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Validation of Stresses Caused by Thermal Gradients in Segmental Concrete Bridges

University of Florida Institutional Repository
Permanent Link: http://ufdc.ufl.edu/UFE0021684/00001

Material Information

Title: Validation of Stresses Caused by Thermal Gradients in Segmental Concrete Bridges
Physical Description: 1 online resource (253 p.)
Language: english
Creator: Mahama, Farouk
Publisher: University of Florida
Place of Publication: Gainesville, Fla.
Publication Date: 2007

Subjects

Subjects / Keywords: bridges, concrete, gradient, prestressed, segmental, stress, temperature, thermal
Civil and Coastal Engineering -- Dissertations, Academic -- UF
Genre: Civil Engineering thesis, Ph.D.
bibliography   ( marcgt )
theses   ( marcgt )
government publication (state, provincial, terriorial, dependent)   ( marcgt )
born-digital   ( sobekcm )
Electronic Thesis or Dissertation

Notes

Abstract: This dissertation presents the results of a series of tests aimed at quantifying self equilibrating thermal stresses caused by AASHTO design nonlinear thermal gradients in segmental concrete bridges. Negative gradients (deck cooler than web) can cause significant tensile stresses to develop in the top few inches of bridge decks, leading to requirements for large prestressing forces to counteract this tension. Design gradients are based on field measurement of temperature variations on both a seasonal and diurnal basis. There is, however, little data in which actual stresses have been measured during these peak gradients to verify that the stresses are indeed as high as predicted by analysis. One reason for this is the difficulty of stress measurement in concrete. Stress is generally estimated by measuring strain, which is then converted to stress by applying an elastic modulus. This works well for homogeneous elastic materials but there is less confidence in this procedure when applied to concrete due to material variability at the scale of the strain gauge, temperature compensation of strain gauges, creep, and shrinkage. A 20 ft long 3 ft deep segmental T beam was constructed and tested in the laboratory for the purpose of quantifying self equilibrating thermal stresses caused by the AASHTO design nonlinear thermal gradients. The beam was made of four 5 ft segments externally post tensioned together with four high strength steel bars. By embedding rows of copper tubing into two of the beam segments, and passing heated water through the tubes, the desired thermal gradients were imposed on the heated segments. Two independent methods were used to measure stresses at the dry joint between the heated segments. The first was to convert measured stress inducing thermal strains to stresses using the elastic modulus. Stresses determined using this method were referred to as elastic modulus derived stresses (E stresses). The second method was a more direct measure of stress using the known stress state at incipient opening of the joint. This method of determining stresses was referred to as joint opening derived stresses (J stresses). Stresses determined using both methods are compared with AASHTO predicted self equilibrating thermal stresses and discussed.
General Note: In the series University of Florida Digital Collections.
General Note: Includes vita.
Bibliography: Includes bibliographical references.
Source of Description: Description based on online resource; title from PDF title page.
Source of Description: This bibliographic record is available under the Creative Commons CC0 public domain dedication. The University of Florida Libraries, as creator of this bibliographic record, has waived all rights to it worldwide under copyright law, including all related and neighboring rights, to the extent allowed by law.
Statement of Responsibility: by Farouk Mahama.
Thesis: Thesis (Ph.D.)--University of Florida, 2007.
Local: Adviser: Consolazio, Gary R.
Local: Co-adviser: Hamilton, Homer R.

Record Information

Source Institution: UFRGP
Rights Management: Applicable rights reserved.
Classification: lcc - LD1780 2007
System ID: UFE0021684:00001

Permanent Link: http://ufdc.ufl.edu/UFE0021684/00001

Material Information

Title: Validation of Stresses Caused by Thermal Gradients in Segmental Concrete Bridges
Physical Description: 1 online resource (253 p.)
Language: english
Creator: Mahama, Farouk
Publisher: University of Florida
Place of Publication: Gainesville, Fla.
Publication Date: 2007

Subjects

Subjects / Keywords: bridges, concrete, gradient, prestressed, segmental, stress, temperature, thermal
Civil and Coastal Engineering -- Dissertations, Academic -- UF
Genre: Civil Engineering thesis, Ph.D.
bibliography   ( marcgt )
theses   ( marcgt )
government publication (state, provincial, terriorial, dependent)   ( marcgt )
born-digital   ( sobekcm )
Electronic Thesis or Dissertation

Notes

Abstract: This dissertation presents the results of a series of tests aimed at quantifying self equilibrating thermal stresses caused by AASHTO design nonlinear thermal gradients in segmental concrete bridges. Negative gradients (deck cooler than web) can cause significant tensile stresses to develop in the top few inches of bridge decks, leading to requirements for large prestressing forces to counteract this tension. Design gradients are based on field measurement of temperature variations on both a seasonal and diurnal basis. There is, however, little data in which actual stresses have been measured during these peak gradients to verify that the stresses are indeed as high as predicted by analysis. One reason for this is the difficulty of stress measurement in concrete. Stress is generally estimated by measuring strain, which is then converted to stress by applying an elastic modulus. This works well for homogeneous elastic materials but there is less confidence in this procedure when applied to concrete due to material variability at the scale of the strain gauge, temperature compensation of strain gauges, creep, and shrinkage. A 20 ft long 3 ft deep segmental T beam was constructed and tested in the laboratory for the purpose of quantifying self equilibrating thermal stresses caused by the AASHTO design nonlinear thermal gradients. The beam was made of four 5 ft segments externally post tensioned together with four high strength steel bars. By embedding rows of copper tubing into two of the beam segments, and passing heated water through the tubes, the desired thermal gradients were imposed on the heated segments. Two independent methods were used to measure stresses at the dry joint between the heated segments. The first was to convert measured stress inducing thermal strains to stresses using the elastic modulus. Stresses determined using this method were referred to as elastic modulus derived stresses (E stresses). The second method was a more direct measure of stress using the known stress state at incipient opening of the joint. This method of determining stresses was referred to as joint opening derived stresses (J stresses). Stresses determined using both methods are compared with AASHTO predicted self equilibrating thermal stresses and discussed.
General Note: In the series University of Florida Digital Collections.
General Note: Includes vita.
Bibliography: Includes bibliographical references.
Source of Description: Description based on online resource; title from PDF title page.
Source of Description: This bibliographic record is available under the Creative Commons CC0 public domain dedication. The University of Florida Libraries, as creator of this bibliographic record, has waived all rights to it worldwide under copyright law, including all related and neighboring rights, to the extent allowed by law.
Statement of Responsibility: by Farouk Mahama.
Thesis: Thesis (Ph.D.)--University of Florida, 2007.
Local: Adviser: Consolazio, Gary R.
Local: Co-adviser: Hamilton, Homer R.

Record Information

Source Institution: UFRGP
Rights Management: Applicable rights reserved.
Classification: lcc - LD1780 2007
System ID: UFE0021684:00001


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VALIDATION OF STRESSES CAUSED BY THERMAL GRADIENTS INT SEGMENTAL
CONCRETE BRIDGES





















By

FAROUK MAHAMA


A DISSERTATION PRESENTED TO THE GRADUATE SCHOOL
OF THE UNIVERSITY OF FLORIDA IN PARTIAL FULFILLMENT
OF THE REQUIREMENTS FOR THE DEGREE OF
DOCTOR OF PHILOSOPHY

UNIVERSITY OF FLORIDA

2007




































O 2007 Farouk Mahama






























To Mom and Dad









ACKNOWLEDGMENTS

I would first like to thank Dr. G. R. Consolazio and Dr. H.R. Hamilton for their help and

guidance throughout the course of my study at The University of Florida. I would also like to

thank the members of my supervisory committee: Dr. B. Sankar of the mechanical and aerospace

engineering department, Dr. R. Cook and Dr. K. Gurley of the civil and coastal engineering

department, for their insightful suggestions. I would like to acknowledge and thank the Florida

Department of Transportation for funding this research. I would especially like to thank Mr.

Marcus Ansley of the FDOT Structures Research Center, Tallahassee, for his invaluable support

and contributions to this study. Sincere thanks to Mr. Frank Cobb, Mr. David Allen, Mr. Steve

Eudy, Mr. Tony Johnston, and Mr. Paul Tighe also of the FDOT Structures Research Center,

Tallahassee, for their help in constructing and transporting the laboratory specimen from

Tallahassee to Gainesville, Florida. Thanks to DYWIDAG Systems Incorporated (DSI) for

donating the post-tensioning bars which were used to post-tension the laboratory specimen. In

addition, I would like to thank Mr. Richard M. DeLorenzo of the FDOT Materials Laboratory,

Gainesville, for his assistance in determining material properties of the test specimen. Finally, I

would like to express my sincere gratitude to Mr. Charles "Chuck" Broward of the University of

Florida Structures Laboratory, his staff of undergraduate students, and Mr. Hubert "Nard" Martin

for their various contributions towards the successful execution of experiments in the laboratory.












TABLE OF CONTENTS


page

ACKNOWLEDGMENT S .............. ...............4.....


LI ST OF T ABLE S ................. ...............8.__. .....


LIST OF FIGURES .............. ...............10....


AB S TRAC T ......_ ................. ............_........2


CHAPTER


1 INTRODUCTION ................. ...............22.......... ......


2 SCOPE AND OBJECTIVES............... ...............2


3 BACKGROUND .............. ...............26....


Thermal Gradients .............. ....... ..... .............2
Structural Response to Thermal Gradients ................. ...............29........... ...
Selected Field Studies on Thermal Gradients............... ...............3
The North Halawa Valley Viaduct Proj ect ........................_. .....................3
The San Antonio "Y" Proj ect .................. ..... ...._ .... ...............35.
Northbound IH-35S/Northbound US 183 Flyover Ramp Proj ect ................. ................ .36
Sum m ary ................. ...............39.......... ......

4 BEAM DE SIGN ................. ...............47................


Cross Section Design ................. ...............47........... ....
Segment Design ................. ............. ...............49.......
Design of Segment Heating System .............. ...............50....
Prestress Design ................. ...............51.................

5 BEAM CONSTRUCTION ................. ...............61........... ....


Placement of Steel Reinforcement, Thermocouple Cages, and Copper Tubes ......................61
Casting of Concrete .............. ...............62....
Material Tests and Properties .............. ...............62....
Application of Prestress ................. ...............65......._. ....

6 IN STRUMENTATION ................. ...............74.......... ......


Therm ocouples .............. ...... ..... ... .. .........7
Electrical Resistance Concrete Strain Gauges and Strain Rings .............. .....................7
Linear Variable Displacement Transducers (LVDT) .............. ...............76....
Load Cells............... ...............76.











Data Acquisition ................ ...............77.................

7 SETUP AND PROCEDURES FOR MECHANICAL LOADING................. ...............8


Opening of Joint between Segments 2 and 3 ................ ...............88..............

8 SETUP AND PROCEDURES FOR THERMAL LOADING ................. ............ .........93


Uniform Temperature Distribution............... ..............9
Linear Thermal Gradient .............. ...............95...
AASHTO Positive Thermal Gradient............... ...............95
AASHTO Negative Thermal Gradient ................. ...............96................

9 IN-SITU COEFFICIENT OF THERMAL EXPANSION ................ ........................102

10 RESULT S PRESTRES SING ................. ...............116......... .....

11 RESULTS MECHANICAL LOADING ................. ...............129........... ...


Detection of Joint Opening Strain Gauges Close to Joint at Midspan .............. .... ...........129
Detection of Joint Opening LVDTs Across Joint at Midspan ................. ............... .....13 5
Strains at M id-Segment .............. ...............137....
D election .............. ...............138....
Sum m ary ................. ...............139......... ......

12 RESULTS UNIFORM TEMPERATURE CHANGE ................. ......................._15 1

13 RESULTS AASHTO POSITIVE THERMAL GRADIENT ........._. ..... ...._._.........163


Elastic Modulus Derived Stresses (E stresses) ...._.._.._ ..... .._._. .... .._._.........16
Joint Opening Derived Stresses (J Stresses) ........._.._.. ....._.. ......_.._..........6

14 RESULTS AASHTO NEGATIVE THERMAL GRADIENT ........._.._.. .. ......._.._.. ....195


Elastic Modulus Derived Stresses (E stresses) ...._.._.._ ..... .._._. .... .._._.........19
Joint Opening Derived Stresses (J Stresses) ........._.._.. ....._.. ......_.._..........0

15 SUMMARY AND CONCLUSIONS ........._._. ...._... ...............222...

APPENDIX

A BEAM SHOP DRAWINGS .............. ...............227....

B LOADING FRAME DRAWINGS ................. ...............231...............


C LOAD RESPONSE CURVES AT MID-SEGMENT (MECHANICAL LOADING).........236

D LOAD RESPONSE CURVES (POSITIVE THERMAL GRADIENT) .............. ...............241












E LOAD RESPONSE CURVES (NEGATIVE THERMAL GRADIENT) ..........................246

LIST OF REFERENCES ........._._.... ...............251._._.. ......


BIOGRAPHICAL SKETCH .............. ...............253....










LIST OF TABLES


Table page

3-1 Positive thermal gradient magnitudes ................. ...............40........... ...

3-2 Modulus of elasticity values for selected Ramp P segments .............. .....................4

3-3 Coefficient of thermal expansion values for selected Ramp P segments ................... .......40

3-4 Comparison of measured and calculated stresses from measured thermal gradients ........40

3-5 Comparison of measured and design Stresses ................. ................ ......... ...._41

4-1 Approximate Service I stresses in Santa Rosa Bay Bridge............... ...............53.

5-1 Segment cast dates .............. ...............67....

5-2 Concrete pump mix proportions .............. ...............67....

5-3 Compressive strengths and moduli of elasticity of Segment 1 .............. ....................6

5-4 Compressive strengths and moduli of elasticity of Segment 2..........._..._ ........._...__....67

5-5 Compressive strengths and moduli of elasticity of Segment 3 .............. ....................6

5-6 Compressive strengths and moduli of elasticity of Segment 4 ................ ........._...__....67

5-7 Coefficient of thermal expansion (CTE) of Segment 3 (AASHTO TP 60-00) ...............68

5-8 Selected post-tensioning force increments ................. ...............68........... ...

9-1 Experimentally determined coefficients of thermal expansion .............. ....................10

10-1 Prestress magnitudes and horizontal eccentricities............... ............12

11-1 Comparison of measured strains due to prestress and measured strains when j oint
opens .............. ...............140....

12-1 Average measured coefficients of thermal expansion (CTE) of concrete segments .......156

12-2 Calculated modulus of elasticity (MOE) of concrete segments ................. ................. .156

12-3 Changes in prestress due to heating of Segments 2 and 3 .............. ....................15

12-4 Changes in prestress due to cooling of Segments 2 and 3 .............. ....................15

13-1 Comparison of E stresses and extrapolated stresses on top of segment flanges near
joint J2 (laboratory positive thermal gradient) ................. ...............178........... ..










13-2 Comparison of E stresses and predicted self-equilibrating thermal stresses caused by
laboratory positive thermal gradient near j oint J2 ........._.._.. ......_. ......._.._......178

13-3 J stresses in top 4 in. of flange ................. ...............178..........

13-4 Comparison of J stresses and predicted stresses in top 4 in. of flange ............................178

13-5 Comparison of J stresses and E stresses in top 4 in. of flange .........._ ....... ............ ...179

14-1 Comparison of E stresses and extrapolated stresses on top of segment flanges near
joint J2 (laboratory negative thermal gradient) ................. ...............205........... ..

14-2 Comparison of E stresses and predicted self-equilibrating thermal stresses caused by
laboratory negative thermal gradient near j oint J2 ........._.._.. ....._. ........_.._.....205

14-3 J stresses in top 4 in. of flange ................. ...............205.._._. .

14-4 Comparison of J stresses and predicted stresses in top 4 in. of flange ............................205

14-5 Comparison of J stresses and E stresses in top 4 in. of flange..........._.._.. ........._.._.....206










LIST OF FIGURES


Figure page

3-1 Conditions for the development of positive thermal gradients ................. ..........___....42

3-2 Conditions for the development of negative thermal gradients ................ ................ ...42

3-4 Comparison of AASHTO gradients for zone 3 (for superstructure depths greater than
2 ft) ............... ...............43..

3-5 Positive vertical temperature gradient for concrete superstructures ................ ...............43

3-6 Decomposition of a nonlinear thermal gradient ................. ...............44........... ..

3-7 Development of self-equilibrating thermal stresses for positive thermal gradient ............44

3-8 Development of self-equilibrating thermal stresses for negative thermal gradient.......... .45

3-9 Thermocouple locations ................. ...............45........... ....

3-10 Comparison of maximum daily positive temperature differences and negative
temperature differences with design gradients .............. ...............46....

3-11 Thermocouple locations ................. ...............46........... ....

4-1 Typical cross-section of Santa Rosa Bay Bridge ................. ...............54..............

4-2 I-section representation of SRB bridge cross section .............. ...............54....

4-3 Self-equilibrating stresses due to AASHTO positive thermal gradient ................... ..........54

4-4 Self-equilibrating stresses due to AASHTO negative thermal gradient............._.._. .........55

4-5 Cross section of laboratory beam with analytically determined self-equilibrating
thermal stresses due AASHTO design gradients ............_. ......_. ..........__.......5

4-6 Location of shear keys on beam cross section and detailed elevation view of shear
key............... ...............56..

4-7 Beam segments .............. ...............56....

4-8 Copper tube layouts for prototype beam and laboratory segmental beam.........................57

4-9 Copper tube layouts in relation to shape of AASHTO design thermal gradients ..............57

4-10 Typical manifold in flange ........._.._ ...... .___ ...............58...

4-11 Typical manifold in web .............. ...............58....











4-12 Typical flow rates through web manifolds .............. ...............58....

4-13 Typical flow rates through flange manifolds ....._.._.. ......._. _. ...._.._ .........5

4-14 Heating system............... ...............59.

4-15 Cross section view of prestress assembly ........._..... ...._._ ....._ ........_.......59

4-16 Elevation view of prestress assembly ........._..__......._ ...._.. ........_._........60

4-17 Mild steel reinforcements in Segments 1 and 4 ................ ...............60........... .

4-18 Mild steel reinforcement ................. ...............60................

5-1 Open form with mild steel reinforcement, closed form with mild steel reinforcement
and lifting hooks. ............. ...............69.....

5-2 Form for shear keys .............. ...............69....

5-3 Heated segment with copper tubes, thermocouple cages and thermocouples ...................70

5-4 Beam layout with casting sequence ................. ....__. ...............70. ..

5-5 Match-casting of segment ........._.___..... .___ ...............70......

5-6 Finished concrete pours for Segment 1, Segment 2, Segment 3, Segment 4 ........._._........71

5-7 Compressive strength test setup, elastic modulus test setup............... ..................7

5-8 AASHTO TP 60-00 test setup .............. ...............72....

5-9 Bar designations and design eccentricities (West)............... ...............72.

5-10 Pre stress assembly (East) ................. ...............73......... .....

5-11 Elevation view of prestress assembly (North) ................. ................ ........ ...._.73

6-1 Thermocouple cage with attached thermocouples ................. ..............................78

6-2 Layout of thermocouples in relation to shape of positive thermal gradient and
negative thermal gradient ................. ...............78........... ....

6-3 Location of thermocouple cages in Segments 2 and 3 ....._.__._ ... ......__ ................79

6-4 Thermocouple labels in Segments 2 and 3 .............. ...............80....

6-5 Strain (foil) gauge .............. ...............8 1....











6-6 Strain gauges close to j oint at midspan on North flange, South flange, North web,
and South web ................. ...............8.. 1......... ....

6-7 Strain ring............... ...............82..

6-8 Instrumentation details (North side) .............. ...............82....

6-9 Instrumentation details (South side) .............. ...............83....

6-10 Instrumentation at midspan (top flange) ......___ ......._._ ......._ ...........8

6-11 Typical labeling convention for strain gauges ..........._..__......_. .......__ .........8

6-12 Typical labeling convention for strain rings ......._..__ ........_._......._ ..........8

6-13 LVDT for measuring deflection at cantilevered-end of beam ................ ........._...__.....84

6-14 LVDTs mounted across joint at midspan on South side and top flange............._.._...........84

6-15 LVDT labeling convention .............. ...............84....

6-16 Load cell layout. ........._..... ...............85...._. .....

6-17 Load cells for measuring applied load, prestress, mid-support reaction, and
end-support reaction............... ...............85

6-18 Instrumentation layout (North) .............. ...............86....

6-19 Instrumentation layout (South) .............. ...............86....

6-20 DAQ System; Connection of instrumentation to DAQ System............._. .........._._....86

7-1 Test setup .............. ...............90....

7-2 Segmental beam in laboratory .............. ...............90....

7-3 Loading frame and 60-ton jack ........._._.._......_.. ...............91..

7-4 Ideal stress diagrams without thermal loads ...._.._.._ ..... .._._. .... .._._.........9

7-5 Ideal stress diagrams with positive thermal gradient ........._._.._......_.. ........_.._.....91

7-6 Ideal stress diagrams with negative thermal gradient ........._._.._......_.. ........_.._.....92

8-1 Pipe layers ........._._. ._......_.. ...............98....

8-2 Thermocouple locations in heated segments .............. ...............98....

8-3 Thermocouples used at each section ..........._.... ...............99.......... ..




12











8-4 Insulated heated segments............... ...............99

8-5 Piping configuration used to impose initial condition ....._._ ................ ...............100

8-6 Piping configuration used to impose uniform temperature differential ........._................100

8-7 Piping configuration used to impose linear thermal gradient............ ..__ ........._ ....100

8-8 Piping configuration used to impose AASHTO nonlinear positive thermal
gradient .............. ...............101....

8-9 Piping configuration used to impose AASHTO nonlinear negative thermal
gradient .............. ...............101....

9-1 Typical in-situ CTE test setup; Photograph and Details. ........._. ..... ..._. ............108

9-2 Uniform temperature change imposed on Segment 2............... ...............109...

9-3 Measured end-displacements due to uniform temperature change imposed on
Segm ent 2 ................. ...............109..............

9-4 Uniform temperature change imposed on Segment 3 ................ ....___ ................110

9-5 Measured end-displacements due to uniform temperature change imposed on
Segm ent 3 ................. ...............110..............

9-6 Measured concrete temperatures in Segment 2 (uniform profile) ................. ................111

9-7 Measured concrete temperatures in Segment 3 (uniform profile) ................. ................111

9-8 Orientation of Segment 2 during testing (South elevation) ................. ............. .......112

9-9 Orientation of Segment 3 during testing (South elevation) ................. ............. .......112

9-10 Linear temperature gradient imposed on Segment 2 ................ ...._.._ ................11 3

9-11 Measured displacements due to linear thermal gradient imposed on Segment 2 ............113

9-12 Linear thermal gradient imposed on Segment 3 ................. ...............114.............

9-13 Measured displacements due to linear thermal gradient on Segment 3 ................... ........114

9-14 Measured concrete temperatures in Segment 2 (linear profile) ...........__... ...............115

9-15 Measured concrete temperatures in Segment 3 (linear profile) ...........__... ...............115

10-1 Segment support during prestressing ..........__ ........_..........._ ............2

10-2 Beam support for mechanical and thermal load tests .............. ...............122....










10-3 Post-tensioning bar designations and eccentricities ................. ............... 123....._._.

10-4 Measured concrete strains near j oint J2 due to prestress (Segment 2, North) ........._.......123

10-5 Measured concrete strains near j oint J2 due to prestress (Segment 3, North) ........._.......124

10-6 Measured concrete strains near j oint J2 due to prestress (Segment 2, South) ........._.......124

10-7 Measured concrete strains near j oint J2 due to prestress (Segment 3, South) ........._.......125

10-8 Measured concrete strains near j oint J2 due to prestress (Top flange) .........._.._...............125

10-9 Effect of differential shrinkage on top flange strains. ....._._._ ... ....... ..............126

10-10 Measured concrete strains due to prestress through depth of segments
near joint J2 ........... __..... ._ ...............126....

10-11 Measured concrete strains due to prestress across width of segment flanges near joint
J2 (Top flange) ................. ...............127.._._. ......

10-12 Variation of prestress forces with time ..........._._ ......__ ...............127.

10-13 Change in total prestress force with time ..........._..__........__....... .........12

11-1 Expected behavior of strain gauges on side of beam near j oint. .........._.._. ........._......141

11-2 Expected behavior of strain gauges on top of flange near j oint. ........._._............_.....141

11-3 Load vs. Strain near j oint at midspan (North side) ................ ...............142...........

11-4 Load vs. Strain near j oint at midspan (South side) ................ ...............142...........

11-5 Load vs. Strain near j oint at midspan (Top flange) ................. ............................143

11-6 Condition of j oint J2 on top of flange ................. ...............143............

11-7 Measured strain distributions near j oint at midspan (North side) ................. .................144

11-8 Measured strain distributions near j oint at midspan (South side) ................. .................144

11-9 Estimated progression of joint-opening with load (based on strain gauge data) .............145

11-10 Movement of neutral axis (N.A.) with load ................. ...............145.............

11-11 Changes in prestress force with load .............. ...............146....

11-12 Expected behavior of LVDTs across j oint on side of beam .............. .......__.........146

11-13 Expected behavior of LVDTs across j oint on top of flange ................. .........___......147











11-14 Load vs. Joint opening (Side LVDTs) ................ ...............147........... ..

11-15 Load vs. Joint opening (Top flange LVDTs) ................. ...............148.............

11-16 Measured strain distributions at middle of Segment 3 (30 in. from joint J2) on North
side of beam ................. ...............148...............

11-17 Measured strain distributions at middle of Segment 3 (30 in. from joint J2) on South
side of beam ................. ...............149...............

11-18 Forces and moments acting at mid-segment ................. ...............149........... ..

11-19 Measured vertical deflection near cantilevered end of beam ................. ............... ..... 150

12-1 Laboratory beam ................. ...............157...............

12-2 Laboratory imposed temperature changes on Segment 2 .............. .....................5

12-3 Laboratory imposed temperature changes on Segment 3 .............. .....................5

12-4 Measured concrete temperatures in Segment 2 .............. ...............158....

12-5 Measured concrete temperatures in Segment 3 .............. ...............159....

12-6 Measured temperature changes at Section C (Heating phase) ................. ..........._..__...159

12-7 Measured temperature changes at Section D (Heating phase)............... ..................6

12-8 Measured strain distribution on Segment 2 (Section C) due to temperature
changes............... ...............160

12-9 Measured strain distribution on Segment 3 (Section D) due to temperature
changes............... ...............161

12-10 Comparison of measured and calculated strains at Section C due to moderately
nonuniform temperature distribution (Segment 2, Heating)..........._._... ......._._.......161

12-11 Comparison of measured and calculated strains at Section D due to moderately
nonuniform temperature distribution (Segment 3, Heating)..........._._... ......._._.......162

13-1 Sequence of load application (positive gradient test) .............. ...............180....

13-2 Laboratory beam ........._. ...... .... ...............181...

13-3 Laboratory imposed positive thermal gradient ....._._._ .... ... .__ ......_._.........18

13-4 Typical fi eld measured positive thermal gradi ent ....._____ .... ... ..__ ........__ ......8

13-5 Measured temperatures in heated segments (positive thermal gradient) .......................182











13-6 Calculated strain components of the AASHTO positive thermal gradient.............._._....183

13-7 Measured and predicted strains near j oint J2 (Segment 2) ..........._... .......__. ..........183

13-8 Measured and predicted strains near j oint J2 (Segment 3) ..........._... .......__. ..........184

13-9 Plan view of measured and predicted strains near j oint J2 (Top Flange) .........._.._...........184

13-10 Comparison of measured thermal gradient profiles with average .........._.... ................1 85

13-11 E stresses near j oint J2 (Segment 2) ........... ....._.._ ...............185

13-12 E stresses near j oint J2 (Segment 3) ........._.._... ...............186.._._.. .

13-13 Difference in magnitude of imposed thermal gradients at location of maximum slope
change (elevation 32 in.)............... ...............186.

13-14 Superposition of component stress blocks (Mechanical loads only) .............. ..... ........._.187

13-15 Superposition of component stress blocks (Mechanical loads with positive thermal
gradient) ................. ...............187.............

13-16 Uniform opening of joint across section width ................. ....___ .............. .....8

13-17 Non-uniform opening of joint across section width ........._. ............ ........._......188

13-18 Load vs. strain at reference temperature (Segment 3, North) ........___........ ........... ....189

13-19 Load vs. strain with positive thermal gradient (Segment 3, North) ........._..... ...............189

13-20 Load vs. strain at reference temperature (Segment 3, South) ................ ............... ....190

13-21 Load vs. strain with positive thermal gradient (Segment 3, South) ................. ...............190

13-22 Load vs. strain at reference temperature (Top flange) ........................... ...............191

13-23 Load vs. strain with positive thermal gradient (Top flange) ................. .....................191

13-24 Comparison of strain differences on North and South sides of joint J2 (Positive
thermal gradient) ................. ...............192......... ......

13-25 Joint opening loads detected from strain gauges near j oint J2 ................. ................ ..192

13-26 Sign convention for moments and curvature .............. ...............193....

13-27 Contact areas at j oint J2 at incipient opening of joint on South side at
elevation 35.5 in ................. ...............193....._... ...











13-28 Contact areas at j oint J2 at incipient opening of joint on North side at elevation
33.5 in. ............. ...............193....

13-29 Contact areas at j oint J2 at incipient opening of joint on South side at elevation
32.0 in. ............. ...............194....

14-1 Sequence of load application (negative gradient test) .............. ...............207....

14-2 Laboratory beam .............. ...............208....

14-3 Laboratory imposed negative thermal gradient .............. ...............208....

14-4 Measured temperatures in heated segments (negative thermal gradient) ........................209

14-5 Calculated strain components of the AASHTO negative thermal gradient .........._........209

14-6 Measured and predicted strains near j oint J2 (Segment 2) ........._. ..... ..._._..........210

14-7 Measured and predicted strains near j oint J2 (Segment 3) ................ .......__ ........210

14-8 Plan view of measured and predicted strains near j oint J2 (Top Flange) ................... .....21 1

14-9 Measured and predicted strains at midspan and mid-segment (Segment 2, North).........211

14-10 Measured and predicted strains at midspan and mid-segment (Segment 3, North).........212

14-11 Comparison of measured thermal gradient profiles with average profile. .................. .....212

14-12 E stresses near j oint J2 (Segment 2) .............. ...............213...............

14-13 E stresses near j oint J2 (Segment 3) .............. ...............213...............

14-14 E stresses at mid-segment and midspan (Segment 2, North) ................. ............... .....214

14-15 E stresses at mid-segment and midspan (Segment 3, North) ................. ............... .....214

14-16 Difference in magnitude of imposed thermal gradients at location of maximum slope
change (elevation 32 in.)............... ...............215.

14-17 Superposition of component stress blocks (mechanical with uniform temperature
increase) ................. ...............215......... ......

14-18 Superposition of component stress blocks (mechanical with uniform temperature
increase and negative thermal gradient) .............. ...............216....

14-19 Load vs. strain at reference temperature (Segment 3, North) ................ ............... ....216

14-20 Load vs. strain with negative thermal gradient (Segment 3, North) ............... .... ........._..217











14-21 Load vs. strain at reference temperature (Segment 3, South)..........._ .. ......._.._.. ....217

14-22 Load vs. strain with negative thermal gradient (Segment 3, South) ........._...... ..............218

14-23 Load vs. strain at reference temperature (Top flange) ........................... ...............218

14-24 Load vs. strain with negative thermal gradient (Top flange) ................. ............... .....219

14-25 Comparison of strain differences on North and South sides of joint J2 (Negative
thermal gradient) ................. ...............2.. 19..............

14-26 Joint opening loads detected from strain gauges near j oint J2 ................. ................ ..220

14-27 Sign convention for moments and curvature .............. ...............220....

14-28 Contact areas at j oint J2 at incipient opening of joint on South side at elevation
35.5 in. ............. ...............220....

14-29 Contact areas at j oint J2 at incipient opening of joint on North side at elevation
33.5 in. ............. ...............221....

14-30 Contact areas at j oint J2 at incipient opening of joint on South side at elevation
32.0 in. ............. ...............221....

A-1 Prestress reinforcement details .............. ...............228....

A-2 Manifold and copper tube details. ................ ...._.._ ...............229 ...

A-3 Shear key details .............. ...............230....

B-1 Loading frame details .............. ...............232....

B-2 Details of cross channels............... ...............23

B-3 Mid-support details ....... ................ ........___.........23

B-4 End-support details .............. ...............235....

C-1 Load vs. strain at middle of Segment 2 on North side............... ...............237.

C-2 Load vs. strain at middle of Segment 2 on South side............... ...............237.

C-3 Measured strain distributions at middle of Segment 2 on North side..............................238

C-4 Measured strain distributions at middle of Segment 2 on South side..............................238

C-5 Load vs. strain at middle of Segment 3 on North side............... ...............239.

C-6 Load vs. strain at middle of Segment 3 on South side............... ...............239.











C-7 Measured strain distributions at middle of Segment 3 on North side..............................240

C-8 Measured strain distributions at middle of Segment 3 on South side..............................240

D-1 Load vs. strain at reference temperature (Segment 2, North)..........._._. ........._._.....242

D-2 Load vs. strain with positive thermal gradient (Segment 2, North) ............... ... ........._...242

D-3 Load vs. strain at reference temperature (Segment 2, South) ................ ............... ....243

D-4 Load vs. strain with positive thermal gradient (Segment 2, South) ........._.._... ..............243

D-5 Load vs. joint opening at reference temperature (Top flange) ................. ................ ..244

D-6 Load vs. joint opening with positive thermal gradient (Top flange) .............. ..... ........._.244

D-7 Load vs. joint opening at reference temperature (South side).........._.._.._ ........_.._.. ...245

D-8 Load vs. joint opening with positive thermal gradient (South side) ........._..... ..............245

E-1 Load vs. strain at reference temperature (Segment 2, North).........._.._.._ ......._.._.. ....247

E-2 Load vs. strain with negative thermal gradient (Segment 2, North) ........._...... ..............247

E-3 Load vs. strain at reference temperature (Segment 2, South).........._.._.._ ......._.._.. ....248

E-4 Load vs. strain with negative thermal gradient (Segment 2, South) ........._...... ..............248

E-5 Load vs. joint opening at reference temperature (Top flange) ................. ............... ..249

E-6 Load vs. joint opening with negative thermal gradient (Top flange) .........._.._.. .............249

E-7 Load vs. joint opening at reference temperature (South side).........._.._.._ ........_.._.. ...250

E-8 Load vs. joint opening with negative thermal gradient (South side) .........._.... .............250









Abstract of Dissertation Presented to the Graduate School
of the University of Florida in Partial Fulfillment of the
Requirements for the Degree of Doctor of Philosophy

VALIDATION OF STRESSES CAUSED BY THERMAL GRADIENTS INT SEGMENTAL
CONCRETE BRIDGES

By

Farouk Mahama

December 2007

Chair: Gary R. Consolazio
Cochair: H. R. Hamilton
Major: Civil Engineering

This dissertation presents the results of a series of tests aimed at quantifying

self-equilibrating thermal stresses caused by AASHTO design nonlinear thermal gradients in

segmental concrete bridges. Negative gradients (deck cooler than web) can cause significant

tensile stresses to develop in the top few inches of bridge decks, leading to requirements for large

prestressing forces to counteract this tension.

Design gradients are based on Hield measurement of temperature variations on both a

seasonal and diurnal basis. There is, however, little data in which actual stresses have been

measured during these peak gradients to verify that the stresses are indeed as high as predicted

by analysis. One reason for this is the difficulty of stress measurement in concrete. Stress is

generally estimated by measuring strain, which is then converted to stress by applying an elastic

modulus. This works well for homogeneous elastic materials but there is less confidence in this

procedure when applied to concrete due to material variability at the scale of the strain gauge,

temperature compensation of strain gauges, creep, and shrinkage.

A 20 ft-long 3 ft-deep segmental T beam was constructed and tested in the laboratory for

the purpose of quantifying self-equilibrating thermal stresses caused by the AASHTO design










nonlinear thermal gradients. The beam was made of four 5 ft segments externally post-tensioned

together with four high-strength steel bars. By embedding rows of copper tubing into two of the

beam segments, and passing heated water through the tubes, the desired thermal gradients were

imposed on the heated segments.

Two independent methods were used to measure stresses at the dry joint between the

heated segments. The first was to convert measured stress-inducing thermal strains to stresses

using the elastic modulus. Stresses determined using this method were referred to as elastic

modulus derived stresses (E stresses). The second method was a more direct measure of stress

using the known stress state at incipient opening of the joint. This method of determining

stresses was referred to as joint opening derived stresses (J stresses). Stresses determined using

both methods are compared with AASHTO predicted self-equilibrating thermal stresses and

discussed.









CHAPTER 1
INTTRODUCTION

Thermal stresses are the result of restraint to deformations caused by temperature

changes. In general, stresses are generated in bridges when the temperature of all or part of the

superstructure varies significantly from the temperature at which it was constructed. Seasonal

and diurnal variations in temperature are usually the cause of these temperature changes. In

typical beam-slab concrete bridges, temperature variations lead to uniform expansion and

contraction of the superstructure. This is because the shallow decks of such bridges allow

uniform heating and cooling of the superstructure under environmental conditions. Segmental

bridges, however, are comprised of deep box-girder sections. Such bridges experience not only

uniform temperature changes, but also nonlinear distributions of temperature through the depth

of the superstructure cross-section, known as nonlinear thermal gradients. Bridge deformations

due to uniform temperature changes are well understood and easily accounted for in design by

providing sliding j points and flexible piers, among other methods, to accommodate such

movements. Nonlinear temperature distributions, however, present a more complex engineering

problem. In simply-supported spans, nonlinear thermal gradients lead to internal

self-equilibrating thermal stresses that cannot be relieved through support conditions. In

continuous spans, nonlinear gradients lead to continuity stresses due to restraint to curvature in

addition to self-equilibrating thermal stresses.

Designing continuous segmental concrete bridges for stresses due to thermal gradients is

typically accomplished by making use of the American Association of State Highway and

Transportation Officials (AASHTO) Load and Resistance Factor Design (LRFD) Specifications

(AASHTO 2004) and the AASHTO Guide Specifications for Design and Construction of

Segmental Concrete Bridges (AASHTO 1999). These specifications require the consideration of










nonlinear thermal gradient load cases when analyzing a segmental bridge for serviceability.

Gradients that must be considered are positive (deck warmer than web) and negative (deck

cooler than web). Stresses due to thermal gradients are analytically determined using concepts

from classical mechanics. The magnitudes of thermal stresses determined in this manner can

sometimes equal those due to live loads. This is of particular concern in the negative gradient

case, which causes high tensile stresses to develop in the top few inches of the bridge deck. Due

to limitations on the allowable tensile stress in segmental bridges, as stipulated by design codes,

large prestress forces are needed to counteract the tension generated by the negative gradient.

From the perspective that nonlinear thermal gradients are considered only in serviceability

checks, and do not affect the ultimate strength condition of a bridge, designing for thermal

stresses as high as those determined analytically can produce overly-conservative and costly

structures.

To gain a better understanding of the effects of nonlinear thermal gradients on concrete

bridges, it is first necessary to accurately quantify stresses that are generated by such gradients.

This will not only aid in the development of improved methods for predicting thermal stresses in

segmental concrete bridges (e.g. should actual stresses be less severe than predicted with current

analysis procedures), but will also aid in investigating the effects of stresses caused by nonlinear

thermal gradients on the durability of concrete (e.g. cracking and associated crack widths).









CHAPTER 2
SCOPE AND OBJECTIVES

Past research leading to the determination of design thermal gradients for segmental

concrete bridges has focused mainly on collection of temperature data over varying periods of

time, and selection of the maximum observed gradients as design gradients. There is, however,

little data with which to determine whether the peak gradients produce stresses that are as high as

those predicted analytically. One reason for this is the difficulty of stress measurement in

concrete. Stress is generally estimated by measuring strain, which is then converted to stress by

applying an elastic modulus. This works well for homogeneous elastic materials but there is less

confidence in this procedure when applied to concrete due to material variability at the scale of

the strain gauge.

A primary obj ective of this research was to determine whether experimentally determined

self-equilibrating thermal stresses caused by application of the AASHTO nonlinear thermal

gradients, are as severe as predicted by analysis. To this end an experimental program was

carried out to quantify self-equilibrating stresses caused by the thermal gradients.

A 20 ft-long, 3 ft-deep segmental concrete T-beam was constructed and laboratory-tested

for this study. The beam was made of four 5 ft segments externally post-tensioned together with

four high-strength steel bars. By embedding rows of copper tubing into two of the beam

segments, and passing heated water through the tubes, the desired thermal gradients were

imposed on the heated segments. These segments were also instrumented with thermocouples to

monitor concrete temperatures during the application of thermal loads. The beam was supported

on one end and at midspan. Mechanical loads were applied at the cantilevered end with the

obj ective of creating a known (zero) stress state at the dry j oint (at midspan) between the two

heated segments from which the effects of thermal gradients could be determined.









In-situ tests utilizing non-stress-inducing temperature profiles (uniform and linear

temperature distributions) were performed on selected simply supported segments of the beam,

to determine coefficients of thermal expansion. The post-tensioned beam was initially tested

under the action of mechanical loads to establish a baseline condition from which the effect of

thermal loads could be determined. Data from these tests were also used to evaluate the most

suitable method of determining loads at which the dry j oint at the midspan of the beam opened at

specified depths. Accurate determination of loads at which the joint opened was important in

quantifying stresses at the joint caused by nonlinear thermal gradients. A uniform temperature

increment was imposed to investigate the expansion behavior of the beam under thermal loading.

Though the beam was statically determinate with respect to support conditions, expansion or

contraction of the concrete segments relative to the post-tensioning bars was expected to lead to

the development of additional stresses that had to be accounted for in quantifying

self-equilibrating thermal stresses. Subsequently a combination of AASHTO nonlinear thermal

gradients and mechanical loads were applied to the beam. Self-equilibrating thermal stresses

determined with results from these tests were then compared with corresponding thermal stresses

determined using the AASHTO recommended method for calculating stresses caused by

nonlinear thermal gradients.









CHAPTER 3
BACKGROUND

Thermal Gradients

Thermal gradients in concrete bridges are largely the result of the low thermal conductivity

of concrete. By convention, a positive gradient is defined as a condition in which the

temperature of the top deck is higher than the temperature of the webs. A negative gradient

exists when the temperature of the web is warmer than that of the top deck and bottom flange.

Climate, bridge material, and the shape of the cross section all affect the shape and

magnitude of thermal gradients. Climatic factors of importance include solar radiation, ambient

temperature, wind speed, and precipitation. Climatic conditions leading to the development of

positive and negative thermal gradients in concrete bridges are illustrated in Figure 3-1 and

Figure 3-2, respectively. Material properties such as thermal conductivity, density, absorptivity,

and specific heat influence thermal gradients in concrete. The effect of cross sectional shape on

the development of thermal gradients is complex and has not been the focus of extensive

research. However, from thermocouple data taken from existing segmental box-girder bridges, it

is known that in addition to vertical temperature gradients, box girder sections also experience

transverse temperature gradients due to the effects of differential temperature inside and outside

the section (see points A and B in Figure 3-1 and Figure 3-2). Furthermore, the effect of

enclosed air inside concrete box girders causes slightly different temperatures between the deck

above the cavity and the exposed (cantilevered) deck overhang (points C and D in Figure 3-1 and

Figure 3-2).

AASHTO specifications for the design of bridges for thermal gradients were first

introduced in 1989. In 1983 Potgieter and Gamble developed a two-dimensional Einite

difference program to calculate the distribution of temperature in a concrete section using









weather station data from around the United States. They determined conditions at each site that

would produce the maximum temperature differences, shapes, and magnitudes of nonlinear

(positive) temperature gradients. The analytical model was validated with data taken from the

Kishwaukee River Bridge in Illinois. In 1985 the National Cooperative Highway Research

Program (NCHRP) published Report 276, Thermal Effects in Concrete Bridge Superstructures

(Imbsen et al. 1985), which provided guidelines for the consideration of thermal gradients in the

design of concrete bridges. The recommendations in NCHRP Report 276 were based largely on

the work by Potgieter and Gamble (1983). In 1989 AASHTO published their Guide

Specifications, thermal Effects in Concrete Bridge Superstructures (AASHTO 1989a), which

was based on NCHRP Report 276. The AASHTO Guide Specifications for Design and

Construction ofSegmental Concrete Bridges (AASHTO 1989b), a derivative of the AASHTO

(1989a) specifications, required the consideration of thermal gradients in the design of all

segmental bridges.

In the AASHTO Guide Specif ications, Thermal Effects in Concrete Bridge Superstructures

(AASHTO 1989a), the United States is divided into four solar radiation zones (see Figure 3-3),

and a positive and negative gradient magnitude is specified for each zone. At the time of

publication of the AASHTO (1989a) Guide Specifieations, very little Hield data were available to

substantiate the nonlinear thermal gradients utilized by the specifications. Since then, several

Hield studies have been conducted on existing segmental bridges in the United States (e.g.

Shushkewich 1998) that generally agree with the positive gradients stipulated by AASHTO.

Negative gradients in the AASHTO (1989a) Guide Specifieations were based on the

British Standard BS 5400 (1978). The shape of negative thermal gradients has since been

modified and the magnitudes reduced to both simplify the design process and reduce the









magnitude of stresses caused by these gradients, which are tensile in the top few inches of

superstructure cross sections. The AASHTO Guide Specifications for Design and Construction

of Segmental Concrete Bridges (AASHTO 1999), and the AASHTO LRFD Bridge Design

Specifications (AASHTO 1998a) specify the negative gradient as a fractional multiple of the

positive gradient (-0.30 for plain concrete surfaces and -0.20 for surfaces with 2-in. asphalt

topping). Magnitudes of the negative gradients in each geographic zone depend on

categorization into one of two superstructure surface conditions: plain concrete surface, and 2-in.

asphalt topping. Asphalt toppings tend to insulate the flanges of bridge superstructures. This

reduces loss of heat from the surface of the flange, thereby reducing the severity of the thermal

gradient. Thermal gradient shapes are essentially the same for all cross sections.

Thermal gradients in the AASHTO Guide Specif ications, Thermal Effects in Concrete

Bridge Superstructures (AASHTO 1989b) are applicable only to superstructure depths greater

than 2 ft. Thermal gradients in the AASHTO Guide Specifications for Design and Construction

ofSegmental Concrete Bridges (AASHTO 1999), and the AASHTO LRFD Bridge Design

Specifications (AASHTO 1994a), which are derivatives of the AASHTO (1989b) Guide

Specifications, are not restricted to superstructure depths greater than 2 ft. (see Figure 3-4 for a

comparison of AASHTO gradients). Instead, different superstructure depths are taken into

account by means of a vertical dimension, "A" (see Figure 3-5). The dimension "A" is taken as

12 in. for superstructure depths greater than 16 in. For superstructures with depth less than

16 in., "A" is taken as 4 in. less than the depth of the superstructures.

Magnitudes of T1 and T2 for the four solar radiation zones into which the United States is

divided (see Figure 3-3) are shown in Table 3-1 (Florida is located in zone 3). The AASHTO

(1999) Guide Specifications specify the value of T3 aS zero, unless a site-specific study is









conducted to determine an appropriate value. Furthermore, should a site-specific study be

conducted, the maximum value of T3 aS required by the specifications is 5 oF. It is worth

mentioning that T3 is usually taken as zero in design since it is unlikely that design engineers will

have the necessary site data to determine otherwise.

Nonlinear thermal gradients in AASHTO specifications published after 1999 are identical

to the gradients in the AASHTO (1999) Guide Specifications. The AASHTO (1999) thermal

gradients were therefore used in this study since they are currently being used in the design of

segmental concrete bridges.

Structural Response to Thermal Gradients

Nonlinear thermal gradients are usually divided into three components for analysis

purposes (Figure 3-6): uniform temperature, linear thermal gradient and, self-equilibrating

temperature distribution. The uniform temperature component causes uniform expansion or

contraction of the unrestrained superstructure. If the structure is restrained against this

deformation, axial forces may develop. A linear temperature gradient causes uniform curvature

in an unrestrained superstructure. If the structure is restrained against curvature (restraints from

vertical supports, e.g. bridge piers), then secondary moments develop as the result of a linear

gradient.

The self-equilibrating temperature gradient, as the name implies, leads to the development

of stresses in the structure that are internally in self-equilibrium. The resultant force and moment

due to these stresses are both zero because the stresses are developed as the result of inter-fiber

compatibility and are not associated with external forces and moments. The development of

self-equilibrating thermal stresses is discussed in the following paragraphs.

Consider the beam cross section shown in Figure 3-7 and assume the fibers of the section

are free to deform independently. Under the action of a nonlinear positive thermal gradient the










section fibers would deform in the shape of the gradient with the top fibers undergoing greater

elongations than the middle and bottom fibers. In a real beam, however, inter-fiber bonds resist

the free deformation of section fibers. If the cross section of the beam is able to resist

out-of-plane flexural distortion (which is the case for a beam made of a homogeneous isotropic

material undergoing uniform bending), the fibers of the beam will undergo a uniform curvature

plus elongation. For deformations of the fibers to be consistent with the resistance of the cross

section to out-of-plane flexural distortion, stresses are developed. These stresses, which are

self-equilibrating, are compressive in the top and bottom fibers and tensile in the middle fibers of

the cross section.

The development of self-equilibrating thermal stresses under the action of a nonlinear

negative thermal gradient is illustrated in Figure 3-8. In this case, if the fibers of the section are

free to deform independently, they would shorten with the top fibers undergoing greater

shortening than the middle and bottom fibers. For deformations of the fibers of the beam to be

consistent with the resistance of the cross section to out-of-plane flexural distortion,

self-equilibrating stresses are developed. These stresses are tensile in the top and bottom fibers

and compressive in the middle fibers of the beam.

The AASHTO approach to calculating stresses due to thermal gradients, which is based on

one-dimensional Bernoulli beam theory, is outlined in the AASHTO Guide Specifications,

Thermal E~ffects in Concrete Bridge Superstructures (AASHTO 1989b). The following

assumptions regarding concrete material behavior (for segmental box girder bridges, the

construction material typically used is concrete) are made in the calculations:

1. Concrete is homogeneous and isotropic.

2. The material properties of concrete are independent of temperature.

3. Concrete has linear stress-strain and temperature-strain relationships.









4. The Navier-Bernoulli hypothesis; that initially plane sections remain plane after bending, is
valid.

5. Temperature varies vertically with depth, but is constant at all points of equal depth.

6. Longitudinal and transverse thermal stress fields are independent of each other.

The shape of box-girder sections leads to the development of transverse thermal gradients

because of differential temperatures between parts of the section that are inside and outside the

box. Analysis for the effects of transverse thermal gradients is generally considered unnecessary

(AASHTO 1999). For relatively shallow bridges with thick webs, however, such an analysis

may be necessary. The AASHTO 1999 specifications recommend a plus or minus 10 oF

transverse temperature differential in such cases. Generally, the primary stresses of interest in

design are usually longitudinal stresses. To determine self-equilibrating longitudinal stresses

using the AASHTO approach, a sectional analysis is performed. The structure is first assumed to

be fully restrained against rotation and translation and the thermal stresses determined using

Equation 3-1:

fRT (y)= -1-(E-a- TG(y)) (3-1)

where; fRT(YliS the thermal stress assuming a fully restrained structure, y is the vertical distance

measured from the z axis, E is the elastic modulus, a is the coefficient of thermal expansion, and

TG(y) is the vertical thermal gradient. Axial force and bending moment required to maintain full

restraint are then determined from the resulting stress distribution using Equation 3-2 and

Equation 3-3:

NR RT ,(y) b(y)dy (3-2)

MtR RT'j, (y) b(y) ydy 3-3

where; NR is the restraining axial force, MEZR is the restraining moment about the z axis, and b(y)

is the width of the cross section. Stresses due to the axial force and bending moment are then









subtracted from the fully restrained thermal stresses to give self-equilibrating thermal stresses as

shown in Equation 3-4:


fsE (y) = fRT () RR(3 -4)
A I

where; A is the area of the cross section and I, is the moment of inertia of the cross section about

the z axis. In statically determinate structures, this superposition yields the complete internal

stress state. The strain distribution and curvature of the structure are given by Equation 3-5 and

Equation 3-6, respectively:

-1 N, 2Mz y35
E(y) = R (-5
EA I

~= R(3-6)
E-I

Strains the structure does not undergo (i.e. strains corresponding to self-equilibrating thermal

stresses) are calculated from Equation 3-7:

SE (y) = E(y) a -TG(y) (3 -7)

where ESE(YI is the strain distribution corresponding to the self-equilibrating thermal stresses. In

statically indeterminate (continuous) structures, additional continuity stresses must be

determined by performing a structural analysis using the negative of the restraining axial force

and bending moment as loads at the ends of the continuous structure. This is usually done using

structural analysis software. Stresses computed from the structural analysis are then

superimposed on stresses due to the restraining axial force and bending moment in the primary

(sectional) analysis to give continuity stresses. Alternatively, the indeterminate structure can be

allowed to undergo continuity deformations due to the nonlinear gradient (which can be obtained

from Equation 3-5) by removing enough redundant supports to make the structure statically









determinate. Reactions necessary to enforce displacement compatibility and accompanying

continuity stresses can then be subsequently determined (e.g. using the flexibility method). The

sum of the self-equilibrating stresses (determined previously via sectional analysis) and

continuity stresses gives the total stress state in the continuous structure due to the nonlinear

thermal gradient.

If the thermal gradient varies through the depth and width of the cross section,

self-equilibrating thermal stresses are determined using Equation 3-8 through Equation 3-12,

which are two-dimensional versions of Equation 3-1 through Equation 3-4, respectively.

fRT (z, y) = -1- (E -a TG(z, y)) (3-8)
NR RT ,(z, y)dzdy (3-9)

MtR RTf.(z, y) ydzdy (3-10)

MyR RTf,(z, y)- zdzdy (3-11)

NR MlzR y MlyR -z
fSE ( Y RT RZ R R (3-12)
A I I,

Where TG(z,y) is the two dimensional thermal gradient in the cross section, fRT(Z,YI is the

thermal stress distribution assuming a fully restrained structure, MEzR is the restrained moment

about the z axis, MyR is the restrained moment about the y axis, I, is the moment of inertia of

section about the z axis, ly is the moment of inertia of the section about the y axis, and fSE(z,yl is

the two dimensional self-equilibrating thermal stress distribution.

Selected Field Studies on Thermal Gradients

Past studies on thermal gradients in continuous concrete segmental bridges have focused

on determining the magnitude and shape of positive and negative thermal gradients. The

frequencies at which maximum positive and negative gradients occur, due to variations in

environmental heating, have also been investigated. The studies vary in location, duration,









number and type of thermocouples, and placement of thermocouples. Bridge cross sections most

frequently considered were of the concrete box-girder type. Three such field studies are

discussed here.

The North Halawa Valley Viaduct Project

The North Halawa Viaduct consists of twin prestressed concrete segmental bridges on the

island of Oahu in Hawaii. As part of the instrumentation set up to measure various bridges

responses, two sections along a five-span unit were heavily instrumented with thermocouples

(Shushkewich, 1998). One section, E, with 26 gauges, was near midspan (location of maximum

positive moment under service loads), while another section, F, with 32 gauges, was near a

support (location of maximum negative moment under service loads).

Thermocouple readings were first recorded in late 1994 and were to be recorded through

the end of 1999. Initially readings were taken at 2-hour intervals but this was increased to 6-hour

intervals when it was felt that too much data was being gathered. When it became apparent that

the critical positive thermal gradient was being underestimated the recording interval was again

reduced to 2 hours (for design gradients in Hawaii, see Figure 3-5 and Table 3-1, zone 3).

According to Shushkewich (1998), negative gradient readings were not as sensitive to the time

interval as positive gradient readings. Thus, all the negative gradient readings were considered

useful. Positive gradient readings taken during the period when the time interval between

readings was 6 hours were considered unreliable. A 2-in. thick concrete topping was later placed

on the instrumented sections. The topping was instrumented with thermocouples at the top,

middle, and bottom.

Monthly and daily positive thermal gradient data were seen to be slightly higher for

Section E than they were for Section F. Shushkewich (1998) attributed this to the higher thermal

inertia of Section F (larger depth). Critical positive and negative thermal gradient profiles









determined during the study were plotted for gauges along the centerlines of the web, top and

bottom slabs. The gradients were also compared to design gradients in the then-proposed

AASHTO (1998b) Segmental Guide Specifications. Because construction traffic interfered with

the gauges at the top of the deck, Shushkewich (1998) considered readings from those gauges

unreliable and suggested that readings at the deck surface be obtained by extrapolating data from

gauges 2.5 in. from the deck surface. Considering the positive and negative thermal gradient

profiles, it was clear that in general, the slab readings were very close to the design gradients.

The same could not be said for the web readings. The overall measured positive thermal

gradient profile matched the design gradient more than the measured negative gradient profile

matched the design negative gradient. The results of this study substantiated the reduction of the

negative thermal gradient from -0.5 (AASHTO 1994a) to -0.3 times the positive gradient: the

value used in the AASHTO Segmental Guide Specifications (AASHTO 1998b) and the

AASHTO LRFD Bridge Design Specifications (AASHTO 1998a).

The San Antonio "Y" Project

As part of a field study (Roberts, C. L.; Breen J. E.; Cawrse J. (2002)), four segments of a

three-span continuous unit in the extensive upgrade to the intersection of interstate highways

I-3 5 and I-10 in downtown San Antonio, Texas (the San Antonio "Y" proj ect) were heavily

instrumented with thermocouples. The instrumented segments were part of elevated viaducts

comprised of precast segmental concrete box girders constructed using span-by-span techniques.

Thermocouples in a web of one instrumented segment (Figure 3-9) were connected to a data

logger. Temperatures were recorded every 30 minutes for 2 years and 6 months. There were

gaps in the data due to limited memory of the data logger.

Maximum positive and negative temperature differences were determined for each day that

thermocouple readings were recorded. Maximum positive temperature differences were









computed from the difference between the largest top thermocouple reading (located 1 inch from

the deck surface) and the coolest web thermocouple reading. Maximum negative temperature

differences were computed from the difference between the coolest top thermocouple reading

and the warmest web thermocouple reading.

Measured positive thermal gradient magnitudes were found by Roberts et al. (2002) to be

smaller than the design gradients in the AASHTO (1994a) LRFD specifications and the

AASHTO (1999) segmental guide specifications (for design gradients in Texas, see Figure 3-5

and Table 3-1, zone 2). The gradient shapes were found to be similar to the older tri-linear shape

in the Guide Specifications for 7zermal Effects in Concrete Superstructures (AASHTO 1989b).

Measured maximum negative thermal gradients were also compared to the design gradient. It

was found that the field measured magnitudes were less than the AASHTO (1994b) LRFD

specifications but slightly greater than the AASHTO (1999) segmental specifications. Figure

3-10 shows a comparison between design gradient magnitudes and the recorded maximum

positive and negative temperature difference for each day in the data record, respectively. Data

from the top most thermocouple (1 in. below the deck surface) were extrapolated to estimate

deck surface temperatures using a fifth order polynomial equation based on earlier work by

Priestley (1978).

Northbound IH-35/Northbound US 183 Flyover Ramp Project

A field study was conducted by Thompson et al. (1998) on a five-span continuous precast

segmental horizontally curved concrete bridge erected using balanced cantilever construction.

The bridge was part of a flyover ramp between interstate highway I-3 5 and US highway 183 in

Austin, Texas. Three segments designated Pl6-2, Pl6-10, and Pl6-17 in one span of the

structure were instrumented with thermocouples (see Figure 3-11). Segment Pl6-2 was at the

base of the cantilever where the maximum negative moment (tension in the top fiber of the









section) occurred during construction. Segment Pl6-10 was near the quarter point of the

completed span where an inflection point in the load moment diagram was expected to occur.

Segment Pl6-17 was located near the midpoint of the completed span where the maximum

moment from gravity load was expected to occur. Response of the structure was studied under

the actions of daily thermal gradients that occurred over a 9-month period.

From the temperature data gathered during the course of monitoring the bridge, daily

temperature gradients were evaluated. The average temperature at the junction between the webs

and the top flange was used as baseline reference and deducted from the measured average top

and bottom temperatures. These resulting temperatures were taken as the basis for determining

the thermal gradients.

Longitudinal stresses from the design gradients and stresses from the maximum measured

thermal gradients were calculated. The calculations were based on the technique recommended

in the AASHTO LRFD Bridge Design Specifications (1994a). The calculated stresses were

compared to measured thermal gradient stresses. The measured stresses were determined by

making use of measured concrete strains (from strain gauges), a determined coefficient of

thermal expansion, and elastic modulus determined from concrete test cylinders. To make

calculated stresses comparable to measured stresses, calculated stress results were adjusted by

adding a uniform temperature to the nonlinear AASHTO gradients. According to the

investigators, measured stresses came from readings taken between the time of peak gradient

occurrence and some baseline time when the temperature distribution in the section was fairly

uniform. Since a uniform change in temperature occurred within this time, the adjustment was

necessary to make comparisons between measured and calculated stresses reasonable. Average

values of elastic modulus and coefficient of thermal expansion determined during the course of









the field study are shown in Table 3-2 and Table 3-3, respectively. Table 3-4 compares

measured stresses with stresses calculated from the measured thermal gradients (tension is

positive and compression is negative). Table 3-5 compares measured stresses with stresses

calculated from application of the design gradients. It can be seen that measured stresses for

Pl6-10 and Pl6-17 are high compared to those at Pl6-2. Furthermore, they do not compare well

with the stresses determined using the AASHTO design technique. Thompson et al. (1998)

attributed this to warping of the box girder. Of the three sections, Pl6-2 was the only one

restrained by an anchorage diaphragm from section distortion. Since the AASHTO design

specifications assume plane sections remain plane, stresses at Pl6-10 and Pl6-17, which were

free to undergo out-of-plane distortion, could not be expected to match stresses computed using

the AASHTO recommended design technique.

In spite of the observed high stresses, Thompson et al. (1998) did not observe any distress

in the structure that could be attributed to thermal effects. The maximum and minimum top

flange stresses, under load combinations of dead load, prestress, live load, and thermal gradient

were computed. The field load combinations were not necessarily the same for each segment.

From the computations, it was clear that no tension existed in the bridge under the load

combinations considered. A design 28-day concrete compressive strength, f'c, of 6.5ksi was used

in the design of the bridge. However, compressive strength cylinder tests revealed that concrete

strengths of 10 ksi were common. The maximum allowable compressive stress, 0.45f'c, was

exceeded in Pl6-10 and Pl6-17 under full service loads. The approximate limit of elastic

behavior in concrete, 0.7f'c, was also exceeded in a small (about foot wide) part of Pl6-10.

Based on the range of compressive strengths obtained from tests, the investigators felt the true

compressive strength of concrete in the segments was probably much greater than the average










design compressive strength. They therefore decided the stress distributions needed no

adjustment.

Summary

The subsequent chapters will discuss the study conducted at the University of Florida that

is the subject of this dissertation. Previous studies have confirmed the existence of nonlinear

thermal gradients in segmental concrete bridges. The shape and magnitudes of the positive

thermal gradients have also, in large measure, been verified with field measurements on existing

segmental concrete bridges in the United States. However, few attempts at measuring stresses

caused by nonlinear thermal gradients have been made. This indicates a need to further

investigate stresses caused by nonlinear thermal gradients.

In the following chapters, design of the laboratory setup and a series of tests aimed at

quantifying stresses caused by the AASHTO design nonlinear thermal gradients are presented

and discussed. Stresses quantified from laboratory test data are then compared with stresses

predicted with the AASHTO recommended method.










Table 3-1. Positive thermal gradient magnitudes
Plain Concrete Surface or Asphalt Topping
Zone T, (oF) T, (oF)
1 54 14
2 46 12
3 41 11
4 38 9
*AASHTO (1999)., "Guide Specifications for Design and Construction of Segmental Concrete Bridges,"
2nd Ed., Washington, D.C., Table 6-1, pg. 10.

Table 3-2. Modulus of elasticity values for selected Ramp P segments
Test Date Pl6-2 Pl6-10 Pl6-17
(Cast 5/24/96) (Cast 6/4/96) (Cast 6/10/96)
9/24/1996 6350 ksi 5900 ksi 5950 ksi
6/17/1997 6080 ksi 5470 ksi 5570 ksi
*Thompson, M. K., Davis, R. T., Breen, J. E., and Kreger, M. E. (1998)., "Measured Behavior of a
Curved Precast Segmental Concrete Bridge Erected by Balanced Cantilevering," Research Rep. 1404-2,
Center for Transportation Research, Univ. of Texas at Austin, Texas, Table 3.1, pg. 55.

Table 3-3. Coefficient of thermal expansion values for selected Ramp P segments
Pl6-2 Pl6-10 Pl6-17 Average
Coefficient of (5.0E-6/oF) (5.4E-6f"F) (5.2E-6/oF) (5.2E-6f"F)
Thermal Expansion (u) 9.0E-6f"C 9.7E-6/oC 9.4E-6/oC 9.4E-6/oC
*Thompson, M. K., Davis, R. T., Breen, J. E., and Kreger, M. E. (1998)., "Measured Behavior of a
Curved Precast Segmental Concrete Bridge Erected by Balanced Cantilevering," Research Rep. 1404-2,
Center for Transportation Research, Univ. of Texas at Austin, Texas, Table 3.2, pg. 56

Table 3-4. Comparison of measured and calculated stresses from measured thermal gradients
Positive Thermal Gradient Negative Thermal Gradient
Segment Average Average Measured/ Average Average Measured/
Measured Calculated Calculated Measured Calculated Calculated
Pl6-2 (368 psi) (441 psi) 086(-251 psi) (-220 psi) 1.3
2.54 Mpa 3.04 Mpa -1.73 Mpa -1.52 Mpa
Pl6-10 (669 psi) (458 psi) 149(-466 psi) (-225 psi) 2.7
4.61 Mpa 3.16 Mpa -3.21 Mpa -1.55 Mpa
Pl6-17 (609 psi) (451 psi) 1.350 (-316 psi) (-219 psi) 1.444
4.20 Mpa 3.11 Mpa -2.18 Mpa -1.51 Mpa

Peak Peak Measured/ Peak Peak Measured/
Measured Calculated Calculated Measured Calculated Calculated
Pl6-2 (584 psi) (624 psi) 0.937 (-426 psi) (-292 psi) 1.463
4.03 Mpa 4.30 Mpa -2.94 Mpa -2.01 Mpa
Pl6-10 (1874 psi) (640 psi) 290(-1144 psi) (-297 psi) 3.4
12.92 Mpa 4.41 Mpa -7.89 Mpa -2.05 Mpa
Pl6-17 (1291 psi) (627 psi) 200(-483 psi) (-287 psi) 1.8
8.90 Mpa 4.32 Mpa -3.33 Mpa -1.98 Mpa
*Thompson, M. K., Davis, R. T., Breen, J. E., and Kreger, M. E. (1998)., "Measured Behavior of a
Curved Precast Segmental Concrete Bridge Erected by Balanced Cantilevering," Research Rep. 1404-2,
Center for Transportation Research, Univ. of Texas at Austin, Texas, Table 7.1, pg. 138.











Table 3-5. Comparison of measured and design stresses (after Thompson et al. (1998))
Positive Thermal Gradient Negative Thermal Gradient
Segment Peak Design Measured/ Peak Design Measured/
Measured Calculated Design Measured Calculated Design
Pl6-2 (584 psi) (518 psi) 129(-426 psi) (-264 psi) 1.5
4.03 Mpa 3.57 Mpa -2.94 Mpa -1.82 Mpa
Pl6-10 (1874 psi) (518 psi) 3.619 (-1144 psi) (-263 psi) 4.359
12.92 Mpa 3.57 Mpa -7.89 Mpa -1.81 Mpa
Pl6-17 (1291 psi) 515 psi 257(-483 psi) (-260 psi) 1.6
8.90 Mpa (3.55 Mpa) -3.33 Mpa -1.79 Mpa
*Thompson, M. K., Davis, R. T., Breen, J. E., and Kreger, M. E. (1998)., "Measured Behavior of a
Curved Precast Segmental Concrete Bridge Erected by Balanced Cantilevering," Research Rep. 1404-2,
Center for Transportation Research, Univ. of Texas at Austin, Texas, Table 7.2, pg. 138.


































strong winds


radiation


light wind


Temperature Distribution
through depth of superstructure
-_ Ttop >Tmiddle


Figure 3-1. Conditions for the development of positive thermal gradients


precipitation


Temperature Distribution
through depth of superstructure
Ttop < Tmiddle


Figure 3-2. Conditions for the development of negative thermal gradients


Figure 3-3. Solar radiation zones for the United States (AASHTO (1989a)., "AASHTO Guide
Specifications, Thermal Effects in Concrete Bridge Superstructures," Washington D.C.,
Figure 4, pg. 5)









AASHTO 1989

39.36" 81 I oF


AASHTO 1994


AASHTO 1999

I ~4~loF


1 "


loF lF2"' 4"


8"I h5oF


Positive Gradients


, 20 .5 o5F


12.3oF 1 4"


Negative Gradients
d = superstructure depth

Figure 3-4. Comparison of AASHTO gradients for zone 3 (for superstructure depths greater than
2 ft)

Top of Concrete Section


o f ~ e p h T ,T ,



Super-
structure


S8"


Figure 3-5. Positive vertical temperature gradient for concrete superstructures (AASHTO
(1999)., "Guide Specifications for Design and Construction of Segmental Concrete
Bridges," 2nd Ed., Washington, D.C., Figure 6-4, pg. 11.)










T, + T2 + T3 = Top


Neutral Axis


Non-Linear
Self-Equilibrating
Temperature
Distribution


Cross Section Thermal Uniform Linear
Gradient Temperature Temperature
Gradient



Figure 3-6. Decomposition of a nonlinear thermal gradient


exATxL


+A


Compression


Tension


Compression


Cross Section


Temperature Strain distribution
Distribution when section fibers are
free to deform independently


Self-equilibrating stresses
develop when compatibility
between fibers is enforced


Figure 3-7. Development of self-equilibrating thermal stresses for positive thermal gradient










laxATxL


-T


SCompression





Tension


Temperature Strain distribution
Distribution when section fibers are
free to deform independently


Self-equilibrating stresses
develop when compatibility
between fibers is enforced


Cross Section


Figure 3-8. Development of self-equilibrating thermal stresses for negative thermal gradient


305


4572


Type Ill Segment Thermocouple Layout
Segments 44A-6 and 44A-15
all dimensions In mm


Figure 3-9. Thermocouple locations (Roberts, C. L., Breen, J. E., Cawrse J. (2002).,
"Measurement of Thermal Gradients and their Effects on Segmental Concrete
Bridge," ASCE Journal of Bridge Engineering, Vol. 7, No. 3, Figure 3, pg. 168.)














JV / .. ~r.: rl.-.;;, ..-;.-a...... :.i


O -~ I ''';''' ''''
ra:ar r:;01
%20



;lull~
e
X5
lJI


__ i

--;~': LI~C l~i:~~.~ ;J~


TB09 THO 0
T852,\ T828,
TB53, L Ta29,
T854 mIg nB
TB49, T831
Tr50, 1 3832
Tg4g T843, TB40, TB37, TB36
TS44, TB41, T83B,
T843 T842 TB39
Section D-D


I


7115/92 11/14/92 3/16/93 7/16/93 11/15/93 3/17/94 7/17/4 11/16/94


Figure 3-10. Comparison of maximum daily A) positive temperature difference. B) negative
temperature difference with design gradients (Roberts, C. L., Breen, J. E., Cawrse J.
(2002)., "Measurement of Thermal Gradients and their Effects on Segmental
Concrete Bridge," ASCE Journal of Bridge Engineering, Vol. 7, No. 3, Figure 6 and
Figure 7, pg. 169-170.)


topto borrom
T802, TSO5, TB10, TS13, TB16,
TSOS, TSO@, T11, T814, T817,
T801 T$O4 TSO? 2808 T~lZ TS15 1818


Ts21, Tsa4,
TB22. TR25.
'89 B2 T2


Figure 3-11. Thermocouple locations (Thompson, M. K., Davis, R. T., Breen, J. E., and Kreger,
M. E. (1998)., "Measured Behavior of a Curved Precast Segmental Concrete Bridge
Erected by Balanced Cantilevering," Research Rep. 1404-2, Center for Transportation
Research, Univ. of Texas at Austin, Texas, Figure 3.14, pg. 53.)


O 9
t FY


t jl
D 81 1a I Y~ 3liTI:l 1114 rCi Idl
e,
r r 131I"''j
f
-81 -(04:
AASHTOLRFO
,,topping: -1 `.lomm asphan ~cpping
placed uzas3
15 L- ------------------
7115192 11114192 3115193 m6183 11115193 3H7184 7117194 IlilWB~
Date


46 ca
Upstation









CHAPTER 4
BEAM DESIGN

Cross Section Design

The Santa Rosa Bay (SRB) Bridge, located near Milton, Florida, was used as a prototype

for design of the laboratory segmental beam that was tested in this study. Laboratory space and

equipment constraints ruled out the use of a full scale replica of the cross-section of the bridge

(see Figure 4-1) as the test specimen. A scaled model of the box-girder section was considered.

This, however, required scaling of the AASHTO design thermal gradients such that

self-equilibrating thermal stresses in the model, determined using the AASHTO recommended

procedure, matched those in the full size bridge. The logistics of imposing scaled AASHTO

thermal gradients on a scaled model of the bridge (e.g. difficulties of scaling aggregates, steel

reinforcement, etc.) eliminated this as a viable option.

Past research constituting the basis of thermal gradients in the design codes were

conducted mainly on segmental box girder bridges. The design codes, however, do not restrict

the use of the gradients to box girder bridges. Furthermore, the codes assume that the gradients

vary only through the depth of the section. This means two cross-sections of different shapes,

with the same depths, section properties, and material properties will experience identical

self-equilibrating thermal stresses due to a nonlinear thermal gradient (from classical Bernoulli

beam theory). For the purpose of determining longitudinal stresses due to bending about the

weak axis, the cross-section of the SRB Bridge can be simplified to that of an un-symmetric

I-section (see Figure 4-2) with the same cross sectional area and flexural stiffness about the weak

axis as the box-girder section. The results of an analysis on the simplified section for

self-equilibrating thermal stresses under the action of the AASHTO positive and negative design

thermal gradients (for Florida) are shown in Figure 4-3 and Figure 4-4, respectively. The









positive gradient leads to the development of compressive stresses (negative) in the top and

bottom fibers of the section while tensile stresses (positive) develop in intermediate parts of the

section. The negative gradient leads to the development of tensile stresses in the top and bottom

fibers of the section and compressive stresses in the intermediate parts of the section.

Throughout this document tensile stresses will be considered positive, and compressive stresses

negative. Of primary interest in this study were the tensile stresses created in the top few inches

of the section by the negative thermal gradient. Consequently, a segmental T-beam with cross

sectional geometry matching the top portion of the modified SRB Bridge section (illustrated by

the hatching in Figure 4-3 and Figure 4-4) was constructed. Analytically determined

self-equilibrating thermal stresses developed in the T-section by the AASHTO design gradients

are also shown in the figures. The key aspects of the thermal stress profile in the SRB Bridge are

captured in the laboratory segmental beam, including stress magnitudes in the top four inches of

the flange, where the thermal gradient is steepest. Details of the cross-section of the laboratory

beam together with analytically determined self-equilibrating thermal stresses due to the

AASHTO design gradients are shown in Figure 4-5.

The flange width of the laboratory test beam was chosen based on recommendations in the

AASHTO LRFD Bridge Design Specifications (AASHTO 2004), which are similar to

recommendations in the ACI Committee 318, Building Code Requirements for Structural

Concrete and Commentary (ACI 318-02). In prestressed beams with very wide flanges, shear

deformations tend to relieve extreme fibers in the flange of longitudinal compressive stress,

leading to a non-uniform distribution of stress (often referred to as "shear lag" effect). Therefore,

for simplicity in design calculations it is recommended that an "effective flange width", which

may be smaller than the actual physical flange width, be used together with the assumption of









uniform stress distribution in the flange. For symmetrical T-beams it is recommended that the

width of slab effective as a T-beam flange not exceed one-quarter of the span length of the beam,

and the effective overhanging flange width on each side of the web not exceed eight times the

slab thickness nor one-half the clear distance to the next web. A width of 2 ft was chosen so that

the entire flange of the beam could be considered effective in resisting the prestress force.

Heating time and thermal energy required to impose the AASHTO nonlinear thermal gradients

on the beam were also considered in limiting the width of the flange to 2 ft.

Segment Design

A 20-foot long segmental beam was designed for use in laboratory testing. The length of

the beam was chosen based on the length of a typical segment of the Santa Rosa Bay Bridge.

The beam was constructed as four 5 ft segments that were post-tensioned together. Equal

segment lengths allowed a single set of forms to be used in casting the segments. The design of

the segments included shear keys (see Figure 4-6), which were used to fit the segments together

and prevent relative vertical sliding during load tests. Details of the shear keys on each segment

can be found in Appendix A. Figure 4-7 shows the segments as designed to fit together for

laboratory testing. Two of the segments (segments 1 and 4) were designated "ambient"

segments because they remained at the ambient laboratory temperature throughout testing.

These segments were reinforced with steel to resist the high prestress forces arising in the

anchorage zones. The remaining two segments (segments 2 and 3) were designated "heated"

segments because they were thermally controlled during tests that involved the application of

thermal loads. The heated segments contained copper tubes for thermal control but did not

contain steel reinforcement, except for three thermocouple positioning steel cages.









Design of Segment Heating System

Thermal control was achieved by passing heated water through layers of copper tubes

embedded in the heated segments of the beam. The number of copper tubes in each layer was

minimized to reduce any reinforcing effect and reduction in concrete cross-sectional properties.

Tests were first conducted on a 5 ft long, 2 ft deep prototype beam to optimize the number of

copper tubes used in the laboratory segmental beam. AASHTO positive and negative design

thermal gradients were imposed on the prototype beam using a varying number of copper tubes

in each layer. The number of tubes in each layer that minimized piping while not sacrificing the

ability to achieve the gradients in a reasonable amount of time, was chosen for use in the

laboratory segmental beam. Copper tube layouts in the prototype and laboratory beam are

shown in Figure 4-8 (A) and (B), respectively. As shown in Figure 4-9, layers 1, 2, and 4 were

located near the slope changes in the AASHTO design thermal gradients. Additional layers of

tubes were positioned to aid in heating the entire beam and in shaping the AASHTO gradients.

The top layer of tubes was placed as close to top of the flange of the segments as possible while

retaining adequate concrete cover (1 in.). This resulted in a slight kink in the thermal gradients

near the top surface of the beam. Test results indicated that this may have affected the

magnitude of measured strains caused by the AASHTO nonlinear thermal gradients in the

extreme top flange fibers of the heated segments (see Chapter 13 and Chapter 14 for a complete

discussion).

Manifold systems were designed to distribute approximately equal flow of heated water to

each pipe, which was key in achieving a uniform distribution of temperature across the width of

the beam. Typical manifolds in the flange and web of the heated segments are shown in Figure

4-10 and Figure 4-11i, respectively. The web manifolds consisted of constant-diameter inlet and

outlet pipes. The flange manifolds required the use of varying-diameter inlet and outlet pipes to









maintain approximately equal flow rates, due to the significant number of tubes in each layer in

the flanges. Typical flow rates through the manifolds in the web and flange of the heated

segments are shown in Figure 4-12 and Figure 4-13, respectively. Tests conducted on the

manifolds showed that they were adequate in uniformly distributing heat across the web and

along the length of the heated segments.

Heat energy was supplied to the beam by pumping water through on-demand electrical

water heaters (see Figure 4-14). The heating system comprised of two S-H-7 Seisco electric

heaters and one DHC-E Stiebel Eltron heater. The Seisco heaters (referred to as Heaters 1 and 2)

could deliver water at temperatures as high asl35 oF. The Stiebel Eltron heater (referred to as

Heater 3) could instantly deliver water at temperatures as high as 125 oF. Pressurized water was

supplied to the heaters (and beam) by 0.5 horsepower Depco submersible pumps. The pumps

were able to operate at temperatures as high as 200 oF, which was required to re-circulate hot

water through the beam. Hoses used with the pumps and the heaters were flexible plastic

braided tubing, which could also operate at high temperatures.

Prestress Design

An external post-tensioning system was designed for post-tensioning the segmental beam.

The choice to use an external post-tensioning system, rather than an embedded internal system

using ducts, was made to avoid problems with concrete void space and interference with internal

instrumentation (thermocouples). Stress levels considered in the design of the post-tensioning

system were AASHTO Service I stresses at the midspan and first interior support of a typical

five-span unit of the Santa Rosa Bay Bridge (see Table 4-1). The Santa Rosa Bay Bridge was

designed using HS20-44 vehicular loads, however, HL-93 vehicular loads (AASHTO LRFD)

were considered in the prestress design of the laboratory beam. In Table 4-1, M/St and M/Sb









refer to stresses in the extreme top and bottom fibers of the cross section of the Santa Rosa Bay

Bridge, respectively.

Four 1-3/8 in.-diameter high-strength DYWIDAG threaded bars were used to post-tension

the beam. An anchorage system fabricated from structural steel shapes was designed to hold the

bars in place during post-tensioning (see Figure 4-15 and Figure 4-16). Steel channels were

placed back-to-back with sufficient space to allow for passage of the DYWIDAG bars. A pair of

back-to-back channels was used for the top and another pair for the bottom bars. Stiffeners were

welded to the channels under the bar bearing plates. The design of the channel systems allowed

the prestress force to be evenly distributed over the web of the beam.

Steel reinforcement was required to resist the high post-tensioning forces in segments 1

and 4, where the post-tensioning systems were anchored. The AASHTO LRFD Bridge Design

Specifications (AASHTO 2004a) was used in the design of reinforcement in the prestress

anchorage zones. Number 3 vertical stirrups were placed 1.75 in. on center to resist principal

tensile stresses that developed in the general anchorage zones. This reinforcement was placed

within 27 in. from the bearing ends of the segments. The approximate method, which is

permitted by the AASHTO LRFD specifications, was the basis of the design. Outside the

anchorage zone, vertical stirrups were placed at 12 in. on center. Stresses in the local zones were

determined using guidelines from the AASHTO (2004a) specifications. A set of three

confinement spirals were used to resist the high local zone stresses. The reinforcement design is

shown in Figure 4-17 and Figure 4-18.











Table 4-1. Approximate Service I stresses in Santa Rosa Bay Bridge
Effective Prestress (psi) Dead + Live Load (psi)
Support Midspan Support Midspan
P/A M/St M/Sb P/A M/St M/Sb M/St M/Sb M/St M/Sb
HS20-44 -700 -338 680 -700 460 -940 810 -1630 -610 1230
HL-93 -700 -338 680 -700 460 -940 810 -1735 -684 1380











24 ft


9 ft-6 5 In


1. ft-3 In 1ft-3n 85 In


r 1 8 In
53 21 13 ft-6 In
4 ft-6 In

100 1 0 14 ft-11 25 In 8f
59 26 7I


16 ft


Figure 4-1. Typical cross-section of Santa Rosa Bay Bridge

517.2 in.

8- in

8inI 31.5 in.

N.A.



26.4 in.




7 inr


196.8 in.


Figure 4-2. I-section representation of SRB bridge cross section

+41 -622 -568
114 In 117 1181 7


12 In
/+111



60 In


-106

Temperature gradient SRB Laboratory beam
(oF) (psi) (psi)


Figure 4-3. Self-equilibrating stresses due to AASHTO positive thermal gradient













41n

121n




20 1n61 .


Temperature gradient
(oF)


Laboratory beam
(psi)


Figure 4-4. Self-equilibrating stresses due to AASHTO negative thermal gradient


4 In


12 In


36 In


20 In


I 1 9

10 In


Cross section of laboratory
segmental beam


Self-Equillbrating Stresses for
AASHTO Negative Thermal Gradlent
(psl)


Self-Equillbrating Stresses for
AASHTO Positive Thermal Gradlent
(psl)


Figure 4-5. Cross section of laboratory beam with analytically determined self-equilibrating
thermal stresses due AASHTO design gradients


S24 In










24 In












28 In I









1 25 1n
10 In ~A B


Figure 4-6. A) Location of shear keys on beam cross section. B) Detailed elevation view of shear
key.


PresressSegment 1 Segment 2 Segment 3 Segment 4Prses

(Ambient) (Heated) (Heated) (Ambient)

5ft 5ft 5ft 5ft


Figure 4-7. Beam segments


















24 in.


1.75 in. 1.5 in.


24 in.

3.5 in.


1. in


3 in 0 a 0
3 in.


8 in.








28 in.


6 in.






18 in.


0000000000

0000000000

000DO

coon,

DD0DD

00000

00000-
1- 3 in.
00000-

, 1.5 in.
10 in.


24 in


to


O ,


2 in. a


2" 3" 3" 2"

10 in.


Figure 4-8. Copper tube layouts for A) Prototype beam. B) Laboratory segmental beam.

24 in.

+41 oF -12.3 oF


8 in.






28 in.


Layer 1
Layer 2
Layer 3


Layer 4



Layer 5



Layer 6


-3.3 oF



0 oF


4I in.


12 in.





20 in.


36 in.


20 in.


* *


AASHTO negative
thermal gradient


AASHTO positive
thermal gradient


Figure 4-9. Copper tube layouts in relation to shape of AASHTO design thermal gradients


1.5 in -


I


~3 in. .6 i


*~r **


._
10In.





10 in.


SEGMENT 2 SEGMENT 3


5ft 5ft

SEGMENT 2 SEGMENT 3


I I


-



-

-

-

-


WATER IN
FROM HEATERS


WATER RETURN
TO TANKS


1.375 in.


0.25 in. I.D. COPPER
TUBES


WATER OUT OF SEGMENT 2
INTO SEGMENT 3 THROUGH
FLEXIBLE PLASTIC TUBING


Figure 4-10. Typical manifold in flange


WATER IN
FROM HEATERS


WATER RETURN
TO TANKS


0.25 in. I.D. COPPER
TUBES


WATER OUT OF SEGMENT 2
INTO SEGMENT 3 THROUGH
FLEXIBLE PLASTIC TUBING


Figure 4-11. Typical manifold in web


1.4

1.2



0.8

P0 0.6

.o 0.4

0.2

0
Incoming
Flow s


2
Longitudinal tube number


Figure 4-12. Typical flow rates through web manifolds

















-


-


-


-


-


0.6


0.5


E 0.4


'3 0.3


E' 0.2


0.1


Incoing1


2 3 4 5 6 7

Longitudinal tube number


Figure 4-13. Typical flow rates through flange manifolds


Figure 4-14. Heating system


y=1.67in

3/81n




'-BACK TO BACK

C8X18.75 CHANNELS


PRESTRESS BAR

_L_

1 1/2 In


Figure 4-15. Cross section view of prestress assembly


L

i i

i i
















C

C


II


CHAIR (NOT SHOWN) LOAD CELL 3 nin 4 i.
HYDRAULIC CYLINDER -

21 in.

1-38 n. DIA. DYWIDG
1-34 in. PLATE D -TRA A
NUT FROM DSIC8X1.75 in. EMBED PLAT

CHANNEL


P3 in. PLATE


Figure 4-16. Elevation view of prestress assembly


5ft


27 in.


129 in.


I24 in.


#3 CONFINEMENT
SPIRALS



'# 3 BARS


36 in


28 in.


r


# 3 STIRRUPS @1.75 in. -# 3 STIRRUPS @ 12 in.


10 in.


Figure 4-17. Mild steel reinforcements in Segments 1 and 4


Figure 4-18. Mild steel reinforcement









CHAPTER 5
BEAM CONSTRUCTION

The segmental laboratory test beam was constructed at the Florida Department of

Transportation (FDOT) Structures Research Center in Tallahassee, Florida. Beam design plans

(see Appendix A) prepared by the University of Florida, were submitted to the FDOT personnel

in the summer of 2005. Construction began in December, 2005 and was completed in February,

2006. Formwork, reinforcement, and thermocouple cages were fabricated by FDOT personnel.

After the segments were cast and cured, they were transported to the University of Florida Civil

Engineering Structures Laboratory in Gainesville.

Placement of Steel Reinforcement, Thermocouple Cages, and Copper Tubes

Because the segments were of equal length, a single set of re-usable wooden forms was

used to cast each of the four segments of the beam. Segments 1 and 4 contained a steel bearing

plate to distribute the anchorage force to the prestress anchorage zones, which contained mild

steel confinement reinforcement (Figure 5-1 (A)). Two steel lifting hooks were placed 1 ft from

each end of the segments as shown in Figure 5-1 (B). The segment joints contained two shear

keys to assist in alignment during prestressing and to transfer shear during load tests (Figure

5-2). The heated segments (Segment 2 and 3) each contained three thermocouple positioning

steel cages (Figure 5-3). In addition, six copper tube manifolds were tied to the thermocouple

cages to ensure that their positions were maintained during concrete placement. Three manifolds

were placed in the flange and three were placed in the web.









Casting of Concrete

The casting sequence of the segments of the laboratory beam is shown in Figure 5-4 and in

Table 5-1 in ascending order. The ambient segments (1 and 4) were cast first so that the heated

segments (2 and 3) could be match cast against them.

A 7000-psi concrete pump mix was used for all four segments. The design mix

proportions are shown in Table 5-2. Delivery tickets for each mix are provided in Appendix C.

Although the slump of the concrete is listed as 5 in. in Table 5-2, the mix was delivered with a

slightly lower water content and slump to allow for adjustments prior to casting. Each segment

was left in the forms for a week in the FDOT research laboratory before being removed and

re-positioned for match-casting the next segment (see Figure 5-5). Finished pours for Segments

1 through 4 are shown in Figure 5-6 (A) through (D), respectively.

Material Tests and Properties

During the casting of each segment, fifteen 6 in. diameter by 12 in. long cylinders were

cast for later use in determining material properties. The material properties determined for the

ambient segments (1 and 4) were the compressive strength and modulus of elasticity (MOE).

For the heated segments (2 and 3), the coefficient of thermal expansion (CTE) was determined in

addition to the compressive strength and elastic modulus. The test setup for compressive

strength and elastic modulus tests are shown in Figure 5-7 (A) and Figure 5-7 (B), respectively.

Compressive strength tests were conducted in accordance with the Standard Test Method

for Compressive Strength of Cylindrical Concrete Specimens (ASTM C 39-01). Modulus of

elasticity tests were conducted in accordance with the Standarddddd~~~~~~dddddd Test M~ethod for Static M~odulus

ofla~sticity and Poisson 's Ratio of Concrete in Compression (ASTM C 469-94). Coefficient of

thermal expansion tests were conducted on each heated segment under laboratory conditions

(in-situ CTE) and on 4 in. diameter by 8 in. long cylinders in accordance with the Standard~~dddddddddddddd









Method of Test for Coefficient of Thermal Expansion of Hydraulic Cement Concrete

(AASHTO TP 60-00). The in-situ CTE tests are discussed in Chapter 9. Cylinders meeting the

specifications of the AASHTO TP 60-00 test method were not taken for Segment 2 therefore

results from this test are only available for Segment 3. The AASHTO TP 60-00 test setup is

shown in Figure 5-8. Tests were conducted in the FDOT Materials Testing Laboratory in

Gainesville, Florida.

The results of compressive strength and modulus of elasticity tests for Segment 1 through

Segment 4 are shown in Table 5-3 through Table 5-6, respectively. Three sets of compressive

strength and elastic modulus tests were conducted for all segments except for Segment 3, the last

segment to be cast. The first two sets of tests were conducted in early 2006 soon after the

cylinders were transported from Tallahassee to Gainesville. The last set of tests was conducted

in late 2006 during the course of conducting experiments on the laboratory segmental beam. In

each test, one cylinder from each segment was used to determine the compressive strength and

two cylinders were used for determining the elastic modulus. The elastic modulus values shown

in the table are the average of elastic moduli determined from two cylinders. Because of

scheduling conflicts, the ages of cylinders at the times tests were conducted were generally not

the same. However, test results for segments 1 and 4 which were cast 11 days apart, match

closely (maximum difference of 2% and 6% in compressive strength and modulus of elasticity

values, respectively). The same is true for segments 2 and 3, which were also cast 11 days apart

(maximum difference of 12% and 5% in compressive strength and modulus of elasticity values,

respectively).

The coefficient of thermal expansion (CTE) of Segment 3 was determined using the

AASHTO TP 60-00 test method. The focus of the test method is the measurement of the change









in length of a fully water-saturated concrete cylinder over a specified temperature range. The

length change is then divided by the product of the original length of the specimen and the

temperature change to give the CTE.

The AASHTO TP 60-00 test procedure is conducted as follows. The tests specimens

consist of concrete cylinders that are 7.0 f 1 in. long and 4 in. in diameter. The specimens are

submerged in saturated limewater at 73 f 4 oF for at least two days. After the cylinders are fully

saturated, they are wiped dry and their lengths measured at room temperature to the nearest

0.004 in. The specimens are then placed in the measuring apparatus shown in Figure 5-8, which

is positioned in a prepared water bath. The temperature of the water bath is set to 50 f 2 oF. The

bath is allowed to remain at this temperature until the specimen reaches thermal equilibrium,

which is indicated by consistent readings of a linear variable displacement transducer (LVDT) to

the nearest 0.00001 in, taken every 10 minutes over a half hour time period. The temperature of

the water bath and the consistent LVDT readings are taken as initial readings. The temperature

of the water bath is then set to 122 f 2 oF. The bath is allowed to remain at this temperature

until the specimen reaches thermal equilibrium in the same manner as for the initial readings.

The temperature of the water bath and LVDT readings are taken as the second readings. The

temperature of the water bath is finally set back to 50 f 2 oF. After thermal equilibrium is

reached the temperature of the water bath and LVDT readings are taken as final readings.

The CTE is calculated using the following equations:

CTE = (Ma /L~o)AT (5-1)
Ma, = s + &L, (5-2)
My, = C, x L, AT (5-3)

where MLa is the actual length change of the specimen during the temperature change, La

is the measured length of specimen at room temperature, AT is the measured temperature










change (increase is positive, decrease is negative), ML,, is the measured length change of

specimen during the temperature change (increase is positive, decrease is negative), Myf is the

length change of the measuring apparatus during the temperature change, and Cf is a correction

factor accounting for the change in length of the measurement apparatus with temperature.

The correction factor (Cr) in Equation 5-3 is usually taken as 9.6E-6/oF, the coefficient of

thermal expansion of stainless steel. CTEs are determined from the expansion (initial and

second readings) and contraction (second and final readings) segments of the test. The two CTE

values thus obtained are averaged to give the CTE of the test specimen, provided the values are

within 0.5E-6/oF of each other. If the CTEs obtained from the expansion and contraction phases

are not within 0.5E-6/oF of each other, the test is repeated until this criterion is satisfied. Results

for the coefficient of thermal expansion of Segment 3 determined using the AASHTO TP 60-00

test procedure are given in Table 5-7. Three cylinders were used for the test.

Application of Prestress

The goal of prestressing was to produce a net prestress with a selected vertical eccentricity

and no net horizontal eccentricity. The magnitude and vertical eccentricity of prestress were

chosen to impose a negative curvature (less compression in the extreme top fibers than in the

bottom of the web) on the beam with stresses comparable to Service I stresses at a typical

interior support of a four-span unit of the Santa Rosa Bay (SRB) bridge. The total prestress force

was also required to provide sufficient compression in the extreme top fibers of the beam such

that an appreciably high load at the cantilevered end of the beam, which could be accurately

measured in the laboratory, would be required to open the joint at midspan. To achieve the stress

state described above, a total prestress force of 376 kips (94 kips per bar) with a vertical

eccentricity of 1.5 in. below the centroid of the beam was applied to the beam (see Figure 5-9).









Prior to post-tensioning, the segments were placed on wooden blocks at the same elevation

with matching joint faces in contact. This reduced the possibility of excessive movement as the

joints closed during post-tensioning. The prestress anchorage systems were suspended from the

ends of Segments 1 and 4 using a pair of threaded bars connected to two steel channels, which

were bolted to the ends of the segments (Figure 5-10 and Figure 5-11). This arrangement

allowed the vertical eccentricity of prestress to be varied as necessary. Four DYWIDAG

post-tensioning bars were then installed. Tandem 60-ton Enerpac hollow core single-acting

jacks, pressurized with a manifold system attached to a single pump, were used to stress two bars

on either side of the web at a time. The set of four bars were stressed sequentially, 2 bars on

either side of the beam at a time. Prestressing was applied incrementally as shown in Table 5-8

with the force monitored using 200 kip hollow core load cells mounted on each bar (Figure

5-11). Prestressing forces in opposing bars were slightly different (less than 8%) due to

construction imperfections and variations in bar placement.










Table 5-1. Segment cast dates
Segment Number Date Cast
1 12/01/2005
4 12/12/2005
2 01/19/2006
3 02/02/2006

Table 5-2. Concrete pump mix proportions
Mix Number FC82JC
Strength (psi) 7000
W/C Ratio 0.31
Slump (in) 5 +/- 1"
Air Content (%) 4.5 +/- 1.5%
Plastic Unit Weight (lbs/cf) 140. 1 +/- 1.5

Material ASTM Type
Cement C 150 I/II 820
Cement C 618 F. Ash 160
Water -- -- 304
Fine Aggregate C 33 Sand 1095
Aggregate C 33 #89STONE 1400
Admixture C 260 AIR Dosage rates vary with
Admixture C 494 W/Reducer manufacturers recommendations

Table 5-3. Compressive strengths and moduli of elasticity of Segment 1
SEGMENT 1 (Cast 12/01/2005)
Age (days) Compressive Strength (psi) Modulus of Elasticity (ksi)
77 9300 4862
124 9820 5000
350 10210 5362

Table 5-4. Compressive strengths and moduli of elasticity of Segment 2
SEGMENT 2 (Cast 01/19/2006)
Age (days) Compressive Strength (psi) Modulus of Elasticity (ksi)
28 7090 3785
75 8360 4000
319 9690 5180

Table 5-5. Compressive strengths and moduli of elasticity of Segment 3
SEGMENT 3 (Cast 02/02/2006)
Age (days) Compressive Strength (psi) Modulus of Elasticity (ksi)
28 7150 3836
62 7950 4000
361 10970 5443

Table 5-6. Compressive strengths and moduli of elasticity of Segment 4


SEGMENT 4 (Cast 12/12/2005)
Age (days) Compressive Strength (psi) Modulus of El
66 9110 4575


lasticity (ksi)










Table 5-6. Continued
SEGMENT 4 (Cast 12/12/2005)
Age (days) Compressive Strength (psi) Modulus of Elasticity (ksi)
113 10030 5000
339 10250 5158

Table 5-7. Coefficient of thermal expansion (CTE) of Segment 3 (AASHTO TP 60-00)
CTE (per oF)
Cylinder 1 7.92E-6
Cylinder 2 7.77E-6
Cylinder 3 7.83E-6
Average 7.84E-6

Table 5-8. Selected post-tensioning force increments
Post-tensioning Load Cell Readings(kips)
Step P1 P2 P3 P4
1 ~29.2 18---
2 29.2 18 43.8 46.7
3 48.3 32.2 43.8 46.7
4 48.3 32.2 76.3 68.8
5 76.7 68.8 76.3 68.8
6 76.7 68.8 97.6 93.2
7 94.6 100.8 97.6 93.2
8 94.6 100.8 107.7 100.9
9 106.5 112.1 107.7 100.9
10 106.5 112.1 111.8 106.1
Final Loads 97.2 89.2 93.3 92.4
























Figure 5-1. A) Open form with mild steel reinforcement. B) Closed form with mild steel
reinforcement and lifting hooks.


Figure 5-2. Form for shear keys





























Figure 5-3. Heated segment with copper tubes, thermocouple cages and thermocouples



SEGMENT 1 SEGMENT 2 SEGMENT 3 SEGMENT 4
December 1, 2005 January 19, 2006 February 2, 2006 December 12, 2005


Figure 5-4. Beam layout with casting sequence


Figure 5-5. Match-casting of segment








































----"I 'r


Figure 5-6. Finished concrete pours for A) Segment 1. B) Segment 2. C) Segment 3.
D) Segment 4.














r- dia4 A i B

Figure 5-7. A) Compressive strength test setup. B) Elastic modulus test setup.












Baea Plato Die.= 10`-


SprinA Landed 1.VDT





4" DAs. Concrets
Core shown


3 Semi-ophancel sigport
Butlans equLliy spaced
labout 2" Da. Obrle


Frmne Helit=


Front Visrw


Figure 5-8. AASHTO TP 60-00 test setup


LOAD




-----------beam centroid


RESS

CELL


jBAR


ch ch




eh ,eh


P.T. system centroid


Figure 5-9. Bar designations and design eccentricities (West)


L



























Figure 5-10. Prestress assembly (East)


Figure 5-11i. Elevation view of prestress assembly (North)









CHAPTER 6
INTSTRUMENTATION

Segments 2 and 3 of the laboratory segmental beam, designated "heated segments"

because they were thermally controlled during testing, were internally instrumented with

thermocouples prior to being cast, and externally instrumented with strain gauges, strain rings,

and linear variable displacement transducers (LVDTs) prior to post-tensioning of the beam.

Load cells were used to monitor reactions, applied mechanical loads, and prestress forces in the

post-tensioning bars. This chapter presents a detailed description of the instrumentation used.

Thermocouples

Laboratory-fabricated thermocouples were embedded in the heated segments to monitor

temperatures during thermal loading of the beam. The range of temperature that was to be

measured was 50 oF to 130 oF. A Teflon-neoflon type T thermocouple wire, produced by

OMEGA Engineering, Inc., was used for fabrication of the thermocouples due to its wide range

of temperature sensitivity (-150 oF to 392 oF). Thermocouples were positioned in the segments

with the aid of cages made of small-diameter steel, which were then placed in the forms at

desired locations before concrete was cast (see Figure 6-1).

Thermocouples were vertically positioned to monitor temperature changes at heights

corresponding to slope changes in the imposed thermal gradients. Additional thermocouples

were placed at intermediate points between slope changes to facilitate control of the shape of the

thermal gradient being imposed. The layout of thermocouples in relation to the shape of the

AASHTO positive and negative thermal gradients is in shown in Figure 6-2. Three

thermocouple cages were embedded in each of the two heated segments and total of thirty nine

thermocouples were attached to each cage. Thermocouple cages were placed 3 in, away from

the ends and at the middle of each segment (see Figure 6-3). This arrangement was used to









ensure the thermal gradient being imposed was longitudinally uniform. Thermocouple labels at

the sections in Figure 6-3 are shown in Figure 6-4.

Electrical Resistance Concrete Strain Gauges and Strain Rings

Foil type electrical resistance strain gauges (Figure 6-5) were bonded to the surfaces of the

heated segments of the beam for monitoring beam behavior under mechanical and thermal

loading (Figure 6-6). The strain gauges were of type PL-60-1 1-5LT, manufactured by Tokyo

Sokki Kenkyuj o Co., Ltd. The gauges had a gauge length of 60 mm (2.4 in.), and a temperature

compensation number of 11, which is adequate for eliminating strains due to unrestrained

thermal expansion/contraction of steel and concrete from measured strain values. To eliminate

the influence of temperature variations (of the lead wires) on measured strains, three-wire type

gauges were used.

In addition to strain gauges, four Strainstall Type-5745 sealed strain rings (Figure 6-7)

were mounted at the centroid of the beam at midspan (Figure 6-6 (C) and (D)). Data from the

strain rings were used to validate readings from strain gauges mounted at the same location. The

detailed locations of strain gauges and strain rings through the depth of the beam on either side

are shown in Figure 6-8, Figure 6-9, and Figure 6-10. The strain gauges located in the vicinity of

the j oint at midspan, (J2), were of particular importance in determining the load at which the

joint opened. Strain gauges and strain rings located at the centroid of the beam at midspan were

used to monitor movement of the neutral axis of the beam after the midspan j oint began to open.

With the exception of gauges located at the centroid of the beam, strain gauges located on the

North and South of joint J2 were placed such that the center of each gauge was 2 in, away from

the joint. Strain gauges located at the centroid at midspan were centered beneath strain rings,

which had a greater gauge length (4.5 in.). Thus, the distance from the common center of these

gauges to the j oint at midspan was 3.6 in. Strain gauges on top of the flange were located 5.5 in.










away from the j oint. Because of the presence of copper tubes protruding from the concrete on

the North side of the beam, two strain gauges were installed on the North side of the flange while

three were installed on the South side. Therefore, a total of three strain gauges were located

above the neutral axis of the section on the North side compared with four on the South side.

The labeling convention used for strain gauges is explained in Figure 6-11. Strain rings were

labeled in a similar manner by replacing the "S" for strain gauge with "R" for strain ring (see

Figure 6-12).

Linear Variable Displacement Transducers (LVDT)

DCTH Series LVDTs, produced by RDP Electrosense, were used in measuring deflections

and opening of the joint at the midspan of the beam. The LVDTs had a stroke of 1 in. Four

LVDTs were used to measure the vertical deflection at the cantilevered end of the beam (see

Figure 6-13), relative sliding (if any) between Segments 2 and 3, deflections close to the mid-

support, and deflections close to the end-support. To detect and track the depth of joint-opening

at the midspan of the beam, six LVDTs were mounted on the South side and three were mounted

on the top flange across the j oint (see Figure 6-14). The labeling convention used for LVDTs is

shown in Figure 6-15.

Load Cells

Load cells used to measure the magnitudes of applied loads and reactions were Model

3000 load cells, manufactured by Geokon, Inc. The layout of load cells on the post-tensioned

beam is illustrated in Figure 6-16. The force in the hydraulic jack, which was used to load the

beam at the cantilevered end, was measured using a 200-kip load cell (Figure 6-17 (A)). 200-kip

load cells were mounted on each of the four DYWIDAG post-tensioning bars (Figure 6-17 (B)).

These load cells were used to monitor prestress levels in the beam. 150-kip and 75-kip load cells









were installed at the mid-support (Figure 6-17 (C)) and end-support (Figure 6-17 (D)) of the

beam, respectively, for measuring reactions under the effect of applied loads.

Data Acquisition

The instrumentation layout for the prestressed beam is shown in Figure 6-18 and Figure

6-19. Data from the variety of instruments shown in the figures were collected using the

National Instruments model SCXI-1000DC Data Acquisition (DAQ) System (see Figure 6-20).

Data were collected from a total of 192 thermocouples (32 per section), 15 LVDTs, and 7 load

cells. Forty-one data acquisition channels were reserved for collecting data from strain gauges,

which were connected to the DAQ system based on the cross section of interest in test being

conducted. During the application of thermal loads, the DAQ system was set to acquire 3600

samples of data from each instrument in five minutes, which were then averaged and recorded at

the end of each 5 minute interval. During the application of mechanical loads, the system was

set to acquire 100 samples of data from each instrument, which were averaged and recorded

every second. Compared with mechanical loading a lower data acquisition rate was used during

thermal loading because of the longer time needed to heat or cool the concrete.
































Figure 6-1. Thermocouple cage with attached thermocouples


24"
1" I -12.3 F



9"


24"


1" I
.

9'







o" B


+41 F

+11 F


O.F


lo"


Figure 6-2. Layout of thermocouples in relation to shape of A) positive thermal gradient.
B) negative thermal gradient.














SEGMENT 2 SEGMENT 3


THERMOCOUPLE CAGE

-I3 in.


SECTION A SECTION B SECTION C SECTION D

Figure 6-3. Location of thermocouple cages in Segments 2 and 3


SECTION E


SECTION F


- 3 in.















A-T-1


A-T-6


A-T-2 A-T-3 A-T-4 A-T-5


A-T-7 A-T-8 A-T-9 A-T-10
A-T-12 A-T-13 A-T-14 A-T-15


A-T-16 A-T-17 IA-T-18
A-T-19 A-T-20 IA-T-21

A-T-22 A-T-23 IA-T-24
A-T-25 A-T-26 A-T-27



A-T-28 A-T-29 IA-T-30


B-T-1 B-T-2 B-T-3 B-T-4 B-T-5


B-T-6 B-T-7 B-T-8 B-T-9 B-T-10
B-T-11 B-T-12 B-T-13 B-T-14 B-T-15


B-T-16 B-T-17m B-T-18
B-T-19 mB-T-20 m B-T-21

B-T-22 mB-T-23 m B-T-24
B-T-25 mB-T-26 m B-T-27



B-T-28 B-T-29 IB-T-30


C-T-1 C-T-2 C-T-3 C-T-4 C-T-5


C-T-6 C-T-7 C-T-8 C-T-9 C-T-10
C-T-11 C-T-12 C-T-13 C-T-14 C-T-15


C-T-1 6 C-T-17 IC-T-18
-T-19 C-T-20 C-T-21

C-T-22 C-T-23 IC-T-24
C-T-25 C-T-26 C-T-27



C-T-28 C-T-29 IC-T-30


A--1 AT3 --3

A-T-34 A-T-35 IA-T-36




A-T-37 A-T-38 IA-T-39



SECTION A


B-T-31 B-T-32 IB-T-33



B-T-34 B-T-35 IB-T-36

B-T-37 B-T-38 IB-T-39



SECTION B


C--3 C--2CT3

C-T-34 C-T-35 IC-T-36




C-T-37 C-T-38 IC-T-39



SECTION C


D-T-1 D-T-2 D-T-3 D-T-4 D-T-5


D-T-6 D-T-7 D-T-8 D-T-9 D-T-10
D-T-11 D-T-12 D-T-13 D-T-14 D-T-15


b-T-16 D-T-17 DD-T-18
b-T-19 D-T-20 ID-T-21

b-T-22 D-T-23 ID-T-24
b-T-25 D-T-26 ID-T-27


E-T-1 E-T-2 E-T-3 E-T-4 E-T-5


E-T-6 E-T-7 E-T-8 E-T-9 E-T-10
E-T-11 E-T-12 E-T-13 E-T-14 E-T-15


E-T-16 mE-T-17 m E-T-18
E-T-19 mE-T-20 m E-T-21

E-T-22 E-T-23m E-T-24
E-T-25 mE-T-26 m E-T-27



E-T-28 E-T-29 IE-T-30


F-T-1 F-T-2 F-T-3 F-T-4 F-T-5


F-T-6 F-T-7 F-T-8 F-T-9 F-T-10
F-T-11 F-T-12 F-T-13 F-T-14 F-T-15


F-T-16 mF-T-17 m F-T-18
-T-19 F-T-20 F-T-21

-T-22 F-T-23 F-T-24
-T-25 F-T-26 F-T-27



F-T-28 F-T-29 IF-T-30


D-T-28 D-T-29 ID-T-30



D-T-31 D-T-32 ID-T-33



b-T-34mD-T-35m D-T-36


D-T-37 mD-T-38m D-T-39



SECTION D


E-T-31 E-T-32 IE-T-33



E-T-34 E-T-35 IE-T-36


mE-T-37 nE-T-38 m E-T-39


SECTION E


F-T-31 F-T-32 IF-T-33



-T-34 -T-35m IF-T-36


F-T-37 mF-T-38 m F-T-39



SECTION F


Figure 6-4. Thermocouple labels in Segments 2 and 3


























Figure 6-5. Strain (foil) gauge


Figure 6-6. Strain gauges close to joint at midspan; A) North flange. B) South flange. C) North
web. D) South web.













































S2-T-D1 S3-T-D1


S2-N-S-58-35 5 2NS3-55S2-N-S-02-35 5"0o S3-N-S-02-35 5 S3-N-S-30-35 5 S---83
SEGMENT 2 S2-N-S-02-32H0 00 S3-N-S-02-32 SEGMENT 3
S2-N-S-58-2 2NS3-28 5 S2-N-S-02-28 5 oo S3-N-S-02-28 5 S3-N-S-30-28 5 S---82
14./"S2-N-S-02-27 3 S3-N-S-02-27 3
S2-N-S-58-21 3 C.G~ _S2-N-S-30-21 3 S2-N-R-03-21 3 S3-N-R-03-21 3 C.G S3-N-S-30-21 3 S3-N-S-58-21 3



S2-N-S-02-815 H H S3-N-S-02-815

MS-N-S-58-6 3 H S2-N-S-30-6 3 0 S3-N-S-30-6 3 S3-N-S-58-6 3

S-N-S-58-0 6 S2-N-S-30-0 6 S2-N-S-02-0 6 L;LS3-N-S-02-0 6 S3-N-S-30-0 6 S3-N-S-58-06



L2 Li


Figure 6-8. Instrumentation details (North side)


Figure 6-7. Strain ring


LVDT

LOAD CELL

FOIL GAUGE
STRAIN RING


I


J2


J3


30 in.


30 in.


30 in.


30 in.


8 in.





28 in.























1 S3-T-D1 S2-T-D1



o 3SS5-5 S3s-S--30-355 S3-S-S-02-35 5 MS2-S-S-0323355 "S2-S-S-30-35 5 S-S583 o
a SEGMENT 3 S3s-S-S-2-32 H HS2-S-S-02-32 SEGMENT 2 o
S3-S-S-58-28 5 ,,0 J2-S-D-30 2 S2-S-S-58-28 5
on S3-S-S-30-285 14.67" S3-S-S-02-28 5 S2-S-S-02-28 5 MS2-S-S-30-28 5 o


Figure 6-9. Instrumentation details (South side)

FOIL GAUGE

IHLVDT


t i 'J2-TS-D-9 5
| S2-TS-S-5 5-8 25 0 | e0 S3-TS-S-5 5-7 25


I


- -


LVDT

LOAD CELL

FOIL GAUGE

STRAIN RING


J3


J2


J1


30 in.


30 in.


30 in.


S3-S-S-02-27 3
S3-S-R-03-21


S3-S-S-02-15 6


S3-S-S-02-8 1 M


S3-S-S-02-0 6 U


IS2-S-S-02-27 3
SJ-S-D-235
S2-S-R-03-21 3

0 S2-S-S-02-15 6


M S2-S-S-02-8 1

O J2-S-D-04
a S2-S-S-02-0 6


S3-S-S-58-21 3 S3-S-S-30-21 3 C.G.
o


0 S3-S-58-138 S3-S-S-30-13 80


C.G. S2-S-S-30-21 3


S2-S-S-58-21 3


28 In.


0 S2-S-S-30-13 8 S2-S-S-58-13 8 0

0 S -S--306 3 S2--S-8-63

H S2-S-S-30-06 S2-S-S-58-0 6


H S3-S-S-58-6 3

SS3-S-S-58-0 6


S3-S-S-30-6 30

S3-S-S-30-0 6m


SOUTH 12 in.





NORTH 12 in.


J2-T-D -te S3-T-S-5 5-0 75 BA
CENTERLINE


S2-TN-S-5 5-7 75 e0 I S3-TN-S-5 5-7 25
I H J2-TN-D-9 5


Figure 6-10. Instrumentation at midspan (top flange)


Segment Number

North (N) or South (S) Z

Strain Gauge vo

Distance from Joint 2 ul

Distance Above Bottom of Beam




Figure 6-11. Typical labeling convention for strain gauges


1. L2










Segment Number
North (N) or South (S) Face
Strain Gauge
Distance from Joint 2
Distance Above Bottom of Beam


Figure 6-12. Typical labeling convention for strain rings


Figure 6-13. LVDT for measuring deflection at cantilevered-end of beam


Figure 6-14. LVDTs mounted across joint at midspan on A) South side and B) top flange


Joint (J) or Seg. (S) Number

Location (T = Top, S = Side)

Displacement Device Number


Figure 6-15. LVDT labeling convention









0 LOAD CELL


Figure 6-16. Load cell layout


Figure 6-17. Load cells for measuring; A) applied load. B) prestress. C) mid-support reaction.
D) end-support reaction.










LVDT
LOAD CELL
FOIL GAUGE
e- STRAIN RING
DIAL GAUGE


Figure 6-18. Instrumeentation layout (North)

LVDT
LOAD CELL
FOIL GAUGE
-e STRAINRING
DIAL GAUGE



S4-T-D1P OL1 S3-T-D1S2T-1


S1-T-D1


I li_ _Ir: _il I


SL5
L6
L7


L4


SEG 2


SEG 4


SEG 1


L2 J


d~b


Figure 6-19. Instrumeentation layout (South)


Figure 6-20. A) DAQ System. B) Connection of instrumentation to DAQ System.


SEG 3









CHAPTER 7
SETUP AND PROCEDURES FOR MECHANICAL LOADING

The setup for conducting laboratory experiments is illustrated in Figure 7-1. A picture of

the post-tensioned beam in the laboratory is shown in Figure 7-2. The beam was supported 1.7 ft

from the end of Segment 1 (end-support) and 10.5 ft from the cantilevered-end of the beam

(mid-support). It was mechanically loaded 2.7 ft from the cantilevered-end. Fabrication details

of the support systems and loading frame can be found in Appendix B.

The end-support consisted of back-to-back channels supported by four all-thread bars

bolted to the laboratory strong floor. A 75-kip load cell was placed between the back-to-back

channels and a 3/8-in. thick, 12 in. by 12 in, steel plate. Between the steel plate and the surface

of the beam a 5/8-in. thick, 12 in. by 12 in. neoprene pad was used to distribute the reaction to

the concrete. The mid-support consisted of a 1.5 in.-thick, 10 in. by 10 in, steel plate supported

by four all-thread rods. The rods were 0.5 in, shorter than the 150-kip load cell at mid-support,

which was placed between the steel plate and a C15 x 33.9 channel bolted to the laboratory

strong floor. The 0.5 in. clearance between the load cell and the steel rods allowed the load cell

to fully carry loads due to the self-weight of the beam and the actuator without any contribution

from the steel rods. A 5/8-in. thick, 12 in. by 12 in. neoprene pad was placed between the steel

plate and the bottom web of the beam to distribute the mid-support reaction to the concrete. The

loading frame, which was designed to carry loads up to 400 kips, consisted of two steel columns

and two deep channel beams. For convenience, a temporary I-section was bolted to the load

frame columns below the deep channel beams, to support a 60 ton manually pressurized jack,

which was used to apply mechanical loads to the beam (see Figure 7-3). A 200-kip load cell was

placed directly under the jack to measure applied loads. A 3/8-in. thick, 12 in. by 12 in, steel










plate and 5/8-in. thick, 12 in. by 12 in. neoprene pad were used to distribute the applied load to

the concrete.

Opening of Joint between Segments 2 and 3

The primary aim of applying mechanical loads to the beam was to open the joint between

segments 2 and 3 (j oint J2), creating zero stress conditions from which the effects of thermal

loads could be quantified. This is illustrated in Figure 7-4 through Figure 7-6.

Stresses at j oint J2 created by prestress and the self-weight of the beam were taken as the

baseline or reference stresses. Stresses due to the AASHTO nonlinear thermal gradients, which

were expected to be uniformly distributed across the width of joint J2, were quantified relative to

the baseline stresses at joint J2. Quantifying average stresses caused by the AASHTO nonlinear

thermal gradients in the extreme top fibers of the beam at j oint J2 required the determination of

the load corresponding to the average reference stress, QNT, (See Figure 7-4). In addition, loads

corresponding to average stresses in the extreme top fibers created by the superposition of the

AASHTO nonlinear positive thermal gradient on the reference stresses QPG, (See Figure 7-5)

and the AASHTO nonlinear negative thermal gradient on the reference stresses, QNG, (See Figure

7-6) had to be determined. Average stresses due to the thermal gradients were quantified from

the difference in loads initiating j oint opening (QPG QNT for the positive gradient and

QNG QNT for the negative gradient) through back calculation. Though the concept of

quantifying thermal stresses by opening the joint between segments 2 and 3 is illustrated for the

extreme top fibers in Figure 7-4 through Figure 7-6, it is applicable at any depth at joint J2 where

loads which cause the section fibers to loose contact at that depth can be determined.

It was determined from sectional analysis using conventional beam theory that a maximum

load of about 40 kips was required to relieve the average longitudinal stress in the extreme top

fibers of the beam at the j oint (i.e. open the j oint) created by the superposition of stresses due to









the self-weight of the beam, prestress, and the AASHTO nonlinear positive or negative thermal

gradient. To allow for the possibility that the experimental setup might deviate somewhat from

beam theory, loads of up to 60 kips were applied during the tests. The configuration of load and

support points ensured that the maximum moment due to applied loads occurred at the joint at

midspan (joint J2). This eliminated the development of high tensile stresses within the beam

segments since tensile stresses could not be transmitted across the j oint.










Thermal Loads


Figure 7-2. Segmental beam in laboratory


Figure 7-1. Test setup






































C.G.


Figure 7-3. A) Loading frame. B) 60-ton j ack


Apply load QNT to create
zero stress at top fiber


Compression Tennsion


Cetroid


Prestress (P) Self-weight (SW) Joint-opening
load (QNT)


Figure 7-4. Ideal stress diagrams without thermal loads


SUM (P +SW +QNT)


Apply load QPG to create
zero stress at top fiber


Compression | Tension


Centroid


Prestress (P) Self-weight (SW) Positive Joint-opening SUM (P +SW +PG +QPG)
gradient (PG) load (QPG)


Figure 7-5. Ideal stress diagrams with positive thermal gradient


Z










Compression Tennsion


Apply load QNG to create
zero stress at top fiber


Prestress (P) Self-weight (SW) Negative Joint-opening SUM (P +SW +NG +QNG)
gradient (NG) load (QNG)


Figure 7-6. Ideal stress diagrams with negative thermal gradient









CHAPTER 8
SETUP AND PROCEDURES FOR THERMAL LOADING

Thermal profiles were imposed on the heated segments of the beam by passing heated

water at laboratory controlled temperatures through strategically placed copper tubes embedded

in the concrete. Four thermal profiles were imposed on the heated segments: uniform

temperature distribution, linear thermal gradient, AASHTO nonlinear positive thermal gradient,

and AASHTO nonlinear negative thermal gradient.

This chapter describes the methods and piping arrangements used to impose each thermal

profile. Throughout this chapter, thermocouple locations, pipe layers, and heaters are referenced.

Three water heaters were used to heat the water pumped through the beam. Heaters 1 and 2 (H1

and H2) were capable of supplying water at temperatures as high as 135 oF. These heaters were

used to provide high temperatures typically ranging from 105 oF to 135 oF. Heater 3 (H3) was

capable of supplying water at temperatures as high as 125 oF, and was utilized for temperatures

ranging from 86 oF to 100 oF. Pipe layer designations, thermocouple section locations, and the

layout of thermocouples at each section are shown in Figure 8-1 through Figure 8-3,

respectively. The "x" markings in Figure 8-3 represent thermocouples that were not connected

to the DAQ system because they were not needed to capture pertinent data. To minimize heat

loss from the beam, 0.5-in. thick Styrofoam boards were used to insulate the surfaces of the

beam (see Figure 8-4).

Uniform Temperature Distribution

Before the beam was prestressed, initial thermal testing was conducted that involved

heating the segments uniformly to determine the in-situ CTE. The uniform heating was also one

part of the AASHTO negative thermal gradient.










Changing laboratory temperatures (i.e. from early morning through noon till evening) and

the fact that the heated segments were insulated prevented the segments from being at a uniform

temperature prior to the start of imposing prescribed thermal profiles. This was because the large

mass and low thermal conductivity of the concrete segments prevented them from rapidly

adjusting to changing laboratory temperatures. In particular, the bottom webs of the segments

were generally cooler than the top flanges of the segments. Tap water, which ranged in

temperature from 74 oF to 85 oF, depending on the month in which tests were conducted, was

used to bring the entire segments to a uniform reference temperature by circulating the water

through the segments overnight using the piping configuration shown in Figure 8-5. After the

desired thermal configuration had been imposed, this same approach was then used to cool the

segments back to the reference temperature.

The piping configuration shown in Figure 8-6 was used to uniformly heat the segments.

This created a temperature differential that was uniform over the height of the segment. With

Heaters 1 and 2 set to the target temperature, water was continuously circulated through the

segments. Heater 3 was not used in this setup primarily because of limitations on the heat energy

that it could deliver at the high flow rates which were required to uniformly heat the segments

longitudinally. Temperatures in the concrete were monitored from thermocouple readings.

Thermal profiles at each section were also periodically plotted using an average of readings

taken from each row of thermocouples throughout the depth of the beam. Heater settings were

then updated to offset deviations from the target temperature. When the desired profile was

achieved at each section, temperatures were held in steady state for about 30 to 45 minutes as

readings were taken periodically. The segments were then cooled to the reference temperature.









The average time it took to impose a uniform profile on a single heated segment was about

10 hours. In the case of two segments, the system was kept running for between 20 to 30 hours.

Linear Thermal Gradient

A second set of thermal tests were conducted that involved imposing a linear thermal

gradient from 0 oF at the bottom of the web to +41 oF at the top of the flange. This gradient,

which leads to no stress development in a simply supported structure, was also used in

determining the in-situ coefficients of thermal expansion of the heated segments.

The piping configuration shown in Figure 8-7 was used to impose the linear thermal

gradient after circulating tap water through the segment to establish a uniform reference

temperature. Heaters 1, 2, and 3 were set to temperatures 41 oF, 23 oF, and 12 oF above the

reference temperature, respectively. Water from Heaters 1 and 2 was mixed and circulated

through pipe layer 3. The temperature of mixed water was about 32 oF above the reference

temperature. There was no flow in pipe layers 2 and 6. Thermocouple readings and thermal

profiles at each section were monitored and changes to the heater settings made when necessary.

When the target thermal gradient was achieved, temperatures were held in steady state for about

30 to 45 minutes as readings were taken periodically. The segment was then cooled back to the

reference temperature. The average time it took to impose the linear profiles on a single heated

segment was about 9 hours.

AASHTO Positive Thermal Gradient

The piping shown in Figure 8-8 was used to impose the AASHTO nonlinear positive

thermal gradient on the heated segments of the beam. Before circulating heated water through

the segments, tap water was circulated overnight to establish the reference temperature.

Heaters 1 and 3 were set to 41 oF and 11 oF above the reference temperature, respectively.

Although tap water was pumped from a reservoir through Heater 2, the heater was turned off for









the duration of the test. The water pumped through Heater 2 was mixed with water from

Heater 1 and circulated through layer 3, which was required to be at a temperature about 7 oF

above the reference temperature. The temperature of mixed water was regulated by controlling

contributions to the mix from Heater 1 (turned on) and Heater 2 (turned off). The bottom 20-in.

portion of the beam was maintained at the reference temperature by circulating tap water through

layers 4, 5, and 6. This produced the 0 oF temperature change in the gradient (relative to the

reference temperature). Thermocouple readings and the shape of the gradient at each section

were monitored and changes to heater settings were made when necessary. When the AASHTO

positive thermal gradient profile was achieved, temperatures were kept at steady state for about

30 to 45 minutes as readings were taken periodically. The beam was then cooled to the reference

temperature. The average time it took to impose the AASHTO positive thermal gradient on the

heated segments was about 7 hours.

AASHTO Negative Thermal Gradient

The AASHTO nonlinear negative thermal gradient was imposed on the heated segments

using the setup shown in Figure 8-9. To impose this gradient, the segments had to be cooled

from the reference temperature rather than heated. Since the setup for thermal control could only

be used to heat the segments, two reference temperatures were involved in imposing the negative

gradient. The first reference temperature (referred to as the low reference temperature) was

imposed by circulating tap water through the segments using the piping configuration previously

shown in Figure 8-5. The low reference temperature was imposed to maintain consistency with

procedure for imposing the thermal profiles discussed previously. After establishing the low

reference temperature, a uniform temperature increase of about 40 oF was imposed on the

segments using the plumbing in Figure 8-6. The temperature of the segments after the 40 oF

increase was referred to as the high reference temperature. Heater settings and layer










temperatures required to impose the gradient were based on the high reference temperature.

Heater 1 was set to a temperature 12.3 oF below the high reference temperature. This

corresponded to the -12.3 oF temperature change in the AASHTO nonlinear thermal gradient.

The bottom 20-in. portion of the beam was maintained at the high reference temperature by

circulating water at that temperature through layers 4, 5, and 6, using Heater 2. This

corresponded with the 0 oF temperature change in the gradient. Heater 3 was connected to layer

2 and was only used when needed to bring the temperature of layer 2 to 3.3 oF below the high

reference temperature. Water from heaters 1 and 2 was mixed and circulated through layer 3.

Thermocouple readings and the shape of the gradient were monitored throughout the test, and

changes to heater settings were made as necessary. When the target gradient was achieved,

temperatures were kept in steady state for about 30 to 45 minutes as readings were periodically

taken. The beam was then cooled to the low reference temperature. The average time required

to impose the AASHTO negative thermal gradient after imposing the high reference temperature

was about 7 hours.


































-THERMOCOUPLE CAGE

13 in. 3 in.

SEGMENT 2 SEGMENT 3


24 in.


8 in. * *



36 in. ***

28 in.







10in.


Figure 8-1. Pipe layers


Layer 2
Layer 3

Layer43


Layer 5


Layer 6


SECTION A


SECTION B SECTION C SECTION D


SECTION E


SECTION F


Figure 8-2. Thermocouple locations in heated segments















X

X








~


SECTION A


SECTION B


SECTION C


SECTION D


SECTION E


SECTION F


Figure 8-3. Thermocouples used at each section


Figure 8-4. Insulated heated segments












-* * *O*-TAP WATER
coooomIN

TAP WATER OUT o o a o a o e




o ** TAP WATER IN









TAP WATER OUT o a .



Figure 8-5. Piping configuration used to impose initial condition




a D a O a O~HEATER 1IN

HEATER 1OUT o ao o o o a



-O a **HEATER 2IN a




VALVE CLOSED

HEATER OUT -o a as.



Figure 8-6. Piping configuration used to impose uniform temperature differential




HEATER 1OUT O a O a O a OtHEATER 1 I
coooooo
MIXED OUT o * o+MIXE



HEATER 2OUT o a HEATER I



HEATER 3 OUT o a o* EATER 3 IN



TAP WATER OUT O a O* -TAP WATER IN VALVE PARTIALLY OPEN
TO MIX WATER


Figure 8-7. Piping configuration used to impose linear thermal gradient















HEATER 1OUT o a o a o o o~HEATER 1IN
HEATER30UTl o o a o o O ~HEATER31N
MIXED OUT MIE


* CTAP WATER IN


- *


~O O 0~


TAP WATER OUTI o


-k VALVE PARTIALLY OPEN
TO MIX WATER


Figure 8-8. Piping configuration used to impose AASHTO nonlinear positive thermal gradient




HEATER 1OUT o a o a o a THEATER 1IN H1 P
HEATER 3OUTl o o a o a THEATER 3 IN *O
MIXED OUT* **** MIE



HEATER 2 IN I


~00-


HEATER OUTloOP


TO MIX WATER


Figure 8-9. Piping configuration used to impose AASHTO nonlinear negative thermal gradient


































101









CHAPTER 9
IN-SITU COEFFICIENT OF THERMAL EXPANSION

In-situ CTE tests were conducted to determine coefficients of thermal expansion that were

representative of the composite behavior of the concrete segments, copper tubes, and

thermocouple cages embedded in segments 2 and 3 of the laboratory test beam. The setup for

the in-situ CTE tests is shown in Figure 9-1. The segment being tested was supported on two

wooden blocks 6 in, away from the ends. LVDTs were placed vertically along the centerline of

the cross section on both ends of the segment to record the elongation of the segment. Initially

three LVDTs were used to record displacements at locations 0.5 in. below the top of the flange,

at the centroid of the segment (21.3 in. from the bottom of the segment), and 0.5 in, above the

bottom of the segment. Subsequently, with the acquisition of additional LVDTs, four and then

five LVDTs were used in the testing. The three and four LVDT setups were used in tests

conducted on Segment 2. The four LVDT setup was used in one test conducted on Segment 3.

In the remaining tests conducted on Segment 3, the five LVDT setup was used.

Two non-stress inducing thermal profiles were imposed on the segment: a uniform

temperature change of about 41 oF above the reference temperature (about 85 oF) of the segment,

and a linear thermal gradient varying from 0 oF at the bottom of the web to +41 oF at the top of

the flange. The uniform and linear thermal profiles were imposed using the piping setups in

Figure 8-6 and Figure 8-7, respectively. The composite CTE of the segment was calculated as:

3rotoz~dA,
A (9-1)
avg Ac




TG ra (9-3)
avg A,










a m (9-4)
TG


where Ams is the average axial elongation of the segment, Ears is the average engineering

strain of the segment, TGg is the average temperature differential, a is the coefficient of

thermal expansion, 3roto is the total measured axial elongation at the location of the LVDT, L is

the length of the segment, Tgrad iS the temperature gradient/change imposed on the segment, and

A, is the cross sectional area of the segment.

It was expected that both uniform and linear temperature distributions would produce the

same CTE values since neither involved nonlinearity of temperature profile, and since it was

assumed that the segments had uniform distributions of moisture content.

A laboratory imposed uniform temperature change on Segment 2 and the corresponding

measured end displacements are shown together with the target thermal profile and calculated

longitudinal displacement in Figure 9-2 and Figure 9-3, respectively. A uniform temperature

change imposed on Segment 3 and the corresponding measured end displacements are shown

together with the target thermal profile and calculated longitudinal displacement in Figure 9-4

and Figure 9-5, respectively. Measured concrete temperatures after uniform profiles were

imposed on segments 2 and 3 are shown in Figure 9-6 and Figure 9-7, respectively. Laboratory

imposed thermal profiles were within 2% of the target profiles for both segments. In Figure 9-3

and Figure 9-5, calculated displacements were determined using CTEs determined from

measured data and target temperature profiles. There was more variability in measured total

displacements for Segment 3 (see Figure 9-5) about the calculated displacement than for

Segment 2 (see Figure 9-3). This was partly because five LVDTs were used at each end of

Segment 3 whereas only three LVDTs were used at each end of Segment 2. In addition, the









coefficient of variation of the temperature profie imposed on Segment 3 with respect to the

target (1.9%) was higher than the coefficient of variation of the temperature profie imposed on

Segment 2 (1.4%). The variability in measured displacements was also partially attributed to

nonlinearities in the laboratory imposed thermal profies and varying moisture contents

throughout the volume of the segments.

It should be noted that in the AASHTO standard test method for determining the

coefficient of thermal expansion of concrete (AASHTO TP 60-00) the influence of moisture

content on CTE is eliminated by fully saturating the concrete test cylinders (and thus ensuring a

uniform distribution of moisture in the test specimen). In the in-situ CTE tests, measured end

displacements were higher at the ends where heated water entered the segments than at the ends

where water exited the segments. The orientations of Segment 2 and Segment 3 together with

the inlet and outlet of heated water during testing are shown in Figure 9-8 and Figure 9-9,

respectively. Measured end displacements were higher on the West end of Segment 2 than on

the East end of the segment (see Figure 9-3). For Segment 3 measured end displacements were

higher on the East end than on the West end of the segment (see Figure 9-5). This was because

prior to achieving a constant temperature profile longitudinally, the inlet sections of each

segment experienced higher temperatures than the outlet sections, which led to higher measured

elongations at the inlet ends than at the outlet ends of the segments.

A laboratory imposed linear temperature profile on Segment 2 and the corresponding

measured end displacements are shown together with the target thermal profile and calculated

longitudinal displacement in Figure 9-10 and Figure 9-11, respectively. A linear temperature

change imposed on Segment 3 and the corresponding measured end displacements are shown

together with the target thermal profile and calculated longitudinal displacement in Figure 9-12









and Figure 9-13, respectively. Measured concrete temperatures after linear profiles were

imposed on segments 2 and 3 are shown in Figure 9-14 and Figure 9-15, respectively.

Laboratory imposed linear temperature gradients were within 2% of the target temperature

profile for both segments. The coefficients of variation of the laboratory imposed thermal

gradients with respect to the target gradients were 3.7% and 4% for Segment 2 and Segment 3,

respectively. This is in agreement with the closer match between calculated and measured total

displacements for Segment 2 (see Figure 9-11) than for Segment 3 (see Figure 9-13). In

calculating the coefficient of variation of laboratory imposed linear gradients, the standard error

about the target gradient was used in place of the standard deviation about the mean. This

explains the higher coefficients of variation for laboratory imposed linear temperature gradients

compared with laboratory imposed uniform temperature changes. In Figure 9-11, measured

displacements at the West end of Segment 2 were lower than measured displacements at the East

end in the lower half of the segment, which was expected since the inlet of heated water to the

segment was at the East end. In the upper half of the segment, however, measured displacements

were higher at the West end than at the East end of the segment. This was because the target

temperature at the top of the flange was exceeded in imposing the linear thermal gradient. In an

attempt to cool the top flange to the target temperature it was slightly overcooled, leading to

lower temperatures and corresponding lower elongations at sections close to the inlet (East end)

of water to the segment than at sections close to the outlet (West end) of water from the segment.

For Segment 3, measured displacements were higher at the East end than at the West end of the

segment. This was consistent with higher temperatures developing at the inlet of heated water to

the segment (East end) than at the outlet of heated water from the segment (West end) prior to

achieving a constant thermal profile longihtdinally.










The coefficients of thermal expansion determined from in-situ tests and the

AASHTO TP 60-00 procedure, which was discussed in Chapter 5, are summarized in Table 9-1.

In-situ CTEs determined with linear thermal gradients were generally higher than in-situ CTEs

determined with uniform temperature distributions. The slight increase in CTE (an average of

about 8%) associated with linear thermal gradients was attributed to the influence of copper

tubes on the longitudinal expansion of the concrete segments and non-uniform moisture contents

of the segments. The influence of thermocouple positioning steel cages on the longitudinal

expansion of the segments was deemed insignificant since they were placed transversely in the

segments.

The CTE for Segment 3, determined using the uniform temperature profie, was equal to

the CTE of the segment determined using the AASHTO standard method (AASHTO TP 60-00).

It is, however, likely that a repeat of the in-situ test would have yielded a slightly different CTE

for the segment. In the AASHTO procedure, the tolerance within which two CTEs determined

from the same cycle can be averaged is 0.5E-6/oF. The differences between CTEs determined

with the linear profie and CTEs determined with the uniform temperature distribution were

0.7E-6/oF and 0.5E-6/oF for segments 2 and 3, respectively. Since the in-situ CTEs were

determined from different tests using different temperature distributions, these differences were

deemed acceptable. The arithmetic average of the CTEs of each segment determined using the

procedures discussed above was used in predicting thermal stresses and strains later in this study.










Table 9-1. Experimentally determined coefficients of thermal expansion
Uniform Temp. Linear Thermal Gradient AASHTO TP 60-00
Distribution (In-situ) (In-situ) Method
Segment 2 7.3E-6/oF 8.0E-6/oF N/A
Segment 3 7.8E-6/oF 8.3E-6/oF 7.8E-6/oF

























































LVDT
FOIL GAUGE
SSTRAIN RING
LVDT
) 5 n


4In X4 In STEEL o HEATED SEGMENT
COLUMN *- 14 67 In








o 01n41

























1081












-b Section A
M Section B
M Section C Flange
- Target



Web


)I so
O 0.005 0.01


.


0 5 10 15 20 25 30
Temperature Difference (deg. F)


35 40 45


Figure 9-2. Uniform temperature change imposed on Segment 2


- Measured (West)
Measured (East)
,, Measured (Total)
WC Calculated


0.015 0.02
Displacement (in.)


0.025 0.03 0.035


Figure 9-3. Measured end-displacements due to uniform temperature change imposed on
Segment 2

































0 5 10 15 20 25 30
Temperature Difference (deg.F)


35 40 45


Figure 9-4. Uniform temperature change imposed on Segment 3


0 0.005 0.01 0.015 0.02
Displacement (in.)


0.025 0.03 0.035


Figure 9-5. Measured end-displacements due to uniform temperature change imposed on
Segment 3











M ecio

35 M Section B
M TargetFlange
30


2 25 Web




W 15


10





85 90 95 100 105 110 115 120 125 130
Temperature (deg. F)


Figure 9-6. Measured concrete temperatures in Segment 2 (uniform profile)


90 95 100 105 110
Temperature (deg.F)


115 120 125 130


Figure 9-7. Measured concrete temperatures in Segment 3 (uniform profile)
















































I


~tr"~


10 4



10 9
o~ 05m


C"LVDT
FOIL GAUGE
SSTRAIN RING


WATER OUTLET


WATER INLET


Figure 9-8. Orientation of Segment 2 during testing (South elevation)

C~LVDT

WATSO A AR G WATER INLET
WAE STANRN


LVDT



41n X4 1n STEEC o 1
COLUMN -


\\FS ND


0 5 n


SEGM ENT3


14 67


'In

EAST N

In



In


C G


SHORING-



Figure 9-9. Orientation of Segment 3 during testing (South elevation)




























112


































0 5 10 15 20 25 30
Temperature Difference (deg. F)


35 40 45


Figure 9-10. Linear temperature gradient imposed on Segment 2


0 0.005 0.01 0.015 0.02
Displacement (in.)


0.025 0.03 0.035


Figure 9-11. Measured displacements due to linear thermal gradient imposed on Segment 2


































0 5 10 15 20 25 30 35 40 45
Temperature Difference (deg. F)


Figure 9-12. Linear thermal gradient imposed on Segment 3


0 0.005 0.01 0.015 0.02
Displacement (in.)


0.025 0.03 0.035


Figure 9-13. Measured displacements due to linear thermal gradient on Segment 3



























10





85 90 95 100 105 110 115 120 125 130
Temperature (deg. F)


Figure 9-14. Measured concrete temperatures in Segment 2 (linear profile)


85 90 95 100 105 110
Temperature (deg. F)


115 120 125 130


Figure 9-15. Measured concrete temperatures in Segment 3 (linear profile)









CHAPTER 10
RESULTS PRE STRESSING

In this chapter strains recorded during prestressing of the laboratory segmental beam are

presented and discussed. The four segments of the beam were supported on wooden blocks as

shown in Figure 10-1 during prestressing. This support system was changed to that shown in

Figure 10-2 prior to the beginning of mechanical and thermal load tests on the laboratory beam.

Labels assigned to the DYWIDAG post-tensioning bars and the design eccentricities of the bars

from the centroid of the beam were presented in Chapter 5. They are duplicated in Figure 10-3

for convenience. Final forces in the prestress bars and measured horizontal eccentricities

immediately after tensioning are given in Table 10-1. The vertical eccentricity of the four-bar

group was 1.5 in. below the centroid of the beam.

Concrete strains near (j oint J2) were continuously recorded as the beam was prestressed.

The strain data collected during prestressing provided important information regarding the

distribution of strains at the joint. This information was vital in interpreting data collected during

later mechanical load tests in which the joint was slowly opened to relieve stresses due to the

initial pre-compression and self-weight of the beam. The locations of strain gauges on the beam

can be found in Chapter 6.

Figure 10-4 and Figure 10-5 show the increase in strain at j oint J2 on the North side of the

beam. Figure 10-6 and Figure 10-7 show the strains at the same joint on the South side and

Figure 10-8 shows the strains on top of the top flange. Also included in Figure 10-4 through

Figure 10-8 are calculated strains at the top flange at joint J2. Strains were calculated using

laboratory determined concrete material properties (e.g. elastic modulus) and measured prestress

forces. Gaps, if any, at joint J2 prior to prestressing were neglected in the calculations. In these

figures negative strains indicate compression. The top two bars, which were located above the









centroid of the beam, were tensioned first (up to a total prestress of about 50 kips). As shown in

Figure 10-8 the top flange strain gauges detected very little strain until the prestress force was

between 50 kips and 125 kips. One explanation for this behavior is differential shrinkage of

concrete at the edges of the beam segments. As Figure 10-9, shows the top surfaces of the

segments were exposed to the laboratory environment after segment casting. It is likely that

shrinkage was greater in the exposed portion of the top flange than in other surfaces which

remained covered during curing. It is believed that this differential shrinkage led to a narrow gap

between the top flanges of segments 2 and 3. Consequently, no strain was detected until

sufficient prestress force had been applied to close the gap.

Differential shrinkage is also believed to be the reason for the systematically lower strains

measured at the top flange compared with calculated strains (see Figure 10-8). This may have

been due to the assumption in the calculations, that contact surfaces at j oint J2 were smooth and

in full contact (with no gaps). Calculated strains at the top flange close to j oint J2 were higher

than measured strains at the top flange for all prestress levels. The same was not the case for

measured strains close to the top flange on the sides of the j oint (see Figure 10-4 through Figure

10-7). Comparison of data from gauges on the sides of the j oint with calculated top flange

strains was more representative of expected behavior. This was because the 1.5 in. vertical

eccentricity in prestressing was expected to lead to the development of lower compressive strains

on top of the flange than at lower elevations.

Measured concrete strains through the depth of the beam segments near j oint J2 are shown

in Figure 10-10. These readings were taken immediately after prestressing was completed. Also

shown in the plot are calculated strain profiles determined with the measured prestress forces and

eccentricities (horizontal as well as vertical) shown in Table 10-1. Two observations can be









made when comparing the measured and calculated strains. The first is that strains vary

considerably with depth. The other is that the average measured strains on the North side are

greater in magnitude than those on the South side with calculated strains along the vertical line of

symmetry of the beam between the two.

Differences in the average measured strains on the North and South sides of the segments

can be attributed to the unequal total prestress forces on the North (190.4 kips) and South (181.6

kips) sides of the beam, and the 0.5 in. net horizontal eccentricity in prestressing (see Figure 10-3

and Table 10-1). As Figure 10-10 shows, calculated strains on the North and South sides of joint

J2 determined with measured prestress forces and measured horizontal and vertical eccentricities

were higher on the North side than on the South side of the j oint. It was explained in Chapter 5

that the goal of applying an equal prestress force to each bar was not achieved because the

prestress anchorage system prevented independent post-tensioning of the DYWIDAG bars. The

0.5 in. net horizontal eccentricity was most likely the result of movement of the suspended

post-tensioning anchorage system as the beam was prestressed. The moment due to the

unintended horizontal eccentricity caused the development of compressive strains on the North

side and tensile strains on the South side of the vertical axis of the beam. This moment, together

with the moment developed as a result of the inequality in the total prestress on the North and

South sides of the beam, led to the development of lower magnitude strains on the South side of

the beam compared to the North side.

A likely explanation for the variation in measured strains through the depth of the

segments is an imperfect fit (segment-to-segment contact) at j oint J2. This could have occurred

during the match-casting process or during positioning of the segments for prestressing. An

imperfect fit would lead to data from the strain gauges being influenced by stress concentrations









in the surface fibers of the beam segments. The unusually high strains measured on the North

side of Segment 3 from strain gauges located 1.1 in, and 21.3 in. from the bottom of the segment

(see Figure 10-10) might have been due to localized effects at those points on the segment. The

exact causes of the high measured strains at these locations are unknown, however, at about 7%

of the total prestress force the strain gauges designated S3-N-S-02-1.1 and S3-N-S-3.6-21.3 (see

Figure 10-5) had registered about 36% and 55% of the respective total measured strains at their

locations. Except for the two high strain points in the profile of Segment 3 on the North side,

strain profiles on identical sides of segments 2 and 3 compared quite well.

Strains measured transversely across the width of the flanges of segments 2 and 3 near

joint J2 are shown in Figure 10-11. Also shown in the figure are calculated strains that take into

account the vertical eccentricity in prestressing only (shown as average calculated strains in the

legend) and calculated strains that take into account both vertical and net horizontal eccentricities

in prestressing (shown as calculated strains in the legend). Data in Figure 10-11 were collected

from three strain gauges on Segment 3 and two strain gauges on Segment 2. The presence of

LVDT mounts on Segment 2 prevented the placement of a strain gauge close to the center of the

flange of that segment. In an ideal situation, strains measured across the width of the flanges

near j oint J2 should be uniform (see the average calculated strains in Figure 10-11). Because of

the measured net horizontal eccentricity in prestressing, the distribution of measured strains

across the width of the flange was expected to look like the calculated strains in the figure. A

possible reason for the nonlinear distribution of measured strains across the width of the flange is

a lack of a full contact fit at the joint.

The nonlinearities in the measured strains were not expected to affect the quantification of

thermal stresses caused by the AASHTO nonlinear thermal gradients. As discussed in Chapter 7,









stresses due to prestress, self-weight, and any additional forces that may have been induced at

j oint J2 when the support system of the beam was changed (see Figure 10-1 and Figure 10-2),

were taken as reference stresses. These stresses were then relieved when joint J2 was opened,

and therefore did not directly enter into calculations of thermally induced stresses.

Partial losses in prestressing force were initially measured over a period of approximately

three weeks and are plotted for each bar in Figure 10-12. The percentage change in total

prestress with time is shown in Figure 10-13. Fluctuations about the general downward trend in

Figure 10-12 and Figure 10-13 were the result of daily temperature variations. Prestress levels

were also checked before and after each mechanical and thermal load test conducted after the

initial monitoring period. The maximum percentage reduction in total prestress over the course

of the 4-month period during which tests were conducted on the laboratory segmental beam was

about 3.5% of the initial total prestress.










Table 10-1. Prestress magnitudes and horizontal eccentricities
Bar Designation Force (kips) Horizontal Eccentricity Designation Horizontal
Eccentricity (in.)
Pl 97.2 el 8.6
P2 89.2 e2 8.1
P3 93.2 e3 8.6
P4 92.4 e4 8.1


















---- ---'
(AMBIENT)


SEGMENT 1 SEGMENT 2 SEGMENT 3 SEGMENT 4


Location of
interest
(Joint J2)


Beam centroid


Centroid of 4 prestress bars


(H EATED)


(H EATED)


(AMBIENT)


Lab. floor10.5ft
Wooden block L~b:lo
Mid-support


East


- West


20'
PT: Post Tensioning Force

Figure 10-1. Segment support during prestressing
Thermal Loads


20'
PT: Post Tensioning Force

Figure 10-2. Beam support for mechanical and thermal load tests


i


PT 3f


PT--










North~ South


;S BAR

L


LOAD CELI



------------beam centroid



P.T. system centroid


el e



e3 ,e4


Figure 10-3. Post-tensioning bar designations and eccentricities


S300

S250

200

150
O
I-


0 1-
-600


-500 -400 -300 -200 -100 0 100
Strain (microstrain)


Figure 10-4. Measured concrete strains near j oint J2 due to prestress (Segment 2, North)


L














400

350

S300

S250

Z 200

S150
O


-600 -500 -400 -300 -200 -100 0 100
Strain (microstrain)


Figure 10-5. Measured concrete strains near j oint J2 due to prestress (Segment 3, North)


S300

S250

S200


o s


O U
-600


-500 -400 -300 -200 -100 0 100
Strain (microstrain)


Figure 10-6. Measured concrete strains near j oint J2 due to prestress (Segment 2, South)














400

350

S300

S250

Z 200

S150
O


-600 -500 -400 -300 -200 -100 0 100
Strain (microstrain)


Figure 10-7. Measured concrete strains near j oint J2 due to prestress (Segment 3, South)


S300

S250

S200


o s


O U
-600


-500 -400 -300 -200 -100 0 100
Strain (microstrain)


Figure 10-8. Measured concrete strains near j oint J2 due to prestress (Top flange)









Differential shrinkage caused by top flange
exposure to environment during curing


ELEVATION


SECTION


Figure 10-9. Effect of differential shrinkage on top flange strains


-600 -550


-500 -450 -400 -350 -300 -250 -200 -150 -100 -50
Strain (microstrain)


Figure 10-10. Measured concrete strains due to prestress through depth of segments near j oint J2


Top flange exposed




Formwork coverage
~ During curing













- Segment 2(Measured)
N Segment 3 (Measured)
H Calculated
& aeragle CalcullatedJ


Soutfh




North


-550 -500 -450 -400 -350 -300 -250 -200 -150 -100 -50 0
Strain (microstrain)


-101

12 *
-600


Figure 10-11. Measured concrete strains due to prestress across width of segment flanges near
joint J2 (Top flange)


0 10 20 30 40 50 60 70 80 90 100 110 120 130 140 150
Time (days)


Figure 10-12. Variation of prestress forces with time














0.25
0.2

-0.25
-0.5
-0.75

o1
LL-1.25
S-1.5
S-1.75
-2
.5 -2.25
S-2.5
c*
O -3
-3.25
-3.5
-3.75
-4
0 10 20 30 40 50 60 70 80 90 100 110 120 130 140 150
Time (days)



Figure 10-13. Change in total prestress force with time









CHAPTER 11
RESULTS -1VIECHANICAL LOADING

The behavior of the laboratory segmental beam under the action of mechanical loads

applied at the cantilevered end of the beam is discussed in this chapter. The objective of the

mechanical load tests was to determine: the load at which the j oint at midspan (j oint J2) opened;

and the effect that this j oint opening had on the overall behavior of the beam. As discussed in

Chapter 7, opening of joint J2 was used to create zero reference stress conditions from which

stresses due to the AASHTO nonlinear thermal gradients could later be quantified.

Two methods of detecting j oint opening were used. One involved the use of strain gauges

mounted close to j oint J2. The other involved the use of LVDTs mounted across j oint J2 at

specified depths. Data collected from the LVDTs and strain gauges are presented and compared

in the following sections. In addition, data collected from strain gauges located at the middle of

segments 2 and 3 (30 in, away from joint J2 on both sides) and vertical deflection data will be

presented and discussed.

In the plots presented in the following sections, loads refer to mechanical loads applied by

the hydraulic j ack. Beam response is also due to loads applied by the hydraulic j ack. The total

vertical mechanical load carried by the beam during tests was the sum of the self-weight of the

beam (measured at about 11 kips) and the load applied by the hydraulic jack. Tensile strains

plotted in this chapter represent relief of initial compressive strains (caused by prestressing) and

are positive. Compressive strains represent additional increments of compression that add to the

initial precompression and are negative.

Detection of Joint Opening Strain Gauges Close to Joint at Midspan

The detection of joint opening with strain gauges is illustrated in Figure 11-1 and Figure

11-2. Prior to opening of the j oint, the change in strain is linear with respect to applied load.









After the joint opens, concrete fibers initially in contact are unable to carry any significant

additional strain. Strain gauges located at the level of joint opening therefore show no change in

strain with increasing load, and the load vs. strain curve becomes almost vertical. The load at

which strains initially stop increasing is the load that causes the joint to open at the location of

the strain gauge. Strain at this load is equal in magnitude, but opposite in sign, to the initial

strain at the same location that was caused by prestress and self-weight.

For strain gauges located on the side of the beam (see Figure 1 1-1), the initial slope of the

load vs. strain curve is inversely proportional to the distance of the gauge from the neutral axis of

the gross section. Strain gauges located farther away from the centroid of the contact area of the

gross section indicate lower j oint-opening loads than strain gauges located closer in distance to

the centroid. In Figure 11-1, Q1 is less than Q2 because SG1 and SG2 are closer in distance to

the centroid of the contact area than SG3 and SG4. This is because the joint starts opening at the

top of the section and slowly progresses downward as indicated by the direction of the moment

in Figure 11-1. The point at which the load vs. strain curve changes slope (becomes vertical) is

dependent on the compressive strain at the location of the strain gauge. In Figure 11-1 it is

assumed that the initial strain, si, at the location of SG1 and SG2 is less than the initial strain, 82,

at the location of SG3 and SG4 (due to the location of the line of action of the post-tensioning

force, i.e. below the centroid of the contact area of the gross cross section).

Strain gauges located on top of the flange have identical load vs. strain curves (see Figure

11-2). This is because strain is uniformly distributed across the width of the flange. The strain at

which the load vs. strain curve becomes vertical, si, is the initial uniform strain in the top fibers

of the flange before the application of mechanical loads.










Though the post-joint-opening curves are shown as vertical in Figure 11-1 and Figure

11-2, this is not always the case. In prestressed beams, the sudden increase in prestress

associated with opening a joint may lead to a slight compression in fibers that are no longer in

contact. The post-joint-opening curve then has a slight curvature, which diminishes as the depth

of joint-opening moves farther away from the location of the fibers (with increasing load).

Typical load vs. strain curves on the North and South sides of joint J2, plotted with

laboratory measured loads and concrete strains, are shown in Figure 11-3 and Figure 11-4,

respectively. Opening of the j oint at the location of each strain gauge was indicated by the point

at which the curves initially became vertical. Generally, strain gauges located above the centroid

of the contact area of the cross section prior to the j oint opening (referred to simply as the

centroid of the gross cross section in the Eigures) indicated opening of the joint. Strain gauges

located below the centroid of the gross cross section registered compressive strains. This was

expected since the moment at joint J2 due to the applied loads led to relief of existing

compressive strains above, and the addition of compressive strains below the centroid of the

contact area at the joint. The high decompression shown by the strain gauge located at the

centroid of the gross cross section in Figure 11-3 (S3-N-S-3.6-21.3) as the depth of joint opening

approached the centroid was consistent with the high compressive strain recorded by the same

gauge during prestressing (see Figure 10-5 and the measured strain profie on the North side of

Segment 3 at elevation 21.3 in. in Figure 10-10).

Figure 11-5 shows the variation of concrete strain with load on top of the flanges of

segments 2 and 3 close to joint J2. Strain gauges located on the top flange generally detected

very low strains with applied load compared with strain gauges on the sides of the segments.

This was expected since low strains were recorded in the extreme top fibers of the segment










flanges during prestressing (see Figure 10-8 and Figure 10-11). Of the Hyve strain gauges on the

top flange, it was possible to detect j oint-opening from two: one on the South of Segment 2 and

the other on the North of Segment 3 (see Figure 11-5). The load vs. strain curves of the other

three strain gauges were almost vertical throughout the entire loading process. Normally, the

behavior of the three gauges with almost vertical load vs. strain curves would indicate that the

joint opened at the top flange almost immediately after the beam was loaded. This, however,

was not the case. As shown in Figure 11-6, some concrete at the top flange at joint J2 had

broken off during transportation and handling of the segments. Gauges at the locations where a

significant amount of concrete had broken off showed almost no change in strain with load even

though the j oint was not open. This was because concrete fibers on opposite sides of the j oint at

the locations were not in contact prior to loading the beam. Strain gauges at other locations

where this condition was less severe registered some strain as the beam was loaded. The

nonlinear behavior of measured strain with load in Figure 1 1-3 through Figure 1 1-5 was the

result of the condition of joint J2 at the top flange as shown in Figure 1 1-6, and changes in the

stiffness of the contact area at the j oint as it was slowly opened.

As discussed in the beginning paragraphs of this section, the strain at which the j oint

opened at the location of a gauge was expected to be equal to the initial compressive strain at that

location. Before beginning mechanical load tests on the beam, the supports were changed from

the system shown in Figure 10-1 to that shown in Figure 10-2. The changes in strain that took

place during this transition were not recorded. Hence the exact distribution of initial strain at

j oint J2 was not known prior to the application of mechanical loads. In spite of the unknown

changes in strain that took place while changing the beam support conditions, the measured

strains at which the joint opened, though not equal in magnitude, were still consistent with the









distribution of strains due to prestress. As shown in Table 11-1, strain gauges near joint J2 on

the sides of the flange, which showed higher strains due to prestress, indicated opening of joint

J2 at higher strains than gauges located in areas of lesser prestrain.

Strain gauges above the centroid of the contact area of the section and at identical locations

on either side of the joint were expected to detect j oint-opening at the same load. Furthermore, it

was expected that gauges at higher elevations would indicate opening of the j oint at lower loads

than gauges at lower elevations (see Figure 11-1). However, strain gauges located above the

centroid of the contact area showed the j oint opening at higher loads on the North side (Figure

11-3) than on the South side (Figure 11-4). This was partly due to differences in the elevations

of the gauges. The strain gauge designated S3-N-S-02-27.4 on the North side of the joint

showed the joint opening at a load of about 48 kips (see Figure 1 1-3), while the strain gauge at

the same location on the South (S3-S-S-02-27.5) showed the joint opening at a load of about

38 kips (see Figure 11-4). Furthermore, the strain gauge located at elevation 28.6 in. on the

South side of the j oint (see Figure 1 1-4) showed joint opening at a lower load (21 kips) than two

strain gauges located above it on the North side of the j oint as shown in Figure 11-3 (3 1 kips for

the gauge at elevation 33.5 in, and 41 kips for the gauge at elevation 30.3 in.). This was

indicative of the j oint opening earlier on the South side than on the North side, and was

consistent with the distribution of measured strains through the depth of the beam due to

prestress (see Figure 10-10).

Because of the distinct change in strain that occurred when the j oint opened, strain gauges

were the instrument of choice in determining j oint-opening loads.

Measured concrete strains through the depth of the beam near j oint J2 on the North and

South sides are shown in Figure 11-7 and Figure 11-8, respectively. Strain data shown in Figure









11-3 through Figure 11-5 were used in plotting the strain profiles in Figure 11-7 and Figure 11-8.

In Figure 1 1-7 and Figure 1 1-8, j oint-opening at each elevation within j oint J2 is indicated when

no further strain change with load occurs at that depth. As explained previously, the fact that top

flange strains were nearly constant with respect to load in Figure 11-8 was not indicative of

opening of joint J2, but was probably the result of the condition at the j oint shown in Figure

11-6.

As shown in Figure 1 1-7 and Figure 1 1-8, the neutral axis of the contact area at j oint J2

(point of intersection of strain profile with zero strain axis) gradually moved downward with

increasing load. Furthermore, the movement of the neutral axis was smaller on the North side of

the j oint (see Figure 1 1-7) than on the South side (see Figure 1 1-8), indicating a rotation of the

neutral axis about the centroid of the contact area. As illustrated in Figure 1 1-9, the downward

movement of the centroid of the contact area at joint J2, as the beam was incrementally loaded,

was due to opening of the j oint. Rotation of the neutral axis about the centroid of the contact

area was attributed to the net out-of-plane horizontal eccentricity in prestressing. Movement of

the neutral axis with load is illustrated in Figure 11-10.

The change in prestress as the beam was incrementally loaded is shown in Figure 11-11.

Bars 1 and 2 were expected to undergo the same change in force with load since they were at the

same elevation. Similarly, bars 2 and 4 were expected to undergo the same change in force.

However, because the opening of joint J2 was greater on the South side than on the North side,

the change in force in the bars on the South side (P2 and P4) was greater than the change in force

in the bars on the North side (Pl and P3, respectively) after the joint opened. The forces in bars

1 and 2 increased with load while forces in bars 2 and 3 generally decreased with load. This was

because bars 1 and 2 were located above the centroid of the gross section and bars 3 and 4 were









located below the centroid of the gross section (see the position of prestress bars in Figure

1 1-1 1). At a load of about 40 kips (see Figure 1 1-9) the depth of joint opening caused the

centroid of the contact area at j oint J2 to move below the location of bars 3 and 4, leading to an

increase in force with load in these bars.

Detection of Joint Opening LVDTs Across Joint at Midspan

Determination of joint-opening using LVDTs mounted across the j oint is illustrated in

Figure 1 1-12 and Figure 11-13. LVDTs mounted across a j oint indicate opening of the j oint at

the location of the LVDT when the initial slope of the load vs. displacement curve changes as a

result of the reduction in stiffness of the section.

Prior to the joint opening, LVDTs measure the displacement between the mounts

(supports) of the LVDT as a result of strain in concrete. The initial slope of the

load vs. displacement curve is inversely proportional to the distance between the mounts of the

LVDT and the distance of the LVDT from the centroid of the contact area at the j oint prior to the

application of mechanical loads (see Figure 11-12). The bending moment in Figure 1 1-12 causes

the joint to start opening at the top flange and gradually progress downward. Therefore, LVDTs

that are farther above the centroid of the contact area prior to the j oint opening indicate lower

j oint-opening loads than LVDTs that are closer to the centroid of the contact area. LVDTs at

identical distances from the centroid of the contact area of the gross section have the same

load vs. displacement curves if the j oint opens uniformly across the width of the section (see

Figure 11-13). After the joint opens, fibers that were initially in contact separate and are unable

to carry any significant additional strain. LVDTs then measure the distance between the

separated fibers or the width of joint opening.

Figure 1 1-14 shows data from LVDTs distributed throughout the depth of joint J2 on the

South side of the beam. In this figure, the last number in each LVDT label indicates the distance









of the LVDT from the bottom of the beam. The centroid of the contact area of the gross section

at joint J2 was 21.3 in. from the bottom of the segments. As expected, LVDTs located at

elevations above the centroid of the contact area of the gross section indicated lower

joint-opening loads than LVDTs at lower elevations. Furthermore, LVDTs located close to the

bottom of the j oint indicated little or no j oint-opening, and in the case of the LVDT at the lowest

elevation (J2-S-D-4.275) some compression. This was because the moment at joint J2 due to

applied mechanical loads caused the relief of compressive strains above the centroid of the

contact area but increased the existing compressive strains below the centroid. At the level of

each LVDT the initial compressive strains had to be relieved by strains due to the applied

moment in order for the joint to open. It was therefore expected that only LVDTs located above

the centroid of the contact area would indicate j oint-opening. This was evident in data from the

top three LVDTs, designated J2-S-D-33.75, J2-S-D-30.25, and J2-S-D-25.0 in Figure 11-14,

which were located above the centroid of the contact area at j oint J2 prior to opening of the joint.

Figure 11-15 shows data from LVDTs mounted across j oint J2 on top of the flanges of

segments 2 and 3. Unlike the ideal curve in Figure 11-13, the load vs. displacement curves in

Figure 11-15 were essentially nonlinear from the beginning of load application. This was most

likely caused by lack of contact between top flange concrete fibers at joint J2 (see Figure 1 1-6).

Similar to the measured strain gauge data, the nonlinear form of the LVDT curves at higher loads

was due to changes in stiffness of the contact area at joint J2 as it was opened. Opening of joint

J2 at the flange top fibers was estimated from the curves in Figure 11-15 by locating the points at

which the various curves initially deviated from one another.

Ideally, if the j oint opened uniformly across the width of the flange, all three LVDTs

would have indicated opening of the j oint at the same load and would have had identical









load vs. displacement curves. As discussed in the previous chapter, however, joint J2 initially

opened on the South side before opening on the North side. This caused displacements recorded

by the LVDT on the South flange, designated J2-TS-D-9.5, to be larger than displacements

recorded by the LVDT at the center of the flange (J2-T-D), and the LVDT at the North flange

(J2-TN-D-9.5).

LVDTs mounted across j oint J2 on top of the flanges of segments 2 and 3, and the LVDTs

designated J2-S-D-33.75 and J2-S-D-30.25 in Figure 11-14 showed two distinct essentially

linear regions after the j oint initially opened. In the first linear region of the curves, which

occurred after the j oint initially opened at the location of each LVDT, the centroid of the

concrete contact area was between the top and bottom post-tensioning bars. Thus, tensile

stresses due to the applied moment were resisted by the post-tensioning bars and existing

compressive stresses at the joint. In the second linear region, which began at a load of about

40 kips, the centroid of the concrete contact area was below the bottom post-tensioning bars (see

Figure 11-9). Tensile stresses due to the applied moment were therefore effectively resisted by

the post-tensioning bars with little contribution from existing concrete compressive stresses,

leading to a significant change in slope (from the first linear region).

Due to nonlinearities in the load vs. displacement curves for LVDTs mounted across joint

J2, there was less confidence in determining joint-opening loads with these instruments

compared to strain gauges located close to the joint. LVDT data were, however, useful in

checking j oint-opening loads determined from strain gauge data.

Strains at Mid-Segment

During tests in which data were collected from strain gauges at the middle of segments 2

and 3, loads applied to the beam did not exceed 40 kips. This was because strain data from the

middle of the segments were not needed for j oint-opening analysis.









Strain distributions 30 in, away from the middle of Segment 3 on the North and South

sides of the beam are shown in Figure 11-16 and Figure 11-17, respectively. Data obtained from

gauges located at the middle of Segment 2 (see Appendix C) were nearly identical to the

Segment 3 data and are therefore not shown here.

Opening of the j oint at the beam midspan (at j oint J2) did not affect on the location of the

neutral axis at the middle of the segments, which remained at elevation 21.3 in. However, the

non-uniform opening of joint J2 across the width of the section at the joint affected the

distribution of strains at mid-segment. Lesser magnitude strains were detected in the North

flange than the South flange, and higher strains were detected in the North web than the South

web. This was indicative of bi-axial bending as illustrated in Figure 11-18. The horizontal

component of the moment at mid-segment equilibrated the moment due to the applied load at the

cantilevered end of the beam. The vertical component of the moment at mid-segment, which

was the result of the net out-of-plane horizontal eccentricity in prestressing and the changes in

prestress shown in Figure 11-11, formed a self-equilibrating system with the concrete.

Deflection

Vertical deflection of the beam, measured at a location 7.25 in. from the cantilevered end,

is shown in Figure 11-19. The initial nonlinear part of the deflection curve was attributed to a

slight deflection at the East end-support of the beam as it was initially loaded. Movement of the

neutral axis at the midspan of the beam, as the j oint opened, was expected to affect the vertical

deflection of the beam. This is indicated by the deviation of the straight line drawn through the

deflection curve from the nonlinear parts of the curve. The initial deviation of the straight line

from the deflection curve occurred at a load of about 9 kips, the load at which the centroid of the

contact area at joint J2 initially began to move downward. After this point the deflection curve

was almost linear with load until the depth of joint opening was sufficient enough to cause the









centroid of the contact area to move below the bottom prestress bars (bars 3 and 4 in Figure

1 1-1 1) at a load of about 41 kips. Though the section stiffness at joint J2 continuously changed

in the linear part of the deflection curve, the change in stiffness was local to the j oint and did not

affect the overall stiffness of the beam, and therefore the cantilever tip deflection.

Summary

Results from mechanical load tests on the laboratory beam indicated elastic behavior of the

beam. The tests were also repeatable (i.e. neglecting small changes of prestress that occurred

with time, the response of the beam under the action of mechanical loads was repeatable across

tests). The distinct change in strain with load at incipient opening of the j oint at midspan (j oint

J2) resulted in the use of strain gauges near the joint as instruments for detecting joint-opening

loads. The contact area at j oint J2 could also be estimated using j oint-opening loads and

elevations of strain gauges near the j oint. The relative magnitude of joint-opening loads at

identical elevations on the North side and South side of joint J2 together with the shape of

contact areas at the joint showed that the beam underwent biaxial bending when mechanically

loaded. Measured strain distributions through the height of contact areas at joint J2 showed that

strain was a linear function of curvature.

These experimental observations made it possible for normal stresses at incipient opening

of joint J2 to be determined without explicitly using material properties (e.g. elastic modulus and

coefficient of thermal expansion) of segments 2 and 3.











Table 11-1. Comparison of measured strains due to prestress and measured strains when j oint
opens
Gauge Location Gauge Designation Strains due to Prestress (psE) Strains measured at joint


opening condition (CLs)
-304 210
-209 151


North Flange


South Flange


S3-N-S-02-33.5
S3-N-S-02-30.3

S3-N-S-02-35.3
S3-N-S-02-32.0
S3-N-S-02-28.6


-185
-200
-110














SG1M HIj:MSG2
SG3 er, 0SG4


joint

Segment 2 Segment 3


Joint J2 (closed)


Ei Strai n PLAN VIEW


Figure 1 1-2. Expected behavior of strain gauges on top of flange near j oint


0 Strain gauge

SG1,SG2 SG3, SG4


/Joint J2 (closed)


--\after joint
opens


M


Centroid of
gross cross
section


3M


Strain E, E2 ELEVATION VIEW


Figure 1 1-1. Expected behavior of strain gauges on side of beam near j oint

SG1 SGSG Strain gauge
SG4, SG5, SG6,
.24 S5 G


-- after joint opens








Q = Joi nt-openi ng Load


0 SG2
Open
~joint


0 SG4

Segment 3


0 SG6


SG1 0 :





7 SG3 0


Segment 2 i


SG5 MI '













55 ,,~f gross5 c.ro:ss 5sectlion

50

45

40

~i35

30

3 25










-700 -600 -500 -400 -300 -200 -100 0
Strain (microstrain)


100 200 300 400


Figure 1 1-3. Load vs. Strain near j oint at midspan (North side)


~C~ S:-S-S-il~-:F:
S:-S-S-O~-:~
^ S:-S-S-O~-~8G

S:-S-S-:G-~I :
~6 5:-S-S-il~-I-IE


0
-700


-600 -500 -400 -300 -200 -100 0 100 200 300 400
Strain (microstrain)


Figure 11-4. Load vs. Strain near joint at midspan (South side)














S2-Trl-S-F F-~ ~F
TS-S-
rl I-S-F F-T ~f
5:-T-S-F F-0 TF
5 :-TS-S-



i:ii ii i
H

~ ct I I
iii ITiii: I1I Iii
111-in 111
H
ill '


60







40

S35

30

S 25


10


5

-700 -600


-500 -400 -300 -200 -100 0
Strain (microstrain)


100 200 300 400


Figure 11-5. Load vs. Strain near joint at midspan (Top flange)


Figure 11-6. Condition of joint J2 on top of flange





~C~ Okips
lit rlcs

,, L~ rlCs

,, :.Frlcs

~L~FI/IFS
,, Filrlcs


I


10

5


-700 -600 -500 -400 -300 -200 -100 0 100 200 300 400
Strain (microstrain)

Figure 1 1-7. Measured strain distributions near j oint at midspan (North side)


40

35 Hc 0 kips
S10 kips
M 20kipsFlange
M 0 ip


45 kips
S20 M 50 kips

W 15

10





-700 -600 -500 -400 -300 -200 -100 0 100 200 300
Strain (microstrain)

Figure 1 1-8. Measured strain distributions near j oint at midspan (South side)











e- Post-tensioning bar

North South North c ~South North South North --- South



Ple *~ P2 Ple ~ P2 Ple *~ P2 Pl* ~ P2

P3e *~ P4 P3 *nl P4 P3* *y P4 P3* *~1 P4
Centroid of~-;// Centroid of- Centroid of VX/ Centroid of-
contact area contact area contact aea contact area

Prestress only Prestress plus At 30 kips At 40 kips
20 kip tip load


Figure 1 1-9. Estimated progression of joint-opening with load (based on strain gauge data)



Northh South
24 in.


8 in

N.A. before joint opens
C.G.
N.A. after joint
first opens

28 in.
21.3 in.
N.A. as load is further
increased




10 in.


Figure 1 1-10. Movement of neutral axis (N.A.) with load





































0 5 10 15 20 25 30 35 40 45 50 55
Applied Load (kips)


Figure 11-11. Changes in prestress force with load


Jon 2(closed)



Open
joint


LVDT11
LVDT2


M

Centroid of
gross cross
section


..._ M


7 Segment 2 | Segment 3


Q = Joint-opening Load


ELEVATION VIEW


Displacement


Figure 1 1-12. Expected behavior of LVDTs across joint on side of beam
















146












.' ~ ''''''' Joint J2 (closed)



QaQ ~jointpe


LVDT2

Segment 2 Segment 3

Q = Joint-opening Load
LVDT3

Displacement PLAN VIEW

Figure 1 1-13. Expected behavior of LVDTs across joint on top of flange


60
55
50
45
40

S35
30

S25
20


15
10
5
0-
-0.005


0 0.005 0.01 0.015 0.02 0. 025 0.03 0.035 0.04
Relative Longitudinal Displacement (in.)


Figure 11-14. Load vs. Joint opening (Side LVDTs)











60 -

55

50

45

40

S35
30

.8 25

20

15

10

5

0-
-0.005


0 0.005 0.01 0.015 0.02 0.025 0.03 0.035 0.04
Relative Longitudinal Displacement (in.)


Figure 11-15. Load vs. Joint opening (Top flange LVDTs)




35


30


S25


.20


W 15


10


5


-400 -300 -200 -100 0 100 200 300 400 500 600 700 800
Strain (microstrain)


Figure 1 1-16. Measured strain distributions at middle of Segment 3 (30 in. from joint J2) on
North side of beam





Flange




We b



H 0 Okips
S5 kips
M 1 0 kips
M 15 kips
20 kips
25 kips
30 kips
,, 35 kips


------------------- ---- ----------------------------
C


I


10


5



-400


-300 -200 -100 0


100 200 300 400
Strain (microstrain)


500 600 700 800


Figure 1 1-17. Measured strain distributions at middle of Segment 3 (30 in. from joint J2) on
South side of beam


Centroid of
prestress bars

Xi


Q (Applied load)


Segment 3


Segment 4


ELEVATION


CROSS SECTION


C = Resultant concrete compressivee) force
T = Resultant prestress (tensile) force
z = moment arm


Figure 11-18. Forces and moments acting at mid-segment


M h = M, -----


Ma = Q x
Mh =T*z= C*z


C.G.











vu

55

50

45
Movement of centroid of contact
40
area at joint J2 below bottom
S35 prestress bars



25

20

15

101 Joint initially opens
on South flange



0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 0.55 0.6
Deflection (in.)


Figure 11-19. Measured vertical deflection near cantilevered end of beam









CHAPTER 12
RESULTS UNIFORM TEMPERATURE CHANGE

A uniform temperature change was imposed on segments 2 and 3 of the laboratory beam

(Figure 12-1) to investigate the behavior in the absence of self-equilibrating thermally induced

stresses. The goal was to determine the maximum change in prestress that would result from

application of thermal loads on the concrete segments while the DYWIDAG post-tensioning bars

remained essentially at laboratory temperature. Though the beam was statically determinate with

respect to the supports, expansion of the concrete segments relative to the post-tensioning bars

was expected to lead to an increase in prestress and the development of net compressive stresses

in the concrete. Conversely, contraction (due to cooling) of the concrete segments relative to the

post-tensioning bars was expected to lead to a reduction in prestress and the development of net

tensile stresses (i.e. a reduction in compressive stresses) in the concrete. Understanding how

such changes in prestress affected concrete stresses was important in estimating the effects, if

any, of thermally induced changes in prestress on self-equilibrating thermal stresses when the

AASHTO nonlinear thermal gradients were later imposed on the beam.

The test sequence started with the circulation of tap water through segments 2 and 3 for

about 24 hours to establish a uniform reference temperature of about 84 oF (low reference

temperature). Segments 2 and 3 were then heated to an average temperature of about +41 oF

above the low reference temperature using the piping configuration shown in Figure 8-6. Forces

in the post-tensioning bars and concrete strains at joint J2 were continuously recorded during this

period, which will subsequently be referred to as the "heating phase". Following the heating

phase, the temperature of the concrete segments, which was about 125 oF, was taken as the new

reference temperature (high reference). With the data acquisition system still running, the

segments were cooled from the high reference temperature back to the initial (low) reference










temperature using the piping configuration shown in Figure 8-5. This phase of the test will

subsequently be referred to as the "cooling phase". Laboratory imposed temperature changes in

the heating and cooling phases of the test are shown together with target temperature changes for

Segment 2 and Segment 3 in Figure 12-2 and Figure 12-3, respectively. Measured concrete

temperatures in Segment 2 and Segment 3 are shown in Figure 12-4 and Figure 12-5,

respectively. Temperature changes in the Figure 12-2 and Figure 12-3 are with respect to the

low reference temperature (about 84 oF) for the heating phase and the high reference temperature

(about 125 oF) for the cooling phase. The average (uniform) temperature increase during the

heating phase of the test was about 40 oF and the average decrease in temperature during the

cooling phase was about 38 oF. The difference between the average temperature changes in the

heating and cooling phases was due to a slight increase in tap water temperature during the three

day period over which the test was conducted. This slight increase caused segments 2 and 3 to

be cooled to a temperature that was higher than the initial temperature from which they were

heated.

Significant deviation from the target profile occurred at Section A (see Figure 12-1) and

Section F (see Figure 12-3). These deviations were due to the fact that sections A and F were

adjacent to the ambient segments (segments 1 and 4). These segments (1 and 4) acted as heat

sinks because they remained essentially at laboratory temperature during application of the

thermal profiles on the heated segments (Segments 2 and 3). Additionally, the bottom surfaces

of segments 2 and 3 could not be adequately heated at sections C and D because these locations

were close to the mid-support point and could not be adequately insulated with Styrofoam. This

issue was resolved in later tests by using flexible fiberglass to insulate the mid-support area of

the beam. Temperature profiles were non uniform not only through the height of the segments









but also across the width. The distribution of temperature change through the height and across

the width of the beam at Section C and Section D during the heating phase are shown in Figure

12-6 and Figure 12-7, respectively. The color bar in each figure represents change in

temperature (in oF) relative to the low reference temperature. These figures show that

temperatures along the perimeter of each section were generally slightly lower than temperatures

in the interior. This was more pronounced in the web, where the ratio of concrete area to copper

tubes was only about a third of that in the flange. There were two main reasons for this. First,

the segment heating system was designed to efficiently impose the AASHTO nonlinear gradients

while keeping the number of copper tubes embedded in concrete to a minimum. Thus, there was

a higher concentration of copper tubes in the flange (where the maximum temperature changes in

the gradients occur) than in the web (where there was almost no change in temperature). Second,

heating the two concrete segments, by approximately 40 oF, uniformly was the most thermally

demanding situation imposed on the heating system, due to the total volume of concrete and

temperature increase involved.

Average measured temperature changes in the heated segments were used together with the

average measured coefficients of thermal expansion (CTE) in Table 12-1, elastic moduli (MOE)

in Table 12-2, and DYWIDAG bar properties to predict anticipated changes in prestress.

Concrete elastic moduli in Table 12-2 were obtained by linearly interpolating between MOEs

which were derived from cylinder test data between test ages of 28 and 360 days. Moments

caused by the vertical and horizontal eccentricities of the prestress bars and slight curvatures

caused by non-uniformity of the imposed temperature profiles were neglected in the prediction

of prestress change. It was also assumed that for the duration of the test, the prestress bars and

ambient concrete segments did not undergo any changes in temperature. Predicted and measured










changes in prestress during the heating and cooling phases of the test are compared in Table 12-3

and Table 12-4, respectively. Measured total changes in prestress were within 11% of

corresponding calculated values. Calculated changes were of higher magnitude than measured

changes mainly because the ambient segments and prestress bars were subj ected to a slight

temperature increase due to an increase in laboratory temperature during the course of the test. It

was expected that the steel prestress bars would respond to such non-stress-inducing temperature

changes more rapidly than the ambient segments because of the relatively high thermal

conductivity of steel and the small volume of steel compared with concrete (about 1%).

Measured total changes in prestress even under this worst case thermal loading condition were

less than 6% of the initial total prestress.

Measured concrete strains near j oint J2 from strain gauges located on segments 2 and 3

during the heating and cooling phases of the test are shown in Figure 12-8 and Figure 12-9,

respectively. Expected (calculated) strain distributions are also shown in the figures for

comparison. Calculated strains were determined using measured prestress forces and

eccentricities, concrete section properties, and the elastic moduli shown in Table 12-2. Concrete

strains measured during the heating phase were essentially a mirror image of concrete strains

measured during the cooling phase. This showed that strains induced in the heated segments

when the beam was heated were relieved when the beam was cooled; evidence that the beam

remained elastic under the action of the thermal loads. Because the strain gauges installed on the

concrete segments were self-temperature-compensating (STC) gauges, it was expected that the

measured strains (assuming uniformity of temperature distributions) would arise solely from

changes in prestress, and therefore would be compressive during heating and tensile during

cooling. It is, however, evident from Figure 12-8 and Figure 12-9 that the opposite was the case.









Measured concrete strains during the heating phase were instead tensile. A similar reversal was

observed during the cooling phase. Furthermore, the measured strains were non-uniform through

the height of the segments. The observed reversals were attributed to the fact that the

temperature profiles imposed on the segments were somewhat non-uniform over the cross

sectional area of the segments (recall Figure 12-6 and Figure 12-7). Thus, while the total change

in prestress was a result of the average (uniform) temperature change imposed on the heated

segments, strains measured on the surfaces of the sections were affected by non-uniform

temperature changes. Concrete strains measured during the heating phase are compared with

calculated strains which take into account both changes in prestress and the non-uniformity in

temperature distributions in Figure 12-10 and Figure 12-11. The calculated strains in were

determined by superimposing strains caused by the increase in prestress and stress-inducing

strains caused by the non-uniform temperature distributions shown in Figure 12-6 and Figure

12-7, respectively. Stress-inducing strains caused by the two-dimensional thermal gradients in

the figures were calculated using Eqns. 3-8 through 3-12 (see Chapter 3). Though the calculated

strain magnitudes shown in Figure 12-10 and Figure 12-11 do not exactly match the measured

strains they are consistent in sign (i.e. positive, tensile). A possible explanation for the

difference in magnitude of measured and calculated strains is that precise measurements of

temperature at the surface of the concrete sections, where the strains were measured, were not

available. Instead surface temperatures were obtained by extrapolating data from thermocouples

nearest to, but not exactly at, the surface of the concrete. Hence the extrapolated surface

temperatures may have been less than the actual surface temperatures.











Table 12-1. Average measured coefficients of thermal expansion (CTE) of concrete segments
Segment Average CTE
1 N/A
2 7.7E-6f"F
3 8.0E-6f"F
4 N/A


Table 12-2. Calculated modulus of elasticity (MOE) of concrete segments
Segment Age (days) MOE (ksi)
1 268 5231
2 219 4696
3 206 4695
4 257 5101


Table 12-3. Changes in prestress due to heating of Segments 2 and 3
Bar Measured Increase in Percentage Calculated
Designation Initial Measured Increase in Increase in
Prestress Prestress Measured Prestress (kips)
(kips) (kips) Prestress (%)
P1 94.6 5.6 5.9 5.9
P2 87.7 5.2 5.9 5.9
P3 90.8 4.5 5.0 5.9
P4 89.6 5.8 6.5 5.9
Total 362.7 21.1 5.8 23.6


Difference b/n
Measured and
Calculated Increase
in Prestress (%)
-5.1
-11.9
-23.7
-1.7
-10.6


Table 12-4. Changes in prestress due to cooling of Segments 2 and 3
Bar Measured Decrease in Percentage Calculated Difference b/n
Designation Initial Measured Decrease in Decrease in Measured and
Prestress Prestress Measured Prestress Calculated
(kips) (kips) Prestress (%) (kips) Increase in


Prestress (%)
-1.8
-7.1
-26.8
-5.4
-10.7


P1
P2
P3
P4
Total


100.2
93.0
95.3
95.4
384.0


-5.5
-5.2
-4.1
-5.3
-20.0


-5.5
-5.6
-4.3
-5.6
-5.2


-5.6
-5.6
-5.6
-5.6
-22.4

















SEGMENT 1 IjSEGM'ENT 2 1 SEG ENT 3 ii SEGMENT 4


(AMBIENT) II (HEA TED) II (HEATED) II (AMBIENT)


10.5 ft




5ft 5ft


W 15) RM I


101 n I-

5 M i


End-support



1.7ft


Location of
interest
(Joint J2)


Applied Load (Q)


A B


C (D


E F


3f lt


P


d-support


East -


West


P: Post-tensioning force

Figure 12-1. Laboratory beam


Flange







SEc Dlin ct IHctling
SEc Dlin E. I Hctling
SECi tlin =1. I Hiealing I
Seasolin c- IC, coillnal
Section *C. I=C, collngl
T r giel I Hiea l ng I
Targe PC~cling


-50 -40 -30 -20 -10 0 10 20 30 40 50
Temperature Difference Relative to Reference Condition for each Phase (deg. F)

Figure 12-2. Laboratory imposed temperature changes on Segment 2


I


2.7 f


Lab. floor
Mi





I I\\ I, SiEC Din CI IHiealnIn
W 151 n Sec tion E I Hctling
W SEC lon F IHiealng a
,, Secition C liCrcollngl
101 1 Sie lion El Coorillngl
,, Secition FIC~icollng.




-50 -40 -30 -20 -10 0 10 20 30 40 50
Temperature Difference Relative to Reference Condition for each Phase (deg. F)


Figure 12-3. Laboratory imposed temperature changes on Segment 3


Flange


85 90 95 100 105 110 115
Temperature (deg. F)


120 125 130


Figure 12-4. Measured concrete temperatures in Segment 2











40


35
Flange
30


c Web

. 20


W 15 H Section D (Heating)
Section E(Heating)
M Section F (Heating)
101 1 Section D(Cooling)
,, Section E (Cooling)
N Section F (Cooling)
51 1 Target (Heating)
HC Target (Cooling)


80 85 90 95 100 105 110 115 120 125 130
Temperature (deg. F)


Figure 12-5. Measured concrete temperatures in Segment 3




S45
?340- .4
~35 -
~30 -e-3

1 5 -
10-


5 3

405 153

0 -1 10
Beam Height (in.) Beam Width (in.)


Figure 12-6. Measured temperature changes at Section C (Heating phase)





N Sieg 2 Ilorr~hl
,, Sig 2 lorlfh
- Sieg 2 Sirlth
- Sieg 2 Soulth


-350 -300 -250 -200 -150 -100 -50 0
Strain (microstrain)


50 100 150 200


43

42


41




38

37


,45
S40
S35


S20 -
a~15
10
5-
41


35 3

15 10
0 -15


Bearn Helght (In)


Bearn Width (in.)


Figure 12-7.


Measured temperature changes at Section D (Heating phase)


Flange









Hiejlings
PC, cillngl
I Hctling
I C, cillng l
iljt[e~ IHctlingl
lajtiel l*Circing e


10


5



-400


Figure 12-8. Measured strain distribution on Segment 2 (Section C) due to temperature changes





- Se5g. j, N~ortl
H Seg. 3, Nortl
& Seg. 3, Sout
- Seg. 3, Sout
N Average Cal
M Average Cal


35

30

^ 25

. 20

W 15

10

5


-400


-350 -300 -250 -200 -150 -100 -50
Strain (microstrain)


0 50 100 150 200


Figure 12-9. Measured strain distribution on Segment 3 (Section D) due to temperature changes


40

35
Flange~
30

25

20




15

10


-400 -350 -300 -250 -200 -150 -100 -50
Strain (microstrain)


50 100 150 200


Figure 12-10. Comparison of measured and calculated strains at Section C due to moderately
nonuniform temperature distribution (Segment 2, Heating)


;d


Flange








h (Heatlng!
h (Cooling)
:h (Heating)
:h (Cooling)
culated (Heating)
culated (Cooling)










40


35
Flange
30




20


W 15








-400 -350 -300 -250 -200 -150 -100 -50 0 50 100 150 200
Strain (microstrain)


Figure 12-11. Comparison of measured and calculated strains at Section D due to moderately
nonuniform temperature distribution (Segment 3, Heating)









CHAPTER 13
RESULTS AASHTO POSITIVE THERMAL GRADIENT

Results from the application of mechanical loading in combination with the AASHTO

positive thermal gradient are presented and discussed in this chapter. The objective of the

mechanical-thermal load tests was to experimentally quantify the self-equilibrating thermal

stresses caused by the AASHTO nonlinear positive thermal gradient in the top 4 in. of the

combined flanges of segments 2 and 3. Two independent methods were used to quantify

stresses. The first was to convert measured strains using the elastic modulus, which was

determined from tests on cylinders made from the same concrete that was used to construct the

beam. Stresses determined using this method will be referred to as elastic modulus derived

stresses (E stresses). This is the method most often used to determine stresses, but may be

subject to variation from local strain contributions in the concrete surrounding the strain gauge,

size effect between cylinder and specimen, or creep and shrinkage. The second method was a

more direct measure of stress using the known stress state at incipient joint opening. Stresses

determined in this manner will be referred to as joint opening derived stresses (J stresses). In

both methods, concrete behavior was assumed to be linear elastic.

Figure 13-1 illustrates the test sequence that was used. Before mechanical or thermal loads

were applied, the forces acting on the beam consisted of prestress and self-weight. The test

sequence started with partial opening and closing of the j oint at midspan (j oint J2) with the beam

at a constant reference temperature (about 80 oF). As indicated in the figure, strain data from this

step were used to establish a reference stress state at joint J2. The AASHTO positive thermal

gradient was then imposed on segments 2 and 3. After achieving and maintaining the steady

state thermal gradient on the heated segments for 30 to 45 minutes, joint J2 was again partially

opened and closed. Strains at this stage were used to determine the thermal stress state. The









heated segments were then cooled to the original reference temperature at the start of the test,

after which joint J2 was again partially opened and closed, completing the load cycle.

Joint-opening loads and contact areas at j oint J2, as the j oint was gradually opened, which

were determined from data collected from steps 1 and 3 of the load sequence, were used to

calculate self-equilibrating stresses caused by the nonlinear gradient (J stresses). Note that

neither the elastic moduli nor the coeffieients of thermal expansion of segments 2 and 3 were

used in the calculation of the J stresses.

Elastic modulus derived thermal stresses calculated from measured thermal strains close to

joint J2 (E stresses) and joint opening derived thermal stresses (J stresses) are presented and

discussed in the following sections.

Elastic Modulus Derived Stresses (E stresses)

The nonlinear positive thermal gradient imposed on the heated segments of the laboratory

beam (see Figure 13-2) in Step 2 of the load sequence is shown in Figure 13-3. For comparison,

Figure 13-3 also shows the AASHTO design positive gradient. Though it did not exactly match

the AASHTO gradient, the shape of the laboratory gradient was more representative of typical

field measured gradients (see Figure 13-4). Measured temperatures in the heated segments after

the positive thermal gradient was imposed are shown in Figure 13-5.

Temperature data for the laboratory-imposed thermal gradient profile was available up to

an elevation of 3 5.5 in. (0.5 in. below the top surface of the flange): the elevation of the topmost

thermocouples embedded in the heated segments. Thus the concrete temperature at the top

surface of the flanges (at an elevation of 36 in.) was not measured. Because the segments were

heated from the inside, rather than externally from solar radiation, it is likely that the top flange

surface temperature was equal to or even slightly less than the measured temperature at 35.5 in.

For the purpose of calculating theoretical stresses and strains caused by the laboratory gradient,









the magnitude of the thermal gradient at the top surface of the flange was obtained by

extrapolating from measured thermal gradient magnitudes at elevations 32 in, and 35.5 in.

Figure 13-6 shows an ideal representation of the components of strains induced in the

laboratory beam by the AASHTO design gradient. These strains were calculated according to

the procedure outlined in the AASHTO (1989a) guide specifications and the coefficients of

thermal expansion given in Table 12-1 (see Chapter 12) using the equation:

ET = a -3T(z)+ e, (13-1)

where the unrestrained thermal strain profile (adGT(z)) represents the strains that the

section would undergo if the section were layered and the layers were free to deform

independently. The total strains (ET) are generated when compatibility between the layers is

enforced. Assuming that plane sections remain plane under the action of flexural deformations,

this strain distribution is linear. The total strain (ET) includes components caused by axial and

flexural restraint, which were not present in the laboratory set-up. The self-equilibrating strains

(ESE), which are the only strains measurable with temperature compensating strain gauges (see

Chapter 3 for a complete discussion), make up the final component of the total strains.

The change in strain between the beginning and end of Step 2 at joint J2 are plotted in

Figure 13-7 through Figure 13-9. Figure 13-7 and Figure 13-8 show the strain differences along

the height of segments 2 and 3, respectively. Figure 13-9 shows a plan view of the strain

differences on the top flange near the same j oint. Also shown in the figures are two sets of strain

changes predicted using the AASHTO design procedure: one using the AASHTO design thermal

gradient, and the other using the laboratory-imposed thermal gradient. Because the strain gauges

were self-temperature compensating (STC) gauges, and because there was no axial or flexural

restraint on the beam, the measured strains consisted only of the self-equilibrating component of









the total strains. The average laboratory-imposed thermal gradient profile (average of profiles at

Section A through Section F (see Figure 13-3)) was used in calculating the 'laboratory gradient'

strains in Figure 13-7 through Figure 13-9.

No marked difference is apparent between measured and predicted strains below

approximately 20 in. elevation. Compressive strains were present in the bottom of the section up

to an elevation of approximately 10 in. Tensile strains arose in the section mid-height from

about 10 in, to 32 in. elevation. A maximum predicted tensile strain (due to the laboratory

gradient) of about 52 C1s was predicted at elevation 28 in., whereas a maximum measured tensile

strain of about 65 C1s occurred at elevation of 27.5 in. The maximum predicted tensile strain due

to the AASHTO design gradient, of magnitude about 53 C1s, occurred at an elevation of 20 in.

The difference between locations of maximum predicted tensile strains due to the imposed

laboratory gradient and the AASHTO design gradient was due to the difference in the shape of

the laboratory and AASHTO design thermal gradients. In each case maximum tensile strain

occurred at the location where the change in slope (in units of oF/in.) of the thermal gradient

profile was algebraically at a maximum. This occurred between elevations of 27.5 in, and

28.5 in. for the laboratory gradient and at an elevation of 20 in. for the AASHTO design

gradient. Compressive strains also occurred above the mid-thickness of the flange with a

gradient steeper than that of the remainder of the profile.

Some additional differences between the measured and predicted strains are also notable.

Measured compressive strains were significantly smaller in magnitude than predicted at the top

of the section in both segments (see Figure 13-9). This was also the case during prestressing (see

Chapter 10) and mechanical load tests (see Chapter 11). One explanation for the lower measured

compressive strains at the top of the section is the shape of the thermal gradient in the top 4 in. of










the flange. The placement of copper tubes in the flange allowed for a linear gradient between

elevations of 32 in, and 35.5 in. The shape and magnitude of the thermal gradient in the top 0.5

in. of the flange was, however, not known. To predict top fiber strains, the magnitude of the

thermal gradient in the top flange was obtained by extrapolating from the linear thermal gradient

between elevations 32 in, and 35.5 in.

Another possibility is that differential shrinkage on top of the flange at joint J2 contributed

to the lower measured strains. Between elevations of 32 in, and 35.5 in., the measured

compressive strains more or less followed a linear distribution as did the predicted strains. The

measured strains were, however, generally larger than predicted strains between elevations 32 in,

and 34 in, and smaller than predicted strains above 34 in. This was attributed to variations

between the measured thermal gradients at sections A through F, and the average of these

gradients (see Figure 13-10), which was used to predict strains per the AASHTO design

procedure.

The uniform and linear sub-components of the overall nonlinear thermal gradient were

expected to lead to additional stresses in the concrete as segments 2 and 3 were heated during

Step 2. Expansion of the segments relative to the prestressing caused a net increase in

prestressing force. However, the measured peak increase was only 0.4% of the initial prestress

and was therefore considered negligible.

Elastic modulus derived stresses (E stresses) were the self-equilibrating thermal stresses

caused by the positive thermal gradient, and were determined by multiplying the measured

strains in Figure 13-7 and Figure 13-8 by the elastic moduli of Segment 2 (4760 ksi) and

Segment 3 (4760 ksi), respectively. The elastic moduli were calculated by linearly interpolating










cylinder modulus of elasticity data between test ages of 28 and 360 days. At the time of the test,

the ages of segments 2 and 3 were 232 and 219 days, respectively.

Figure 13-11 and Figure 13-12 show E stress distributions near joint J2 on Segment 2 and

Segment 3, respectively. For comparison, self-equilibrating thermal stresses were also calculated

using the AASHTO recommended procedure discussed in Chapter 3, the laboratory thermal

gradient, and the AASHTO design gradient. CTEs from Table 12-1 and the segment MOEs

noted above were used in these calculations.

Table 13-1 compares E stresses computed at the top of the flanges of segments 2 and 3

with similar stresses obtained by extrapolating from the linear E stress distributions between

elevations 32 in, and 35.5 in. (see Figure 13-11 and Figure 13-12) on the sides of the segment

flanges. E stresses in the extreme top flange fibers were significantly lower than stresses

extrapolated to the same location. This condition follows from the relatively smaller

stress-inducing thermal strains that were measured at the top surfaces of the flanges (see Figure

13-9). As discussed previously, the smaller strains were attributed to differential shrinkage at

j oint J2 and to a lower thermal gradient magnitude than was targeted for the top of the flanges of

the segments. At an elevation of 32 in., E stresses in segments 2 and 3 (see Figure 13-11 and

Figure 13-12) were compressive whereas predicted stresses were tensile. This was attributed to

the difference in magnitude of the laboratory thermal gradients at sections A through F (from the

average thermal gradient used in predicting stresses) at that elevation; the location of the

maximum slope change in the thermal gradients (see Figure 13-13).

E stresses and predicted stresses caused by the laboratory-imposed thermal gradient in the

top 4 in. of the flanges of segments 2 and 3 are compared in Table 13-2. Predicted stresses in the

extreme top flange fibers (where the maximum compressive stresses were expected to occur had










the gradient been linear in the top 4 in. of the flanges) are not shown in the table because the

shape and magnitude of the thermal gradient at that location were not measured. E stresses

0.5 in. below the top flange (maximum E stresses) were approximately 3% and 8% less than

corresponding predicted stresses in Segment 2 and Segment 3, respectively. Taking into

consideration the possible effects of differential shrinkage at joint J2, these differences were

considered to be within the limits of experimental error.

Joint Opening Derived Stresses (J Stresses)

The known stress state at incipient j oint opening was used to determine stresses caused by

the laboratory positive thermal gradient without converting measured strains to stresses using the

elastic moduli of the concrete segments. The magnitude of stresses caused by the thermal

gradient in the top 4 in. of segments 2 and 3 at joint J2 were quantified using data collected from

steps 1 and 3 of the load sequence shown in Figure 13-1. This was accomplished by loading the

specimen until j oint J2 began to open. At the condition of joint opening, it is known that the

normal concrete stress near the joint face is zero (due to lack of contact). Assuming linear elastic

behavior for subsequent short-term loads (thermal or mechanical), it was possible to extrapolate

concrete stresses from the known (zero) stress state. Section properties of the contact area at

j oint J2, after j oint opening, were used to calculate these stresses (J stresses).

Figure 13-14 and Figure 13-15 illustrate the J stress calculation procedure using

component stress blocks. Stresses at joint J2 prior to Step 1 of the load sequence consisted of

stresses caused by prestress (P) and the self-weight (SW) of the beam. In Step 1, joint J2 was

opened and closed at the reference temperature of the beam. The state of stress in the contact

area at the joint caused by the joint-opening load, QR, will be referred to as the reference stress

state (see Figure 13-14). In Step 2 the positive thermal gradient was applied. Stresses at j oint J2

consisted of stresses caused by prestress (P), self-weight (SW), and the nonlinear positive









thermal gradient (PG). In Step 3 of the load sequence, joint J2 was again opened and closed.

The state of stress in the contact area at the j oint caused by the j oint-opening load, Qr, will be

referred to as the thermal stress state (see Figure 13-15). At incipient joint opening, flexural

stresses caused by QR and Qr in the extreme top flange fibers were equal, but opposite, to the

existing normal stresses caused by (P + SW) and (P + SW + PG), respectively, at the same

location. This condition was used to quantify self-equilibrating thermal stresses caused by the

nonlinear positive thermal gradient. Though the concept of creating a zero stress condition at

joint J2 is illustrated for the extreme top flange fibers, it is generally applicable to any shape of

contact area. A general discussion of joint-opening and its uses in quantifying self-equilibrating

thermal stresses follows.

Figure 13-16 shows uniform opening of joint J2 to a known depth 'h' below the extreme

top flange fibers. Because the j oint opens uniformly across the width of the section, the

boundary (referred to as the contact boundary in the figure) between open and closed parts of the

j oint is perpendicular to the sides of the segments. The j oint opens in this manner when the line

of action of the j oint-opening load passes through the axis of symmetry of the contact area, and

normal stresses existing prior to opening the joint are a function of depth only (i.e. uniformly

distributed across the width of the section at all depths). If these conditions hold true for load

cases without the thermal gradient (P + SW) and with the thermal gradient (P + SW + PG), then

the contact area at the reference and thermal stress states is the same (Figure 13-16 (B)). If the

distribution of existing normal stresses at the joint caused by (P + SW) and/or (P + SW + PG)

varies across the depth and width, the depth of joint opening would not be uniform across the

width of the segments, as was found to be the case for the laboratory beam. As shown in Figure









13-17, the contact areas at the reference and thermal stress states are in general not the same

under these conditions.

The zero stress condition created by superimposing stresses caused by the joint-opening

loads QR and Qr (see Figure 13-14 and Figure 13-15) on existing normal stresses along

corresponding contact boundaries is shown mathematically in the following equations:

J,(y, z)+ J,, (y, z-)+ Jk(y, Z)= 0, ((y, z) R) (13-2)
f(y, z) + fsw (y, z) + f, (y, z) + f, (y, z) = 0, ((y, z) E T) (13-3)
Then,
f,(y, z) = fR(y, z) fT (y, Z), ((y, z) E R n T) (13-4)

where fp is the concrete stress in the contact area due to prestressing force, fs is the stress

caused by self-weight, fJ is the J stress (self-equilibrating concrete stress caused by nonlinear

positive thermal gradient), fR is the reference stress state, fris the thermal stress state, R is the

contact boundary at the reference stress state, T is the contact boundary at the thermal stress

state, and y and : are vertical and horizontal coordinates of points on contact boundaries,

respectively.

These equations are valid only along the contact boundary corresponding to each stress

state. For example, Equation 13-2 and Equation 13-3 are applicable along line AB in Figure

13-16. In Figure 13-17, however, Equation 13-2 is applicable along line AB while

Equation 13-3 is applicable along line AC. Equation 13-4, which is obtained by taking the

difference between the reference stress state and thermal stress state, is valid only at point A in

Figure 13-17, where the contact boundary at the reference stress state is at the same elevation as

the contact boundary at the thermal stress state. Equation 13-4 shows that self-equilibrating

thermal stresses caused by the nonlinear positive thermal gradient at the points of intersection of

the contact boundaries can be determined if stresses caused by QR and QT are known.









The load that caused j oint J2 to open at a known depth 'h' at the reference and final stress

states was determined from load vs. strain curves of strain gauges adj acent to the j oint. Because

the laboratory beam was statically determinate, the bending moment at j oint J2 was determined

from the j oint-opening load without taking the change in stiffness of the beam, caused by

opening the j oint, into account. Assuming that plane sections remained plane under the actions

of the forces and moments acting at the j oint, stresses caused by j oint-opening loads at the

reference and final stress states along corresponding contact boundaries were determined with

the aid of stress-strain diagrams of the concrete segments and equations of statics. Assuming

further that the behavior of the beam was linear elastic under the action of the applied loads, it

became possible to determine stresses without measuring strain.

For stresses due to joint-opening loads to be determined without explicitly using the

elastic/tangent modulus of concrete (i.e. without the stress-strain curve), the material behavior of

concrete within the load ranges considered had to be linear elastic. Furthermore, the distribution

of strain through the depth of the contact area at j oint J2 (after opening the j oint) had to be a

linear function of curvature (i.e. plane sections remain plane). It was assumed that concrete was

homogeneous and isotropic. Linear elastic material behavior of the beam segments within the

range of mechanical loads applied during testing was supported by data from cylinder tests,

which showed that the beam segments were linear elastic up to stresses of about 6000 psi

(uniaxial compression). Distributions of measured concrete strain through the depth of evolving

contact areas near j oint J2 were approximately linear as the j oint was opened. This was evidence

of plane sections remaining plane, within the contact area, under flexure. Data collected from

in-situ CTE tests conducted on the heated segments showed that, within the temperature ranges

to which the segments were subj ected during testing, plane sections remained plane and thermal









strains were a linear function of temperature difference. Based on these observations flexural

stresses due to j oint-opening loads were determined using classical flexural stress formulas.

Figure 13-18 and Figure 13-19 show variations of concrete strain with applied load near

joint J2 on the North side of Segment 3 at the reference stress state (reference temperature) and

thermal stress state (with positive thermal gradient), respectively. Similar plots near the same

joint on the South side of Segment 3 are shown in Figure 13-20 and Figure 13-21, respectively.

The variation of concrete strain with applied load on top of the flanges of segments 2 and 3 near

joint J2 at the reference and thermal stress states are shown in Figure 13-22 and Figure 13-23,

respectively. Data collected from strain gauges near j oint J2 on Segment 2 (which were similar

to those from Segment 3), LVDTs mounted across j oint J2 on top of the flanges of segments 2

and 3, and LVDTs mounted across the same joint on the South side can be found in Appendix D.

The variation of measured strains and measured displacements with load near j oint J2 on the

South side, North side, and on top of the flanges of segments 2 and 3 was discussed in detail in

Chapter 11.

Two general observations can be made when measured concrete strains at the same side of

joint J2 and LVDT readings at the reference and thermal stress states are compared. These

observations are illustrated in Figure 13-24 with data from the strain gauges at elevations 33.5 in,

and 3 5.3 in. on the North and South sides of joint J2, respectively. The first is that at the same

elevation in the top 4 in. of the flange, the j oint opened at higher loads at the thermal stress state

than it did at the reference stress state (i.e. QTN > QRN and QTS > Rs). This is also evident in the

top flange strains shown in Figure 13-22 and Figure 13-23, and LVDT data (see Figure D-5

through Figure D-8 in Appendix D). Opening of joint J2 at higher loads at the thermal stress









state was consistent with the development of compressive strains in the top concrete fibers

caused by the positive thermal gradient.

The second observation is that although smaller strains were recorded on the South side of

the joint than on the North side (i.e. SRS < RN and STS < TN in Figure 13-24), the strain

difference between vertical portions of strain diagrams at the reference and thermal stress states

(Ess and Ass) was independent of the side of the j oint on which strain gauges were located. The

strain difference was, however, dependent on the distribution of stress-inducing concrete strains

caused by the positive thermal gradient at j oint J2 (and therefore the elevation of gauges). In

Figure 13-24 the strain difference on the North side at elevation 33.5 in. (Ass) was less than the

strain difference on the South side of the joint at elevation 35.3 in. (Ess). This was because the

gauge on the South side was at a higher elevation than the gauge on the North side.

Since the strain difference between vertical portions of strain curves at the reference and

thermal stress states represented strains caused by the positive thermal gradient at joint J2, it was

evident that within the top 4 in. of the flange, these strains (and corresponding stresses)

decreased in compression, with the maximum strains and stresses occurring in the top fibers of

the section. This was consistent with the expected distribution of self-equilibrating thermal

stresses within the top 4 in. of the flange (see predicted strains and stresses in the discussion of

E stresses)

Loads that caused j oint J2 to open at the reference and thermal stress states were detected

using load vs. strain data (detection of joint-opening loads using strain gauges was discussed in

Chapter 11). LVDT data were mainly used to check joint-opening loads determined with strain

gauges, especially on top of the flange, where very low strains were recorded at the reference

stress state. Applied loads at the cantilevered-end of the test beam, that caused joint J2 to open at









various depths, are shown in Figure 13-25. Each point in the figure shows the average load

(determined from gauges on segments 2 and 3 on the same side (North or South) of the j oint) at

which the change in strain at that location became zero. These points were used to define the

boundary of the contact area at varying loads. The sign convention for moments and curvatures

is shown in Figure 13-26. Tensile stresses caused by joint-opening loads are positive and

compressive stresses are negative. Recall that tensile stresses are actually reductions of the

initial compressive stresses caused by prestressing.

Figure 13-27 through Figure 13-29 show estimated contact areas at joint J2 at the reference

and thermal stress states just as opening of the j oint was detected from strain gauges at elevations

of 35.5 in. (South), 33.5 in. (North), and 32.0 in. (South), respectively. Contact boundaries are

indicated by dashed lines. Contact areas were estimated by interpolating between joint-opening

loads and the positions of the strain gauges from which the loads were determined (see Figure

13-25). Total stresses caused by moments at joint J2 due to joint-opening loads and changes in

prestress were determined using the contact area cross sections and Equation 13-5 through

Equation 13-11.

f (z, y,Mz\~,M,,'It, Iv, Izy p, A) =
(MY It +M2, Izy) Z (M~, I, +M Izy) y (13-5)
2 N, (Ap, A)

My = AMP v(13-6)
Mz2 = M -A~P~h (13-7)

4~
f, (p, A) = (13-8)

aMP h(p y,=() ey ) (13-9)

AMP, v z~~e)C~ z ) (13-10)

MQ= xJ2 Q (13-11)











Where, f is the total stress caused by the joint-opening load (Q), fN is the stress caused by

changes in prestress at load Q, MyQ is the moment of joint-opening load (Q) at j oint J2, Ap is the

change in prestress at load Q, ei,- is the vertical eccentricity of post-tensioning bar 'i', ei, is the

horizontal eccentricity of post-tensioning bar 'i', A2~p ,is the moment about the vertical axis due

to changes in prestress, AM~P h is the moment about the horizontal axis due to changes in

prestress, I, is the moment of inertia of the section about the horizontal axis, 13. is the moment of

inertia of the section about the vertical axis, I,, is the product of inertia of the section, z is the

horizontal coordinate of the point at which stress is calculated, y is the vertical coordinate of

point at which stress is calculated, and xxz is the moment arm of the j oint-opening load from j oint

J2.

Though data from strain gauges and LVDTs on top of the flanges of segments 2 and 3

were useful in estimating contact areas, top flange stresses could not be determined with these

equations. This was because the condition of the j oint at the top of the flanges (see Figure 1 1-6)

violated the assumptions under which the equations could be used.

Table 13 -3 shows calculated J stresses at the locations of strain gauges on the sides of the

beam within the top 4 in. of the flange. Though the total stresses (stresses determined from

Equation 13-5 are positive, indicating tension, they actually represent relief of

prestressing-induced compressive stresses at J2 that were present prior to the application of

joint-opening loads. The J stresses were then determined by taking the difference between total

stresses at the reference stress state and total stresses at the final stress state.

In Equation 13.5, the total stress is made of two components; the stress component due to

the joint opening load and the stress component due to changes in prestress. Changes in

prestress (determined from measured prestress forces and section properties) accounted for less









than 0.5% of total stresses. The calculated total stresses were therefore essentially dependent on

the magnitude of joint opening loads. J stresses, however, were dependent only on the difference

between the joint-opening loads at the reference and thermal stress states. For example, the

loads initiating opening of joint J2 on the North side at an elevation of 33.5 in. were greater than

on the South side at an elevation of 3 5.5 in, as can be seen from the magnitudes of the moments

in Table 13-3. However, calculated J stresses at an elevation of 33.5 in. were lower than

J stresses at an elevation of 35.5 in. This was expected since the distribution of self-equilibrating

thermal stresses within the top 4 in. of the flanges of segments 2 and 3 was expected to increase

linearly (in compression) from a minimum magnitude at an elevation of 32 in, to a maximum

magnitude at the top flange (elevation 36 in.).

J stresses and predicted stresses in the top 4 in. of the flange are compared in Table 13-4.

J stresses 0.5 in. below the top of the flange (maximum J stresses) were approximately 10% and

15% less than corresponding predicted stresses in Segment 2 and Segment 3, respectively. At

elevation 32 in., J stresses were about 82% less than predicted stresses. Both predicted and J

stresses were, however, tensile. As was the case for E stresses, this was attributed mainly to the

difference in magnitude between the measured thermal gradients and the average thermal

gradient (with which stresses were predicted).

J stresses and E stresses in the top 4 in. of the flange are compared in Table 13-5. Both

sets of stresses compared well except at elevation 32 in. A possible reason for this discrepancy

was noted above. Maximum J stresses (at elevation 35.5 in.) were about 7% and 8% less than

maximum E stresses on Segment 2 and Segment 3, respectively.










Table 13-1. Comparison of E stresses and extrapolated stresses on top of segment flanges near
joint J2 (laboratory positive thermal gradient)
Measured (psi) Extrapolated (psi) Measured/Extrapolated
Segment 2, North -307 -786 0.391
Segment 2, South -438 -732 0.598


Segment 3, North
Segment 3, Middle
Segment 3, South


-463
-518
-499


-772
-751
-729


0.600
0.690
0.684


Table 13-2. Comparison of E stresses and predicted self-equilibrating thermal stresses caused by
laboratory positive thermal gradient near j oint J2


Segment 2
Elevation (in.)

36
35.5
33.5
32
Segment 3
Elevation (in.)

36
35.5
33.5
32


Average E Stress (psi)


Average Predicted
(psi)
N/A
-693
-219
137

Average Predicted
(psi)
N/A
-729
-230
144


E Stress/Predicted

N/A
0.968
1.461
-0.416

E Stress/Predicted

N/A
0.925
1.604
-0.972


-373
-671
-320
-57


Average E Stress (psi)

-493
-674
-369
-140


Table 13-3. J stresses in top 4 in. of flange
Gauge Elevation Moments due to
Joint-opening Loads (kip-in.)
Reference Thermal
35.5 in. S 1399 2889
33.5 in. N 2790 4063
32.0 in. S 1833 2645


Total Stresses (psi)


J Stress (psi)


-623
-323
25


Reference
366
801
558


Thermal
989
1124
533


Table 13-4. Comparison of J stresses and predicted stresses in top 4 in. of flange
Segment 2
Gauge Elevation J Stress (psi) Predicted Stress (psi) J Stress/Predicted Stress
35.5 in. S -623 -693 0.899
33.5 in. N -323 -219 1.475
32.0 in. S 25 137 0.182
Segment 3
Gauge Elevation J Stress (psi) Predicted Stress (psi) J Stress/Predicted Stress
35.5 in. S -623 -729 0.855
33.5 in. N -323 -230 1.404
32.0 in. S 25 144 0.174












Table 13-5. Comparison of J stresses and E stresses in top 4 in. of flange
Segment 2
Gauge Elevation J Stress (psi) E Stress (psi) J Stress/E Stress
35.5 in. S -623 -671 0.928
33.5 in. N -323 -320 1.009
32.0 in. S 25 -57 -0.439
Segment 3
Gauge Elevation J Stress (psi) E Stress (psi) J Stress/E Stress
35.5 in. S -623 -674 0.924
33.5 in. N -323 -369 0.875
32.0 in. S 25 -140 -0.179











Measured strains due to
mechanical and thermal loading


Measured
reference


Confirmed


strains


Time


15 hrs


mi ns


9 hrs


5 mins


5 mins


P +SW: Pretress + Self-weight

Applied Loads:
Step 1: Opening and closing of joint J2 (application and removal of mechanical loads)
Step 2: Positive thermal gradient (application of thermal load)
Step 3: Opening and closing of joint J2 (application and removal mechanical loads)
Step 4: Cooling to reference temperature at start of test (removal of thermal loads)
Step 5: Opening and closing of joint J2 (application and removal of mechanical loads)


Figure 13-1. Sequence of load application (positive gradient test)












End-support


Location of
interest
(Joint J2)


P: Post-tensioning force


Figure 13-2. Laboratory beam


40


35


30


S25






10

W 5


10
-

-5


0 5 10 15 20 25 30
Temperature Difference (deg. F)


35 40 45


Figure 13-3. Laboratory imposed positive thermal gradient












i 5~= ?~c !Se 2qOC


AASHTO LRFD
& 993 Segrnental


o a c ,
Ma)dmum on Aug 11, 1992


ly 16, 1992
h 25 1993


Figure 13-4. Typical field measured positive thermal gradient (Roberts, C. L., Breen, J. E.,
Cawrse J. (2002)., "Measurement of Thermal Gradients and their Effects on
Segmental Concrete Bridge," ASCE Journal of Bridge Engineering, Vol. 7, No. 3,
Figure 4a, pg. 168)


40

35

30

^ 25


.) 2 0

m 15

10

5


80 85 90 95 100 105
Temperature (deg. F)


110 115 120 125


Figure 13-5. Measured temperatures in heated segments (positive thermal gradient)


Measured
Maximum




Readlngs fIromr Ju
tn M rr




























101 *!*I





-500 -400 -300 -200 -100 0 100 200 300 400 500
Strain (microstrain)


Figure 13-6. Calculated strain components of the AASHTO positive thermal gradient


0L
-300


-200 -100 0 100
Strain (microstral


200 300 400 500


Figure 13-7. Measured and predicted strains near j oint J2 (Segment 2)






































































0 50 100 150 200 250 300 350 400 450
Strain (microstrain)


101 1 esueiISg3 o~
,, Measturi.L1Seg :. Soullhl

5~ Pred~ltd I aboHratorj*rdlentl



-300 -200 -100 0 100 200 300 400 500
Strain (microstrain)


Figure 13-8. Measured and predicted strains near j oint J2 (Segment 3)


12

10

8

6

4

2

0-

-2

-4

-6

-8

-10

-12
-250 -200 -150 -100 -50


- Seg. 2(Measured)
SSeg. 2 (Calculated, Lab. Gradient)
- Seg 2 C.IClil8[ad uuSHT.I.=: I3rjdltntl
HS~ Seg .ICnij5ltidlatdLt rdet
MC Seg :.ijilljatilad uuSHT.I.=*3 Irjdltntl


p =,enterllne ojf beam1


Figure 13-9. Plan view of measured and predicted strains near j oint J2 (Top Flange)

































-5 0 5 10 15 20 25 30 35 40 45
Temperature Difference (deg. F)

Figure 13-10. Comparison of measured thermal gradient profiles with average


-2000 -1800 -1600 -1400 -1200 -1000 -800 -600 -400 -200 0 200 400
Stress (psi)


Figure 13-11i. E stresses near j oint J2 (Segment 2)






























10
,,E Strc aScgmcntt 3.i lo1h a1
,, E Stre i''lSi gment 3. Soulthl
5 M P'ried-letid I Laboiratorri Gradjient
& Freditiad 1u.uSHTC.= Gradientl


-2000 -1800 -1600 -1400 -1200 -1000 -800 -600 -400 -200 0 200 400
Stress (psi)


Figure 13-12. E stresses near j oint J2 (Segment 3)


D~~f r n.: In mag~nltudr of~ [nh rmB
~~gradents fromll a ~rag~ I 5t 1:: localln o:f
1 1 11*Illlt 11:im slpe:hr) ng~ lea535 t

p''rjdicted 5train5 are [ nglle



'- Sectlon c-
SSiectlon E.
Mi~ Secin C.
M Seclion DI
M Seclion E
SSiectlon F


-5 0 5 10 15 20 25 30
Temperature Difference (deg. F)


35 40 45


Figure 13-13. Difference in magnitude of imposed thermal gradients at location of maximum
slope change (elevation 32 in.)














------------ '-------------------


Apply load Q, to create
zero stress at top fiber


Compression Tennsion


Centroid


Prestress (P)


Self-weight (SW) Joint-opening SUM (P +SW +Q )
load (Q,)
(Reference Stress state)


Figure 13-14. Superposition of component stress blocks (Mechanical loads only)


Apply load QT to create
zero stress at top fiber


Compression~ Tension


Prestress (P) Self-weight (SW) Positive Joint-opening SUM (P +SW +PG +QT)
gradient (PG) load (QT)
(Thermal stress state)


Figure 13-15. Superposition of component stress blocks (Mechanical loads with positive thermal
gradient)


z


C G.












h = depth of joint opening Compression Tenslon
.....,, zero stress at


zero stress at
depth 'h' from


(d)
Total stress distribution at
Joint J2
(Thermal stress state)


(a) (b) (c)
Beam deformation near Cross section Total stress distribution at
joint J2 at joint J2 Joint ]2
(Elevation view) (reference and (reference stress state)
thermal stress states)


Figure 13-16. Uniform opening of joint across section width

hA, h,, ha = depth of joint opening on sides of cross section


hII cntcboundary hA bou~Lndaryl hA

B/ /A C \A








contact area 1/// contact area





Cross section at joint J2 Cross section at joint J2
(Reference stress state) (Thermal stress state)


Figure 13-17. Non-uniform opening of joint across section width













55

50

45

40

S35
30

3 25









-700 -600 -500 -400 -300 -200 -1 00 0 100 200 300 400
Strain (microstrain)


Figure 13-18. Load vs. strain at reference temperature (Segment 3, North)


-600 -500 -400 -300 -200 -100 0
Strain (microstrain)


100 200 300 400


Figure 13-19. Load vs. strain with positive thermal gradient (Segment 3, North)



























-~HC ~?-~-~-01'-?5?



~?-~-i-?li.-l~l?


0-


-700 -600 -500 -400 -300 -200 -1 00 0 100 200 300 400
Strain (microstrain)


Figure 13-20. Load vs. strain at reference temperature (Segment 3, South)


-600 -500 -400 -300 -200 -1 00 0 100 200 300 400
Strain (microstrain)


Figure 13-21. Load vs. strain with positive thermal gradient (Segment 3, South)












































































Figure 13-23. Load vs. strain with positive thermal gradient (Top flange)


~c~ F~-Tr]-F-:5-~~5


~ ~ ?-T-~ -S 5-0 ;S


-


35

30

4 5

20

1 5

10



15



0
-70


-600 -500 -400


-300 -200 -100
Strain (microstrain)


0 100 200 300 400


Figure 13-22. Load vs. strain at reference temperature (Top flange)


-600 -500 -400 -300 -200 -100 0
Strain (microstrain)


100 200 300 400













H S3-N-S-02-33 5 (Referencel









'-


m
-500 -400 -300 -200 -100 0
Strain (microstrain)


100 200 300 400


55



45

40

~i35

S30

S 25


51


-700 -600


Figure 13-24. Comparison of strain differences on North and South sides of joint J2 (Positive
thermal gradient)


North | South

(25.1 kips, 36 in.) ,(15.8 kipsi 36 in.),(13.0 kips, 36 in.)
(30.9 kips, 33.5 in.) (15.5 kips, 35.5 in.)
(41.0 kips, 30.4 in.) (20.6 kips, 32.0 in.)
(22.6 kips, 28.5 in.)
(44.2 kips, 27.5 in.)' r (37.9 kips, 27.5 in.)










Reference stress state


North | South

(43.3 kips, 36 in.) (32.7 kip 36 in; (30.2 kips, 36 in.)
(44.6 kips, 33.5 in.) (32.0 kips, 35.5 in.)
(44.4 kips, 30.4 in.) (28.9 kips, 32.0 in.)
(20 kips, 28.5 in.)
(47.6 kips, 27.5 in.)' r (38.0 kips, 27.5 in.)










Thermal stress state


Figure 13-25. Joint opening loads detected from strain gauges near j oint J2





Positive
cu rvatu re


Positive
curvature


z (SOUTH)


x: longitudinal axis of beam


Figure 13-26. Sign convention for moments and curvature


S-S-S-02-35.5


North~ South

I 14.6 in. I 9.4 in. I

75 in.


7 in. AM,


North I South
S14.2 in. 9.8 in.


7.5 in.


7 in I 1 12.2in.

AMP hI C.G. M, z







10 in.
Thermal stress state


8 in.





28 in.


8 in.





28 in.


C.G.




Y


M, z


10 in.
Reference stress state


Figure 13-27. Contact areas at j oint J2 at incipient opening of joint on South side at
elevation 35.5 in.


S-S-S-02-32.0


North | South


North~ South
24 in.


4 in.
AM,
(4 in.
7 in.
AMP hI C.G. M, z


8 in.





28 in.


8 in.





28 in.


10 in.
Thermal stress state


Reference stress state


Figure 13-28. Contact areas at j oint J2 at incipient opening of joint on North side at elevation
33.5 in.




193













S-N-S-02-33.5


North | South

19.6 in.




7 in. AM .


North | South


17 in.

--. 3 in.





AMP hI C.G. M, z


5.5 in.





28 in.


5.5 in.





28 in.


C G


M, z


10 in.
Thermal stress state


10in.
Reference stress state


Figure 13-29. Contact areas at j oint J2 at incipient opening of joint on South side at elevation
32.0 in.









CHAPTER 14
RESULTS AASHTO NEGATIVE THERMAL GRADIENT

Results from the application of mechanical loading in combination with the AASHTO

negative thermal gradient are presented and discussed in this chapter. The objective of the

mechanical-thermal load tests was to experimentally quantify the self-equilibrating thermal

stresses caused by the AASHTO nonlinear negative thermal gradient in the top 4 in. of the

flanges of segments 2 and 3. As with the positive gradient, two independent methods were used

to quantify stresses. Elastic modulus derived stresses (E stresses) were determined by converting

measured strains into stresses using the elastic modulus of concrete. Independently, joint

opening derived stresses (J stresses) were determined using the known stress state at incipient

joint opening. In both methods concrete behavior was assumed to be linear elastic.

The test sequence, illustrated in Figure 14-1, shows that before mechanical or thermal

loads were applied, the only forces acting on the beam were prestress and self-weight. The test

sequence started with partial opening and closing of the j oint at midspan (j oint J2) with the beam

at the ambient temperature of the laboratory (about 80 oF). This was followed by application of a

uniform temperature increase of about 45 oF on segments 2 and 3 of the beam, after which the

top portion of the segments could be cooled to impose the negative thermal gradient (see

Chapter 8). Joint J2 was partially opened and closed after achieving and maintaining the steady

state uniform temperature increase on the heated segments for 30 to 45 minutes. Data from this

step of the load sequence were used to establish a zero reference stress state at j oint J2. The top

of the segments were then cooled to impose the AASHTO negative thermal gradient. After

achieving and maintaining the steady state negative thermal gradient on the heated segments for

30 to 45 minutes, joint J2 was partially opened and closed to determine the thermal stress state.









The heated segments were then cooled to the reference temperature (tap water temperature) at

the start of the test, after which j oint J2 was again opened and closed, completing the load cycle.

Data collected from steps 3 and 5 of the load sequence were used to quantify

self-equilibrating thermal stresses caused by the laboratory-imposed negative thermal gradient.

Joint-opening loads and contact areas at j oint J2, as the j oint was gradually opened, were used to

calculate self-equilibrating stresses caused by the nonlinear gradient (J stresses). Neither elastic

moduli, nor coefficients of thermal expansion of segments 2 and 3 were used in the calculation

of J stresses.

Elastic modulus derived thermal stresses calculated from measured thermal strains close to

joint J2 (E stresses) and joint opening derived thermal stresses (J stresses) are presented and

discussed in the following sections.

Elastic Modulus Derived Stresses (E stresses)

The nonlinear negative thermal gradient imposed on the heated segments of the laboratory

beam (see Figure 14-2) in Step 4 of the load sequence is shown in Figure 14-3. For comparison,

Figure 14-3 also shows the AASHTO design negative gradient. Measured temperatures in the

heated segments after imposing the negative thermal gradient are shown in Figure 14-4.

As was done for the positive gradient (described in Chapter 13) temperature on top of the

flange was obtained by extrapolating the measured temperature data from elevations 32 in, and

35.5 in. The idealized strain components induced by the AASHTO design negative thermal

gradient are shown in Figure 14-5 (A detailed description of the strain components is given in

Chapter 3 and Chapter 13).

The change in measured strain between Step 3 and 5 at joint J2 are plotted in Figure 14-6

through Figure 14-8. Figure 14-6 and Figure 14-7 show the strain difference along the height of

segments 2 and 3, respectively. Figure 14-8 shows a plan view of the strain differences on the










top flange near the same joint. Also shown in the figures are the two sets of strain changes

predicted using the AASHTO design procedure: one using the AASHTO design thermal

gradient, and the other using the laboratory-imposed thermal gradient. Because the strain gauges

installed on the beam were self-temperature compensating (STC) gauges, and because there was

no axial or flexural restraint on the beam, the measured strains consisted only of the

self-equilibrating strain component of the total strains. The average laboratory-imposed thermal

gradient profile (average of profiles at Section A through Section F (Figure 14-3)) was used in

calculating the 'laboratory gradient' strains in Figure 14-6 through Figure 14-8.

No marked difference is apparent between measured and predicted strains due to the

laboratory gradient below approximately 28 in. elevation. Tensile strains were present in the

bottom of the section up to an elevation of about 10 in. Compressive strains arose in the section

mid-height from about 10 in, to 32 in. elevation. A maximum compressive strain (due to the

laboratory gradient) of about 21 C1s was predicted at elevation 27.5 in. whereas a maximum

measured compressive strain of about 26 C1s occurred at the same elevation. The maximum

predicted tensile strain due to the AASHTO design gradient, of magnitude about 15 C1s, occurred

at an elevation of 20 in.

The difference between locations of maximum predicted compressive strains due to the

imposed laboratory gradient and the AASHTO design gradient was due to the difference in the

shape of the laboratory and AASHTO design thermal gradients. In each case, the maximum

compressive strain occurred at the location where the change in slope (in units of oF/in.) of the

thermal gradient profile was algebraically at a maximum. This occurred at an elevation of

27.5 in. for the laboratory gradient and at an elevation of 20 in. for the AASHTO design









gradient. Tensile strains also occurred above the mid-thickness of the flange with a steeper

gradient than that of the remainder of the profile.

Some additional differences between the measured and predicted strains are also notable.

Measured tensile strains were significantly smaller than predicted at the top of the section in both

segments except for the North top flange of Segment 3 (see Figure 14-8). As with the positive

thermal gradient, the smaller measured tensile strains on top of the section were thought to be

caused by a likely discontinuity in the shape of the thermal gradient in the top 0.5 in. of the

flange. Although not measured, it is probable that the temperature at the top surface of the

flange was less than that of the temperature of the topmost thermocouples (located at an

elevation of 35.5 in.). In determining predicted strains, however, the magnitude of the thermal

gradient in the top flange was obtained by extrapolating the linear thermal gradient between

elevations of 32 in, and 35.5 in. The approximately 53% difference between strains measured on

the North and South top flange of Segment 3 was attributed to the condition at the top surface of

the flange at joint J2 shown in Figure 11-6.

Measured concrete strains on the North side at midspan (j oint J2) and at mid-segment of

segments 2 and 3 are compared in Figure 14-9 and Figure 14-10, respectively. The distributions

of measured strain on the side of the flange at mid-segment did not match the predicted strain

profile as well as the measured strains at midspan because only two strain gauges were located

on the side of the flange at mid-segment. Additionally, measured tensile strains on top of the

flange at mid-segment were significantly less than predicted strains at the same locations.

Measured strains on top of the flange at mid-segment were, however, generally greater than

corresponding measured tensile strains at joint J2. This observation reinforces the possibility

that differential shrinkage at joint J2 led to a greater discrepancy between measured and










predicted strains at the joint. Between elevations 32 in, and 35.5 in., measured tensile strains

followed a linear distribution as did the predicted strains. The measured strains were, however,

generally larger than predicted strains between elevations 32 in, and 33 in, and smaller than

predicted strains above 33 in. As discussed in Chapter 13, a possible reason for the difference

between measured and predicted strains in this region of the flange was a variation between

measured thermal gradients and the average thermal gradient (see Figure 14-11), which was used

to predict strains per the AASHTO design procedure.

The uniform and linear sub-components of the overall negative thermal gradient were

expected to lead to additional stresses in the concrete as the top portions of segments 2 and 3

were cooled during Step 4. Contraction of the segments relative to the prestressing caused a net

reduction in prestressing force, however the measured peak reduction was only 0.2% of the

initial prestress and was therefore considered negligible.

Elastic modulus derived stresses (E stresses) were the self-equilibrating thermal stresses

caused by the negative thermal gradient, and were determined by multiplying the measured

strains in Figure 14-6 and Figure 14-7 by the elastic moduli of Segment 2 (4850 ksi) and

Segment 3 (4850 ksi), respectively. The elastic moduli were calculated by linearly interpolating

between cylinder modulus of elasticity data between test ages of 28 and 360 days. At the time of

the test, the ages of segments 2 and 3 were 251 and 238 days, respectively.

Figure 14-12 and Figure 14-13 show E stress distributions near joint J2 on Segment 2 and

Segment 3, respectively. E stresses at midspan and mid-segment on the North side of segments 2

and 3 are compared in Figure 14-14 and Figure 14-15, respectively. Also for comparison,

self-equilibrating thermal stresses due to the laboratory thermal gradient and the AASHTO

design gradient were calculated using the AASHTO recommended procedure discussed in










Chapter 3, and are shown in the figures. CTEs from Table 12-1 and the segment MOEs noted

above were used in these calculations.

Table 14-1 compares E stresses computed at the top of the flanges of segments 2 and 3

with similar stresses obtained by extrapolating from the linear E stress distributions between

elevations 32 in, and 35.5 in. (see Figure 14-12 and Figure 14-13) on the sides of the segment

flanges. E stresses in the extreme top flange fibers were significantly lower than stresses

extrapolated to the same location. This condition follows from the relatively smaller

stress-inducing thermal strains that were measured at the top surfaces of the flanges (see Figure

14-8). As discussed previously, the smaller strains were attributed to differential shrinkage at

joint J2 and to a lower thermal gradient magnitude than was targeted (as prescribed by the

AASHTO gradient) for the top of the flanges of the segments. At an elevation of 32 in., the

E stress on Segment 2 was about 88% less than the predicted stress. Both stresses were

compressive. The E stress on Segment 3 at the same elevation, however, was tensile whereas the

predicted stress was compressive. As was the case for the positive thermal gradient, this was

attributed to the difference in magnitude of the laboratory thermal gradients at sections A

through F (from the average thermal gradient used in predicting stresses) at that elevation; the

location of the maximum slope change in the thermal gradients (see Figure 14-16).

E stresses and predicted stresses caused by the laboratory-imposed nonlinear negative

thermal gradient in the top 4 in. of the flanges of segments 2 and 3 are compared in Table 14-2.

Predicted stresses in the extreme top flange fibers (where the maximum tensile stresses were

expected to occur, had the gradient been linear in the top 4 in. of the flanges) are not shown in

the table because the shape and magnitude of the thermal gradient in this region were not

measured. E stresses 0.5 in. below the top of the flange (maximum E stresses) were









approximately 25% and 14% less than corresponding predicted stresses in Segment 2 and

Segment 3, respectively. E stresses caused by the positive thermal gradient (see Chapter 13) at

the same location were 3% and 8% less than corresponding stresses predicted in Segment 2 and

Segment 3, respectively. Beam response was more sensitive to small errors in thermocouple

readings in the negative thermal gradient case than in the positive thermal gradient case because

of the relatively lesser magnitude (temperature change) of the negative thermal gradient. This

was thought to be the reason for the greater discrepancy between maximum E stresses and

corresponding predicted stresses due to the negative gradient. Taking into consideration the

effects of differential shrinkage at j oint J2, small errors in measuring strain gauge elevations, and

differences between measured thermal gradients (at sections A through F) and the average

thermal gradient within the top 4 in. of the segment flanges, these differences were considered to

be within the limits of experimental error.

Joint Opening Derived Stresses (J Stresses)

Joint-opening derived stresses (J stresses) were determined using the procedure outlined in

Chapter 13 and data collected from steps 3 and 5 of the load sequence shown in Figure 14-1. For

the thermal loading sequence used in the negative gradient tests, Eqns. 13-1 and 13-2 were

modified as follows:

fP (y, Z) + Jsw (y, z')+ Jr, (y, z') + fR (r, Z) = 0, ((y, z) R) (14-1)
fP f, Z) + fsw (y, z) + f, (y, z) + f, (y, z) + f, (y, z) = 0, ((y, z) E T) (14-2)

where, for represents stresses caused by the expansion of the concrete segments (against

the restraint of the prestress bars) due to a uniform temperature increase (see Figure 14-17 and

Figure 14-18) and all other quantities are as described in Chapter 13. The for term was added to

account for the fact that the negative gradient was imposed by first heating the entire section and

then cooling the top portion.










Figure 14-19 and Figure 14-20 show variations of concrete strain with applied load near

joint J2 on the North side of Segment 3 at the reference stress state (reference temperature) and

thermal stress state (with negative thermal gradient), respectively. Similar plots near the same

joint on the South side are shown in Figure 14-21 and Figure 14-22, respectively. The variation

of concrete strain with applied load on top of the flanges of segments 2 and 3 near j oint J2 at the

reference and thermal stress states are shown in Figure 14-23 and Figure 14-24, respectively.

Data collected from strain gauges near j oint J2 on Segment 2, LVDTs mounted across joint J2 on

top of the flanges of segments 2 and 3, and LVDTs mounted across the same j oint on the South

side can be found in Appendix E.

A comparison of concrete strains at same side of joint J2 at the reference and thermal stress

states shows that at identical elevations in the top 4 in. of the flange, the j oint opened at lower

loads at the thermal stress state than it did at the reference stress state. This is illustrated in

Figure 14-25 with data taken from the strain gauges at elevations 33.5 in. on the North and

3 5.3 in. on the South side of the j oint. The same is true of the top flange strains shown in Figure

14-23 and Figure 14-24. LVDTs on the sides and top of the flange (see Appendix E) also show

the joint opening at lower loads at the thermal stress state than at the reference stress state. This

was indicative of the development of tensile stresses in the top concrete fibers at j oint J2 due to

the negative thermal gradient. It is also evident in Figure 14-25 that, similar to the positive

thermal gradient, the strain difference between vertical portions of strain diagrams, at the

reference and thermal stress states, was dependent only on the elevation of the gauge and not on

the side (North/South) of the j oint on which the gauge was located.

Loads that caused j oint J2 to open at the reference and thermal stress states were detected

using the strain data shown in Figure 14-19 through Figure 14-24 above, and Figure E-1 through










Figure E-8 in Appendix E. Applied loads at the cantilevered-end of the test beam, which caused

joint J2 to open at various depths, are shown in Figure 14-26. The sign convention for moments

and curvatures, which is the same as that used in Chapter 13, is shown (for convenience) in

Figure 14-27.

Figure 14-28 through Figure 14-30 show estimated contact areas at joint J2 at the reference

and thermal stress states just as opening of the j oint was detected from strain gauges at elevations

of 35.5 in. (South), 33.5 in. (North), and 32.0 in. (South), respectively. These plots were

developed using the same approach detailed in Chapter 13.

In Table 14-3 calculated J stresses are presented for the locations of strain gauges on the

sides of the beam within the top 4 in. of the flange. As for the positive thermal gradient, the total

stresses (stresses determined from Equation 13-5) though positive, indicating tension, actually

represent relief of existing compressive stresses at J2 prior to the application of joint-opening

loads. J stresses were determined by taking the difference between total stresses at the reference

stress state and total stresses at the final stress state.

Changes in prestress (as the beam was mechanically loaded and joint J2 opened) accounted

for less than 1% of total stresses (see Equation 13.5). Calculated total stresses were, therefore,

essentially dependent on the magnitude of joint-opening loads. J stresses, however, were

dependent on the difference between the j oint-opening loads at the reference and thermal stress

states. For example, the loads initiating opening of joint J2 on the North side at an elevation of

33.5 in. were greater than they were on the South side at an elevation of 35.5 in, as can be seen

from the magnitudes of the moments in Table 14-3. However, calculated J stresses at an

elevation of 33.5 in. were lower than J stresses at an elevation of 35.5 in. because the difference










in joint-opening moments at elevation 33.5 in. was lower than the difference in moments

required to open the joint at elevation 35.5 in.

J stresses and stresses predicted with the AASHTO procedure using the laboratory thermal

gradient, in the top 4 in. of the flange, are compared in Table 14-4. J stresses 0.5 in. below the

top of the flange (maximum J stresses) were approximately 17% and 23% less than

corresponding predicted stresses in Segment 2 and Segment 3, respectively. At elevation 32 in.,

J stresses were about 82% less than predicted stresses. Both predicted and J stresses

compressive.

J stresses and E stresses in the top 4 in. of the flanges are compared in Table 14-5.

Maximum J stresses were within 1 1% of maximum E stresses. J stresses were, in general, higher

than E stresses on Segment 2 and lower than E stresses on Segment 3. This could possibly be

due to small errors in estimating contact areas and determining joint-opening loads. Another

possibility is that J stresses represented the average stress between segments 2 and 3 at joint J2

whereas E stresses represented stresses on each segment about 2 in, away from joint J2.










Table 14-1. Comparison of E stresses and extrapolated stresses on top of segment flanges near
joint J2 (laboratory negative thermal gradient)
E Stress (psi) Extrapolated (psi) Measured/Extrapolated
Segment 2, North 38 252 0.151
Segment 2, South 71 191 0.372


Segment 3, North
Segment 3, Middle
Segment 3, South


0.921
0.260
0.476


Table 14-2. Comparison of E stresses and predicted self-equilibrating thermal stresses caused by
laboratory negative thermal gradient near joint J2


Segment 2
Elevation (in.)

36
35.5
33.5
32
Segment 3
Elevation (in.)

36
35.5
33.5
32


Average E Stress (psi)


Average Predicted
(psi)
N/A
258
80
-54

Average Predicted
(psi)
N/A
272
84
-57


E Stress/Predicted

N/A
0.748
0.994
0.116

E Stress/Predicted

N/A
0.865
1.413
-0.539


Average E Stress (psi)

148
235
118
31


Table 14-3.
Gauge
Elevation

35.5 in. S
33.5 in. N
32.0 in. S


J stresses in top 4 in. of flange
Moments due to
Joint-opening Loads (kip-in.)
Reference Thermal
1679 885
2961 2510
1986 1896


Total Stresses (psi)


J Stress
(psi)

214
121
-10


Reference
443
861
625


Thermal
229
740
635


Table 14-4. Comparison of J stresses and predicted stresses in top 4 in. of flange
Segment 2
Gauge Elevation J Stress (psi) Predicted Stress (psi) J Stress/Predicted Stress
35.5 in. S 214 258 0.829
33.5 in. N 121 80 1.500
32.0 in. S -10 -54 0.185
Segment 3
Gauge Elevation J Stress (psi) Predicted Stress (psi) J Stress/Predicted Stress
35.5 in. S 214 272 0.787
33.5 in. N 121 84 1.440
32.0 in. S -10 -57 0.175












Table 14-5. Comparison of J stresses and E stresses in top 4 in. of flange


Segment 2
Gauge Elevation
35.5 in. S
33.5 in. N
32.0 in. S
Segment 3
Gauge Elevation
35.5 in. S
33.5 in. N
32.0 in. S


J Stress (psi)


E Stress (psi)
193
79
-6

E Stress (psi)
235
118
31


J Stress/E Stress
1.109
1.532
1.667

J Stress/E Stress
0.911
0.975
-0.323


J Stress (psi)
214
121
-10











Measured strains due to
mechanical loading and uniform
temperature change


Measured strains due to mechanical loading,
uniform temperature change, and AASHTO
negative thermal gradient

-8Measured
m reference Confirmed
strains i \referen ce
.2I i i strains










S Step 1i Step 2 Stp3 Step 4 Stp5 Step 6 Step 7~





5 mins 24 hrs 5 mins 6 hrs 5 mins 15 hrs 5 mins
Time

P +SW: Pretress + Self-weight
Applied Loads:
Step 1: Opening and closing of joint J2 (application and removal of mechanical loads)
Step 2: Uniform temperature change (application of thermal load)
Step 3: Opening and closing of joint J2 (application and removal mechanical loads)
Step 4: Negative thermal gradient (application of thermal load)
Step 5: Opening and closing of joint J2 (application and removal of mechanical loads):
Step 6: Cooling to reference temperature at start of test (removal of thermal loads)
Step 7: Opening and closing of joint J2 (application and removal of mechanical loads)


Figure 14-1. Sequence of load application (negative gradient test)
















SEGMENT 1 Ij SEGMENT 2 1 SEG ENT 3 ii SEGMENT 4


(AMBIENT) Ij (HEA TED) Il (HEATED) jl (AMBIENT)


10.5 ft



5ft 5ft


H Section A
M Section B
M Section C
M Section D
M Section E
RB Section F
M AASHTO


End-support



1.7ft


Location of
interest
(Joint J2)


Applied Load (Q)


A B


C (D


E F


_i lit


P


Lab. floors


id-support


East -


West


P: Post-tensioning force

Figure 14-2. Laboratory beam


40

35

30

S25



m 15


-45 -40 -35 -30 -25 -20 -15 -10
Temperature Difference (deg. F)


-5 0 5


Figure 14-3. Laboratory imposed negative thermal gradient


2.7 f















35


30


^ 25





m 15
Ht Section A
M Section B
10 Section C
Section D
M Section E
H Section F
Target

80 85 90 95 100 105 110 115 120 125 130
Temperature (deg. F)


Figure 14-4. Measured temperatures in heated segments (negative thermal gradient)


0 1-
-200


-160 -120 -80 -40 0 40
Strain (microstrain)


80 120 160 200


Figure 14-5. Calculated strain components of the AASHTO negative thermal gradient


































































0 50 100 150


Figure 14-7. Measured and predicted strains near j oint J2 (Segment 3)


We b







- Measured (Seg. 2, North)
- Measured (Seg. 2, South)
M Predicted (Laboratory Gradient)
- Predicted (AASHTO Gradient)


Flange



We b








- Measured (Seg. 3, North)
- Measured (Seg. 3, South)
N Predicted (Laboratory Gradient)
- Predicted (AASHTO Gradient)


-350 -300 -250 -200 -150 -100 -50
Strain (microstrain)


O


0 50 100 150


Figure 14-6. Measured and predicted strains near j oint J2 (Segment 2)


-350 -300 -250 -200 -150 -100 -50
Strain (microstrain)













,, Sig ~lnnij5~lridl
- Si~g ~IFri~~liti~~ Ljt~';rj,-jli~ntl
- Si~g ~lfri~~liti~~ c~.~SHTi:j ~;rj~-Jlintl
- Sig:lnni~jS~lridl
Si~g : Ifri~~liti~~ Ljt~ ~,rj~~lintl
,, Si~g: IFri~~liti~~ ~.~SHTi::~ ~;rj~~lintl

~rlith



I]ortll


Flange



W~eb







H Measured (Mid-segment, Seg. 2)
- Measured (Midspan, Seg. 2)
N Predicted (Laboratory Gradient)
& Predicted (AASHTO Gradient)


-8

-10

-12L


-350 -300 -250 -200 -150 -100 -50 0 50 100 150
Strain (microstrain)


Figure 14-8. Plan view of measured and predicted strains near j oint J2 (Top Flange)


-350 -300 -250 -200 -150 -100 -50
Strain (microstrain)


0 50 100 150


Figure 14-9. Measured and predicted strains at midspan and mid-segment (Segment 2, North)





































































-5 0 5


Figure 14-11. Comparison of measured thermal gradient profiles with average profile


Flange




Web







M Measured (Mid-segment, Seg. 3)
M Measured (Midspan, Seg. 3)
N Predicted (Laboratory Gradient)
& Predicted (AASHTO Gradient)


-350 -300 -250 -200 -150 -100 -50
Strain (microstrain)


O


0 50 100 150


Figure 14-10. Measured and predicted strains at midspan and mid-segment (Segment 3, North)


1Flange


Web






Section A
M Section B
M Section C
Section D
M Section E
H Section F
M Average


10


5



-45


-40 -35 -30 -25 -20 -15 -10
Temperature Difference (deg. F)




























10
,,E StrC aSegme~nt 2 I lorfh e
,, E Stre i''lSigment 2t Soulthl
5 MPried~ltd l1aboraTor; *3rjdients


-1000 -800 -600 -400 -200 0 200
Stress (psi)


Figure 14-12. E stresses near j oint J2 (Segment 2)


OM
-1000


-800 -600 -400 -200 0 200
Stress (psi)


Figure 14-13. E stresses near j oint J2 (Segment 3)




























10


5


0-
-1000


-800 -600 -400 -200 0 200
Stress (psi)


Figure 14-14. E stresses at mid-segment and midspan (Segment 2, North)


0 1
-1000


-800 -600 -400 -200 0 200
Stress (psi)


Figure 14-15. E stresses at mid-segment and midspan (Segment 3, North)





-5 0 5



gradients at location of maximum


Apply load Q, to create
zero stress at top fiber



Centroid










Joint-opening SUM (P +SW+ Q,)


Elevation 32 in.
Flange



Dl~ferenc~ In magni'tude':' .:.F115 [hemB grdint-
(from average) at location of maximum
slope change leads to measured tensile
strains whereas predicted strains are
compressive

Section A
^' Section B


10 Section C
M Section D
M Section E
5 Section F
Average

-45 -40 -35 -30 -25 -20 -15 -10
Temperature Difference (deg. F)


Figure 14-16. Difference in magnitude of imposed thermal
slope change (elevation 32 in.)


Compression tTension


temperature. load (Q,)
increase (UT)
(Reference Stress state)


Prestress (P) Self-weight (SW) Uniform


Figure 14-17. Superposition of component stress blocks (mechanical with uniform temperature
increase)














-----~--------------


Compression Tennsion


Apply load QT to create
zero stress at top fiber


L


Centroid


Prestress (P) Self-weight (SW)


Uniform
temperature.
increase (UT)


Negative Joint-opening SUM (P +SW+NG +QT)
gradient (NG) load (QT)
(Thermal Stress State)


Figure 14-18. Superposition of component stress blocks (mechanical with uniform temperature
increase and negative thermal gradient)


-600 -500 -400 -300 -200 -100 0
Strain (microstrain)


100 200 300 400


Figure 14-19. Load vs. strain at reference temperature (Segment 3, North)













55

50

45

40

S35
30

3 25









-700 -600 -500 -400 -300 -200 -1 00 0 100 200 300 400
Strain (microstrain)


Figure 14-20. Load vs. strain with negative thermal gradient (Segment 3, North)


-700 -600 -500 -400 -300 -200 -1 00 0 100 200 300 400
Strain (microstrain)


Figure 14-21. Load vs. strain at reference temperature (Segment 3, South)
































-600 -500 -400 -300 -200 -100 0
Strain (microstrain)


0-

-700


100 200 300 400


Figure 14-22. Load vs. strain with negative thermal gradient (Segment 3, South)

6o.


~c~ ~ _-TI]-~ -S 5-;;5


15
10
5
0 -
-700


-300 -200 -1 00 0 100 200
Strain (microstrain)


-600 -500 -400


300 400


Figure 14-23. Load vs. strain at reference temperature (Top flange)














~c~ ~ I-TI]-~ -S 5-;;5


10
5
0-
-700


-600 -500 -400


-300 -200 -100 0
Strain (microstrain)


100 200 300 400


Figure 14-24. Load vs. strain with negative thermal gradient (Top flange)


60

55

50

45

40

S35
30

S25


51

0'
-700 -600


-500 -400 -300 -200 -100 0
Strain (microstrain)


100 200 300 400


Figure 14-25. Comparison of strain differences on North and South sides of joint J2 (Negative
thermal gradient)






































I


North | South

(25.0 kips, 36.0 in. (15.2 kips, 36.0 in.)(13.5 kips, 36.0 in.)
(32.8 kips, 33.5 in.) (17.7 kips, 35.5 in.)
(41.2 kips, 30.4 in.) (22.5 kips, 32.0 in.)
(24.1 kips, 28.5 in.)
(45.9 kips, 27.5 in.)' (38.7 kips, 27.5 in.)


North | South

(19.7 kips, 36.0 in (.kis360n)(6.0 kips, 36.0 in.)
(27.5 kips, 33.5 in.) (9.8 kips, 35.5 in.)
(41.5 kips, 30.4 in.) (21.3 kips, 32.0 in.)
(22.6 kips, 28.5 in.)
(44.9 kips, 27.5 in.)' r (38.5 kips, 27.5 in.)










Thermal stress state


Reference stress state


Figure 14-26. Joint opening loads detected from strain gauges near j oint J2


Positive
cu rvatu re


Positive
curvature


(SOUTH)


x: longitudinal axis of beam


Figure 14-27. Sign convention for moments and curvature


S-S-S-02-35.5


North | South
12.6 in. 11.4 in.


AM 7.5 in.


S7 in. a,
AMP h G. M, z


8 in.





28 in.


7 in. AM .


AMP hI C.G. M,





10 in.
Reference stress state


z


10 in.
Thermal stress state


Figure 14-28. Contact areas at j oint J2 at incipient opening of joint on South side at elevation
35.5 in.


North~ South
11 in. 13 in.


~~i7.5 in.


I












S-N-S-02-33.5


North~ South


North~ South

22.3 in.





7 in.

AMP hI C.G. M, z


5.5 in.





28 in.


5.5 in.





28 in.


10 in.
Thermal stress state


10 in.
Reference stress state


Figure 14-29. Contact areas at j oint J2 at incipient opening of joint on North side at elevation
33.5 in.


S-S-S-02-32.0


North | South
4.7 in. 16.1 in.


North | South
19.3 in.


8 in.





28 in.


10 in.
Reference stress state


10 In.
Thermal stress state


Figure 14-30. Contact areas at j oint J2 at incipient opening of joint on South side at elevation
32.0 in.









CHAPTER 15
SUMMARY AND CONCLUSIONS

Results from a series of tests conducted on a 20 ft-long 3 ft-deep segmental concrete

T-beam, aimed at quantifying self-equilibrating thermal stresses caused by AASHTO design

nonlinear thermal gradients, have been presented and discussed. The beam consisted of four 5 ft

long segments that were post-tensioned together. Layers of copper tubes, which would later

carry water, were embedded in the middle two segments of the beam (Segments 2 and 3),

designated "heated" segments. Thermocouples were also cast into the heated segments to

monitor the distribution of temperature. The two end segments of the beam (Segments 1 and 4),

which were designated "ambient" segments, were strengthened using steel reinforcing bars to

carry loads at the prestress anchorage zones. The beam was vertically supported at midspan and

at the end of one ambient segment. Mechanical loads were applied at the cantilevered end and

thermal profiles were imposed on the heated segments by passing water at specific temperatures

through each layer of copper tubes. The region of interest in the experimental program was the

dry j oint between the two heated segments of the beam (designated j oint J2), which was heavily

instrumented with surface strain gauges and LVDTs. Detection of opening of the j oint was of

primary importance in quantifying stresses caused by the application of AASHTO nonlinear

thermal gradients.

The experimental program consisted of determining the in-situ coefficient of thermal

expansion (CTE) of the heated segments; investigating the behavior of the beam under the action

of mechanical loads; applying a uniform temperature change on the heated segments to

investigate the free expansion behavior of the beam; and imposing the AASHTO design

nonlinear thermal gradients in combination with mechanical loads for the purpose of quantifying

self-equilibrating thermal stresses due to the thermal gradients.









In-situ CTEs of Segments 2 and 3 were determined by imposing uniform and linear

temperature distributions on each segment. The CTE of Segment 3 was also determined using a

procedure specified by AASHTO. Good agreement was found between the in-situ CTEs

determined using uniform and linear thermal profiles for both segments. Good agreement was

also found between the CTE determined using the AASHTO method and the average in-situ

CTE of Segment 3. AASHTO CTE testing was not conducted for Segment 2 because the

cylinders required for the test were not cast for this segment.

Mechanical load tests indicated that strain gauges mounted on the side surfaces of the

beam close to the j oint at midspan (j oint J2) were the most reliable instruments in detecting

opening of the joint. However, strain gauges mounted on the top surfaces of the segment flanges

near the joint showed little change in strain with increasing applied load. This was attributed to

an imperfect fit (despite match-casting of the segments) at the j oint, and differential shrinkage in

the top flange fibers which were unsealed and exposed to the laboratory environment during

curing of the segments. Strain distributions through the height of the contact area at the j oint

(before and after the joint opened) were generally found to be linearly dependent on applied load,

which allowed for the use of classical flexural stress formulas in quantifying stresses due to the

AASHTO nonlinear thermal gradients. Observations and conclusions that were drawn from the

directly measured experimental data are as follows:


* A uniform temperature increase of 41 oF increased the prestress force by about 6% of the
initial prestress due to differential movement and heating between the bars and concrete
segments. The measured change in prestress compared well with predicted values
determined using in-situ CTEs and laboratory determined concrete elastic moduli.

* Measured concrete strains caused by the uniform temperature increase were generally
tensile, whereas predicted strains (determined using the AASHTO recommended
procedure) were compressive. The difference was attributed primarily to slight variations
in temperature between the inner core and the outer perimeter of the heated segments.










* Measured stress-induced concrete strains caused by the laboratory-imposed nonlinear
thermal gradients on top of the flanges of the heated segments near j oint J2 were
significantly less than predicted for both positive and negative thermal gradients. For the
positive thermal gradient, average measured strains on top of the flanges of segments 2 and
3 were about 56% and 39% less than predicted strains, respectively. For the negative
thermal gradient, average measured strains at the same locations on segments 2 and 3 were
about 81% and 53% less than predicted. The differences were attributed both to
differential shrinkage in the top flange fibers and a probable discontinuity in the thermal
gradients (positive and negative) within the top 0. 5 in. of the flanges of the heated
segments .

* At elevations below 0.5 in. from the top surface of the segment flanges near j oint J2,
measured stress-induced concrete strains caused by the laboratory-imposed nonlinear
thermal gradients agreed well with strains predicted using the AASHTO recommended
method for the analysis of nonlinear thermal gradients. Maximum measured stress-induced
concrete strains (which occurred at elevation 3 5.5 in.) under the action of the positive
thermal gradient were about 3% and 7% less than predicted strains on segments 2 and 3,
respectively. For the negative thermal gradient, maximum measured stress-induced
concrete strains (at the same location as for the positive thermal gradient) were about 25%
and 14% less than predicted strains on segments 2 and 3, respectively.

Two independent methods were also used to quantify concrete stresses caused by the

laboratory-imposed nonlinear thermal gradients at the joint between the heated segments. The

first method involved multiplying measured thermal stress-induced concrete strains by elastic

moduli (E stresses) whereas the second method involved determining stresses at the j oint using

the known stress state at incipient joint opening (J stresses). E stresses were determined

throughout the height of the heated segments at a distance of about 2 in, away, the location of

strain gauges from j oint J2. J stresses were quantified within the top 4 in. of the flanges of the

heated segments at joint J2. Conclusions from quantifying the E stresses and J stresses are as

follows:

* J stresses in the extreme top flange fibers at the j oint, where the maximum stresses caused
by the nonlinear thermal gradients were expected to occur, could not be quantified because
of the effects of differential shrinkage and because pieces of concrete had broken off the
top surface during transportation and handling of the segments. Though E stresses on top
of the flanges of the heated segments near j oint J2 were determined, they did not agree
well with predicted stresses because of reasons given in the third bulleted paragraph above.










* Maximum E stresses caused by the positive thermal gradient, which occurred at elevation
35.5 in. (i.e. 0.5 in. below the top surface of the segment flanges), were about 3% and 8%
less than corresponding predicted self-equilibrating thermal stresses in Segment 2 and
Segment 3, respectively. Maximum J stresses caused by the positive thermal gradient (also
at elevation 35.5 in.) were about 10% and 15% less than the predicted self-equilibrating
thermal stresses in segments 2 and 3, respectively.

* In the case of the negative thermal gradient, maximum E stresses (which also occurred at
elevation 35.5 in.) were about 25% and 14% less than corresponding predicted
self-equilibrating thermal stresses in segments 2 and 3, respectively. Maximum J stresses
(at the same elevation) were about 17% and 23% less than predicted stresses in segments 2
and 3, respectively.

* The percentage difference between maximum measured and maximum predicted negative
gradient stresses was higher than that for the positive thermal gradient because the negative
thermal gradient was more sensitive to local deviations of temperature from the width-wise
average temperatures that were used in predicting the self-equilibrating thermal stresses.
The difference in sensitivity was due to the magnitude of the negative thermal gradient
being only 30% the magnitude of the positive thermal gradient.

E stresses and J stresses in the top few inches of the flanges of segments 2 and 3 were in

general lower than stresses predicted using the AASHTO recommended procedure. In particular,

the maximum quantified stresses due to the negative thermal gradient were on the average about

20% less than corresponding predicted stresses (at the same location). These differences

between quantified and AASHTO predicted stresses could, however, not be attributed to any

flaws in the AASHTO method. They were considered to be likely the result of experimental

error. Based on the effects of differential shrinkage at joint J2, and the slight damage to the top

flange surfaces of the segments at the j oint on the magnitude of quantified stresses, it is possible

that self-equilibrating thermal stresses in the top section fibers at dry joints in segmental concrete

bridges may be smaller in magnitude than stresses predicted using the AASHTO method.

This study focused mainly on quantifying self-equilibrating stresses caused by the

AASHTO nonlinear thermal gradients. Some suggestions on future research are proposed:

* The current AASHTO nonlinear thermal gradients are computationally inconvenient and
do not work well with most structural analysis software. Furthermore, the stresses of
importance in design are the stresses in the top 4 in. of box-girder flanges. A study on









simplifying the nonlinear thermal gradients into a combination of linear gradients, such
that stresses of equal magnitude (especially the maximum stresses) caused by the nonlinear
gradients in the top 4 in, are generated by the combination of linear gradients, would
greatly simplify the computational effort that currently goes into calculating
self-equilibrating stresses in complex box-girder sections.

*The effect on concrete durability of tensile stresses generated by the AASHTO negative
thermal gradient in the top few inches of the flanges of segmental concrete bridges needs
investigation. Though tensile stresses have been known to cause damage to concrete, this
damage has been difficult to quantify. A study into the effect of the relatively steep
self-equilibrating stress gradient in the top few inches of concrete (compared to typical
bending stresses) on the potential for cracking would lead to a better understanding of the
level of damage that gradient-induced tensile stresses may cause.









APPENDIX A
BEAM SHOP DRAWINGS

In this appendix, design plans for the construction of the laboratory segmental beam are

presented. Steel reinforcement in prestress anchorage zones, thermocouple cages, copper tube

locations, plans for the loading mechanism, and shear keys are shown.












gag 41 <17
:Pcon 1b?1ut.1=TI. L* B A
Il ~ ip Lt* J.p-O-E


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a ;5 g la


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El~

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a
`i~-" 48

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lj z~
z





L
e

E
r3



Q


I $ I


g


Z
O


w
y
cs

JI
w
y.
in

g p,


su


Figure A-1. Prestress reinforcement details














I .ilM I p~Uu~
Kt)i :~~LC Y'3'8 ''NI'O "J'W :Mfd~L H3tlmS~RI rsslreanrr~
o
Ma ;o 5tl'EIP H~L;I'H: s.ld 1331~0tld BEQTF1J ~rV~9~D
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ouo*w ;Icr?


3

i vl
z


rs
w
cn






r-l
13
2
m


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J
r~xr


~uurCI


Figure A-2. Manifold and copper tube details


t3~



9




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II I I
I-~-I L I


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rt
i

b
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B


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c-5~,"~


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Figure A-3. Shear key details









APPENDIX B
LOADING FRAME DRAWINGS

Details of the loading frame which was used to apply mechanical loads at the cantilevered

end of the test beam are shown in this appendix.












































0lo 0 W16x89 0 0





oo1 olo




1oo olo


I1 16




Figure B-1. Loading frame details













232






































OO


O O

' 04


COLUMN (TYP.)


rmrm


rmrm


W16x8,


~-MC18x45.8


1" DI BOL
HOLES


STRONG-FLOOR BOLT HOLESllol
LOCATED IN LAB


O


W16x89




O


-PL 2"x1'-1"x1'-7"


Figure B-2. Details of cross channels




































SEGMENT
INTERFACE


DRILLED AND TAPPED
FOR 0.5" DIA


Figure B-3. Mid-support details













C15x33.9


-- LOAD CELL


1/2" X 9" X 9"1
PLATE






STACKED
NEOPRENE PADS


1,
1'-84


LOAD CELL


STACKED
NEOPRENE PADS


Figure B-4. End-support details









APPENDIX C
LOAD RESPONSE CURVES AT MID-SEGMENT (MECHANICAL LOADING)

In this appendix load versus strain response curves at the middle of Segment 2 and

Segment 3 (30 in, away from joint J2) are presented.














30


25


S20





~ 5






-400 -300 -200 -100 0 100 200 300 400 500 600 700 800 900
Strain (microstrain)


Figure C-1. Load vs. strain at middle of Segment 2 on North side





30


25


~i20


o 15









-400 -300 -200 -100 0 100 200 300 400 500 600 700 800 900
Strain (microstrain)


Figure C-2. Load vs. strain at middle of Segment 2 on South side















35


30


^ 25



lil. I. 0kips
.2 5 kips
W 15) YMr 10 kips








-400 -300 -200 -100 0 100 200 300 400 500 600 700 800 900
Strain (microstrain)


Figure C-3. Measured strain distributions at middle of Segment 2 on North side


40


35


30


S25


.P 20


S15


-200 -1 00 0 100 200 300 400 500 600 700 800 900
Strain (microstrain)


Figure C-4. Measured strain distributions at middle of Segment 2 on South side















30


25


S20


o 15









-400 -300 -200 -100 0 100 200 300 400 500 600 700 800 900
Strain (microstrain)


Figure C-5. Load vs. strain at middle of Segment 3 on North side





30


25


~i20


o 15




-400~~~~~~~~~ -300 -20 -10010 0 0 405060-? 70 0 0
strain (microstrain

FiueC6 od s tana idl fSget nSuhsd















35


30



S 25












-400 -300 -200 -100 0 100 200 300 400 500 600 700 800 900
Strain (microstrain)


Figure C-7. Measured strain distributions at middle of Segment 3 on North side


10


35


30


S25


.P 20




W 5





-400 -300 -200 -100 0 100 200 300 400 500 600 700 800 900
Strain (microstrain)


Figure C-8. Measured strain distributions at middle of Segment 3 on South side









APPENDIX D
LOAD RESPONSE CURVES (POSITIVE THERMAL GRADIENT)

Load vs. beam response curves which were derived from strain gauge and LVDT data are

shown here. These curves were used to determine loads at which the joint at midspan

(designated j oint J2) opened. The curves were also used to determine effective concrete contact

areas at j oint J2, which were then used to quantify J stresses due to the AASHTO nonlinear

positive thermal gradient.













55

so

45

40

S35
30






15



-700 -600 -500 -400 -300 -200 -1 00 0 100 200 300 400
Strain (microstrain)


Figure D-1. Load vs. strain at reference temperature (Segment 2, North)


-600 -500 -400 -300 -200 -100 0
Strain (microstrain)


100 200 300 400


Figure D-2. Load vs. strain with positive thermal gradient (Segment 2, North)














55

50

45

40

S35
30



20







-700 -600 -500 -400 -300 -200 -1 00 0 100 200 300 400
Strain (microstrain)


Figure D-3. Load vs. strain at reference temperature (Segment 2, South)


-600 -500 -400 -300 -200 -100 0
Strain (microstrain)


100 200 300 400


Figure D-4. Load vs. strain with positive thermal gradient (Segment 2, South)














55

50

45

40

35

30

25

20

15

10

5

0-
-0.005


0 0.005 0.01 0.015 0.02 0.025 0.03 0.035 0.04
Relative Longitudinal Displacement (in.)


Figure D-5. Load vs. joint opening at reference temperature (Top flange)


5L

-0.005


0 0.005 0.01 0.015 0.02 0.025 0.03 0.035
Relative Longitudinal Displacment (in.)


Figure D-6. Load vs. joint opening with positive thermal gradient (Top flange)









244



































-0.005 0 0.005 0.01 0.015 0.02 0.025 0.03 0.035 0.04
Relative Longitudinal Displacement (in.)


Figure D-7. Load vs. joint opening at reference temperature (South side)


5L

-0.005


0 0.005 0.01 0.015 0.02 0.025 0.03 0.035
Relative Longitudinal Displacement (in.)


Figure D-8. Load vs. joint opening with positive thermal gradient (South side)









245









APPENDIX E
LOAD RESPONSE CURVES (NEGATIVE THERMAL GRADIENT)

Load vs. beam response curves which were derived from strain gauge and LVDT data are

shown here. These curves were used to determine loads at which the joint at midspan

(designated j oint J2) opened. The curves were also used to determine effective concrete contact

areas at j oint J2, which were then used to quantify J stresses due to the AASHTO nonlinear

negative thermal gradient.















60

55





40

35

30

25




10


10


-700 -600 -500


r 1-~ -01-?0 J


-400 -300 -200 -1 00 0 100 200 300 400
Strain (microstrain)


Figure E-1. Load vs. strain at reference temperature (Segment 2, North)


-600 -500 -400 -300 -200 -100 0
Strain (microstrain)


100 200 300 400


Figure E-2. Load vs. strain with negative thermal gradient (Segment 2, North)







247













55

50

45

40

S35
30




251





-700 -600 -500 -400 -300 -200 -1 00 0 100 200 300 400
Strain (microstrain)


Figure E-3. Load vs. strain at reference temperature (Segment 2, South)


-600 -500 -400 -300 -200 -100 0
Strain (microstrain)


100 200 300 400


Figure E-4. Load vs. strain with negative thermal gradient (Segment 2, South)














55

50

4E.

40


S30



20



10




0 0.005 0.01 0.015 0.02 0.025 0.03 0.035 0.04 0.045
Relative Longitudinal Displacement (in.)


Figure E-5. Load vs. joint opening at reference temperature (Top flange)


60

55

50

4E.

40



30



20


10~


101


U 0.005 0.01 0.015 0.02 0.025 0.03 0.035 0.04 0.045
Relative Longitudinal Displacement (in.)


Figure E-6. Load vs. joint opening with negative thermal gradient (Top flange)














55

50

45

40

35

30

25

20

15

10

5

0-
-0.005


0 0.005 0.01 0.015 0.02 0.025 0.03
Relative Longitudinal Displacement (in.)


0.035 0.04


Figure E-7. Load vs. joint opening at reference temperature (South side)


5L

-0.005


0 0.005 0.01 0.015 0.02 0.025 0.03
Relative Longitudinal Displacement (in.)


0.035 0.04


Figure E-8. Load vs. joint opening with negative thermal gradient (South side)









250









LIST OF REFERENCES


AASHTO (1989a)., "AASHTO Guide Specifieations, Thermal Effects in Concrete Bridge
Superstructures," Washington D.C.

AASHTO (1989b)., "Guide Specifications for Design and Construction of Segmental Concrete
Bridges," 1st Ed., Washington, D.C.

AASHTO (1994a)., "AASHTO LRFD Bridge Design Specifieations," Washington, D.C

AASHTO (1994b)., "Interim Specifieations for the Guide Specifieations for Design and
Construction of Segmental Concrete Bridges," 1st Ed., Washington, D.C.

AASHTO (1998a)., "AASHTO LRFD Bridge Design Specifieations," Washington, D.C.

AASHTO (1998b)., "Guide Specifieations for Design and Construction of Segmental Concrete
Bridges," Proposed 2nd Ed., Washington, D.C.

AASHTO (1999)., "Guide Specifieations for Design and Construction of Segmental Concrete
Bridges," 2nd Ed., Washington, D.C.

AASHTO (2004)., "AASHTO LRFD Bridge Design Specifieations," 3rd Ed., Washington, D.C.

AASHTO TP 60-00. (2004), "Standard Method of Test for Coefficient of Thermal Expansion of
Hydraulic Cement Concrete," Washington, D.C.

ACI Committee 318 (2002)., "Building Code Requirements for Structural Concrete (318-02) and
Commentary (318R-02)." American Concrete Institute, Farmington Hills, Michigan.

ASTM C 469-94 (1994), "Standard Test Method for Static Modulus of Elasticity and Poisson' s
Ratio of Concrete in Compression," American Society of Testing and Materials, West
Conshohocken, PA.

ASTM C 39-01 (2001)., "Standard Test Method for Compressive Strength of Concrete Cylinders
Cast in Place in Cylindrical Molds," American Society of Testing and Materials, West
Conshohocken, PA.

Imbsen, R. A., Vandershof, D. E., Schamber, R. A., and Nutt, R.V. (1985)., "Thermal Effects in
Concrete Bridge Superstructures," NCHRP 276, Transportation Research Board,
Washington, D.C.

Potgieter, I. C., and Gamble, W. L. (1983)., "Response of Highway Bridges to Nonlinear
Temperature Distributions," Rep. No. FHWA/IL/UI-201, University of Illinois at Urbana-
Champaign, Urbana-Champaign, Ill.

Priestley, M. J. N. (1978)., "Design of Concrete Bridges for Thermal Gradients," ACI Journal,
75(5), 209-217.










Roberts, C.L., Breen, J. E., and Kreger, M.E. (1993)., "Measurement Based Revisions for
Segmental Bridge Design and Construction Criteria," Research Rep. 1234-3F, Center for
Transportation Research, Univ. of Texas at Austin, Austin, Texas.

Roberts, C. L., Breen, J. E., Cawrse J. (2002)., "Measurement of Thermal Gradients and their
Effects on Segmental Concrete Bridge," ASCE Journal of Bridge Engineering, Vol. 7,
No. 3, 166-174.

Shushkewich, K.W. (1998)., "Design of Segmental Bridges for Thermal Gradient," PCI Journal,
43(4), 120-137.

"Steel, Concrete and Composite Bridges, Part I, General Statement." British Standard BS 5400.
British Standards Institution. Crowthorne, Berkshire, England (1978).

Thompson, M. K., Davis, R. T., Breen, J. E., and Kreger, M. E. (1998)., "Measured Behavior of
a Curved Precast Segmental Concrete Bridge Erected by Balanced Cantilevering,"
Research Rep. 1404-2, Center for Transportation Research, Univ. of Texas at Austin,
Texas .









BIOGRAPHICAL SKETCH

The author began his undergraduate education in 1997 at Orta Dogu Teknik Universitiesi

in Ankara, Turkey. On graduating with a Bachelor of Science degree in civil engineering in June

2001, he moved to Ohio where he obtained a Master of Science in civil engineering at The

University of Akron in August, 2003. Later in August 2003 the author began studying at the

University of Florida towards obtaining a Doctor of Philosophy degree in civil engineering, with

a concentration in structural engineering. The author anticipates obtaining this degree in

December, 2007. Upon graduating, the author plans to pursue a career in structural engineering

at a design firm.





PAGE 1

1 VALIDATION OF STRESSES CAUSED BY THERMAL GRADIENTS IN SEGMENTAL CONCRETE BRIDGES By FAROUK MAHAMA A DISSERTATION PRESENTED TO THE GRADUATE SCHOOL OF THE UNIVERSITY OF FLOR IDA IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY UNIVERSITY OF FLORIDA 2007

PAGE 2

2 2007 Farouk Mahama

PAGE 3

3 To Mom and Dad

PAGE 4

4 ACKNOWLEDGMENTS I would first like to thank Dr. G. R. Consol azio and Dr. H.R. Hamilton for their help and guidance throughout the course of my study at The Un iversity of Florida. I would also like to thank the members of my supervisory committee: Dr. B. Sankar of the mechanical and aerospace engineering department, Dr. R. Cook and Dr. K. Gurley of the civil and coastal engineering department, for their insightful suggestions. I would like to acknowledge and thank the Florida Department of Transportation for funding this re search. I would especially like to thank Mr. Marcus Ansley of the FDOT Structures Research Center, Tallahassee, for his invaluable support and contributions to this study. Sincere thanks to Mr. Frank Cobb, Mr. David Allen, Mr. Steve Eudy, Mr. Tony Johnston, and Mr. Paul Tighe also of the FDOT Structures Research Center, Tallahassee, for their help in constructing and transporting the laboratory specimen from Tallahassee to Gainesville, Florida. Thanks to DYWIDAG Systems Incorporated (DSI) for donating the post-tensioning bars which were used to post-tension the laboratory specimen. In addition, I would like to thank Mr. Richard M. DeLorenzo of the FDOT Materials Laboratory, Gainesville, for his assistance in determining mate rial properties of the test specimen. Finally, I would like to express my sincere gratitude to Mr. Charles Chuck Broward of the University of Florida Structures Laboratory, his staff of undergraduate students, and Mr. Hubert Nard Martin for their various contributions to wards the successful execution of experiments in the laboratory.

PAGE 5

5 TABLE OF CONTENTS page ACKNOWLEDGMENTS...............................................................................................................4 LIST OF TABLES................................................................................................................. ..........8 LIST OF FIGURES................................................................................................................ .......10 ABSTRACT....................................................................................................................... ............20 CHAPTER 1 INTRODUCTION..................................................................................................................22 2 SCOPE AND OBJECTIVES..................................................................................................24 3 BACKGROUND....................................................................................................................26 Thermal Gradients.............................................................................................................. ....26 Structural Response to Thermal Gradients.............................................................................29 Selected Field Studies on Thermal Gradients.........................................................................33 The North Halawa Valley Viaduct Project......................................................................34 The San Antonio Y Project..........................................................................................35 Northbound IH-35/Northbound US 183 Flyover Ramp Project.....................................36 Summary........................................................................................................................ .........39 4 BEAM DESIGN.................................................................................................................... .47 Cross Section Design........................................................................................................... ...47 Segment Design................................................................................................................. .....49 Design of Segment Heating System.......................................................................................50 Prestress Design............................................................................................................... .......51 5 BEAM CONSTRUCTION.....................................................................................................61 Placement of Steel Reinforcement, Thermocouple Cages, and Copper Tubes......................61 Casting of Concrete............................................................................................................ ....62 Material Tests and Properties.................................................................................................62 Application of Prestress....................................................................................................... ...65 6 INSTRUMENTATION..........................................................................................................74 Thermocouples.................................................................................................................. .....74 Electrical Resistance Concrete St rain Gauges and Strain Rings............................................75 Linear Variable Displacement Transducers (LVDT).............................................................76 Load Cells..................................................................................................................... ..........76

PAGE 6

6 Data Acquisition............................................................................................................... ......77 7 SETUP AND PROCEDURES FO R MECHANICAL LOADING........................................87 Opening of Joint between Segments 2 and 3..........................................................................88 8 SETUP AND PROCEDURES FOR THERMAL LOADING...............................................93 Uniform Temperature Distribution.........................................................................................93 Linear Thermal Gradient........................................................................................................95 AASHTO Positive Thermal Gradient.....................................................................................95 AASHTO Negative Thermal Gradient...................................................................................96 9 IN-SITU COEFFICIENT OF THERMAL EXPANSION...................................................102 10 RESULTS PRESTRESSING............................................................................................116 11 RESULTS MECHANICAL LOADING...........................................................................129 Detection of Joint Opening Strain Gauges Close to Joint at Midspan..............................129 Detection of Joint Opening LVDTs Across Joint at Midspan...........................................135 Strains at Mid-Segment........................................................................................................137 Deflection..................................................................................................................... ........138 Summary........................................................................................................................ .......139 12 RESULTS UNIFORM TEMPERATURE CHANGE.......................................................151 13 RESULTS AASHTO POSITI VE THERMAL GRADIENT............................................163 Elastic Modulus Derived Stresses (E stresses).....................................................................164 Joint Opening Derived Stresses (J Stresses)......................................................................169 14 RESULTS AASHTO NEGATIVE THERMAL GRADIENT..........................................195 Elastic Modulus Derived Stresses (E stresses).....................................................................196 Joint Opening Derived Stresses (J Stresses)......................................................................201 15 SUMMARY AND CONCLUSIONS...................................................................................222 APPENDIX A BEAM SHOP DRAWINGS.................................................................................................227 B LOADING FRAME DRAWINGS.......................................................................................231 C LOAD RESPONSE CURVES AT MIDSEGMENT (MECHANICAL LOADING).........236 D LOAD RESPONSE CURVES (POS ITIVE THERMAL GRADIENT)..............................241

PAGE 7

7 E LOAD RESPONSE CURVES (NEGATIVE THERMAL GRADIENT)............................246 LIST OF REFERENCES.............................................................................................................251 BIOGRAPHICAL SKETCH.......................................................................................................253

PAGE 8

8 LIST OF TABLES Table page 3-1 Positive thermal gradient magnitudes................................................................................40 3-2 Modulus of elasticity values for selected Ramp P segments.............................................40 3-3 Coefficient of thermal expansion va lues for selected Ramp P segments..........................40 3-4 Comparison of measured and calculated st resses from measured thermal gradients........40 3-5 Comparison of measured and design Stresses...................................................................41 4-1 Approximate Service I stresses in Santa Rosa Bay Bridge................................................53 5-1 Segment cast dates......................................................................................................... ....67 5-2 Concrete pump mix proportions........................................................................................67 5-3 Compressive strengths and modu li of elasticity of Segment 1..........................................67 5-4 Compressive strengths and modu li of elasticity of Segment 2..........................................67 5-5 Compressive strengths and modu li of elasticity of Segment 3..........................................67 5-6 Compressive strengths and modu li of elasticity of Segment 4..........................................67 5-7 Coefficient of thermal expansion (CTE) of Segment 3 (AASHTO TP 60-00).................68 5-8 Selected post-tensioning force increments.........................................................................68 9-1 Experimentally determined coefficients of thermal expansion.......................................107 10-1 Prestress magnitudes and horizontal eccentricities..........................................................121 11-1 Comparison of measured strains due to prestress and measured strains when joint opens.......................................................................................................................... ......140 12-1 Average measured coeffici ents of thermal expansion (C TE) of concrete segments.......156 12-2 Calculated modulus of elastic ity (MOE) of concrete segments.......................................156 12-3 Changes in prestress due to heating of Segments 2 and 3...............................................156 12-4 Changes in prestress due to cooling of Segments 2 and 3...............................................156 13-1 Comparison of E stresses and extrapolated stresses on top of segment flanges near joint J2 (laboratory pos itive thermal gradient).................................................................178

PAGE 9

9 13-2 Comparison of E stresses and predicted self-equilibrating thermal stresses caused by laboratory positive thermal gradient near joint J2...........................................................178 13-3 J stresses in top 4 in. of flange.........................................................................................178 13-4 Comparison of J stresses and predic ted stresses in top 4 in. of flange............................178 13-5 Comparison of J stresses and E stresses in top 4 in. of flange.........................................179 14-1 Comparison of E stresses and extrapolated stresses on top of segment flanges near joint J2 (laboratory negative thermal gradient)................................................................205 14-2 Comparison of E stresses and predicted self-equilibrating thermal stresses caused by laboratory negative thermal gradient near joint J2..........................................................205 14-3 J stresses in top 4 in. of flange.........................................................................................205 14-4 Comparison of J stresses and predic ted stresses in top 4 in. of flange............................205 14-5 Comparison of J stresses and E stresses in top 4 in. of flange.........................................206

PAGE 10

10 LIST OF FIGURES Figure page 3-1 Conditions for the development of positive thermal gradients..........................................42 3-2 Conditions for the development of negative thermal gradients.........................................42 3-4 Comparison of AASHTO gradients for zone 3 (for superstructure depths greater than 2 ft).......................................................................................................................... ...........43 3-5 Positive vertical temperature grad ient for concrete superstructures..................................43 3-6 Decomposition of a nonlinear thermal gradient.................................................................44 3-7 Development of self-equilibrating ther mal stresses for positive thermal gradient............44 3-8 Development of self-equilibrating therma l stresses for negative thermal gradient...........45 3-9 Thermocouple locations.....................................................................................................45 3-10 Comparison of maximum daily positiv e temperature differences and negative temperature differences with design gradients..................................................................46 3-11 Thermocouple locations.................................................................................................... .46 4-1 Typical cross-section of Santa Rosa Bay Bridge...............................................................54 4-2 I-section representation of SRB bridge cross section........................................................54 4-3 Self-equilibrating stresses due to AASHTO positive thermal gradient.............................54 4-4 Self-equilibrating stresses due to AASHTO negative thermal gradient............................55 4-5 Cross section of laboratory beam with analytically determined self-equilibrating thermal stresses due AASHTO design gradients...............................................................55 4-6 Location of shear keys on beam cross s ection and detailed elevation view of shear key............................................................................................................................ ..........56 4-7 Beam segments.............................................................................................................. ....56 4-8 Copper tube layouts for prototype be am and laboratory segmental beam.........................57 4-9 Copper tube layouts in relation to sh ape of AASHTO design thermal gradients..............57 4-10 Typical manifold in flange................................................................................................ .58 4-11 Typical manifold in web................................................................................................... .58

PAGE 11

11 4-12 Typical flow rates through web manifolds........................................................................58 4-13 Typical flow rates through flange manifolds.....................................................................59 4-14 Heating system............................................................................................................ .......59 4-15 Cross section view of prestress assembly..........................................................................59 4-16 Elevation view of prestress assembly................................................................................60 4-17 Mild steel reinforcements in Segments 1 and 4.................................................................60 4-18 Mild steel reinforcement.................................................................................................. ..60 5-1 Open form with mild steel reinforcement, closed form with mild steel reinforcement and lifting hooks.............................................................................................................. ..69 5-2 Form for shear keys........................................................................................................ ...69 5-3 Heated segment with copper tubes, thermocouple cages and thermocouples...................70 5-4 Beam layout with casting sequence...................................................................................70 5-5 Match-casting of segment..................................................................................................70 5-6 Finished concrete pours for Segment 1, Segment 2, Segment 3, Segment 4.....................71 5-7 Compressive strength test se tup, elastic modulus test setup..............................................71 5-8 AASHTO TP 60-00 test setup...........................................................................................72 5-9 Bar designations and design eccentricities (West).............................................................72 5-10 Prestress assembly (East)................................................................................................. ..73 5-11 Elevation view of prestress assembly (North)...................................................................73 6-1 Thermocouple cage with attached thermocouples.............................................................78 6-2 Layout of thermocouples in relation to shape of positive thermal gradient and negative thermal gradient...................................................................................................78 6-3 Location of thermocouple cages in Segments 2 and 3.......................................................79 6-4 Thermocouple labels in Segments 2 and 3........................................................................80 6-5 Strain (foil) gauge........................................................................................................ ......81

PAGE 12

12 6-6 Strain gauges close to joint at midspa n on North flange, South flange, North web, and South web.................................................................................................................. ..81 6-7 Strain ring................................................................................................................ ...........82 6-8 Instrumentation details (North side)..................................................................................82 6-9 Instrumentation details (South side)..................................................................................83 6-10 Instrumentation at midspan (top flange)............................................................................83 6-11 Typical labeling convent ion for strain gauges...................................................................83 6-12 Typical labeling conve ntion for strain rings......................................................................84 6-13 LVDT for measuring deflecti on at cantilever ed-end of beam...........................................84 6-14 LVDTs mounted across joint at mi dspan on South side and top flange............................84 6-15 LVDT labeling convention................................................................................................84 6-16 Load cell layout.......................................................................................................... ........85 6-17 Load cells for measuring applied lo ad, prestress, mid-support reaction, and end-support reaction...........................................................................................................85 6-18 Instrumentation layout (North)..........................................................................................86 6-19 Instrumentation layout (South)..........................................................................................86 6-20 DAQ System; Connection of in strumentation to DAQ System.........................................86 7-1 Test setup................................................................................................................. ..........90 7-2 Segmental beam in laboratory...........................................................................................90 7-3 Loading frame and 60-ton jack..........................................................................................91 7-4 Ideal stress diagrams without thermal loads......................................................................91 7-5 Ideal stress diagrams with positive thermal gradient.........................................................91 7-6 Ideal stress diagrams with negative thermal gradient........................................................92 8-1 Pipe layers................................................................................................................ ..........98 8-2 Thermocouple locations in heated segments.....................................................................98 8-3 Thermocouples used at each section..................................................................................99

PAGE 13

13 8-4 Insulated heated segments..................................................................................................99 8-5 Piping configuration used to impose initial condition.....................................................100 8-6 Piping configuration used to impos e uniform temperature differential...........................100 8-7 Piping configuration used to impose linear thermal gradient..........................................100 8-8 Piping configuration used to impose AASHTO nonlinear positive thermal gradient....................................................................................................................... .....101 8-9 Piping configuration used to impos e AASHTO nonlinear negative thermal gradient....................................................................................................................... .....101 9-1 Typical in-situ CTE test se tup; Photograph and Details..................................................108 9-2 Uniform temperature change imposed on Segment 2......................................................109 9-3 Measured end-displacements due to uniform temperature change imposed on Segment 2...................................................................................................................... ...109 9-4 Uniform temperature change imposed on Segment 3......................................................110 9-5 Measured end-displacements due to uniform temperature change imposed on Segment 3...................................................................................................................... ...110 9-6 Measured concrete temperatures in Segment 2 (uniform profile)...................................111 9-7 Measured concrete temperatures in Segment 3 (uniform profile)...................................111 9-8 Orientation of Segment 2 dur ing testing (South elevation).............................................112 9-9 Orientation of Segment 3 dur ing testing (South elevation).............................................112 9-10 Linear temperature gradient imposed on Segment 2.......................................................113 9-11 Measured displacements due to linear thermal gradient imposed on Segment 2............113 9-12 Linear thermal gradient imposed on Segment 3..............................................................114 9-13 Measured displacements due to linear thermal gradient on Segment 3...........................114 9-14 Measured concrete temperatures in Segment 2 (linear profile).......................................115 9-15 Measured concrete temperatures in Segment 3 (linear profile).......................................115 10-1 Segment support during prestressing...............................................................................122 10-2 Beam support for mechani cal and thermal load tests......................................................122

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14 10-3 Post-tensioning bar desi gnations and eccentricities.........................................................123 10-4 Measured concrete strains near joint J2 due to prestress (Segment 2, North).................123 10-5 Measured concrete strains near joint J2 due to prestress (Segment 3, North).................124 10-6 Measured concrete strains near joint J2 due to prestress (Segment 2, South).................124 10-7 Measured concrete strains near joint J2 due to prestress (Segment 3, South).................125 10-8 Measured concrete strains near jo int J2 due to prestress (Top flange)............................125 10-9 Effect of differential shri nkage on top flange strains.......................................................126 10-10 Measured concrete strains due to prestress through de pth of segments near joint J2.................................................................................................................. ....126 10-11 Measured concrete strains due to prestre ss across width of segment flanges near joint J2 (Top flange)................................................................................................................ .127 10-12 Variation of prestress forces with time............................................................................127 10-13 Change in total prestress force with time.........................................................................128 11-1 Expected behavior of strain ga uges on side of beam near joint.......................................141 11-2 Expected behavior of strain ga uges on top of flange near joint.......................................141 11-3 Load vs. Strain near joint at midspan (North side)..........................................................142 11-4 Load vs. Strain near joint at midspan (South side)..........................................................142 11-5 Load vs. Strain near joint at midspan (Top flange).........................................................143 11-6 Condition of joint J2 on top of flange..............................................................................143 11-7 Measured strain distributions ne ar joint at midspan (North side)....................................144 11-8 Measured strain distributions ne ar joint at midspan (South side)....................................144 11-9 Estimated progression of joint-opening w ith load (based on strain gauge data).............145 11-10 Movement of neutral axis (N.A.) with load.....................................................................145 11-11 Changes in prestress force with load...............................................................................146 11-12 Expected behavior of LVDT s across joint on side of beam............................................146 11-13 Expected behavior of LVDT s across joint on top of flange............................................147

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15 11-14 Load vs. Joint opening (Side LVDTs).............................................................................147 11-15 Load vs. Joint opening (Top flange LVDTs)...................................................................148 11-16 Measured strain distributions at middle of Segment 3 (30 in. from joint J2) on North side of beam................................................................................................................... ..148 11-17 Measured strain distributions at middle of Segment 3 (30 in. from joint J2) on South side of beam................................................................................................................... ..149 11-18 Forces and moments acting at mid-segment....................................................................149 11-19 Measured vertical deflection near cantilevered end of beam...........................................150 12-1 Laboratory beam........................................................................................................... ...157 12-2 Laboratory imposed temperature changes on Segment 2................................................157 12-3 Laboratory imposed temperature changes on Segment 3................................................158 12-4 Measured concrete temp eratures in Segment 2...............................................................158 12-5 Measured concrete temp eratures in Segment 3...............................................................159 12-6 Measured temperature change s at Section C (Heating phase).........................................159 12-7 Measured temperature change s at Section D (Heating phase).........................................160 12-8 Measured strain distribution on Segm ent 2 (Section C) due to temperature changes........................................................................................................................ .....160 12-9 Measured strain distribution on Segm ent 3 (Section D) due to temperature changes........................................................................................................................ .....161 12-10 Comparison of measured and calculated strains at Section C due to moderately nonuniform temperature distribut ion (Segment 2, Heating)............................................161 12-11 Comparison of measured and calculated strains at Section D due to moderately nonuniform temperature distribut ion (Segment 3, Heating)............................................162 13-1 Sequence of load applicati on (positive gradient test)......................................................180 13-2 Laboratory beam........................................................................................................... ...181 13-3 Laboratory imposed positive thermal gradient................................................................181 13-4 Typical field measured positive thermal gradient............................................................182 13-5 Measured temperatures in heated segments (positive thermal gradient).........................182

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16 13-6 Calculated strain components of the AASHTO positive thermal gradient......................183 13-7 Measured and predicted strain s near joint J2 (Segment 2)..............................................183 13-8 Measured and predicted strain s near joint J2 (Segment 3)..............................................184 13-9 Plan view of measured and predicte d strains near joint J2 (Top Flange)........................184 13-10 Comparison of measured thermal gradient profiles with average...................................185 13-11 E stresses near joint J2 (Segment 2)................................................................................185 13-12 E stresses near joint J2 (Segment 3)................................................................................186 13-13 Difference in magnitude of imposed ther mal gradients at loca tion of maximum slope change (elevation 32 in.)..................................................................................................186 13-14 Superposition of component stre ss blocks (Mechanical loads only)...............................187 13-15 Superposition of component stress blocks (Mechanical loads with positive thermal gradient)...................................................................................................................... .....187 13-16 Uniform opening of joint across section width................................................................188 13-17 Non-uniform opening of joint across section width........................................................188 13-18 Load vs. strain at referen ce temperature (Segment 3, North)..........................................189 13-19 Load vs. strain with positive thermal gradient (Segment 3, North).................................189 13-20 Load vs. strain at referen ce temperature (Segment 3, South)..........................................190 13-21 Load vs. strain with positive thermal gradient (Segment 3, South).................................190 13-22 Load vs. strain at refere nce temperature (Top flange).....................................................191 13-23 Load vs. strain with positive thermal gradient (Top flange)............................................191 13-24 Comparison of strain differences on No rth and South sides of joint J2 (Positive thermal gradient)..............................................................................................................192 13-25 Joint opening loads detected from strain gauges near joint J2.........................................192 13-26 Sign convention for moments and curvature...................................................................193 13-27 Contact areas at joint J2 at inci pient opening of joint on South side at elevation 35.5 in.............................................................................................................. .193

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17 13-28 Contact areas at joint J2 at incipient opening of join t on North side at elevation 33.5 in........................................................................................................................ ......193 13-29 Contact areas at joint J2 at incipient opening of join t on South side at elevation 32.0 in........................................................................................................................ ......194 14-1 Sequence of load applicati on (negative gradient test).....................................................207 14-2 Laboratory beam........................................................................................................... ...208 14-3 Laboratory imposed negative thermal gradient...............................................................208 14-4 Measured temperatures in heated segments (negative thermal gradient)........................209 14-5 Calculated strain components of the AASHTO negative thermal gradient.....................209 14-6 Measured and predicted strain s near joint J2 (Segment 2)..............................................210 14-7 Measured and predicted strain s near joint J2 (Segment 3)..............................................210 14-8 Plan view of measured and predicte d strains near joint J2 (Top Flange)........................211 14-9 Measured and predicted strains at mi dspan and mid-segment (Segment 2, North).........211 14-10 Measured and predicted strains at mi dspan and mid-segment (Segment 3, North).........212 14-11 Comparison of measured thermal grad ient profiles with average profile........................212 14-12 E stresses near joint J2 (Segment 2)................................................................................213 14-13 E stresses near joint J2 (Segment 3)................................................................................213 14-14 E stresses at mid-segment and midspan (Segment 2, North)...........................................214 14-15 E stresses at mid-segment and midspan (Segment 3, North)...........................................214 14-16 Difference in magnitude of imposed ther mal gradients at loca tion of maximum slope change (elevation 32 in.)..................................................................................................215 14-17 Superposition of component stress bloc ks (mechanical with uniform temperature increase)...................................................................................................................... .....215 14-18 Superposition of component stress bloc ks (mechanical with uniform temperature increase and negative thermal gradient)..........................................................................216 14-19 Load vs. strain at referen ce temperature (Segment 3, North)..........................................216 14-20 Load vs. strain with negative th ermal gradient (Segment 3, North)................................217

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18 14-21 Load vs. strain at referen ce temperature (Segment 3, South)..........................................217 14-22 Load vs. strain with negative th ermal gradient (Segment 3, South)................................218 14-23 Load vs. strain at refere nce temperature (Top flange).....................................................218 14-24 Load vs. strain with negativ e thermal gradient (Top flange)...........................................219 14-25 Comparison of strain differences on Nort h and South sides of joint J2 (Negative thermal gradient)..............................................................................................................219 14-26 Joint opening loads detected from strain gauges near joint J2.........................................220 14-27 Sign convention for moments and curvature...................................................................220 14-28 Contact areas at joint J2 at incipient opening of join t on South side at elevation 35.5 in........................................................................................................................ ......220 14-29 Contact areas at joint J2 at incipient opening of join t on North side at elevation 33.5 in........................................................................................................................ ......221 14-30 Contact areas at joint J2 at incipient opening of join t on South side at elevation 32.0 in........................................................................................................................ ......221 A-1 Prestress reinforcement details........................................................................................228 A-2 Manifold and copper tube details.....................................................................................229 A-3 Shear key details.......................................................................................................... ....230 B-1 Loading frame details......................................................................................................232 B-2 Details of cross channels..................................................................................................233 B-3 Mid-support details........................................................................................................ ..234 B-4 End-support details........................................................................................................ ..235 C-1 Load vs. strain at middl e of Segment 2 on North side.....................................................237 C-2 Load vs. strain at middl e of Segment 2 on South side.....................................................237 C-3 Measured strain distributions at middle of Segment 2 on North side..............................238 C-4 Measured strain distributions at middle of Segment 2 on South side..............................238 C-5 Load vs. strain at middl e of Segment 3 on North side.....................................................239 C-6 Load vs. strain at middl e of Segment 3 on South side.....................................................239

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19 C-7 Measured strain distributions at middle of Segment 3 on North side..............................240 C-8 Measured strain distributions at middle of Segment 3 on South side..............................240 D-1 Load vs. strain at referen ce temperature (Segment 2, North)..........................................242 D-2 Load vs. strain with positive thermal gradient (Segment 2, North).................................242 D-3 Load vs. strain at referen ce temperature (Segment 2, South)..........................................243 D-4 Load vs. strain with positive thermal gradient (Segment 2, South).................................243 D-5 Load vs. joint opening at refe rence temperature (Top flange).........................................244 D-6 Load vs. joint opening with posit ive thermal gradient (Top flange)...............................244 D-7 Load vs. joint opening at refe rence temperature (South side).........................................245 D-8 Load vs. joint opening with posit ive thermal gradient (South side)................................245 E-1 Load vs. strain at referen ce temperature (Segment 2, North)..........................................247 E-2 Load vs. strain with negative th ermal gradient (Segment 2, North)................................247 E-3 Load vs. strain at referen ce temperature (Segment 2, South)..........................................248 E-4 Load vs. strain with negative th ermal gradient (Segment 2, South)................................248 E-5 Load vs. joint opening at refe rence temperature (Top flange).........................................249 E-6 Load vs. joint opening with negati ve thermal gradient (Top flange)..............................249 E-7 Load vs. joint opening at refe rence temperature (South side).........................................250 E-8 Load vs. joint opening with negati ve thermal gradient (South side)...............................250

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20 Abstract of Dissertation Pres ented to the Graduate School of the University of Florida in Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy VALIDATION OF STRESSES CAUSED BY THERMAL GRADIENTS IN SEGMENTAL CONCRETE BRIDGES By Farouk Mahama December 2007 Chair: Gary R. Consolazio Cochair: H. R. Hamilton Major: Civil Engineering This dissertation presents th e results of a series of tests aimed at quantifying self-equilibrating thermal stre sses caused by AASHTO design nonlinear thermal gradients in segmental concrete bridges. Negative gradients (deck cooler than web) can cause significant tensile stresses to develop in the top few inches of bridge decks, leading to requirements for large prestressing forces to counteract this tension. Design gradients are based on field measurement of temper ature variations on both a seasonal and diurnal basis. Ther e is, however, little data in wh ich actual stresses have been measured during these peak gradients to verify th at the stresses are indeed as high as predicted by analysis. One reason for this is the difficulty of stress measur ement in concrete. Stress is generally estimated by measuring st rain, which is then converted to stress by applying an elastic modulus. This works well for homogeneous elastic materials but there is less confidence in this procedure when applied to concrete due to materi al variability at the s cale of the strain gauge, temperature compensation of strain gauges, creep, and shrinkage. A 20 ft-long 3 ft-deep segmental T beam was c onstructed and tested in the laboratory for the purpose of quantifying self-equilibrating thermal stresses caused by the AASHTO design

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21 nonlinear thermal gradients. The beam was made of four 5 ft se gments externally post-tensioned together with four high-strength steel bars. By embedding rows of copper tubing into two of the beam segments, and passing heated water through the tubes, the desired thermal gradients were imposed on the heated segments. Two independent methods were used to meas ure stresses at the dry joint between the heated segments. The first was to convert measur ed stress-inducing thermal strains to stresses using the elastic modulus. Stresses determined using this method were referred to as elastic modulus derived stresses (E stresses). The sec ond method was a more direct measure of stress using the known stress state at incipient opening of the joint. This method of determining stresses was referred to as joint opening derived stresses (J stresses). Stresses determined using both methods are compared with AASHTO predicted self-equilibrating thermal stresses and discussed.

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22 CHAPTER 1 INTRODUCTION Thermal stresses are the result of restraint to deforma tions caused by temperature changes. In general, stresses are generated in bridges when the temp erature of all or part of the superstructure varies significantly from the te mperature at which it wa s constructed. Seasonal and diurnal variations in temper ature are usually the cause of th ese temperature changes. In typical beam-slab concrete bridges, temperatur e variations lead to uniform expansion and contraction of the supers tructure. This is because the sh allow decks of such bridges allow uniform heating and cooling of the superstructure under environmental conditions. Segmental bridges, however, are comprised of deep box-girder sections. Such bridges experience not only uniform temperature changes, but also nonlinear distributions of temper ature through the depth of the superstructure cross-sec tion, known as nonlinear thermal grad ients. Bridge deformations due to uniform temperature changes are well understood and easily accounted for in design by providing sliding joints and flexible piers, among other methods, to accommodate such movements. Nonlinear temperat ure distributions, however, presen t a more complex engineering problem. In simply-supported spans, nonlinea r thermal gradients lead to internal self-equilibrating thermal stresses that cannot be relieved through support conditions. In continuous spans, nonlinear gradients lead to continuity stresses due to restraint to curvature in addition to self-equilibrating thermal stresses. Designing continuous segmental concrete bridges for stresses due to thermal gradients is typically accomplished by making use of the American Association of State Highway and Transportation Officials (AASHTO) Load and Resistance Fact or Design (LRFD) Specifications (AASHTO 2004) and the AASHTO Guide Specifications for De sign and Construction of Segmental Concrete Bridges (AASHTO 1999). These specifications require the consideration of

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23 nonlinear thermal gradient load cases when analyzing a segmental bridge for serviceability. Gradients that must be considered are positiv e (deck warmer than web) and negative (deck cooler than web). Stresses due to thermal gradients are analytically determined using concepts from classical mechanics. The magnitudes of thermal stresses determined in this manner can sometimes equal those due to live loads. This is of particular concern in the negative gradient case, which causes high tensile stresses to develop in the top few inches of the bridge deck. Due to limitations on the allowable tensile stress in se gmental bridges, as stipulated by design codes, large prestress forces are needed to counteract the tension generated by th e negative gradient. From the perspective that nonlinear thermal grad ients are considered only in serviceability checks, and do not affect the ultimate strength condition of a bridge designing for thermal stresses as high as those determined analytic ally can produce overly-conservative and costly structures. To gain a better understanding of the effects of nonlinear th ermal gradients on concrete bridges, it is first necessary to accurately quantif y stresses that are generated by such gradients. This will not only aid in the development of impr oved methods for predicting thermal stresses in segmental concrete bridges (e.g. should actual stresse s be less severe than predicted with current analysis procedures), but will also aid in investig ating the effects of stresses caused by nonlinear thermal gradients on the durability of concrete (e.g. cracking and associated crack widths).

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24 CHAPTER 2 SCOPE AND OBJECTIVES Past research leading to the determinati on of design thermal gradients for segmental concrete bridges has focused main ly on collection of temperature data over varying periods of time, and selection of the maximum observed grad ients as design gradients. There is, however, little data with which to determine whether the p eak gradients produce stresses that are as high as those predicted analytically. On e reason for this is the difficu lty of stress measurement in concrete. Stress is generally estimated by measuri ng strain, which is then converted to stress by applying an elastic modulus. This works well for homogeneous elastic materials but there is less confidence in this procedure when applied to concrete due to materi al variability at the scale of the strain gauge. A primary objective of this research was to determine whether experimentally determined self-equilibrating thermal stre sses caused by application of the AASHTO nonlinear thermal gradients, are as severe as predicted by analys is. To this end an e xperimental program was carried out to quantify self-equilibrating st resses caused by the thermal gradients. A 20 ft-long, 3 ft-deep segmental concrete T-be am was constructed and laboratory-tested for this study. The beam was made of four 5 ft segments externally posttensioned together with four high-strength steel bars. By embedding ro ws of copper tubing in to two of the beam segments, and passing heated water through the tubes, the desired th ermal gradients were imposed on the heated segments. These segments were also instrumented with thermocouples to monitor concrete temperatures during the applic ation of thermal loads. The beam was supported on one end and at midspan. Mechanical loads we re applied at the cantilevered end with the objective of creating a known (zero) stress state at the dry join t (at midspan) between the two heated segments from which the effects of thermal gradients could be determined.

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25 In-situ tests utilizing non-s tress-inducing temperature pr ofiles (uniform and linear temperature distributions) were performed on selected simply supported segments of the beam, to determine coefficients of thermal expansion. The post-tensioned beam was initially tested under the action of mechanical loads to establish a baseline condition from which the effect of thermal loads could be determined. Data from th ese tests were also used to evaluate the most suitable method of determining loads at which the dry joint at the midspan of the beam opened at specified depths. Accurate determination of lo ads at which the joint opened was important in quantifying stresses at the join t caused by nonlinear thermal gradients. A uniform temperature increment was imposed to investigate the expansi on behavior of the beam under thermal loading. Though the beam was statically de terminate with respect to s upport conditions, expansion or contraction of the concrete segmen ts relative to the post-tensioning bars was expected to lead to the development of additional stresses th at had to be accounted for in quantifying self-equilibrating thermal stresses. Subsequent ly a combination of AASHTO nonlinear thermal gradients and mechanical loads were applied to the beam. Self-equilibrating thermal stresses determined with results from these tests were then compared with corr esponding thermal stresses determined using the AASHTO recommende d method for calculating stresses caused by nonlinear thermal gradients.

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26 CHAPTER 3 BACKGROUND Thermal Gradients Thermal gradients in concrete bridges are la rgely the result of the low thermal conductivity of concrete. By convention, a positive gradie nt is defined as a condition in which the temperature of the top deck is higher than the temperature of the webs. A negative gradient exists when the temperature of the web is warmer than that of the top deck and bottom flange. Climate, bridge material, and the shape of the cross section all affect the shape and magnitude of thermal gradients. Climatic fact ors of importance include solar radiation, ambient temperature, wind speed, and precipitation. Clim atic conditions leading to the development of positive and negative thermal gradients in concrete bridges are illustrated in Figure 3-1 and Figure 3-2, respectively. Material properties such as thermal conductivity, density, absorptivity, and specific heat influence thermal gradients in c oncrete. The effect of cross sectional shape on the development of thermal gradients is comp lex and has not been the focus of extensive research. However, from thermo couple data taken from existing segmental box-girder bridges, it is known that in addition to vertical temperature gradients, box girder sections also experience transverse temperature gradients due to the effect s of differential temperature inside and outside the section (see points A and B in Figure 3-1 and Figure 3-2). Furtherm ore, the effect of enclosed air inside concrete box girders causes slightly different temperatures between the deck above the cavity and the exposed (cantilev ered) deck overhang (points C and D in Figure 3-1 and Figure 3-2). AASHTO specifications for the design of br idges for thermal gradients were first introduced in 1989. In 1983 Potgieter and Gamb le developed a two-dimensional finite difference program to calculate the distribution of temperature in a c oncrete section using

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27 weather station data from around the United States. They determined conditions at each site that would produce the maximum temperature differe nces, shapes, and magnitudes of nonlinear (positive) temperature gradients. The analytical model was validated with data taken from the Kishwaukee River Bridge in Illinois. In 1985 the National Cooperative Highway Research Program (NCHRP) published Report 276, Thermal Effects in Concre te Bridge Superstructures (Imbsen et al. 1985), which provided guidelines for the consideration of thermal gradients in the design of concrete bridges. The recommendati ons in NCHRP Report 276 were based largely on the work by Potgieter and Gamble ( 1983). In 1989 AASHTO published their Guide Specifications Thermal Effects in Concrete Bridge Superstructures (AASHTO 1989a), which was based on NCHRP Report 276. The AASHTO Guide Specifications for Design and Construction of Segmental Concrete Bridges (AASHTO 1989b), a derivative of the AASHTO (1989a) specifications, required th e consideration of thermal gr adients in the design of all segmental bridges. In the AASHTO Guide Specifications, Thermal Effect s in Concrete Bridge Superstructures (AASHTO 1989a), the United Stat es is divided into four solar radiation zones (see Figure 3-3), and a positive and negative gradient magnitude is specified for each zone. At the time of publication of the AASHTO (1989a) Guide Specifications very little field data were available to substantiate the nonlinear therma l gradients utilized by the speci fications. Since then, several field studies have been conducted on existing segmental bridges in the United States (e.g. Shushkewich 1998) that generally agree with th e positive gradients stipulated by AASHTO. Negative gradients in the AASHTO (1989a) Guide Specifications were based on the British Standard BS 5400 (1978). The shape of negative thermal gradients has since been modified and the magnitudes reduced to both simplify the design process and reduce the

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28 magnitude of stresses caused by these gradients, which are tensile in the top few inches of superstructure cross sections. The AASHTO Guide Specifications for Design and Construction of Segmental Concrete Bridges (AASHTO 1999), and the AASHTO LRFD Bridge Design Specifications (AASHTO 1998a) specify the negative gradient as a fractional multiple of the positive gradient (-0.30 for plain concrete surf aces and -0.20 for surfaces with 2-in. asphalt topping). Magnitudes of the negative grad ients in each geographic zone depend on categorization into one of two superstructure su rface conditions: plain concrete surface, and 2-in. asphalt topping. Asphalt toppings tend to insulate the flanges of bridge superstructures. This reduces loss of heat from the su rface of the flange, thereby reduci ng the severity of the thermal gradient. Thermal gradient shapes are e ssentially the same for all cross sections. Thermal gradients in the AASHTO Guide Specifications, Thermal Effects in Concrete Bridge Superstructures (AASHTO 1989b) are app licable only to superstructure depths greater than 2 ft. Thermal gradients in the AASHTO Guide Specifications for Design and Construction of Segmental Concrete Bridges (AASHTO 1999), and the AASHTO LRFD Bridge Design Specifications (AASHTO 1994a), which are deriva tives of the AASHTO (1989b) Guide Specifications, are not restricted to supers tructure depths greater than 2 ft. (see Figure 3-4 for a comparison of AASHTO gradients). Instead, diffe rent superstructure depths are taken into account by means of a vertical dimension, A (see Figure 3-5). The dimension A is taken as 12 in. for superstructure depths greater than 16 in. For superstructure s with depth less than 16 in., A is taken as 4 in. less than the depth of the superstructure. Magnitudes of T1 and T2 for the four solar radiation zone s into which the United States is divided (see Figure 3-3) are shown in Table 3-1 (Florida is locate d in zone 3). The AASHTO (1999) Guide Specifications specify the value of T3 as zero, unless a site-specific study is

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29 conducted to determine an appropriate value. Furthermore, should a site-specific study be conducted, the maximum value of T3 as required by the specifications is 5 oF. It is worth mentioning that T3 is usually taken as zero in design since it is unlikely that design engineers will have the necessary site data to determine otherwise. Nonlinear thermal gradients in AASHTO speci fications published afte r 1999 are identical to the gradients in the AASHTO (1999) Guid e Specifications. The AASHTO (1999) thermal gradients were therefore used in this study since they are currently being us ed in the design of segmental concrete bridges. Structural Response to Thermal Gradients Nonlinear thermal gradients are usually di vided into three com ponents for analysis purposes (Figure 3-6): uniform temperature, linear thermal gradient and, self-equilibrating temperature distribution. The uniform temper ature component causes uniform expansion or contraction of the unrestrained su perstructure. If the structure is restrained against this deformation, axial forces may develop. A linear temperature gradient causes uniform curvature in an unrestrained superstr ucture. If the structure is restrain ed against curvature (restraints from vertical supports, e.g. bridge pi ers), then secondary moments deve lop as the result of a linear gradient. The self-equilibrating temperature gradient, as the name implies, leads to the development of stresses in the structure that are internally in self-equilibrium. The resultant force and moment due to these stresses are both zer o because the stresses are develope d as the result of inter-fiber compatibility and are not associated with exte rnal forces and moments. The development of self-equilibrating thermal stresses is discussed in the following paragraphs. Consider the beam cross section shown in Figure 3-7 and assume the fibers of the section are free to deform independently. Under the ac tion of a nonlinear positiv e thermal gradient the

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30 section fibers would deform in the shape of th e gradient with the top fibers undergoing greater elongations than the middle and bottom fibers. In a real beam, however, in ter-fiber bonds resist the free deformation of section fi bers. If the cross section of the beam is able to resist out-of-plane flexural dist ortion (which is the case for a beam made of a homogeneous isotropic material undergoing uniform bending), the fibers of the beam will underg o a uniform curvature plus elongation. For deformations of the fibers to be consistent with th e resistance of the cross section to out-of-plane flexural distortion, stresses are develo ped. These stresses, which are self-equilibrating, are compressive in the top and bottom fibers and tensile in the middle fibers of the cross section. The development of self-equilibrating ther mal stresses under the action of a nonlinear negative thermal gradient is illustrated in Figure 3-8. In this case, if the fibers of the section are free to deform independently, they would shor ten with the top fibers undergoing greater shortening than the middle and bottom fibers. For de formations of the fibers of the beam to be consistent with the resistance of the cross section to out-of-plan e flexural distortion, self-equilibrating stresses are develo ped. These stresses are tensil e in the top and bottom fibers and compressive in the middle fibers of the beam. The AASHTO approach to calculating stresses due to thermal gradients, which is based on one-dimensional Bernoulli beam theory, is outlined in the AASHTO Guide Specifications, Thermal Effects in Concre te Bridge Superstructures (AASHTO 1989b). The following assumptions regarding concrete material beha vior (for segmental box girder bridges, the construction material typically used is concrete) are made in the calculations: 1. Concrete is homogeneous and isotropic. 2. The material properties of concrete are independent of temperature. 3. Concrete has linear stress-strain and temperature-strain relationships.

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31 4. The Navier-Bernoulli hypothesis; that initially plane sections remain plane after bending, is valid. 5. Temperature varies vertically with depth, but is constant at all points of equal depth. 6. Longitudinal and transverse thermal stress fields are independent of each other. The shape of box-girder sections leads to the development of transverse thermal gradients because of differential temperatures between parts of the section that are inside and outside the box. Analysis for the effects of transverse therma l gradients is generally considered unnecessary (AASHTO 1999). For relatively sh allow bridges with thick webs however, such an analysis may be necessary. The AASHTO 1999 speci fications recommend a plus or minus 10 oF transverse temperature differential in such cases. Generally, the primary st resses of interest in design are usually longitudinal stresses. To de termine self-equilibrating longitudinal stresses using the AASHTO approach, a sect ional analysis is performed. Th e structure is first assumed to be fully restrained against rotation and transl ation and the thermal stresses determined using Equation 3-1: )) ( ( 1 ) ( y TG E y fRT (3-1) where; fRT(y) is the thermal stress assuming a fully restrained structure, y is the vertical distance measured from the z axis, E is the elastic modulus, is the coefficient of thermal expansion, and TG(y) is the vertical thermal gradient. Axial forc e and bending moment required to maintain full restraint are then determined from the resu lting stress distribution using Equation 3-2 and Equation 3-3: dy y b y f NRT R) ( ) ( (3-2) ydy y b y f MzRT R) ( ) ( (3-3) where; NR is the restraining axial force, MzR is the restraining mome nt about the z axis, and b(y) is the width of the cross section. Stresses due to the axial force and bending moment are then

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32 subtracted from the fully restrained thermal stresses to give self-equilibrating thermal stresses as shown in Equation 3-4: z R R RT SEI y Mz A N y f y f ) ( ) ( (3-4) where; A is the area of the cross section and Iz is the moment of inertia of the cross section about the z axis. In statically determinate structures this superposition yields the complete internal stress state. The strain distribution and curvat ure of the structure are given by Equation 3-5 and Equation 3-6, respectively: z R RI y Mz A N E y 1 ) ( (3-5) z RI E Mz (3-6) Strains the structure does not undergo (i.e. st rains corresponding to se lf-equilibrating thermal stresses) are calculated from Equation 3-7: ) ( ) ( ) ( y TG y ySE (3-7) where SE(y) is the strain distribution corresponding to the self-equilibrating thermal stresses. In statically indeterminate (continuous) structur es, additional continuity stresses must be determined by performing a structural analysis using the negative of the restraining axial force and bending moment as loads at the ends of the co ntinuous structure. This is usually done using structural analysis software. Stresses computed from the structural analysis are then superimposed on stresses due to the restraini ng axial force and bending moment in the primary (sectional) analysis to give continuity stresses. Alternatively, the indeterminate structure can be allowed to undergo continuity deformations due to the nonlinear gradient (which can be obtained from Equation 3-5) by removing enough redundant supports to make the structure statically

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33 determinate. Reactions necessary to enfor ce displacement compatibility and accompanying continuity stresses can then be subsequently dete rmined (e.g. using the flexibility method). The sum of the self-equilibrating stresses (determi ned previously via se ctional anal ysis) and continuity stresses gives the total stress state in the continuous structur e due to the nonlinear thermal gradient. If the thermal gradient varies through th e depth and width of the cross section, self-equilibrating thermal stresses are determin ed using Equation 3-8 through Equation 3-12, which are two-dimensional versions of Equa tion 3-1 through Equation 3-4, respectively. )) ( ( 1 ) ( y z TG E y z fRT (3-8) zy RT Rdzdy y z f N ) ( (3-9) zy RT Rydzdy y z f Mz ) ( (3-10) zy RT Rzdzdy y z f My ) ( (3-11) y R z R R RT SEI z My I y Mz A N y z f y z f ) ( ) ( (3-12) Where TG(z,y) is the two dimensional thermal gradient in the cross section, fRT(z,y) is the thermal stress distribution assuming a fully restrained structure, MzR is the restrained moment about the z axis, MyR is the restrained moment about the y axis, Iz is the moment of inertia of section about the z axis, Iy is the moment of inertia of the section about the y axis, and fSE(z,y) is the two dimensional self-equilibrating thermal stress distribution. Selected Field Studies on Thermal Gradients Past studies on thermal gradie nts in continuous concrete se gmental bridges have focused on determining the magnitude and shape of positi ve and negative thermal gradients. The frequencies at which maximum positive and negative gradients occur, due to variations in environmental heating, have also been investig ated. The studies vary in location, duration,

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34 number and type of thermocouples, and placement of thermocouples. Bridge cross sections most frequently considered were of the concrete box-girder type. Three such field studies are discussed here. The North Halawa Valley Viaduct Project The North Halawa Viaduct consists of twin prestressed concrete segmental bridges on the island of Oahu in Hawaii. As part of the in strumentation set up to measure various bridges responses, two sections along a fi ve-span unit were heavily inst rumented with thermocouples (Shushkewich, 1998). One section, E, with 26 ga uges, was near midspan (location of maximum positive moment under service loads), while another section, F, with 32 gauges, was near a support (location of maximum negative moment under service loads). Thermocouple readings were first recorded in late 1994 and were to be recorded through the end of 1999. Initially readings were taken at 2-hour intervals but this was increased to 6-hour intervals when it was felt that too much data wa s being gathered. When it became apparent that the critical positive thermal gradient was being underestimated the recording interval was again reduced to 2 hours (for desi gn gradients in Hawaii, see Figure 3-5 and Table 3-1, zone 3). According to Shushkewich (1998), ne gative gradient readings were not as sensitive to the time interval as positive gradient readings. Thus, all the negative gradient readings were considered useful. Positive gradient read ings taken during the period when the time interval between readings was 6 hours were considered unreliable. A 2-in. thick concrete topping was later placed on the instrumented sections. The topping was in strumented with thermocouples at the top, middle, and bottom. Monthly and daily positive thermal gradient da ta were seen to be slightly higher for Section E than they were for Section F. Shushkewi ch (1998) attributed this to the higher thermal inertia of Section F (larger depth). Critical positive and negative thermal gradient profiles

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35 determined during the study were plotted for gaug es along the cente rlines of the web, top and bottom slabs. The gradients were also compared to design gradients in the then-proposed AASHTO (1998b) Segmental Guide Specifications. B ecause construction traffic interfered with the gauges at the top of the deck, Shushkewich (1998) considered readings from those gauges unreliable and suggested that readings at the de ck surface be obtained by extrapolating data from gauges 2.5 in. from the deck surface. Considering the positive and negative thermal gradient profiles, it was clear that in general, the slab r eadings were very close to the design gradients. The same could not be said for the web read ings. The overall measured positive thermal gradient profile matched the design gradient more than the measured negative gradient profile matched the design negative gradient. The results of this study substantia ted the reduction of the negative thermal gradient from -0.5 (AASHTO 1994a) to -0.3 times the positive gradient: the value used in the AASHTO Segmental Guide Specifications (AASHTO 1998b) and the AASHTO LRFD Bridge Design Specifications (AASHTO 1998a). The San Antonio Y Project As part of a field study (Roberts, C. L.; Breen J. E.; Cawrse J. (2002)), four segments of a three-span continuous unit in the extensive upgrad e to the intersection of interstate highways I-35 and I-10 in downtown San Antonio, Texas (the San Antonio Y project) were heavily instrumented with thermocouples. The instrument ed segments were part of elevated viaducts comprised of precast segmental concrete box girder s constructed using span -by-span techniques. Thermocouples in a web of one instrumented segment (Figure 3-9) were c onnected to a data logger. Temperatures were r ecorded every 30 minutes for 2 y ears and 6 months. There were gaps in the data due to limited memory of the data logger. Maximum positive and negative temperature differences were determined for each day that thermocouple readings were recorded. Maximum positive temperature differences were

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36 computed from the difference between the largest top thermocouple reading (located 1 inch from the deck surface) and the coolest web thermoc ouple reading. Maximum negative temperature differences were computed from the differen ce between the coolest t op thermocouple reading and the warmest web thermocouple reading. Measured positive thermal gradient magnitude s were found by Roberts et al. (2002) to be smaller than the design gradients in the AASHTO (1994a) LRFD specifications and the AASHTO (1999) segmental guide specifications (for design gradients in Texas, see Figure 3-5 and Table 3-1, zone 2). The gradient shapes were found to be similar to th e older tri-linear shape in the Guide Specifications for Thermal E ffects in Concrete Superstructures (AASHTO 1989b). Measured maximum negative thermal gradients were also compared to the design gradient. It was found that the field measured magnitude s were less than the AASHTO (1994b) LRFD specifications but slightly greater than the AASHTO (1999) segmental specifications. Figure 3-10 shows a comparison between design gradie nt magnitudes and the recorded maximum positive and negative temperature difference for each day in the data record, respectively. Data from the top most thermocouple (1 in. below the deck surface) were ex trapolated to estimate deck surface temperatures using a fifth orde r polynomial equation based on earlier work by Priestley (1978). Northbound IH-35/Northbound US 183 Flyover Ramp Project A field study was conducted by Thompson et al (1998) on a five-spa n continuous precast segmental horizontally curved concrete bridge er ected using balanced can tilever construction. The bridge was part of a flyover ramp between interstate highway I-35 and US highway 183 in Austin, Texas. Three segments designated P16-2, P16-10, and P16-17 in one span of the structure were instrumented with thermocouples (see Figure 3-11). Segment P16-2 was at the base of the cantilever where the maximum nega tive moment (tension in the top fiber of the

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37 section) occurred during construction. Segmen t P16-10 was near the quarter point of the completed span where an inflection point in the load moment diagram was expected to occur. Segment P16-17 was located near the midpoint of the completed span where the maximum moment from gravity load was e xpected to occur. Response of the structure was studied under the actions of daily thermal gradient s that occurred over a 9-month period. From the temperature data gathered during the course of monito ring the bridge, daily temperature gradients were evaluated. The averag e temperature at the j unction between the webs and the top flange was used as baseline refere nce and deducted from th e measured average top and bottom temperatures. These resulting temperat ures were taken as the basis for determining the thermal gradients. Longitudinal stresses from the design gradie nts and stresses from the maximum measured thermal gradients were calculated. The calcu lations were based on the technique recommended in the AASHTO LRFD Bridge Design Specifications (1994a). The calcu lated stresses were compared to measured thermal gradient stresses The measured stresse s were determined by making use of measured concrete strains (from strain gauges), a determined coefficient of thermal expansion, and elastic modulus determin ed from concrete test cylinders. To make calculated stresses comparable to measured stress es, calculated stress results were adjusted by adding a uniform temperature to the nonlinea r AASHTO gradients. According to the investigators, measured stresses came from read ings taken between the time of peak gradient occurrence and some baseline time when the temperature distribution in the section was fairly uniform. Since a uniform change in temperature occurred within this time, the adjustment was necessary to make comparisons between measured and calculated stresses reasonable. Average values of elastic modulus and coefficient of th ermal expansion determined during the course of

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38 the field study are shown in Table 3-2 and Table 3-3, respectively. Table 3-4 compares measured stresses with stresses calculated from the measured thermal gradients (tension is positive and compression is negative). Table 3-5 compares measured stresses with stresses calculated from application of the design gradients. It can be seen that measured stresses for P16-10 and P16-17 are high compared to those at P16-2. Furthermore, they do not compare well with the stresses determined using the AASHT O design technique. T hompson et al. (1998) attributed this to warping of the box girder. Of the three sections, P16-2 was the only one restrained by an anchorage diaphragm from section distortion. Since the AASHTO design specifications assume plane sections remain plan e, stresses at P16-10 and P16-17, which were free to undergo out-of-plane distor tion, could not be expected to match stresses computed using the AASHTO recommende d design technique. In spite of the observed high stresses, Thomps on et al. (1998) did not observe any distress in the structure that could be attributed to thermal effects. The maximum and minimum top flange stresses, under load combinations of dead load, prestress, live load and thermal gradient were computed. The field load combinations we re not necessarily the same for each segment. From the computations, it was cl ear that no tension existed in the bridge under the load combinations considered. A design 28day concrete compressive strength, fc, of 6.5ksi was used in the design of the bridge. However, compressive strength cylinder tests revealed that concrete strengths of 10 ksi were common. The ma ximum allowable compressive stress, 0.45 fc, was exceeded in P16-10 and P16-17 under full service loads. The approximate limit of elastic behavior in concrete, 0.7 fc, was also exceeded in a small (about 1foot wide) part of P16-10. Based on the range of compressive strengths obtained from tests, the investigators felt the true compressive strength of concrete in the segmen ts was probably much gr eater than the average

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39 design compressive strength. They therefore de cided the stress distributions needed no adjustment. Summary The subsequent chapters will discuss the study conducted at the University of Florida that is the subject of this dissertation. Previous studies have confirmed th e existence of nonlinear thermal gradients in segmental concrete bridges. The shape and magnitudes of the positive thermal gradients have also, in large measure, b een verified with field measurements on existing segmental concrete bridges in the United States. However, few attempts at measuring stresses caused by nonlinear thermal gradients have been made. This indicates a need to further investigate stresses caused by nonlinear thermal gradients. In the following chapters, design of the labora tory setup and a series of tests aimed at quantifying stresses caused by the AASHTO desi gn nonlinear thermal gradients are presented and discussed. Stresses quantifie d from laboratory test data are then compared with stresses predicted with the AASHTO recommended method.

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40 Table 3-1. Positive thermal gradient magnitudes Plain Concrete Surface or Asphalt Topping Zone T1 (oF) T2 (oF) 1 54 14 2 46 12 3 41 11 4 38 9 *AASHTO (1999)., Guide Specifications for Design a nd Construction of Segmental Concrete Bridges, 2nd Ed., Washington, D.C., Table 6-1, pg. 10. Table 3-2. Modulus of elasticity valu es for selected Ramp P segments Test Date P16-2 (Cast 5/24/96) P16-10 (Cast 6/4/96) P16-17 (Cast 6/10/96) 9/24/1996 6350 ksi 5900 ksi 5950 ksi 6/17/1997 6080 ksi 5470 ksi 5570 ksi *Thompson, M. K., Davis, R. T., Breen, J. E., a nd Kreger, M. E. (1998)., Measured Behavior of a Curved Precast Segmental Concrete Bridge Erected by Balanced Cantilevering, Research Rep. 1404-2, Center for Transportation Research, Univ. of Texas at Austin, Texas, Table 3.1, pg. 55. Table 3-3. Coefficient of thermal expansion values for selected Ramp P segments P16-2 P16-10 P16-17 Average Coefficient of Thermal Expansion ( (5.0E-6/oF) 9.0E-6/oC (5.4E-6/oF) 9.7E-6/oC (5.2E-6/oF) 9.4E-6/oC (5.2E-6/oF) 9.4E-6/oC *Thompson, M. K., Davis, R. T., Breen, J. E., a nd Kreger, M. E. (1998)., Measured Behavior of a Curved Precast Segmental Concrete Bridge Erected by Balanced Cantilevering, Research Rep. 1404-2, Center for Transportation Research, Univ. of Texas at Austin, Texas, Table 3.2, pg. 56 Table 3-4. Comparison of measured and calcula ted stresses from measured thermal gradients Positive Thermal Gradient Negative Thermal Gradient Segment Average Measured Average Calculated Measured/ Calculated Average Measured Average Calculated Measured/ Calculated P16-2 (368 psi) 2.54 Mpa (441 psi) 3.04 Mpa 0.836 (-251 psi) -1.73 Mpa (-220 psi) -1.52 Mpa 1.138 P16-10 (669 psi) 4.61 Mpa (458 psi) 3.16 Mpa 1.459 (-466 psi) -3.21 Mpa (-225 psi) -1.55 Mpa 2.071 P16-17 (609 psi) 4.20 Mpa (451 psi) 3.11 Mpa 1.350 (-316 psi) -2.18 Mpa (-219 psi) -1.51 Mpa 1.444 Peak Measured Peak Calculated Measured/ Calculated Peak Measured Peak Calculated Measured/ Calculated P16-2 (584 psi) 4.03 Mpa (624 psi) 4.30 Mpa 0.937 (-426 psi) -2.94 Mpa (-292 psi) -2.01 Mpa 1.463 P16-10 (1874 psi) 12.92 Mpa (640 psi) 4.41 Mpa 2.930 (-1144 psi) -7.89 Mpa (-297 psi) -2.05 Mpa 3.849 P16-17 (1291 psi) 8.90 Mpa (627 psi) 4.32 Mpa 2.060 (-483 psi) -3.33 Mpa (-287 psi) -1.98 Mpa 1.682 *Thompson, M. K., Davis, R. T., Breen, J. E., a nd Kreger, M. E. (1998)., Measured Behavior of a Curved Precast Segmental Concrete Bridge Erected by Balanced Cantilevering, Research Rep. 1404-2, Center for Transportation Research, Univ. of Texas at Austin, Texas, Table 7.1, pg. 138.

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41 Table 3-5. Comparison of measured and de sign stresses (after Th ompson et al. (1998)) Positive Thermal Gradient Negative Thermal Gradient Segment Peak Measured Design Calculated Measured/ Design Peak Measured Design Calculated Measured/ Design P16-2 (584 psi) 4.03 Mpa (518 psi) 3.57 Mpa 1.129 (-426 psi) -2.94 Mpa (-264 psi) -1.82 Mpa 1.615 P16-10 (1874 psi) 12.92 Mpa (518 psi) 3.57 Mpa 3.619 (-1144 psi) -7.89 Mpa (-263 psi) -1.81 Mpa 4.359 P16-17 (1291 psi) 8.90 Mpa 515 psi (3.55 Mpa) 2.507 (-483 psi) -3.33 Mpa (-260 psi) -1.79 Mpa 1.860 *Thompson, M. K., Davis, R. T., Breen, J. E., a nd Kreger, M. E. (1998)., Measured Behavior of a Curved Precast Segmental Concrete Bridge Erected by Balanced Cantilevering, Research Rep. 1404-2, Center for Transportation Research, Univ. of Texas at Austin, Texas, Table 7.2, pg. 138.

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42 SUN Temperature Distribution through depth of superstructure Ttop > TmiddleTbottom > Tmiddlelight wind radiation (-) (+) .A B C D Figure 3-1. Conditions for the development of positive thermal gradients Temperature Distribution through depth of superstructure Ttop < TmiddleTbottom < Tmiddle precipitation strong winds (-) (+). .C D A B Figure 3-2. Conditions for the develo pment of negative thermal gradients Figure 3-3. Solar radiation zones for the Un ited States (AASHTO ( 1989a)., AASHTO Guide Specifications, Thermal Effects in Concrete Bridge Superstructures, Washington D.C., Figure 4, pg. 5)

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43 4" 8" 39.36" 8" 4"12"4" 12" 4" 8" 0.45d 4" 8" 0.45dd4" 12" 4" 12" 41oF 11oF 4oF 5oF 41oF 11oF 41oF 11oF 21oF 6oF 2oF 8oF 6oF 2oF 20.5oF 5.5oF 12.3oF 3.3oFAASHTO 1989 AASHTO 1994 AASHTO 1999 Positive Gradients Negative Gradientsd = superstructure depth Figure 3-4. Comparison of AASHTO gradients for zone 3 (for supers tructure depths greater than 2 ft) 4" A 8" Depth of Superstructure Top of Concrete Section T1T2T3 Figure 3-5. Positive vertical temperature grad ient for concrete superstructures (AASHTO (1999)., Guide Specifications for Design a nd Construction of Segmental Concrete Bridges, 2nd Ed., Washington, D.C., Figure 6-4, pg. 11.)

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44 =++ Cross Section Thermal Gradient Uniform Temperature Linear Temperature Gradient Non-Linear Self-Equilibrating Temperature Distribution Neutral Axis z y T1 + T2 + T3 = TTopT1T2TTopT3 Figure 3-6. Decomposition of a nonlinear thermal gradient Cross Section Strain distribution when section fibers are free to deform independently Temperature Distribution Self-equilibrating stresses develop when compatibility between fibers is enforced T L T L Compression Compression Tension Figure 3-7. Development of self-equilibrating thermal stresses for positive thermal gradient

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45 Self-equilibrating stresses Cross Section Strain distribution when section fibers are free to deform independently Temperature Distribution develop when compatibility between fibers is enforced T L T L Tension Tension Compression Figure 3-8. Development of se lf-equilibrating thermal stresses for negative thermal gradient Figure 3-9. Thermocouple loca tions (Roberts, C. L., Breen J. E., Cawrse J. (2002)., Measurement of Thermal Gradients and their Effects on Segmental Concrete Bridge, ASCE Journal of Br idge Engineering, Vol. 7, No. 3, Figure 3, pg. 168.)

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46 A B Figure 3-10. Comparison of maximum daily A) positive temperature difference. B) negative temperature difference with design gradients (Roberts, C. L., Breen, J. E., Cawrse J. (2002)., Measurement of Thermal Gradie nts and their Effects on Segmental Concrete Bridge, ASCE Journal of Bridge Engineering, Vol. 7, No. 3, Figure 6 and Figure 7, pg. 169-170.) Figure 3-11. Thermocouple locations (Thompson, M. K., Davis, R. T., Breen, J. E., and Kreger, M. E. (1998)., Measured Behavior of a Cu rved Precast Segmental Concrete Bridge Erected by Balanced Cantilevering, Research Rep. 1404-2, Center for Transportation Research, Univ. of Texas at Austin, Texas, Figure 3.14, pg. 53.)

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47 CHAPTER 4 BEAM DESIGN Cross Section Design The Santa Rosa Bay (SRB) Bridge, located near Milton, Florida, was used as a prototype for design of the laboratory segmental beam that was tested in this st udy. Laboratory space and equipment constraints ruled out the use of a full s cale replica of the crosssection of the bridge (see Figure 4-1) as the test specimen A scaled model of the box-gi rder section was considered. This, however, required scaling of the AAS HTO design thermal gradients such that self-equilibrating thermal stresses in the mode l, determined using the AASHTO recommended procedure, matched those in th e full size bridge. The logis tics of imposing scaled AASHTO thermal gradients on a scaled mode l of the bridge (e.g. difficulties of scaling aggregates, steel reinforcement, etc.) eliminated this as a viable option. Past research constituting the basis of thermal gradients in the design codes were conducted mainly on segmental box girder bridges. The design codes, however, do not restrict the use of the gradients to box girder bridges. Furthermore, the codes assume that the gradients vary only through the depth of the section. This means two crosssections of different shapes, with the same depths, section properties, a nd material properties will experience identical self-equilibrating thermal stresses due to a nonlinear ther mal gradient (from classical Bernoulli beam theory). For the purpose of determini ng longitudinal stresses du e to bending about the weak axis, the cross-section of the SRB Bridge can be simplified to that of an un-symmetric I-section (see Figure 4-2) with the same cross sectional ar ea and flexural stiffness about the weak axis as the box-girder section. The results of an analysis on the simplified section for self-equilibrating thermal stresses under the action of the AASHTO positive and negative design thermal gradients (for Florida) are shown in Figure 4-3 and Figure 4-4, respectively. The

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48 positive gradient leads to the development of co mpressive stresses (negative) in the top and bottom fibers of the section while tensile stresses (positive) develop in intermediate parts of the section. The negative gradient leads to the development of tensile stresses in the top and bottom fibers of the section and compressive stresses in the intermediate parts of the section. Throughout this document tensile stresses will be considered positive, and compressive stresses negative. Of primary interest in this study were the tensile stresse s created in the top few inches of the section by the negative thermal gradient. Consequently, a segmental T-beam with cross sectional geometry matching the top portion of the modified SRB Bridge section (illustrated by the hatching in Figure 4-3 and Figure 4-4) was constructed. Analytically determined self-equilibrating thermal stresses developed in the T-section by the AASHTO design gradients are also shown in the figures. The key aspects of the thermal stress profile in the SRB Bridge are captured in the laboratory segmental beam, includi ng stress magnitudes in the top four inches of the flange, where the thermal gradient is steepest. Details of the crosssection of the laboratory beam together with analytically determined self-equilibrating thermal stresses due to the AASHTO design gradients are shown in Figure 4-5. The flange width of the laborat ory test beam was chosen based on recommendations in the AASHTO LRFD Bridge Design Specifications (AASHTO 2004), whic h are similar to recommendations in the ACI Committee 318, Building Code Requireme nts for Structural Concrete and Commentary (ACI 318-02). In prestressed beam s with very wide flanges, shear deformations tend to relieve extreme fibers in the flange of longitudinal compressive stress, leading to a non-uniform dist ribution of stress (often referred to as shear lag effect). Therefore, for simplicity in design calculations it is recommended that an effective flange width, which may be smaller than the actual physical flange wi dth, be used together with the assumption of

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49 uniform stress distribution in the flange. For symmetrical T-beams it is recommended that the width of slab effective as a T-beam flange not exceed one-quarter of the span length of the beam, and the effective overhanging flange width on each side of the web not exceed eight times the slab thickness nor one-half the clear distance to the ne xt web. A width of 2 ft was chosen so that the entire flange of the beam could be consider ed effective in resisting the prestress force. Heating time and thermal energy required to impose the AASHTO nonlinear thermal gradients on the beam were also considered in lim iting the width of the flange to 2 ft. Segment Design A 20-foot long segmental beam was designed for use in laboratory testing. The length of the beam was chosen based on the length of a ty pical segment of the Santa Rosa Bay Bridge. The beam was constructed as four 5 ft segmen ts that were post-tensioned together. Equal segment lengths allowed a single set of forms to be used in casting the segments. The design of the segments included shear keys (see Figure 4-6), which were used to fit the segments together and prevent relative vertical sliding during load te sts. Details of the sh ear keys on each segment can be found in Appendix A. Figure 4-7 shows the segments as designed to fit together for laboratory testing. Two of the segments (s egments 1 and 4) were designated ambient segments because they remained at the ambi ent laboratory temperature throughout testing. These segments were reinforced with steel to resist the high prestress forces arising in the anchorage zones. The remaining two segments (segments 2 and 3) were designated heated segments because they were thermally controlled during tests that involved the application of thermal loads. The heated segments containe d copper tubes for therma l control but did not contain steel reinforcement, except for three thermocouple positioning steel cages.

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50 Design of Segment Heating System Thermal control was achieved by passing h eated water through laye rs of copper tubes embedded in the heated segments of the beam. The number of copper tubes in each layer was minimized to reduce any reinforcing effect and re duction in concrete crosssectional properties. Tests were first conducted on a 5 ft long, 2 ft deep prototype beam to optimize the number of copper tubes used in the laboratory segmenta l beam. AASHTO positive and negative design thermal gradients were imposed on the prototype beam using a varying number of copper tubes in each layer. The number of tubes in each laye r that minimized piping while not sacrificing the ability to achieve the gradients in a reasonable amount of time, was chosen for use in the laboratory segmental beam. Copper tube layouts in the prototype and laboratory beam are shown in Figure 4-8 (A) and (B), respectively. As shown in Figure 4-9, layers 1, 2, and 4 were located near the slope changes in the AASHTO de sign thermal gradients. Additional layers of tubes were positioned to aid in heating the enti re beam and in shaping the AASHTO gradients. The top layer of tubes was placed as close to top of the flange of the segments as possible while retaining adequate concrete cover (1 in.). This resulted in a slight kink in the thermal gradients near the top surface of the beam. Test results indicated that this may have affected the magnitude of measured strains caused by th e AASHTO nonlinear thermal gradients in the extreme top flange fibers of the heated segmen ts (see Chapter 13 and Chapter 14 for a complete discussion). Manifold systems were designed to distribute approximately equa l flow of heated water to each pipe, which was key in achieving a uniform di stribution of temperature across the width of the beam. Typical manifolds in the flange a nd web of the heated segments are shown in Figure 4-10 and Figure 4-11, respectively. The web manifold s consisted of constant-diameter inlet and outlet pipes. The flange manifolds required the us e of varying-diameter in let and outlet pipes to

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51 maintain approximately equal flow rates, due to the significant number of tubes in each layer in the flanges. Typical flow ra tes through the manifolds in the web and flange of the heated segments are shown in Figure 4-12 and Figure 4-13, respectively. Tests conducted on the manifolds showed that they were adequate in uniformly distributing heat across the web and along the length of the heated segments. Heat energy was supplied to the beam by pumping water through on-demand electrical water heaters (see Figure 4-14). The heating system comprised of two S-H-7 Seisco electric heaters and one DHC-E Stiebel Eltron heater. The Seisco heaters (re ferred to as Heaters 1 and 2) could deliver water at te mperatures as high as135 oF. The Stiebel Eltron heater (referred to as Heater 3) could instantly deliver wa ter at temperatures as high as 125 oF. Pressurized water was supplied to the heaters (and beam) by 0.5 horse power Depco submersible pumps. The pumps were able to operate at temperatures as high as 200 oF, which was required to re-circulate hot water through the beam. Hoses used with the pumps and the heaters were flexible plastic braided tubing, which could also operate at high temperatures. Prestress Design An external post-tensioning system was desi gned for post-tensioning the segmental beam. The choice to use an external post-tensioning syst em, rather than an embedded internal system using ducts, was made to avoid problems with co ncrete void space and interference with internal instrumentation (thermocouples). Stress levels considered in the desi gn of the post-tensioning system were AASHTO Service I stresses at the midspan and first interi or support of a typical five-span unit of the Sant a Rosa Bay Bridge (see Table 4-1). The Santa Rosa Bay Bridge was designed using HS20-44 vehicular loads, howev er, HL-93 vehicular loads (AASHTO LRFD) were considered in the prestress de sign of the laboratory beam. In Table 4-1, M/St and M/Sb

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52 refer to stresses in the extreme top and bottom fi bers of the cross section of the Santa Rosa Bay Bridge, respectively. Four 1-3/8 in.-diameter high-st rength DYWIDAG threaded bars were used to post-tension the beam. An anchorage system fabricated from structural steel shapes was designed to hold the bars in place during post-tensioning (see Figure 4-15 and Figure 4-16). Steel channels were placed back-to-back with sufficient space to allow for passage of the DYWIDAG bars. A pair of back-to-back channels was used for the top and a nother pair for the bottom bars. Stiffeners were welded to the channels under the bar bearing pl ates. The design of the channel systems allowed the prestress force to be evenly di stributed over the web of the beam. Steel reinforcement was required to resist th e high post-tensioning forces in segments 1 and 4, where the post-tensioning sy stems were anchored. The AASHTO LRFD Bridge Design Specifications (AASHTO 2004a) was used in the design of reinforcement in the prestress anchorage zones. Number 3 ver tical stirrups were placed 1.75 in. on center to resist principal tensile stresses that developed in the general anchorage zones. This reinforcement was placed within 27 in. from the bearing ends of the segments. The approximate method, which is permitted by the AASHTO LRFD specifications, wa s the basis of the design. Outside the anchorage zone, vertical stirrups were placed at 12 in. on center. Stresses in the local zones were determined using guidelines from the AASHT O (2004a) specifications. A set of three confinement spirals were used to resist the high local zone stresses. The reinforcement design is shown in Figure 4-17 and Figure 4-18.

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53 Table 4-1. Approximate Service I stresses in Santa Rosa Bay Bridge Effective Prestress (psi) Dead + Live Load (psi) Support Midspan Support Midspan P/A M/St M/Sb P/A M/St M/Sb M/St M/Sb M/St M/Sb HS20-44 -700 -338 680 -700 460 -940 810 -1630 -610 1230 HL-93 -700 -338 680 -700 460 -940 810 -1735 -684 1380

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54 9 ft-6.5 in. 24 ft9 ft-6.5 in. 4 ft-6 in. 100 59.26 100 53.21 13 ft-6 in. 14 ft-11.25 in. 16 ft 1 ft-3 in. 1 ft-3 in. 7 in. 8 in. 8 ft. 9.75 in. Figure 4-1. Typical cross-secti on of Santa Rosa Bay Bridge 517.2 in. 196.8 in. 26.4 in. 8 in. 7 in. + N.A. 31.5 in. Figure 4-2. I-section representati on of SRB bridge cross section -106 221 330 -622 117 + 41 +11 0 4 in. 12 in. 60 in. 20 in. -568 118 172 -202 Temperature gradient (F) SRB (psi) Laboratory beam (psi) Figure 4-3. Self-equilibrating stresses due to AASHTO positive thermal gradient

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55 32 -66 -99 187 4 in. 12 in. 60 in. 20 in. -35 -12.3 -3.3 0 Temperature gradient (F) SRB (psi) 17 0 -35 -52 61 Laboratory beam (psi) Figure 4-4. Self-equilibra ting stresses due to AASHTO negative thermal gradient 24 in. 61 -52 -35 170 20 in. 8 in. 4 in. 12 in. 10 in. -202 172 -568 117 36 in. Self-Equilibrating Stresses for AASHTO Positive Thermal Gradient (psi) Self-Equilibrating Stresses for AASHTO Negative Thermal Gradient (psi) Cross section of laboratory segmental beam Figure 4-5. Cross section of la boratory beam with analytically determined self-equilibrating thermal stresses due AASHTO design gradients

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56 24 in. 8 in. 28 in. 10 in. 7.5 in. 3.5 in.4 in. 5.5 in. 3.5 in.A 0.5 in. 3.5 in. 1.25 in. B Figure 4-6. A) Location of shear ke ys on beam cross section. B) De tailed elevation view of shear key. Segment 1 Segment 2Segment 3 Segment 4 (Ambient) (Heated) (Heated) (Ambient) Prestress Prestress 5 ft5 ft 5 ft5 ft Figure 4-7. Beam segments

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57 24 in. 6 in. 10 in. 3 in. 1.5 in. 1.5 in. 18 in. 3 in. 1.5 in 24 in1.75 in. A 24 in. 8 in. 10 in. 3 6 in. 3 in.28 in. 2 in. 9 in. 2" 3" 1 in. 3 in. 3" 2" 9 in. 9 in. 3.5 in.1.5 in B Figure 4-8. Copper tube layout s for A) Prototype beam. B) Laboratory segmental beam. +41 oF +11 oF 0 oF 4 in. 12 in. 20 in. 24 in. 8 in. 10 in. 36 in. 28 in. -12.3 oF -3.3 oF 0 oF 4 in. 12 in. 20 in. Layer 1 Layer 2 Layer 3 Layer 4 Layer 5 Layer 6 AASHTO negative thermal gradient AASHTO positive thermal gradient Figure 4-9. Copper tube layouts in relation to shape of AASHTO design thermal gradients

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58 5 ft 2 ft WATER IN FROM HEATERS WATER OUT OF SEGMENT 2 INTO SEGMENT 3 THROUGH FLEXIBLE PLASTIC TUBING WATER RETURN TO TANKS 5 ft COPPER TUBES SEGMENT 2 SEGMENT 3 I.D.0.25 in. 1 .375 in. Figure 4-10. Typical manifold in flange 10 in. WATER OUT OF SEGMENT 2 INTO SEGMENT 3 THROUGH FLEXIBLE PLASTIC TUBING 5 ft WATER IN WATER RETURN TO TANKS 5 ft FROM HEATERS 1 .375 in. COPPER TUBES SEGMENT 2 SEGMENT 3 I.D.0.25 in. Figure 4-11. Typical manifold in web 0 0.2 0.4 0.6 0.8 1 1.2 1.4 123Flow Rate (GPM)Incoming Flow Longitudinal tube number Figure 4-12. Typical flow rates through web manifolds

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59 0 0.1 0.2 0.3 0.4 0.5 0.6 1234567Flow (GPM)Incoming Flow Longitudinal tube number Figure 4-13. Typical flow ra tes through flange manifolds Figure 4-14. Heating system PRESTRESS BAR BACK TO BACK C8X18.75 CHANNELS y=14.67 in. 3 3/8 in. 3 3/8 in. 1 1/2 in. Figure 4-15. Cross section vi ew of prestress assembly

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60 CHAIR (NOT SHOWN) HYDRAULIC CYLINDER LOAD CELL 3 in. 1 2 in. EMBED PLATE 4 in. 21 in. C8X18.75 CHANNEL 20 ft 3 ft 7 ft 13 8 in. DIA. DYWIDAG THREAD BAR 1-3 4 in. PLATE AND NUT FROM DSI 3 in. PLATE Figure 4-16. Elevation view of prestress assembly 27 in. 3 6 in.# 3 STIRRUPS @1.75 in. # 3 STIRRUPS @ 12 in. 5 ft 24 in. 8 in. 28 in. 10 in. 9 3 4 in. 12 in.# 3 BARS 2 1 4 in. 5 1 2 in. #3 CONFINEMENT SPIRALS 2 1 4 in. Figure 4-17. Mild steel reinforcements in Segments 1 and 4 Figure 4-18. Mild steel reinforcement

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61 CHAPTER 5 BEAM CONSTRUCTION The segmental laboratory test beam was c onstructed at the Florida Department of Transportation (FDOT) Structures Research Center in Tallahassee, Florida. Beam design plans (see Appendix A) prepared by the University of Florida, were submitted to the FDOT personnel in the summer of 2005. Construction began in December, 2005 and was completed in February, 2006. Formwork, reinforcement, and thermocoupl e cages were fabricated by FDOT personnel. After the segments were cast and cured, they were transported to the University of Florida Civil Engineering Structures Laboratory in Gainesville. Placement of Steel Reinforcement, Th ermocouple Cages, and Copper Tubes Because the segments were of equal length, a single set of re-usable wooden forms was used to cast each of the four segments of the be am. Segments 1 and 4 contained a steel bearing plate to distribute the anchorage force to the pr estress anchorage zones, which contained mild steel confinement reinforcement (Figure 5-1 (A)). Two steel lifti ng hooks were placed 1 ft from each end of the segments as shown in Figure 5-1 (B). The segment joints contained two shear keys to assist in alignment during prestressi ng and to transfer shear during load tests (Figure 5-2). The heated segments (Segment 2 and 3) each contained three thermocouple positioning steel cages (Figure 5-3). In addition, si x copper tube manifolds were tied to the thermocouple cages to ensure that their positions were maintained during concrete placement. Three manifolds were placed in the flange and three were placed in the web.

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62 Casting of Concrete The casting sequence of the segments of the laboratory beam is shown in Figure 5-4 and in Table 5-1 in ascending order. The ambient segments (1 and 4) were cast first so that the heated segments (2 and 3) could be match cast against them. A 7000-psi concrete pump mix was used fo r all four segments. The design mix proportions are shown in Table 5-2. Delivery tickets for each mix are provided in Appendix C. Although the slump of the concre te is listed as 5 in. in Table 5-2, the mix was delivered with a slightly lower water content and slump to allow fo r adjustments prior to casting. Each segment was left in the forms for a week in the FDOT research laboratory be fore being removed and re-positioned for match-cas ting the next segment (see Figure 5-5). Finished pours for Segments 1 through 4 are shown in Figure 5-6 (A) through (D), respectively. Material Tests and Properties During the casting of each segment, fifteen 6 in. diameter by 12 in. long cylinders were cast for later use in determining material properties. The material properties determined for the ambient segments (1 and 4) were the compressive strength and modulus of elasticity (MOE). For the heated segments (2 and 3), the coefficien t of thermal expansion (CTE) was determined in addition to the compressive strength and elastic modulus. The test setup for compressive strength and elastic modulus tests are shown in Figure 5-7 (A) and Figure 5-7 (B), respectively. Compressive strength tests were conducted in accordance with the Standard Test Method for Compressive Strength of Cylindrical Concre te Specimens (ASTM C 39-01). Modulus of elasticity tests were conducted in accordance with the Standard Test Method for Static Modulus of Elasticity and Poissons Ratio of Concrete in Compression (ASTM C 469-94). Coefficient of thermal expansion tests were conducted on each heated segment under laboratory conditions (in-situ CTE) and on 4 in. diameter by 8 in. long cylinders in accordance with the Standard

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63 Method of Test for Coeffici ent of Thermal Expansion of Hydraulic Cement Concrete (AASHTO TP 60-00). The in-situ CTE tests are di scussed in Chapter 9. Cylinders meeting the specifications of the AASHTO TP 60-00 test method were not taken for Segment 2 therefore results from this test are only available for Segment 3. The AASHTO TP 60-00 test setup is shown in Figure 5-8. Tests were co nducted in the FDOT Materi als Testing Laboratory in Gainesville, Florida. The results of compressive strength and modulus of elasticity tests for Segment 1 through Segment 4 are shown in Table 5-3 through Table 5-6, respectively. Three sets of compressive strength and elastic modulus test s were conducted for all segments except for Segment 3, the last segment to be cast. The firs t two sets of tests were conduc ted in early 200 6 soon after the cylinders were transported from Tallahassee to Gainesville. The last set of tests was conducted in late 2006 during the course of conducting experiments on the laboratory segmental beam. In each test, one cylinder from each segment was used to determine the compressive strength and two cylinders were used for determining the el astic modulus. The elastic modulus values shown in the table are the average of elastic moduli determined from two cylinders. Because of scheduling conflicts, the ages of cylinders at the times tests we re conducted were generally not the same. However, test results for segments 1 and 4 which were cast 11 days apart, match closely (maximum difference of 2% and 6% in compressive strength an d modulus of elasticity values, respectively). The same is true for segmen ts 2 and 3, which were also cast 11 days apart (maximum difference of 12% and 5% in compressive strength and modulus of elasticity values, respectively). The coefficient of thermal expansion (CTE) of Segment 3 was determined using the AASHTO TP 60-00 test method. Th e focus of the test method is the measurement of the change

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64 in length of a fully water-saturated concrete cylinder over a specified temperature range. The length change is then divided by the product of the original length of the specimen and the temperature change to give the CTE. The AASHTO TP 60-00 test procedure is condu cted as follows. The tests specimens consist of concrete cylinders that are 7.0 1 in. long and 4 in. in diameter. The specimens are submerged in saturated limewater at 73 4 oF for at least two days. After the cylinders are fully saturated, they are wiped dry a nd their lengths measured at room temperature to the nearest 0.004 in. The specimens are then placed in the measuring apparatus shown in Figure 5-8, which is positioned in a prepared water bath. The temperature of the water bath is set to 50 2 oF. The bath is allowed to remain at this temperatur e until the specimen reaches thermal equilibrium, which is indicated by consistent readings of a linear variable displacement transducer (LVDT) to the nearest 0.00001 in. taken every 10 minutes over a half hour time period. The temperature of the water bath and the consistent LVDT readings are taken as initial readings. The temperature of the water bath is then set to 122 2 oF. The bath is allowed to remain at this temperature until the specimen reaches thermal equilibrium in the same manner as for the initial readings. The temperature of the water bath and LVDT r eadings are taken as the second readings. The temperature of the water bath is finally set back to 50 2 oF. After thermal equilibrium is reached the temperature of the water bath and L VDT readings are taken as final readings. The CTE is calculated using the following equations: CTE = T L Lo a (5-1) aL = mL + fL (5-2) fL = fC oL T (5-3) whereaL is the actual length change of the specimen during the temperature change, aL is the measured length of specimen at room temperature, T is the measured temperature

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65 change (increase is positi ve, decrease is negative), mL is the measured length change of specimen during the temperature change (incr ease is positive, decrease is negative), fL is the length change of the measuring appara tus during the temperature change, andfCis a correction factor accounting for the change in length of the measurement apparatus with temperature. The correction factor (Cf) in Equation 5-3 is usually taken as 9.6E-6/oF, the coefficient of thermal expansion of stainless st eel. CTEs are determined fr om the expansion (initial and second readings) and contraction (second and final readings) segments of the test. The two CTE values thus obtained are averaged to give the CTE of the test specimen, provided the values are within 0.5E-6/oF of each other. If the CTEs obtained from the expansion and contraction phases are not within 0.5E-6/oF of each other, the test is repeated unt il this criterion is satisfied. Results for the coefficient of thermal expansion of Segment 3 determined using the AASHTO TP 60-00 test procedure are given in Table 5-7. Three cylinders were used for the test. Application of Prestress The goal of prestressing was to produce a net pr estress with a selected vertical eccentricity and no net horizontal eccentricity. The magnitude and vertical eccentricity of prestress were chosen to impose a negative curvature (less comp ression in the extreme top fibers than in the bottom of the web) on the beam with stresses comparable to Service I stresses at a typical interior support of a f our-span unit of the Santa Rosa Bay (SRB) bridge. The total prestress force was also required to provide sufficient compressi on in the extreme top fibers of the beam such that an appreciably high load at the cantilever ed end of the beam, which could be accurately measured in the laboratory, would be required to op en the joint at midspan. To achieve the stress state described above, a total prestress force of 376 kips (94 kips per bar) with a vertical eccentricity of 1.5 in. below the centroid of the beam was applied to the beam (see Figure 5-9).

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66 Prior to post-tensioning, the segments were pl aced on wooden blocks at the same elevation with matching joint faces in contact. This redu ced the possibility of excessive movement as the joints closed during post-tensioni ng. The prestress anchorage systems were suspended from the ends of Segments 1 and 4 using a pair of thread ed bars connected to two steel channels, which were bolted to the ends of the segments (Figure 5-10 and Figure 5-11). This arrangement allowed the vertical eccentricity of prestress to be varied as necessary. Four DYWIDAG post-tensioning bars were then installed. Tandem 60-ton Enerpac hollow core single-acting jacks, pressurized with a manifold system attached to a single pump, were used to stress two bars on either side of the web at a time. The set of four bars were stressed sequentially, 2 bars on either side of the beam at a time. Prestressing was applied incrementally as shown in Table 5-8 with the force monitored using 200 kip hollo w core load cells mounted on each bar (Figure 5-11). Prestressing forces in opposing bars were slightly different (l ess than 8%) due to construction imperfections and variations in bar placement.

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67 Table 5-1. Segment cast dates Segment Number Date Cast 1 12/01/2005 4 12/12/2005 2 01/19/2006 3 02/02/2006 Table 5-2. Concrete pump mix proportions Mix Number FC82JC Strength (psi) 7000 W/C Ratio 0.31 Slump (in) 5 +/1 Air Content (%) 4.5 +/1.5% Plastic Unit Weight (lbs/cf) 140.1 +/1.5 Material ASTM Type Cement C 150 I/II 820 Cement C 618 F. Ash 160 Water --304 Fine Aggregate C 33 Sand 1095 Aggregate C 33 #89STONE 1400 Admixture C 260 AIR Admixture C 494 W/Reducer Dosage rates vary with manufacturers recommendations Table 5-3. Compressive strengths an d moduli of elasticity of Segment 1 SEGMENT 1 (Cast 12/01/2005) Age (days) Compressive Strength (psi) Modulus of Elasticity (ksi) 77 9300 4862 124 9820 5000 350 10210 5362 Table 5-4. Compressive strengths an d moduli of elasticity of Segment 2 SEGMENT 2 (Cast 01/19/2006) Age (days) Compressive Strength (psi) Modulus of Elasticity (ksi) 28 7090 3785 75 8360 4000 319 9690 5180 Table 5-5. Compressive strengths an d moduli of elasticity of Segment 3 SEGMENT 3 (Cast 02/02/2006) Age (days) Compressive Strength (psi) Modulus of Elasticity (ksi) 28 7150 3836 62 7950 4000 361 10970 5443 Table 5-6. Compressive strengths an d moduli of elasticity of Segment 4 SEGMENT 4 (Cast 12/12/2005) Age (days) Compressive Strength (psi) Modulus of Elasticity (ksi) 66 9110 4575

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68 Table 5-6. Continued SEGMENT 4 (Cast 12/12/2005) Age (days) Compressive Strength (psi) Modulus of Elasticity (ksi) 113 10030 5000 339 10250 5158 Table 5-7. Coefficient of thermal expans ion (CTE) of Segment 3 (AASHTO TP 60-00) CTE (per oF) Cylinder 1 7.92E-6 Cylinder 2 7.77E-6 Cylinder 3 7.83E-6 Average 7.84E-6 Table 5-8. Selected post-tensioning force increments Load Cell Readings(kips) Post-tensioning Step P1 P2 P3 P4 1 29.2 18 --2 29.2 18 43.8 46.7 3 48.3 32.2 43.8 46.7 4 48.3 32.2 76.3 68.8 5 76.7 68.8 76.3 68.8 6 76.7 68.8 97.6 93.2 7 94.6 100.8 97.6 93.2 8 94.6 100.8 107.7 100.9 9 106.5 112.1 107.7 100.9 10 106.5 112.1 111.8 106.1 Final Loads 97.2 89.2 93.3 92.4

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69 A B Figure 5-1. A) Open form with mild steel reinforcement. B) Closed form with mild steel reinforcement and lifting hooks. Figure 5-2. Form for shear keys

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70 Figure 5-3. Heated segment with copper t ubes, thermocouple cages and thermocouples SEGMENT 1 December 1, 2005 SEGMENT 2 January 19, 2006 SEGMENT 3 February 2, 2006 SEGMENT 4 December 12, 2005 Figure 5-4. Beam layout with casting sequence Figure 5-5. Match-casting of segment

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71 A B C D Figure 5-6. Finished concrete pours for A) Segment 1. B) Segment 2. C) Segment 3. D) Segment 4. A B Figure 5-7. A) Compressive st rength test setup. B) El astic modulus test setup.

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72 Figure 5-8. AASHTO TP 60-00 test setup LOAD CELL PRESTRESS BAR P1 P2 P3P4 eh eh eheh++ beam centroid P.T. system centroid ev = 1.5 in. ev eh = 8.6 in. Figure 5-9. Bar designations and design eccentricities (West)

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73 Figure 5-10. Prestress assembly (East) Figure 5-11. Elevation view of prestress assembly (North)

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74 CHAPTER 6 INSTRUMENTATION Segments 2 and 3 of the laboratory segmental beam, designated heated segments because they were thermally controlled during te sting, were internally instrumented with thermocouples prior to being cast, and externally instrumented w ith strain gauges, strain rings, and linear variable displacement transducers (L VDTs) prior to post-tensioning of the beam. Load cells were used to monitor reactions, applied mechanical load s, and prestress forces in the post-tensioning bars. This chapter presents a de tailed description of th e instrumentation used. Thermocouples Laboratory-fabricated thermoc ouples were embedded in the heated segments to monitor temperatures during thermal loading of the beam The range of temperature that was to be measured was 50 oF to 130 oF. A Teflon-neoflon type T thermocouple wire, produced by OMEGA Engineering, Inc., was used for fabrication of the thermo couples due to its wide range of temperature sensitivity (-150 oF to 392 oF). Thermocouples were positioned in the segments with the aid of cages made of small-diameter steel, which were then placed in the forms at desired locations before concrete was cast (see Figure 6-1). Thermocouples were vertically positioned to monitor temperature changes at heights corresponding to slope changes in the imposed thermal gradients. Additional thermocouples were placed at intermediate point s between slope changes to facilita te control of the shape of the thermal gradient being imposed. The layout of thermocouples in relatio n to the shape of the AASHTO positive and negative thermal gradients is in shown in Figure 6-2. Three thermocouple cages were embedded in each of the tw o heated segments and total of thirty nine thermocouples were attached to each cage. Thermocouple cages were placed 3 in. away from the ends and at the middle of each segment (see Figure 6-3). This arrangement was used to

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75 ensure the thermal gradient be ing imposed was longitudinally uni form. Thermocouple labels at the sections in Figure 6-3 are shown in Figure 6-4. Electrical Resistance Concrete St rain Gauges and Strain Rings Foil type electrical resistance strain gauges (Figure 6-5) were bonded to the surfaces of the heated segments of the beam for monitoring beam behavior under mechanical and thermal loading (Figure 6-6). The strain gauges were of type PL-60-11-5LT, manufactured by Tokyo Sokki Kenkyujo Co., Ltd. The gauges had a gauge length of 60 mm (2.4 in .), and a temperature compensation number of 11, which is adequate for eliminating strain s due to unrestrained thermal expansion/contraction of steel and concrete from measured strain values. To eliminate the influence of temperature varia tions (of the lead wires) on measured strains, three-wire type gauges were used. In addition to strain gauges, four Stra install Type-5745 sealed strain rings (Figure 6-7) were mounted at the centroid of the beam at midspan (Figure 6-6 (C) and (D)). Data from the strain rings were used to validat e readings from strain gauges mounted at the same location. The detailed locations of strain ga uges and strain rings through the de pth of the beam on either side are shown in Figure 6-8, Figure 6-9, and Figure 6-10. The strain gauges located in the vicinity of the joint at midspan, (J2), were of particular importance in determining the load at which the joint opened. Strain gauges and strain rings locat ed at the centroid of the beam at midspan were used to monitor movement of the neutral axis of the beam after the midspan joint began to open. With the exception of gauges loca ted at the centroid of the beam strain gauges located on the North and South of joint J2 were placed such th at the center of each gauge was 2 in. away from the joint. Strain gauges located at the centroi d at midspan were centere d beneath strain rings, which had a greater gauge length (4.5 in.). Thus, the distance from the common center of these gauges to the joint at midspan wa s 3.6 in. Strain gauges on top of the flange were located 5.5 in.

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76 away from the joint. Because of the presence of copper tubes protruding from the concrete on the North side of the beam, two strain gauges were installed on the North side of the flange while three were installed on the South side. Therefor e, a total of three strain gauges were located above the neutral axis of the se ction on the North side compared with four on the South side. The labeling convention used for strain gauges is explained in Figure 6-11. Strain rings were labeled in a similar manner by replacing the S for strain gauge with R for strain ring (see Figure 6-12). Linear Variable Displacement Transducers (LVDT) DCTH Series LVDTs, produced by RDP Electrosense, were used in measuring deflections and opening of the joint at the midspan of the beam. The LVDTs had a stroke of 1 in. Four LVDTs were used to measure the vertical defl ection at the cantilevered end of the beam (see Figure 6-13), relative sliding (if any) between Segments 2 and 3, deflections close to the midsupport, and deflections close to the end-support. To detect and track the depth of joint-opening at the midspan of the beam, six LVDTs were m ounted on the South side and three were mounted on the top flange across the joint (see Figure 6-14). The labeling c onvention used for LVDTs is shown in Figure 6-15. Load Cells Load cells used to measure the magnitudes of applied loads and reactions were Model 3000 load cells, manufactured by Geokon, Inc. Th e layout of load cells on the post-tensioned beam is illustrated in Figure 6-16. The force in the hydrauli c jack, which was used to load the beam at the cantilevered end, was measured using a 200-kip load cell (Figure 6-17 (A)). 200-kip load cells were mounted on each of the four DYWIDAG post-tensioning bars (Figure 6-17 (B)). These load cells were used to monitor prestress levels in the beam. 150-kip and 75-kip load cells

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77 were installed at the mid-support (Figure 6-17 (C)) and end-support (Figure 6-17 (D)) of the beam, respectively, for measuring reactions under the effect of applied loads. Data Acquisition The instrumentation layout for the prestressed beam is shown in Figure 6-18 and Figure 6-19. Data from the variety of instruments shown in the figures were collected using the National Instruments model SCXI-1000DC Data Acquisition (DAQ) System (see Figure 6-20). Data were collected from a total of 192 thermo couples (32 per section), 15 LVDTs, and 7 load cells. Forty-one data acquisition channels were reserved for collecting data from strain gauges, which were connected to the DAQ system based on the cross section of interest in test being conducted. During the application of thermal loads, the DAQ system was set to acquire 3600 samples of data from each instrument in five minu tes, which were then averaged and recorded at the end of each 5 minute interval. During the a pplication of mechanical loads, the system was set to acquire 100 samples of data from each in strument, which were averaged and recorded every second. Compared with mechanical loadi ng a lower data acquisition rate was used during thermal loading because of the longer time needed to heat or cool the concrete.

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78 Figure 6-1. Thermocouple cage with attached thermocouples +41 F +11 F 0 F 4" 12" 20" 24" 8" 10" 36" 3"28"1" 2" 9" 2" 3" 1" 3" 3" 2" 9" 9" A -12.3 F -3.3 F 0 F 4" 12" 20" 24" 8" 10" 36" 3"28"1" 2" 9" 2" 3" 1" 3" 3" 2" 9" 9"B Figure 6-2. Layout of thermocouples in relati on to shape of A) posit ive thermal gradient. B) negative thermal gradient.

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79 THERMOCOUPLE CAGE 3 in. SECTION ASECTION BSECTION C SECTION DSECTION ESECTION F 3 in. SEGMENT 2SEGMENT 3 Figure 6-3. Location of thermoc ouple cages in Segments 2 and 3

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80 A-T-1 A-T-6 A-T-11 A-T-2 A-T-7 A-T-12 A-T-3 A-T-8 A-T-13 A-T-4 A-T-9 A-T-14 A-T-5 A-T-10 A-T-15 A-T-16A-T-17A-T-18 A-T-19A-T-20A-T-21 A-T-22A-T-23A-T-24 A-T-25A-T-26A-T-27 A-T-28A-T-29A-T-30 A-T-31A-T-32A-T-33 A-T-34A-T-35A-T-36 A-T-37A-T-38A-T-39 B-T-1 B-T-6 B-T-11 B-T-2 B-T-7 B-T-12 B-T-3 B-T-8 B-T-13 B-T-4 B-T-9 B-T-14 B-T-5 B-T-10 B-T-15 B-T-16B-T-17B-T-18 B-T-19B-T-20B-T-21 B-T-22B-T-23B-T-24 B-T-25B-T-26B-T-27 B-T-28B-T-29B-T-30 B-T-31B-T-32B-T-33 B-T-34B-T-35B-T-36 B-T-37B-T-38B-T-39 C-T-6C-T-7C-T-8C-T-9C-T-10 C-T-1 C-T-11 C-T-2 C-T-12 C-T-3 C-T-13 C-T-4 C-T-14 C-T-5 C-T-15 C-T-16C-T-17C-T-18 C-T-19C-T-20C-T-21 C-T-22C-T-23C-T-24 C-T-25C-T-26C-T-27 C-T-28C-T-29C-T-30 C-T-31C-T-32C-T-33 C-T-34C-T-35C-T-36 C-T-37C-T-38C-T-39 E-T-1 E-T-6 E-T-11 E-T-2 E-T-7 E-T-12 E-T-3 E-T-8 E-T-13 E-T-4 E-T-9 E-T-14 E-T-5 E-T-10 E-T-15 E-T-16E-T-17E-T-18 E-T-19E-T-20E-T-21 E-T-22E-T-23E-T-24 E-T-25E-T-26E-T-27 E-T-28E-T-29E-T-30 E-T-31E-T-32E-T-33 E-T-34E-T-35E-T-36 E-T-37E-T-38E-T-39 F-T-6F-T-7F-T-8F-T-9F-T-10 F-T-1 F-T-11 F-T-2 F-T-12 F-T-3 F-T-13 F-T-4 F-T-14 F-T-5 F-T-15 F-T-16F-T-17F-T-18 F-T-19F-T-20F-T-21 F-T-22F-T-23F-T-24 F-T-25F-T-26F-T-27 F-T-28F-T-29F-T-30 F-T-31F-T-32F-T-33 F-T-34F-T-35F-T-36 F-T-37F-T-38F-T-39 D-T-6D-T-7D-T-8D-T-9D-T-10 D-T-1 D-T-11 D-T-2 D-T-12 D-T-3 D-T-13 D-T-4 D-T-14 D-T-5 D-T-15 D-T-16D-T-17D-T-18 D-T-19D-T-20D-T-21 D-T-22D-T-23D-T-24 D-T-25D-T-26D-T-27 D-T-28D-T-29D-T-30 D-T-31D-T-32D-T-33 D-T-34D-T-35D-T-36 D-T-37D-T-38D-T-39SECTION ASECTION BSECTION C SECTION DSECTION ESECTION F Figure 6-4. Thermocouple la bels in Segments 2 and 3

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81 Figure 6-5. Strain (foil) gauge A B C D Figure 6-6. Strain gauges close to joint at midspan; A) North fl ange. B) South flange. C) North web. D) South web.

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82 Figure 6-7. Strain ring STRAIN RING FOIL GAUGE LOAD CELL LVDT SEGMENT 3SEGMENT 214.67" C.G.C.G.8 in. 28 in. S3-N-S-02-35.5 L2 J1 J2 J3S3-N-S-02-32 S3-N-S-02-28.5 S3-N-S-02-27.3 S3-N-S-02-15.6 S3-N-S-02-8.1 S3-N-S-02-0.6 S3-N-R-03-21.3S2-T-D1S3-T-D1S3-N-S-30-35.5 S3-N-S-30-28.5 S3-N-S-30-13.8 S3-N-S-30-6.3 S3-N-S-30-0.6 S3-N-S-30-21.3 S3-N-S-58-35.5 S3-N-S-58-28.5 S3-N-S-58-13.8 S3-N-S-58-6.3 S3-N-S-58-0.6 S3-N-S-58-21.3 S2-N-S-02-35.5 S2-N-S-02-32 S2-N-S-02-28.5 S2-N-S-02-27.3 S2-N-S-02-15.6 S2-N-S-02-8.1 S2-N-S-02-0.6 S2-N-R-03-21.3 S2-N-S-30-35.5 S2-N-S-30-28.5 S2-N-S-30-13.8 S2-N-S-30-6.3 S2-N-S-30-0.6 S2-N-S-30-21.3 S2-N-S-58-35.5 S2-N-S-58-28.5 S2-N-S-58-13.8 S2-N-S-58-6.3 S2-N-S-58-0.6 S2-N-S-58-21.3 30 in.30 in. 30 in. 30 in. Figure 6-8. Instrumentati on details (North side)

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83 14.67" C.G.C.G. SEGMENT 2 SEGMENT 3 S3-T-D1 L2 J3 J2 J1 J2-S-D-33.7 J2-S-D-30.2 J2-S-D-23.5 J2-S-D-04 S3-S-S-02-35.5 S3-S-S-02-32 S3-S-S-02-28.5 S3-S-S-02-27.3 S3-S-S-02-15.6 S3-S-S-02-8.1 S3-S-S-02-0.6 S3-S-R-03-21.3 S3-S-S-30-35.5 S3-S-S-30-28.5 S3-S-S-30-13.8 S3-S-S-30-6.3 S3-S-S-30-0.6 S3-S-S-30-21.3 S3-S-S-58-35.5 S3-S-S-58-28.5 S3-S-S-58-13.8 S3-S-S-58-6.3 S3-S-S-58-0.6 S3-S-S-58-21.3 S2-S-S-02-35.5 S2-S-S-02-32 S2-S-S-02-28.5 S2-S-S-02-27.3 S2-S-S-02-15.6 S2-S-S-02-8.1 S2-S-S-02-0.6 S2-S-R-03-21.3 S2-S-S-30-35.5 S2-S-S-30-28.5 S2-S-S-30-13.8 S2-S-S-30-6.3 S2-S-S-30-0.6 S2-S-S-30-21.3 S2-S-S-58-35.5 S2-S-S-58-28.5 S2-S-S-58-13.8 S2-S-S-58-6.3 S2-S-S-58-0.6 S2-S-S-58-21.3 STRAIN RING FOIL GAUGE LOAD CELL LVDT 8 in. 28 in. 30 in. 30 in. S2-T-D1 30 in. 30 in. Figure 6-9. Instrumentat ion details (South side) LVDT S3-TS-S-5.5-7.25 FOIL GAUGE S3-T-S-5.5-0.75 S3-TN-S-5.5-7.25 SOUTH N ORTHBEAM CENTERLINE S2-TS-S-5.5-8.25 S2-TN-S-5.5-7.75 J2-TS-D-9.5 J2-T-D J2-TN-D-9.512 in. 12 in. Figure 6-10. Instrumentati on at midspan (top flange) Segment Number North (N) or South (S) Strain Gauge Distance from Joint 2 Distance Above Bottom of BeamS2 N S 580.6 Figure 6-11. Typical labeling convention for strain gauges

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84 Segment Number North (N) or South (S) Face Strain Gauge Distance from Joint 2 Distance Above Bottom of BeamS2 N R 3.5 21.3 Figure 6-12. Typical labeling convention for strain rings Figure 6-13. LVDT for measuring defl ection at cantilevered-end of beam A B Figure 6-14. LVDTs mounted acro ss joint at midspan on A) S outh side and B) top flange Joint (J) or Seg. (S) Number Location (T = Top, S = Side) Displacement Device NumberJ2 T D1 Figure 6-15. LVDT labeling convention

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85 LOAD CELL SEG 1 SEG 2 SEG 3 SEG 4 J1 J2 J3 L4 L5 L6 L7 L1 L2 L3 Figure 6-16. Load cell layout A B C D Figure 6-17. Load cells for measuring; A) applie d load. B) prestress. C) mid-support reaction. D) end-support reaction.

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86 STRAIN RING FOIL GAUGE LOAD CELL LVDT SEG 1 SEG 2 SEG 3 SEG 4 J1 J2 J3 DIAL GAUGE L4 L5 L6 L7 L1 L2 L3 S2-T-D1 S3-T-D1 S4-T-D1 S1-T-D1 Figure 6-18. Instrumentation layout (North) SEG 1 SEG 2 SEG 3 SEG 4 J3 J2 J1 L2 L1 L3 S2-T-D1 S3-T-D1 S 4-T-D1 S1-T-D1 STRAIN RING FOIL GAUGE LOAD CELL LVDT DIAL GAUGE L4 L5 L6 L7 Figure 6-19. Instrumentation layout (South) A B Figure 6-20. A) DAQ System. B) Connection of instrumentation to DAQ System.

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87 CHAPTER 7 SETUP AND PROCEDURES FOR MECHANICAL LOADING The setup for conducting laboratory experiments is illustrated in Figure 7-1. A picture of the post-tensioned beam in the laboratory is shown in Figure 7-2. The beam was supported 1.7 ft from the end of Segment 1 (end-support) and 10. 5 ft from the cantileve red-end of the beam (mid-support). It was mechanically loaded 2.7 ft from the cantilevered-end. Fabrication details of the support systems and loading frame can be found in Appendix B. The end-support consisted of back-to-back channels supported by four all-thread bars bolted to the laboratory strong fl oor. A 75-kip load cell was placed between the back-to-back channels and a 3/8-in. thick, 12 in. by 12 in. stee l plate. Between the st eel plate and the surface of the beam a 5/8-in. thick, 12 in. by 12 in. neopr ene pad was used to distribute the reaction to the concrete. The mid-support consisted of a 1. 5 in.-thick, 10 in. by 10 in. steel plate supported by four all-thread rods. The rods were 0.5 in. shorter than the 150-kip lo ad cell at mid-support, which was placed between the steel plate and a C15 x 33.9 channel bolted to the laboratory strong floor. The 0.5 in. clearan ce between the load cel l and the steel rods allowed the load cell to fully carry loads due to the self-weight of the beam and the actuator without any contribution from the steel rods. A 5/8-in. thick, 12 in. by 12 in. neoprene pad was pl aced between the steel plate and the bottom web of the beam to distribu te the mid-support reaction to the concrete. The loading frame, which was designed to carry loads up to 400 kips, consisted of two steel columns and two deep channel beams. For convenience, a temporary I-section was bolted to the load frame columns below the deep channel beams, to support a 60 ton manually pressurized jack, which was used to apply mechanical loads to the beam (see Figure 7-3). A 200-kip load cell was placed directly under the jack to measure applied loads. A 3/8-in. thick, 12 in. by 12 in. steel

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88 plate and 5/8-in. thick, 12 in. by 12 in. neoprene pa d were used to distribute the applied load to the concrete. Opening of Joint between Segments 2 and 3 The primary aim of applying mechanical loads to the beam was to open the joint between segments 2 and 3 (joint J2), creating zero st ress conditions from which the effects of thermal loads could be quantified. This is illustrated in Figure 7-4 through Figure 7-6. Stresses at joint J2 created by prestress and th e self-weight of the beam were taken as the baseline or reference stresses. Stresses due to the AASHTO nonlinear thermal gradients, which were expected to be uniformly distributed across the width of joint J2, were quantified relative to the baseline stresses at joint J2. Quantifying average stresses caused by the AASHTO nonlinear thermal gradients in the extreme top fibers of the beam at joint J2 required the determination of the load corresponding to the average reference stress, QNT, (see Figure 7-4). In addition, loads corresponding to average stresses in the extreme top fibers created by the supe rposition of the AASHTO nonlinear positive thermal gradient on the reference stresses QPG, (see Figure 7-5) and the AASHTO nonlinear negative thermal gradient on the refe rence stresses, QNG, (see Figure 7-6) had to be determined. Av erage stresses due to the therma l gradients were quantified from the difference in loads initiating joint opening (QPG QNT for the positive gradient and QNG QNT for the negative gradient) through ba ck calculation. Though the concept of quantifying thermal stresses by openi ng the joint between segments 2 and 3 is illustrated for the extreme top fibers in Figure 7-4 through Figure 7-6, it is applicable at any depth at joint J2 where loads which cause the section fibers to loose cont act at that depth can be determined. It was determined from sectional analysis us ing conventional beam theory that a maximum load of about 40 kips was required to relieve th e average longitudinal st ress in the extreme top fibers of the beam at the joint (i.e. open the join t) created by the superposi tion of stresses due to

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89 the self-weight of the beam, pr estress, and the AASHTO nonlinea r positive or negative thermal gradient. To allow for the possibility that the experimental setup might deviate somewhat from beam theory, loads of up to 60 kips were applied during the tests. The c onfiguration of load and support points ensured that the ma ximum moment due to applied lo ads occurred at the joint at midspan (joint J2). This eliminated the develo pment of high tensile stresses within the beam segments since tensile stresses could not be transmitted across the joint.

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90 1.7 ft 2.7 ft 20' SEGMENT 1 SEGMENT 2SEGMENT 3SEGMENT 4 Applied Load (Q) 10.5 ft Thermal Loads Beam centroid Centroid of 4 prestress bars 1.5 in. 1.5 in. PT PT East West Lab. floor Mid-support End-support Location of interest 3 ft (AMBIENT) (HEATED)(AMBIENT) (HEATED) Figure 7-1. Test setup Figure 7-2. Segmental beam in laboratory

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91 A B Figure 7-3. A) Loading frame. B) 60-ton jack Prestress (P) Self-weight (SW) Joint-opening load (QNT) SUM (P + SW + QNT)+ + = Apply load QNT to create zero stress at top fiber Centroid Tension Compression y z.C.G. Figure 7-4. Ideal stress diag rams without thermal loads Joint-opening load (QPG) Positive gradient (PG) Prestress (P) Self-weight (SW)SUM (P + SW +PG + QPG).Apply load QPG to create zero stress at top fiber+ + + =Centroid Tension Compression y z.C.G. Figure 7-5. Ideal stress diagrams with positive thermal gradient

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92 Prestress (P) Self-weight (SW)Joint-opening load (QNG) SUM (P + SW +NG + QNG) Negative gradient (NG).Apply load QNG to create zero stress at top fiber = + + +Centroid Tension Compression y z.C.G. Figure 7-6. Ideal stress diagrams with negative thermal gradient

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93 CHAPTER 8 SETUP AND PROCEDURES FOR THERMAL LOADING Thermal profiles were imposed on the heated segments of the beam by passing heated water at laboratory controlled temperatures through strategically pl aced copper tubes embedded in the concrete. Four thermal profiles we re imposed on the heat ed segments: uniform temperature distribution, linear thermal gradie nt, AASHTO nonlinear positive thermal gradient, and AASHTO nonlinear nega tive thermal gradient. This chapter describes the methods and pipi ng arrangements used to impose each thermal profile. Throughout this chapter, thermocouple loca tions, pipe layers, and heaters are referenced. Three water heaters were used to heat the wate r pumped through the beam. Heaters 1 and 2 (H1 and H2) were capable of supplying wa ter at temperatures as high as 135 oF. These heaters were used to provide high temperatur es typically ra nging from 105 oF to 135 oF. Heater 3 (H3) was capable of supplying water at temperatures as high as 125 oF, and was utilized for temperatures ranging from 86 oF to 100 oF. Pipe layer designations, ther mocouple section locations, and the layout of thermocouples at each section are shown in Figure 8-1 through Figure 8-3, respectively. The x markings in Figure 8-3 represent thermocoupl es that were not connected to the DAQ system because they were not needed to capture pertinent da ta. To minimize heat loss from the beam, 0.5-in. thick Styrofoam board s were used to insulate the surfaces of the beam (see Figure 8-4). Uniform Temperature Distribution Before the beam was prestres sed, initial thermal testing was conducted that involved heating the segments uniformly to determine the in-situ CTE. The uniform heating was also one part of the AASHTO nega tive thermal gradient.

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94 Changing laboratory temperatur es (i.e. from early morning through noon till evening) and the fact that the heated segments were insulate d prevented the segments from being at a uniform temperature prior to the start of imposing prescribed thermal profiles. This was because the large mass and low thermal conductivity of the concre te segments prevented them from rapidly adjusting to changing laboratory te mperatures. In particular, th e bottom webs of the segments were generally cooler than the top flanges of the segments. Tap water, which ranged in temperature from 74 oF to 85 oF, depending on the month in wh ich tests were conducted, was used to bring the entire segments to a uniform reference temperature by circulating the water through the segments overnight using the piping configuration shown in Figure 8-5. After the desired thermal configuration had been imposed, this same approach was then used to cool the segments back to the reference temperature. The piping configuration shown in Figure 8-6 was used to uniformly heat the segments. This created a temperature differential that was uniform over the height of the segment. With Heaters 1 and 2 set to the targ et temperature, water was con tinuously circulated through the segments. Heater 3 was not used in this setup primarily because of limitations on the heat energy that it could deliver at the high flow rates which were required to uniformly heat the segments longitudinally. Temperatures in the concrete were monitored from thermocouple readings. Thermal profiles at each section were also peri odically plotted using an average of readings taken from each row of thermocouples throughout the depth of the beam. Heater settings were then updated to offset deviations from the target temperature. When the desired profile was achieved at each section, temperat ures were held in steady state for about 30 to 45 minutes as readings were taken periodically. The segments we re then cooled to the reference temperature.

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95 The average time it took to impose a uniform pr ofile on a single heated segment was about 10 hours. In the case of two segments, the syst em was kept running for between 20 to 30 hours. Linear Thermal Gradient A second set of thermal tests were conducte d that involved imposi ng a linear thermal gradient from 0 oF at the bottom of the web to +41 oF at the top of the flange. This gradient, which leads to no stress development in a simp ly supported structure, was also used in determining the in-situ coefficients of th ermal expansion of the heated segments. The piping configuration shown in Figure 8-7 was used to impose the linear thermal gradient after circulating ta p water through the segment to establish a uniform reference temperature. Heaters 1, 2, and 3 were set to temperatures 41 oF, 23 oF, and 12 oF above the reference temperature, respectively. Water fr om Heaters 1 and 2 was mixed and circulated through pipe layer 3. The temper ature of mixed water was about 32 oF above the reference temperature. There was no flow in pipe layers 2 and 6. Thermocouple readings and thermal profiles at each section were mon itored and changes to the heater settings made when necessary. When the target thermal gradient was achieved, te mperatures were held in steady state for about 30 to 45 minutes as readings were taken periodica lly. The segment was then cooled back to the reference temperature. The average time it took to impose the linear profiles on a single heated segment was about 9 hours. AASHTO Positive Thermal Gradient The piping shown in Figure 8-8 was used to impose the AASHTO nonlinear positive thermal gradient on the heated se gments of the beam. Before circulating heated water through the segments, tap water was circulated overnight to establish the reference temperature. Heaters 1 and 3 were set to 41 oF and 11 oF above the reference temperature, respectively. Although tap water was pumped from a reservoir through Heater 2, the heater was turned off for

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96 the duration of the test. The water pumped through Heater 2 was mixed with water from Heater 1 and circulated through layer 3, which was required to be at a temperature about 7 oF above the reference temperature. The temperat ure of mixed water was regulated by controlling contributions to the mix from Heater 1 (turned on) and Heater 2 (turned off). The bottom 20-in. portion of the beam was maintained at the refe rence temperature by circulating tap water through layers 4, 5, and 6. This produced the 0 oF temperature change in th e gradient (relative to the reference temperature). Thermocouple readings and the shape of the gradient at each section were monitored and changes to heater settings were made when necessary. When the AASHTO positive thermal gradient profile was achieved, temp eratures were kept at steady state for about 30 to 45 minutes as readings were taken periodica lly. The beam was then cooled to the reference temperature. The average time it took to impose the AASHTO positive thermal gradient on the heated segments was about 7 hours. AASHTO Negative Thermal Gradient The AASHTO nonlinear negative thermal gradie nt was imposed on the heated segments using the setup shown in Figure 8-9. To impose this gradient the segments had to be cooled from the reference temperature rather than heated Since the setup for thermal control could only be used to heat the segments, two reference temperatures were involved in imposing the negative gradient. The first reference temperature (refe rred to as the low reference temperature) was imposed by circulating tap water through the segmen ts using the piping configuration previously shown in Figure 8-5. The low reference temperature was imposed to maintain consistency with procedure for imposing the thermal profiles disc ussed previously. After establishing the low reference temperature, a uniform temperature increase of about 40 oF was imposed on the segments using the plumbing in Figure 8-6. The temperature of the segments after the 40 oF increase was referred to as the high referen ce temperature. Heater settings and layer

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97 temperatures required to impose the gradient we re based on the high reference temperature. Heater 1 was set to a temperature 12.3 oF below the high reference temperature. This corresponded to the -12.3 oF temperature change in the AASHTO nonlinear thermal gradient. The bottom 20-in. portion of the beam was maintained at the high reference temperature by circulating water at that temp erature through layers 4, 5, a nd 6, using Heater 2. This corresponded with the 0 oF temperature change in the gradient Heater 3 was connected to layer 2 and was only used when needed to bring the temperature of layer 2 to 3.3 oF below the high reference temperature. Water from heaters 1 an d 2 was mixed and circulated through layer 3. Thermocouple readings and the shape of the gr adient were monitored throughout the test, and changes to heater settings were made as necessary. When the target gradient was achieved, temperatures were kept in stea dy state for about 30 to 45 minute s as readings were periodically taken. The beam was then cooled to the low reference temperature. The average time required to impose the AASHTO negative thermal gradient after imposing the high reference temperature was about 7 hours.

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98 24 in. 8 in. 10 in. 3 6 in. 28 in. Layer 1 Layer 2 Layer 3 Layer 4 Layer 5 Layer 6 Figure 8-1. Pipe layers THERMOCOUPLE CAGE 3 in. SECTION ASECTION BSECTION C SECTION DSECTION ESECTION F 3 in. SEGMENT 2SEGMENT 3 Figure 8-2. Thermocouple locations in heated segments

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99 SECTION ASECTION BSECTION C SECTION DSECTION ESECTION F Figure 8-3. Thermocouples used at each section Figure 8-4. Insulated heated segments

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100 TAP WATER IN TAP WATER IN TAP WATER OUT TAP WATER OUT Figure 8-5. Piping conf iguration used to impose initial condition H1 P1 H2 P2 H3 P3 HEATER 1 IN HEATER 2 IN HEATER 1 OUT HEATER 2 OUT ** *VALVE CLOSED ON ON NOT USED Figure 8-6. Piping configurat ion used to impose uniform temperature differential HEATER 1 IN MIXED HEATER 3 IN H1 P1 H2 P2 H3 P3HEATER 1 OUT MIXED OUT HEATER 3 OUT *VALVE PARTIALLY OPEN TO MIX WATER HEATER 2 IN TAP WATER IN HEATER 2 OUT TAP WATER OUT*ON ON ON Figure 8-7. Piping confi guration used to impose linear thermal gradient

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101 HEATER 1 IN MIXED HEATER 3 IN H1 P1 H2 P2 H3 P3HEATER 1 OUT MIXED OUT HEATER 3 OUT *VALVE PARTIALLY OPEN TO MIX WATER TAP WATER IN TAP WATER OUT ON ON OFF Figure 8-8. Piping configuration used to impose AASHTO nonlinear positive thermal gradient HEATER 1 IN MIXED HEATER 3 IN H1 P1 H2 P2 H3 P3HEATER 1 OUT MIXED OUT HEATER 3 OUT HEATER 2 IN HEATER 2 OUT *VALVE PARTIALLY OPEN TO MIX WATER*ON ON ON Figure 8-9. Piping configurati on used to impose AASHTO nonlinear negative thermal gradient

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102 CHAPTER 9 IN-SITU COEFFICIENT OF THERMAL EXPANSION In-situ CTE tests were conducted to determine co efficients of thermal expansion that were representative of the composite behavior of the concre te segments, copper tubes, and thermocouple cages embedded in segments 2 and 3 of the laboratory test beam. The setup for the in-situ CTE tests is shown in Figure 9-1. The segment bei ng tested was supported on two wooden blocks 6 in. away from the ends. LVDTs were placed vertically along the centerline of the cross section on both ends of the segment to r ecord the elongation of the segment. Initially three LVDTs were used to record displacements at locations 0.5 in. below the top of the flange, at the centroid of the segment (21.3 in. from th e bottom of the segment), and 0.5 in. above the bottom of the segment. Subsequently, with the acquisition of additional LVDTs, four and then five LVDTs were used in the testing. The th ree and four LVDT setups were used in tests conducted on Segment 2. The four LVDT setup wa s used in one test conducted on Segment 3. In the remaining tests conducted on Segment 3, the five LVDT setup was used. Two non-stress inducing thermal profiles we re imposed on the segment: a uniform temperature change of about 41 oF above the reference temperature (about 85 oF) of the segment, and a linear thermal grad ient varying from 0 oF at the bottom of the web to +41 oF at the top of the flange. The uniform and linear thermal prof iles were imposed using the piping setups in Figure 8-6 and Figure 8-7, respectively. The composite CTE of the segment was calculated as: avg = c c totalA dA (9-1) avg = Lavg (9-2) avgTG = c c gradA dA T (9-3)

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103 = avg avgTG (9-4) whereavg is the average axial el ongation of the segment, avg is the average engineering strain of the segment, avgTG is the average temperature differential, is the coefficient of thermal expansion, total is the total measured axial elonga tion at the location of the LVDT, Lis the length of the segment, gradT is the temperature gradient/change imposed on the segment, and cAis the cross sectional area of the segment. It was expected that both uniform and linea r temperature distributions would produce the same CTE values since neither involved nonlinearity of temperature profile, and since it was assumed that the segments had uniform distributions of mo isture content. A laboratory imposed uniform temperature change on Segment 2 and the corresponding measured end displacements are shown together w ith the target thermal profile and calculated longitudinal displacement in Figure 9-2 and Figure 9-3, respectively. A uniform temperature change imposed on Segment 3 and the corresponding measured end displacements are shown together with the target thermal profile and calculated longitudinal displacement in Figure 9-4 and Figure 9-5, respectively. Measured concrete temperatures after uniform profiles were imposed on segments 2 and 3 are shown in Figure 9-6 and Figure 9-7, respectiv ely. Laboratory imposed thermal profiles were within 2% of the target profiles for both segments. In Figure 9-3 and Figure 9-5, calculated displa cements were determined using CTEs determined from measured data and target temperature profiles. There was more variability in measured total displacements for Segment 3 (see Figure 9-5) about the calculated displacement than for Segment 2 (see Figure 9-3). This was partly because fi ve LVDTs were used at each end of Segment 3 whereas only three LVDTs were used at each end of Segment 2. In addition, the

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104 coefficient of variation of the temperature prof ile imposed on Segment 3 with respect to the target (1.9%) was higher than the coefficient of variation of the temperature profile imposed on Segment 2 (1.4%). The variability in measured displacements was also pa rtially attributed to nonlinearities in the laboratory imposed ther mal profiles and varying moisture contents throughout the volume of the segments. It should be noted that in the AASHTO standard test method for determining the coefficient of thermal expansion of concrete (AASHTO TP 60-00) the influence of moisture content on CTE is eliminated by fully saturating th e concrete test cylinders (and thus ensuring a uniform distribution of moisture in the test spec imen). In the in-situ CTE tests, measured end displacements were higher at the ends where heat ed water entered the segments than at the ends where water exited the segments. The orientations of Segment 2 and Segment 3 together with the inlet and outlet of heated water during testing are shown in Figure 9-8 and Figure 9-9, respectively. Measured end displacements were higher on the West end of Segment 2 than on the East end of the segment (see Figure 9-3). For Segment 3 measured end displacements were higher on the East end than on th e West end of the segment (see Figure 9-5). This was because prior to achieving a constant temperature profil e longitudinally, the inlet sections of each segment experienced higher temperatures than th e outlet sections, which led to higher measured elongations at the inlet ends than at the outlet ends of the segments. A laboratory imposed linear temperature pr ofile on Segment 2 and the corresponding measured end displacements are shown together w ith the target thermal profile and calculated longitudinal displacement in Figure 9-10 and Figure 9-11, respectively. A linear temperature change imposed on Segment 3 and the corresponding measured end displacements are shown together with the target thermal profile and calculated longitudinal displacement in Figure 9-12

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105 and Figure 9-13, respectively. Measured concre te temperatures afte r linear profiles were imposed on segments 2 and 3 are shown in Figure 9-14 and Figure 9-15, respectively. Laboratory imposed linear temperature gradients were within 2% of the target temperature profile for both segments. The coefficients of variation of the la boratory imposed thermal gradients with respect to the target gradients were 3.7% and 4% for Segment 2 and Segment 3, respectively. This is in agreement with the closer match between calculated and measured total displacements for Segment 2 (see Figure 9-11) than for Segment 3 (see Figure 9-13). In calculating the coefficient of variation of laborat ory imposed linear gradient s, the standard error about the target gradient was us ed in place of the standard de viation about the mean. This explains the higher coefficients of variation for labor atory imposed linear temperature gradients compared with laboratory imposed uniform temperature changes. In Figure 9-11, measured displacements at the West end of Segment 2 were lower than measured displacements at the East end in the lower half of the segment, which was expected since the inlet of heated water to the segment was at the East end. In the upper half of the segment, however, measured displacements were higher at the West end than at the East e nd of the segment. This was because the target temperature at the top of the flange was exceeded in imposing the linear thermal gradient. In an attempt to cool the top flange to the target te mperature it was slightly overcooled, leading to lower temperatures and correspondin g lower elongations at sections close to the inlet (East end) of water to the segment than at sections close to the outlet (West end) of water from the segment. For Segment 3, measured displacements were higher at the East end than at the West end of the segment. This was consistent with higher temperat ures developing at the in let of heated water to the segment (East end) than at the outlet of heat ed water from the segment (West end) prior to achieving a constant thermal profile longitudinally.

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106 The coefficients of thermal expansion determined from in-situ tests and the AASHTO TP 60-00 procedure, which was disc ussed in Chapter 5, are summarized in Table 9-1. In-situ CTEs determined with linear thermal grad ients were generally higher than in-situ CTEs determined with uniform temperature distributions The slight increase in CTE (an average of about 8%) associated with linear thermal gradients was attribut ed to the influence of copper tubes on the longitudinal expansi on of the concrete segments and non-uniform moisture contents of the segments. The influence of thermocouple positioning steel cages on the longitudinal expansion of the segments was deemed insignificant since they were placed transversely in the segments. The CTE for Segment 3, determined using the uniform temperature profile, was equal to the CTE of the segment determined using the AASHTO standard method (AASHTO TP 60-00). It is, however, likely that a repeat of the in-sit u test would have yielded a slightly different CTE for the segment. In the AASHT O procedure, the tolerance within which two CTEs determined from the same cycle can be averaged is 0.5E-6/oF. The differences between CTEs determined with the linear profile and CTEs determined w ith the uniform temperat ure distribution were 0.7E-6/oF and 0.5E-6/oF for segments 2 and 3, respectivel y. Since the in-situ CTEs were determined from different tests using different temperature distributions, these differences were deemed acceptable. The arithmetic average of the CTEs of each segment determined using the procedures discussed above was used in predicting thermal stresses and strains later in this study.

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107 Table 9-1. Experimentally determined coefficients of thermal expansion Uniform Temp. Distribution (In-situ) Linear Thermal Gradient (In-situ) AASHTO TP 60-00 Method Segment 2 7.3E-6/oF 8.0E-6/oF N/A Segment 3 7.8E-6/oF 8.3E-6/oF 7.8E-6/oF

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108 A HEATED SEGMENT C.G.C.G. LVDT 4 in.X4 in. STEEL COLUMN SHORING 14.67 in. STRAIN RING FOIL GAUGE LVDT 10.9 in. 0.5 in. 0.5 in. 10.4 in. 6 in.B Figure 9-1. Typical in-sit u CTE test setup; A) Ph otograph. B) Details.

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109 Temperature Difference (deg. F)Elevation (in.) 0 5 10 15 20 25 30 35 4045 0 5 10 15 20 25 30 35 40 Section A Section B Section C Target Flange Web Figure 9-2. Uniform temperatur e change imposed on Segment 2 Displacement (in.)Elevation (in.) 0 0.005 0.01 0.015 0.02 0.025 0.03 0.035 0 5 10 15 20 25 30 35 40 Measured (West) Measured (East) Measured (Total) Calculated Flange Web Figure 9-3. Measured end-disp lacements due to uniform temperature change imposed on Segment 2

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110 Temperature Difference (deg.F)Elevation (in.) 0 5 10 15 20 25 30 35 4045 0 5 10 15 20 25 30 35 40 Section D Section E Section F Target Flange Web Figure 9-4. Uniform temperatur e change imposed on Segment 3 Displacement (in.)Elevation (in.) 0 0.005 0.01 0.015 0.02 0.025 0.03 0.035 0 5 10 15 20 25 30 35 40 Measured (West) Measured (East) Measured (Total) Calculated Flange Web Figure 9-5. Measured end-disp lacements due to uniform temperature change imposed on Segment 3

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111 Temperature (deg. F)Elevation (in.) 85 90 95 100 105 110 115 120 125130 0 5 10 15 20 25 30 35 40 Section A Section B Section C Target Flange Web Figure 9-6. Measured concrete temperat ures in Segment 2 (uniform profile) Temperature (deg.F)Elevation (in.) 85 90 95 100 105 110 115 120 125130 0 5 10 15 20 25 30 35 40 Section D Section E Section F Target Flange Web Figure 9-7. Measured concrete temperat ures in Segment 3 (uniform profile)

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112 SEGMENT 2 C.G.C.G. LVDT 4"X4" STEEL COLUMN VERY RIGID SHORING 14.67 in. 6 in. STRAIN RING FOIL GAUGE LVDT 10.9 in. WATER INLET WATER OUTLET 0.5 in. 0.5 in. WEST END EAST END Figure 9-8. Orientation of Segment 2 during testing (South elevation) SEGMENT 3 C.G.C.G. LVDT 4 in.X4 in. STEEL COLUMN SHORING 14.67 in. STRAIN RING FOIL GAUGE LVDT 10.9 in. 0.5 in. 0.5 in. 10.4 in. 6 in. WATER OUTLET WATER INLET WEST END EAST END Figure 9-9. Orientation of Segment 3 during testing (South elevation)

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113 Temperature Difference (deg. F)Elevation (in.) 0 5 10 15 20 25 30 35 4045 0 5 10 15 20 25 30 35 40 Section A Section B Section C Target Flange Web Figure 9-10. Linear temperature gradient imposed on Segment 2 Displacement (in.)Elevation (in.) 0 0.005 0.01 0.015 0.02 0.025 0.03 0.035 0 5 10 15 20 25 30 35 40 Measured (West) Measured (East) Measured (Total) Calculated Flange Web Figure 9-11. Measured displacements due to li near thermal gradient imposed on Segment 2

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114 Temperature Difference (deg. F)Elevation (in.) 0 5 10 15 20 25 30 35 4045 0 5 10 15 20 25 30 35 40 Section D Section F Section E Target Flange Web Figure 9-12. Linear thermal gr adient imposed on Segment 3 Displacement (in.)Elevation (in.) 0 0.005 0.01 0.015 0.02 0.025 0.03 0.035 0 5 10 15 20 25 30 35 40 Measured (West) Measured (East) Measured (Total) Calculated Flange Web Figure 9-13. Measured displacements due to linear thermal gradient on Segment 3

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115 Temperature (deg. F)Elevation (in.) 85 90 95 100 105 110 115 120 125130 0 5 10 15 20 25 30 35 40 Section A Section B Section C Target Flange Web Figure 9-14. Measured concrete temper atures in Segment 2 (linear profile) Temperature (deg. F)Elevation (in.) 85 90 95 100 105 110 115 120 125130 0 5 10 15 20 25 30 35 40 Section D Section F Section E Target Flange Web Figure 9-15. Measured concrete temper atures in Segment 3 (linear profile)

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116 CHAPTER 10 RESULTS PRESTRESSING In this chapter strains recorded during prestr essing of the laboratory segmental beam are presented and discussed. The four segments of the beam were supported on wooden blocks as shown in Figure 10-1 during prestressing. This suppor t system was changed to that shown in Figure 10-2 prior to the beginning of mechanical and thermal load tests on the laboratory beam. Labels assigned to the DYWIDAG post-tensioning bars and the design eccen tricities of the bars from the centroid of the beam were presente d in Chapter 5. They are duplicated in Figure 10-3 for convenience. Final forces in the prestre ss bars and measured hor izontal eccentricities immediately after tensioning are given in Table 10-1. The vertical eccentricity of the four-bar group was 1.5 in. below the centroid of the beam. Concrete strains near (joint J2 ) were continuously recorded as the beam was prestressed. The strain data collected during prestressing provided important information regarding the distribution of strains at the joint. This inform ation was vital in interpreting data collected during later mechanical load tests in which the joint wa s slowly opened to relieve stresses due to the initial pre-compression and self-wei ght of the beam. The locations of strain gauges on the beam can be found in Chapter 6. Figure 10-4 and Figure 10-5 show the increase in strain at joint J2 on the North side of the beam. Figure 10-6 and Figure 10-7 show the stra ins at the same joint on the South side and Figure 10-8 shows the strains on top of the top flange. Also included in Figure 10-4 through Figure 10-8 are calculated strains at the top flange at joint J2. Strains were calculated using laboratory determined concrete material propertie s (e.g. elastic modulus) and measured prestress forces. Gaps, if any, at joint J2 prior to prestressing were neglected in the calculations. In these figures negative strains indicate compression. Th e top two bars, which were located above the

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117 centroid of the beam, were tensione d first (up to a total prestress of about 50 kips). As shown in Figure 10-8 the top flange strain gauges detected very little st rain until the prestress force was between 50 kips and 125 kips. One explanation fo r this behavior is differential shrinkage of concrete at the edges of the beam segments. As Figure 10-9, shows the top surfaces of the segments were exposed to the la boratory environment after segmen t casting. It is likely that shrinkage was greater in the exposed portion of the top flange than in other surfaces which remained covered during curing. It is believed th at this differential shrinkage led to a narrow gap between the top flanges of segments 2 and 3. Consequently, no strain was detected until sufficient prestress force had been applied to close the gap. Differential shrinkage is also believed to be the reason for the systematically lower strains measured at the top flange comp ared with calculated strains (see Figure 10-8). This may have been due to the assumption in the calculations, th at contact surfaces at joint J2 were smooth and in full contact (with no gaps). Calculated strains at the top flange close to joint J2 were higher than measured strains at the top flange for all prestress levels. The same was not the case for measured strains close to the top flange on the sides of the joint (see Figure 10-4 through Figure 10-7). Comparison of data from gauges on the sides of the joint with calculated top flange strains was more representative of expected be havior. This was because the 1.5 in. vertical eccentricity in prestressing was exp ected to lead to the developmen t of lower compressive strains on top of the flange than at lower elevations. Measured concrete strains through the depth of the beam segments near joint J2 are shown in Figure 10-10. These readings were taken immedi ately after prestressing was completed. Also shown in the plot are calculated strain profiles de termined with the measured prestress forces and eccentricities (horizontal as well as vertical) shown in Table 10-1. Two observations can be

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118 made when comparing the measured and calculate d strains. The first is that strains vary considerably with depth. The ot her is that the average measured strains on the North side are greater in magnitude than those on the South side with calculated strains along the vertical line of symmetry of the beam between the two. Differences in the average measured strains on the North and South sides of the segments can be attributed to the unequa l total prestress forces on the No rth (190.4 kips) and South (181.6 kips) sides of the beam, and the 0.5 in. ne t horizontal eccentricity in prestressing (see Figure 10-3 and Table 10-1). As Figure 10-10 shows, calculated strains on the North and South sides of joint J2 determined with measured prestress forces an d measured horizontal and vertical eccentricities were higher on the North side than on the South side of the joint. It was explained in Chapter 5 that the goal of applying an equal prestress force to each bar was not achieved because the prestress anchorage system prevented independe nt post-tensioning of th e DYWIDAG bars. The 0.5 in. net horizontal eccentricity was most lik ely the result of moveme nt of the suspended post-tensioning anchorage system as the beam was prestressed. The moment due to the unintended horizontal eccentricity caused the deve lopment of compressive strains on the North side and tensile strains on the Sout h side of the vertical axis of the beam. This moment, together with the moment developed as a result of the inequality in the total prestress on the North and South sides of the beam, led to the development of lower magnitude strain s on the South side of the beam compared to the North side. A likely explanation for the variation in measured strains thro ugh the depth of the segments is an imperfect fit (segment-to-segment c ontact) at joint J2. This could have occurred during the match-casting process or during positioning of the segm ents for prestressing. An imperfect fit would lead to data from the strain gauges being influenced by stress concentrations

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119 in the surface fibers of the beam segments. The unusually high strains measured on the North side of Segment 3 from strain gauges located 1. 1 in. and 21.3 in. from the bottom of the segment (see Figure 10-10) might have been due to localized effects at those points on the segment. The exact causes of the high measured strains at these locations are unknown, however, at about 7% of the total prestress force the strain gauges designated S3-N-S-02-1.1 and S3-N-S-3.6-21.3 (see Figure 10-5) had registered about 36% and 55% of the re spective total measured strains at their locations. Except for the two high strain points in the profile of Segm ent 3 on the North side, strain profiles on identical sides of segments 2 and 3 compared quite well. Strains measured transversely across the widt h of the flanges of segments 2 and 3 near joint J2 are shown in Figure 10-11. Also shown in the figure ar e calculated strains that take into account the vertical eccentricity in prestressing only (shown as average calculated strains in the legend) and calculated strains that take into account bot h vertical and net hor izontal eccentricities in prestressing (shown as calculated strains in the legend). Data in Figure 10-11 were collected from three strain gauges on Segment 3 and two strain gauges on Segment 2. The presence of LVDT mounts on Segment 2 prevented the placement of a strain gauge close to the center of the flange of that segment. In an ideal situation, strains measured across the width of the flanges near joint J2 should be uniform (see the average calculated strains in Figure 10-11). Because of the measured net horizontal eccentricity in pres tressing, the distribution of measured strains across the width of the flange was expected to look like the calculated strains in the figure. A possible reason for the nonlinear di stribution of measured strains across the width of the flange is a lack of a full contact fit at the joint. The nonlinearities in the measured strains were not expected to affect the quantification of thermal stresses caused by the AASHTO nonlinear therma l gradients. As discussed in Chapter 7,

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120 stresses due to prestress, self -weight, and any additional forces that may have been induced at joint J2 when the support system of the beam was changed (see Figure 10-1 and Figure 10-2), were taken as reference stresses. These stresses were then relieved when joint J2 was opened, and therefore did not directly enter into calculations of ther mally induced stresses. Partial losses in prestressing force were init ially measured over a period of approximately three weeks and are plotted for each bar in Figure 10-12. The percentage change in total prestress with time is shown in Figure 10-13. Fluctuations abou t the general downward trend in Figure 10-12 and Figure 10-13 were the result of daily temperature variat ions. Prestress levels were also checked before and after each mechan ical and thermal load test conducted after the initial monitoring period. The maximum percenta ge reduction in total prestress over the course of the 4-month period during which tests were c onducted on the laboratory segmental beam was about 3.5% of the init ial total prestress.

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121 Table 10-1. Prestress magnitude s and horizontal eccentricities Bar Designation Force (kips) Horizontal Eccentricity Designation Horizontal Eccentricity (in.) P1 97.2 e1 8.6 P2 89.2 e2 8.1 P3 93.2 e3 8.6 P4 92.4 e4 8.1

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122 20' SEGMENT 1 SEGMENT 2SEGMENT 3SEGMENT 4 10.5 ft Beam centroid Centroid of 4 prestress bars PT PT East West Lab. floor Mid-support Location of interest (Joint J2) 3 ft (AMBIENT) (HEATED)(AMBIENT) (HEATED) Wooden block PT: Post Tensioning Force Figure 10-1. Segment support during prestressing 1.7 ft 2.7 ft 20' SEGMENT 1 SEGMENT 2SEGMENT 3SEGMENT 4 Applied Load (Q) 10.5 ft Thermal Loads Beam centroid Centroid of 4 prestress bars 1.5 in. 1.5 in. PT PT East West Lab. floor Mid-support End-support Location of interest (Joint J2) 3 ft (AMBIENT) (HEATED)(AMBIENT) (HEATED) PT: Post Tensioning Force Figure 10-2. Beam support for mechanical and thermal load tests

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123 LOAD CELL PRESTRESS BAR P1 P2 P3 P4 e1 e2 e3e4++ beam centroid P.T. system centroid ev = 1.5 in. ev South North Figure 10-3. Post-tensioning bar designations and eccentricities Strain (microstrain)Total Prestress Force (kips) -600 -500 -400 -300 -200 -100 0100 0 50 100 150 200 250 300 350 400 450 S2-N-S-02-33.4 S2-N-S-02-30.4 S2-N-S-02-27.5 S2-N-S-3.6-21.3 S2-N-S-02-14.5 S2-N-S-02-7.7 S2-N-S-02-1.0 Calculated (Top Flange) Figure 10-4. Measured concrete strains near jo int J2 due to prestress (Segment 2, North)

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124 Strain (microstrain)Total Prestress Force (kips) -600 -500 -400 -300 -200 -100 0100 0 50 100 150 200 250 300 350 400 450 S3-N-S-02-33.5 S3-N-S-02-30.3 S3-N-S-02-27.4 S3-N-S-3.6-21.3 S3-N-S-02-14.6 S3-N-S-02-7.8 S3-N-S-02-1.1 Calculated (Top Flange) Figure 10-5. Measured concrete strains near jo int J2 due to prestress (Segment 3, North) Strain (microstrain)Total Prestress Force (kips) -600 -500 -400 -300 -200 -100 0100 0 50 100 150 200 250 300 350 400 450 S2-S-S-02-35.5 S2-S-S-02-32.0 S2-S-S-02-28.5 S2-S-S-02-27.3 S2-S-S-3.6-21.2 S2-S-S-02-14.5 S2-S-S-02-7.7 S2-S-S-02-0.9 Calculated (Top Flange) Figure 10-6. Measured concrete strains near jo int J2 due to prestress (Segment 2, South)

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125 Strain (microstrain)Total Prestress Force (kips) -600 -500 -400 -300 -200 -100 0100 0 50 100 150 200 250 300 350 400 450 S3-S-S-02-35.5 S3-S-S-02-32 S3-S-S-02-28.5 S3-S-S-02-27.5 S3-S-S-3.6-21.3 S3-S-S-02-14.5 S3-S-S-02-7.7 S3-S-S-02-0.9 Calculated (Top Flange) Figure 10-7. Measured concrete strains near jo int J2 due to prestress (Segment 3, South) Strain (microstrain)Total Prestress Force (kips) -600 -500 -400 -300 -200 -100 0100 0 50 100 150 200 250 300 350 400 450 S2-TN-S-5.5-7.75 S2-TS-5.5-8.25 S3-TN-S-5.5-7.25 S3-T-S-5.5-0.75 S3-TS-S-5.5-7.25 Calculated (Top Flange) Figure 10-8. Measured concrete strains near joint J2 due to prestress (Top flange)

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126 Segment 2, joint formed Segment 3, match cast joint Formwork coverage during curing Differential shrinkage caused by top flange exposure to environment during curing ELEVATION SECTION Top flange exposed Figure 10-9. Effect of differentia l shrinkage on top flange strains Strain (microstrain)Elevation (in.) -600 -550 -500 -450 -400 -350 -300 -250 -200 -150 -100 -500 0 5 10 15 20 25 30 35 40 Segment 2 (North) Segment 3 (North) Segment 2 (South) Segment 3 (South) Calculated (North) Calculated (South) Calculated (Center) Web Flange Figure 10-10. Measured concrete st rains due to prestress through dept h of segments near joint J2

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127 Strain (microstrain)Gauge Location from Center of Beam (in.) -600 -550 -500 -450 -400 -350 -300 -250 -200 -150 -100 -500 -12 -10 -8 -6 -4 -2 0 2 4 6 8 10 12 Segment 2 (Measured) Segment 3 (Measured) Calculated Average Calculated South North Figure 10-11. Measured concrete strains due to prestress across width of segment flanges near joint J2 (Top flange) Time (days)Prestress Force (kips) 0 10 20 30 40 50 60 70 80 90 100 110 120 130 140 150 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 P1 P2 P3 P4 Figure 10-12. Variation of pr estress forces with time

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128 Time (days)Change in Prestress Force (%) 0 10 20 30 40 50 60 70 80 90 100 110 120 130 140 150 -4 -3.75 -3.5 -3.25 -3 -2.75 -2.5 -2.25 -2 -1.75 -1.5 -1.25 -1 -0.75 -0.5 -0.25 0 0.25 0.5 Figure 10-13. Change in total prestress force with time

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129 CHAPTER 11 RESULTS MECHANICAL LOADING The behavior of the laboratory segmental beam under the action of mechanical loads applied at the cantilevere d end of the beam is discussed in this chapter. The objective of the mechanical load tests was to determine: the load at which the joint at mi dspan (joint J2) opened; and the effect that this joint opening had on the overall behavior of the beam. As discussed in Chapter 7, opening of joint J2 was used to create zero reference stress conditions from which stresses due to the AASHTO nonlinear thermal gradients could later be quantified. Two methods of detecting joint opening were used. One involved the use of strain gauges mounted close to joint J2. Th e other involved the use of LVDT s mounted across joint J2 at specified depths. Data collected from the LVDT s and strain gauges are presented and compared in the following sections. In addition, data colle cted from strain gauges located at the middle of segments 2 and 3 (30 in. away from joint J2 on both sides) and vertical deflection data will be presented and discussed. In the plots presented in the following secti ons, loads refer to mech anical loads applied by the hydraulic jack. Beam response is also due to loads applied by the hyd raulic jack. The total vertical mechanical load carried by the beam dur ing tests was the sum of the self-weight of the beam (measured at about 11 kips ) and the load applie d by the hydraulic jack. Tensile strains plotted in this chapter represent relief of initia l compressive strains (caused by prestressing) and are positive. Compressive strains represent addi tional increments of compression that add to the initial precompression and are negative. Detection of Joint Opening Strain Gauges Close to Joint at Midspan The detection of joint opening with strain gauges is illustrated in Figure 11-1 and Figure 11-2. Prior to opening of the join t, the change in strain is linea r with respect to applied load.

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130 After the joint opens, concrete fibers initially in contact are unable to carry any significant additional strain. Strain gauges located at the le vel of joint opening therefore show no change in strain with increasing load, and th e load vs. strain curve becomes almost vertical. The load at which strains initially stop increasing is the load that causes the joint to open at the location of the strain gauge. Strain at this load is equal in magnitude but opposite in sign, to the initial strain at the same location that was caused by prestress and self-weight. For strain gauges located on the side of the beam (see Figure 11-1), the initi al slope of the load vs. strain curve is inversely proportional to the distance of the gauge fr om the neutral axis of the gross section. Strain gauges located farther away from the cen troid of the contact area of the gross section indicate lower joint-opening loads th an strain gauges located closer in distance to the centroid. In Figure 11-1, Q1 is less than Q2 because SG1 and SG2 are closer in distance to the centroid of the contact area than SG3 and SG4. This is because the joint starts opening at the top of the section and slowly progresses downward as indicated by the direction of the moment in Figure 11-1. The point at which the load vs. st rain curve changes slope (becomes vertical) is dependent on the compressive strain at the location of the strain gauge. In Figure 11-1 it is assumed that the initial strain, at the location of SG1 and SG2 is less than the initial strain, at the location of SG3 and SG4 ( due to the location of the line of action of the post-tensioning force, i.e. below the centroid of the c ontact area of the gross cross section). Strain gauges located on top of the flange ha ve identical load vs. strain curves (see Figure 11-2). This is because strain is uniformly distribu ted across the width of the flange. The strain at which the load vs. strain curve becomes vertical, i, is the initial uniform strain in the top fibers of the flange before the app lication of mechanical loads.

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131 Though the post-joint-opening curves are shown as vertical in Figure 11-1 and Figure 11-2, this is not always the cas e. In prestressed beams, th e sudden increase in prestress associated with opening a joint may lead to a s light compression in fibers that are no longer in contact. The post-joint-opening cu rve then has a slight curvature, which diminishes as the depth of joint-opening moves farther aw ay from the location of the fibers (with increasing load). Typical load vs. strain curves on the North and South sides of joint J2, plotted with laboratory measured loads and concrete strains, are shown in Figure 11-3 and Figure 11-4, respectively. Opening of the joint at the locati on of each strain gauge was indicated by the point at which the curves initially be came vertical. Generally, strain gauges located above the centroid of the contact area of the cross section prior to the joint opening (referred to simply as the centroid of the gross cross secti on in the figures) indica ted opening of the jo int. Strain gauges located below the centroid of the gross cross sect ion registered compressive strains. This was expected since the moment at joint J2 due to the applied loads led to relief of existing compressive strains above, and the addition of compressive stra ins below the centroid of the contact area at the joint. The high decompression shown by the strain gauge located at the centroid of the gross cross section in Figure 11-3 (S3-N-S-3.6-21.3) as the depth of joint opening approached the centroid was cons istent with the high compressive strain recorded by the same gauge during prestressing (see Figure 10-5 and the measured strain profile on the North side of Segment 3 at elevation 21.3 in. in Figure 10-10). Figure 11-5 shows the variation of concrete st rain with load on top of the flanges of segments 2 and 3 close to joint J2. Strain ga uges located on the top flan ge generally detected very low strains with applied load compared with strain gauges on the sides of the segments. This was expected since low strains were record ed in the extreme top fibers of the segment

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132 flanges during prestressing (see Figure 10-8 and Figure 10-11). Of the five strain gauges on the top flange, it was possible to detect joint-openin g from two: one on the South of Segment 2 and the other on the North of Segment 3 (see Figure 11-5). The load vs. st rain curves of the other three strain gauges were almost vertical throughout th e entire loading process. Normally, the behavior of the three gauges with almost vertical load vs. strain curves would indicate that the joint opened at the top flange almost immediat ely after the beam was loaded. This, however, was not the case. As shown in Figure 11-6, some concrete at the top flange at joint J2 had broken off during transportation a nd handling of the segments. Gauges at the locations where a significant amount of concrete had broken off showed almost no change in strain with load even though the joint was not open. This was because c oncrete fibers on opposite sides of the joint at the locations were not in contact prior to loadi ng the beam. Strain gauges at other locations where this condition was less seve re registered some strain as the beam was loaded. The nonlinear behavior of measur ed strain with load in Figure 11-3 through Figure 11-5 was the result of the condition of joint J2 at the top fla nge as shown in Figure 11-6, and changes in the stiffness of the contact area at th e joint as it was slowly opened. As discussed in the beginning paragraphs of th is section, the strain at which the joint opened at the location of a gauge wa s expected to be equal to the in itial compressive strain at that location. Before beginning mech anical load tests on the beam, the supports were changed from the system shown in Figure 10-1 to that shown in Figure 10-2. The changes in strain that took place during this transition were not recorded. Hence the exact distribution of initial strain at joint J2 was not known prior to th e application of mechanical lo ads. In spite of the unknown changes in strain that took place while cha nging the beam support conditions, the measured strains at which the joint opened, though not equal in magnitude, we re still consistent with the

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133 distribution of strains due to prestress. As shown in Table 11-1, strain gauges near joint J2 on the sides of the flange, which showed higher strain s due to prestress, indicated opening of joint J2 at higher strains th an gauges located in areas of lesser prestrain. Strain gauges above the centroid of the contact area of the section and at identical locations on either side of the joint were expected to detect joint-opening at the same load. Furthermore, it was expected that gauges at higher elevations would indicate opening of th e joint at lower loads than gauges at lower elevations (see Figure 11-1). However, stra in gauges located above the centroid of the contact area showed the joint opening at higher loads on the North side (Figure 11-3) than on the South side (Figure 11-4). This was partly due to differences in the elevations of the gauges. The strain gauge designated S3 -N-S-02-27.4 on the North side of the joint showed the joint opening at a load of about 48 kips (see Figure 11-3), while the strain gauge at the same location on the South (S 3-S-S-02-27.5) showed the joint opening at a load of about 38 kips (see Figure 11-4). Furthermore, the strain ga uge located at elevation 28.6 in. on the South side of the joint (see Figure 11-4) showed joint opening at a lower load (21 kips) than two strain gauges located above it on the North side of the joint as shown in Figure 11-3 (31 kips for the gauge at elevation 33.5 in. and 41 kips fo r the gauge at elevation 30.3 in.). This was indicative of the joint opening earlier on the South side than on the North side, and was consistent with the distribution of measured strains through the depth of the beam due to prestress (see Figure 10-10). Because of the distinct change in strain that occurred when the joint opened, strain gauges were the instrument of choice in determining joint-opening loads. Measured concrete strains through the depth of the beam near joint J2 on the North and South sides are shown in Figure 11-7 and Figure 11-8, respectively. Strain data shown in Figure

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134 11-3 through Figure 11-5 were used in plot ting the strain profiles in Figure 11-7 and Figure 11-8. In Figure 11-7 and Figure 11-8, joint-opening at each elevati on within joint J2 is indicated when no further strain change with load occurs at that depth. As explai ned previously, the fact that top flange strains were nearly constant with respect to load in Figure 11-8 was not indicative of opening of joint J2, but was probably the resu lt of the condition at the joint shown in Figure 11-6. As shown in Figure 11-7 and Figure 11-8, the neutral axis of the contact area at joint J2 (point of intersection of strain profile with zero strain axis) gradually moved downward with increasing load. Furthermore, the movement of th e neutral axis was smalle r on the North side of the joint (see Figure 11-7) than on the South side (see Figure 11-8), indicati ng a rotation of the neutral axis about the centroid of the contact area. As illustrated in Figure 11-9, the downward movement of the centroid of the contact area at joint J2, as the beam wa s incrementally loaded, was due to opening of the joint. Rotation of th e neutral axis about the centroid of the contact area was attributed to the net out-of-plane horizon tal eccentricity in prestressing. Movement of the neutral axis with load is illustrated in Figure 11-10. The change in prestress as the beam was incrementally loaded is shown in Figure 11-11. Bars 1 and 2 were expected to undergo the same cha nge in force with load since they were at the same elevation. Similarly, bars 2 and 4 were expected to undergo the same change in force. However, because the opening of joint J2 was gr eater on the South side than on the North side, the change in force in the bars on the South side (P2 and P4) was greater than the change in force in the bars on the North side (P1 and P3, respectiv ely) after the joint opened. The forces in bars 1 and 2 increased with load while forces in bars 2 and 3 generally decreased with load. This was because bars 1 and 2 were located above the centr oid of the gross section and bars 3 and 4 were

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135 located below the centroid of the gross sect ion (see the position of prestress bars in Figure 11-11). At a load of about 40 kips (see Figure 11-9) the depth of joint opening caused the centroid of the contact area at join t J2 to move below the location of bars 3 and 4, leading to an increase in force with load in these bars. Detection of Joint Opening LVDTs Across Joint at Midspan Determination of joint-opening using LVDTs mounted across the joint is illustrated in Figure 11-12 and Figure 11-13. LVDTs mounted across a jo int indicate opening of the joint at the location of the LVDT when the initial slope of the load vs. displacement curve changes as a result of the reduction in stiffness of the section. Prior to the joint opening, LVDTs meas ure the displacement between the mounts (supports) of the LVDT as a re sult of strain in concrete. The initial slope of the load vs. displacement curve is inversely proporti onal to the distance between the mounts of the LVDT and the distance of the LVDT from the centroid of the contact area at the joint prior to the application of mechanical loads (see Figure 11-12). The bending moment in Figure 11-12 causes the joint to start opening at the top flange and gradually progre ss downward. Therefore, LVDTs that are farther above the centroid of the cont act area prior to the jo int opening indicate lower joint-opening loads than LVDTs that are closer to the centroid of the contact area. LVDTs at identical distances from the centroid of the c ontact area of the gross section have the same load vs. displacement curves if the joint opens uniformly across the width of the section (see Figure 11-13). After the joint opens, fibers that were initially in contact separate and are unable to carry any significant additional strain. L VDTs then measure the distance between the separated fibers or the width of joint opening. Figure 11-14 shows data from LVDTs distribut ed throughout the depth of joint J2 on the South side of the beam. In this figure, the last number in each LVDT label indicates the distance

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136 of the LVDT from the bottom of the beam. The centroid of the contact area of the gross section at joint J2 was 21.3 in. from the bottom of th e segments. As expected, LVDTs located at elevations above the centroid of the contact area of the gross section indicated lower joint-opening loads than LVDTs at lower elevatio ns. Furthermore, LVDTs located close to the bottom of the joint indicated little or no joint-ope ning, and in the case of the LVDT at the lowest elevation (J2-S-D-4.275) some compression. This was because the moment at joint J2 due to applied mechanical loads caused the relief of compressive strains above the centroid of the contact area but increased the existing compressive strains below the centroid. At the level of each LVDT the initial compressive strains had to be relieved by strain s due to the applied moment in order for the joint to open. It was therefore expected that only LVDTs located above the centroid of the contact area woul d indicate joint-opening. This was evident in data from the top three LVDTs, designated J2-S-D-33. 75, J2-S-D-30.25, and J2-S-D-25.0 in Figure 11-14, which were located above the centroid of the contact area at joint J2 prior to opening of the joint. Figure 11-15 shows data from LVDTs mounted across joint J2 on top of the flanges of segments 2 and 3. Unlike the ideal curve in Figure 11-13, the load vs. displacement curves in Figure 11-15 were essentially nonlinear from the beginning of load application. This was most likely caused by lack of contact between top fl ange concrete fibers at joint J2 (see Figure 11-6). Similar to the measured strain gauge data, the no nlinear form of the LVDT curves at higher loads was due to changes in stiffness of the contact area at joint J2 as it was opened. Opening of joint J2 at the flange top fibers was estimated from the curves in Figure 11-15 by locating the points at which the various curves initiall y deviated from one another. Ideally, if the joint opened uniformly across the width of the fla nge, all three LVDTs would have indicated opening of the joint at the same load and would have had identical

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137 load vs. displacement curves. As discussed in th e previous chapter, however, joint J2 initially opened on the South side before opening on the Nort h side. This caused displacements recorded by the LVDT on the South flange, designated J2-T S-D-9.5, to be larger than displacements recorded by the LVDT at the center of the flange (J2-T-D), and the LVDT at the North flange (J2-TN-D-9.5). LVDTs mounted across joint J2 on top of the fl anges of segments 2 and 3, and the LVDTs designated J2-S-D-33.75 and J2-S-D-30.25 in Figure 11-14 showed two distinct essentially linear regions after the joint initially opened. In the first linear region of the curves, which occurred after the joint initia lly opened at the location of each LVDT, the centroid of the concrete contact area was between the top a nd bottom post-tensioning bars. Thus, tensile stresses due to the applied moment were re sisted by the post-tensi oning bars and existing compressive stresses at the joint. In the sec ond linear region, which be gan at a load of about 40 kips, the centroid of the conc rete contact area was below th e bottom post-tensioning bars (see Figure 11-9). Tensile stresses due to the applied moment were th erefore effectively resisted by the post-tensioning bars with little contributi on from existing concrete compressive stresses, leading to a significant change in sl ope (from the first linear region). Due to nonlinearities in the load vs. displa cement curves for LVDT s mounted across joint J2, there was less confidence in determining joint-opening loads with these instruments compared to strain gauges located close to the joint. LVDT data were, however, useful in checking joint-opening loads determined from strain gauge data. Strains at Mid-Segment During tests in which data were collected from strain gauges at the middle of segments 2 and 3, loads applied to the beam did not exceed 40 kips. This was because strain data from the middle of the segments were not needed for joint-opening analysis.

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138 Strain distributions 30 in. away from the middle of Segment 3 on the North and South sides of the beam are shown in Figure 11-16 and Figure 11-17, respectively. Data obtained from gauges located at the middle of Segment 2 (see Appendix C) were nearly identical to the Segment 3 data and are therefore not shown here. Opening of the joint at the beam midspan (at joint J2) did not affect on the location of the neutral axis at the middle of the segments, whic h remained at elevation 21.3 in. However, the non-uniform opening of joint J2 across the widt h of the section at th e joint affected the distribution of strains at mid-segment. Lesser magnitude st rains were detected in the North flange than the South flange, and higher strains were detected in the North web than the South web. This was indicative of bi-axial bending as illustrated in Figure 11-18. The horizontal component of the moment at mid-segment equilibra ted the moment due to the applied load at the cantilevered end of the beam. The vertical component of the moment at mid-segment, which was the result of the net out-of-plane horizontal e ccentricity in prestressing and the changes in prestress shown in Figure 11-11, formed a self-equilibrating system with the concrete. Deflection Vertical deflection of the beam measured at a location 7.25 in from the cantilevered end, is shown in Figure 11-19. The initial nonlinear part of the deflection curve was attributed to a slight deflection at the East end-support of the be am as it was initially loaded. Movement of the neutral axis at the midspan of the beam, as the jo int opened, was expected to affect the vertical deflection of the beam. This is indicated by the deviation of the straight line drawn through the deflection curve from the nonlinear parts of the curve. The initial deviation of the straight line from the deflection curve occurred at a load of a bout 9 kips, the load at wh ich the centroid of the contact area at joint J2 initially began to move downward. After this point the deflection curve was almost linear with load until the depth of joint opening was sufficient enough to cause the

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139 centroid of the contact area to move below the bottom prestress bars (bars 3 and 4 in Figure 11-11) at a load of about 41 kips. Though the sec tion stiffness at joint J2 continuously changed in the linear part of the deflecti on curve, the change in stiffness was local to the joint and did not affect the overall stiffness of the beam, and therefore the cantilever tip deflection. Summary Results from mechanical load tests on the labora tory beam indicated elastic behavior of the beam. The tests were also repeatable (i.e. ne glecting small changes of prestress that occurred with time, the response of the beam under the ac tion of mechanical load s was repeatable across tests). The distinct change in strain with load at incipient opening of th e joint at midspan (joint J2) resulted in the use of strain gauges near the joint as instru ments for detecting joint-opening loads. The contact area at joint J2 could al so be estimated using joint-opening loads and elevations of strain gauges near the joint. The relative magnitude of joint-opening loads at identical elevations on the North side and South side of joint J2 together with the shape of contact areas at the joint show ed that the beam underwent biax ial bending when mechanically loaded. Measured strain distribut ions through the height of contact areas at joint J2 showed that strain was a linear f unction of curvature. These experimental observations made it possi ble for normal stresses at incipient opening of joint J2 to be determined without explicitly using material properties (e.g. elastic modulus and coefficient of thermal expansion) of segments 2 and 3.

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140 Table 11-1. Comparison of measur ed strains due to prestress a nd measured strains when joint opens Gauge Location Gauge Designation Strains due to Prestress ( ) Strains measured at joint opening condition ( ) S3-N-S-02-33.5 -304 210 North Flange S3-N-S-02-30.3 -209 151 S3-N-S-02-35.3 -185 103 S3-N-S-02-32.0 -200 115 South Flange S3-N-S-02-28.6 -110 60

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141 Open joint Joint J2 (closed) SG1 SG3 Segment 2 Segment 3 StrainApplied LoadQ2 Q = Joint-opening Load SG1,SG2 ELEVATION VIEW SG3, SG4 Q1 SG2 SG4 Strain gauge before joint opens after joint opens Centroid of gross cross section M M Figure 11-1. Expected behavior of strain gauges on side of beam near joint Open joint Joint J2 (closed) SG1 SG3 SG5 Segment 2 Segment 3 StrainApplied LoadQ Q = Joint-opening Load PLAN VIEW SG2 SG4 SG6 SG1, SG2, SG3, SG4, SG5, SG6i Strain gauge after joint opens before joint opens Figure 11-2. Expected behavior of strain gauges on top of flange near joint

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142 Strain (microstrain)Load (kips) -700 -600 -500 -400 -300 -200 -100 0 100 200 300400 0 5 10 15 20 25 30 35 40 45 50 55 60 S3-N-S-02-33.5 S3-N-S-02-30.3 S3-N-S-02-27.4 S3-N-S-3.6-21.3 S3-N-S-02-14.6 S3-N-S-02-7.8 S3-N-S-02-1.1 Depth of open joint quickly approaching centroid Strain gauge at centroid of gross cross section Joint opening at location of strain gauge Figure 11-3. Load vs. Strain near joint at midspan (North side) Strain (microstrain)Load (kips) -700 -600 -500 -400 -300 -200 -100 0 100 200 300400 0 5 10 15 20 25 30 35 40 45 50 55 60 S3-S-S-02-35.3 S3-S-S-02-32 S3-S-S-02-28.6 S3-S-S-02-27.5 S3-S-S-3.6-21.3 S3-S-S-02-14.6 S3-S-S-02-7.9 S3-S-S-02-0.9 Strain gauge at centroid of gross cross section Joint opening at location of strain gauge Figure 11-4. Load vs. Strain near joint at midspan (South side)

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143 Strain (microstrain)Load (kips) -700 -600 -500 -400 -300 -200 -100 0 100 200 300400 0 5 10 15 20 25 30 35 40 45 50 55 60 S2-TN-S-5.5-7.75 S2-TS-S-5.5-8.25 S3-TN-S-5.5-7.25 S3-T-S-5.5-0.75 S3-TS-S-5.5-7.25 S3-TS-S-5.5-7.25 S3-T-S-5.5-0.75 S3-TN-S-5.5-7.25 SOUTH NORTH BEAM CENTERLINE S2-TS-S-5.5-8.25 S2-TN-S-5.5-7.75 12 in. 12 in. Joint J2 Figure 11-5. Load vs. Strain near joint at midspan (Top flange) Figure 11-6. Condition of joint J2 on top of flange

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144 Strain (microstrain)Elevation (in.) -700 -600 -500 -400 -300 -200 -100 0 100 200 300400 0 5 10 15 20 25 30 35 40 0 kips 10 kips 20 kips 25 kips 30 kips 35 kips 40 kips 45 kips 50 kips Flange Web Figure 11-7. Measured strain distributions near joint at midspan (North side) Strain (microstrain)Elevation (in.) -700 -600 -500 -400 -300 -200 -100 0 100 200300 0 5 10 15 20 25 30 35 40 0 kips 10 kips 20 kips 25 kips 30 kips 35 kips 40 kips 45 kips 50 kips Flange Web Figure 11-8. Measured strain distributions near join t at midspan (South side)

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145 Centroid of contact area Centroid of contact area Centroid of contact aea Centroid of contact area Prestress onlyPrestress plus 20 kip tip load At 30 kips .At 40 kips South North South North South North South North P1 P2 P3 P4 P1 P2 P3 P4 P1 P2 P3 P4 P1 P2 P3 P4 Post-tensioning bar Figure 11-9. Estimated progression of joint-openi ng with load (based on strain gauge data) 8 in. 28 in. 21.3 in. 24 in. North South C.G. 10 in. N.A. before joint opens N.A. after joint first opens N.A. as load is further increased Figure 11-10. Movement of neut ral axis (N.A.) with load

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146 Applied Load (kips)Percentage Change in Pretress Force (%) 0 5 10 15 20 25 30 35 40 45 5055 -1 -0.5 0 0.5 1 1.5 2 2.5 3 3.5 P1 P2 P3 P4 Initial Forces: P1 = 95.0 kips P2 = 87.8 kips P3 = 91.4 kips P4 = 89.9 kips Depth of joint opening increases on South side Joint opens on North flange .C.G. P1 P2 P4 P3 NorthSouth Figure 11-11. Changes in prestress force with load Open joint Joint J2 (closed) LVDT1 LVDT2 Segment 2 Segment 3 DisplacementApplied LoadQ1 Q = Joint-opening Load LVDT1 ELEVATION VIEW LVDT2 Q2 M M Centroid of gross cross section Figure 11-12. Expected behavior of LVDTs across joint on side of beam

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147 Open joint Joint J2 (closed) LVDT1 LVDT2 LVDT3 Segment 2 Segment 3 DisplacementApplied LoadQ Q = Joint-opening Load LVDT1, LVDT2, LVDT3 PLAN VIEW Figure 11-13. Expected behavior of LVDTs across joint on top of flange Relative Longitudinal Displacement (in.)Load (kips) -0.005 0 0.005 0.01 0.015 0.02 0.025 0.03 0.0350.04 0 5 10 15 20 25 30 35 40 45 50 55 60 J2-S-D-33.75 J2-S-D-30.25 J2-S-D-25.0 J2-S-D-18.25 J2-S-D-11.375 J2-S-D-4.375 Joint opening Joint opening Joint opening Figure 11-14. Load vs. Joint opening (Side LVDTs)

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148 Relative Longitudinal Displacement (in.)Load (kips) -0.005 0 0.005 0.01 0.015 0.02 0.025 0.03 0.0350.04 0 5 10 15 20 25 30 35 40 45 50 55 60 J2-TN-D-9.5 J2-T-D J2-TS-D-9.5 Joint opening Joint opening Joint opening Figure 11-15. Load vs. Joint opening (Top flange LVDTs) Strain (microstrain)Elevation (in.) -400 -300 -200 -100 0 100 200 300 400 500 600 700800 0 5 10 15 20 25 30 35 40 0 kips 5 kips 10 kips 15 kips 20 kips 25 kips 30 kips 35 kips Flange Web Figure 11-16. Measured strain di stributions at middle of Segment 3 (30 in. from joint J2) on North side of beam

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149 Strain (microstrain)Elevation (in.) -400 -300 -200 -100 0 100 200 300 400 500 600 700800 0 5 10 15 20 25 30 35 40 0 kips 5 kips 10 kips 15 kips 20 kips 25 kips 30 kips 35 kips Flange Web Figure 11-17. Measured strain di stributions at middle of Segment 3 (30 in. from joint J2) on South side of beam T C z R = Q Q (Applied load) MQ MvC.G.ELEVATION CROSS SECTION Segment 3 Segment 4 Centroid of prestress bars C = Resultant concrete (compressive) force T = Resultant prestress (tensile) force z = moment arm MQ = Q x x Mh = T z = C z Mh = MQ Figure 11-18. Forces and mome nts acting at mid-segment

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150 Deflection (in.)Load (kips) 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 0.550.6 0 5 10 15 20 25 30 35 40 45 50 55 60 Joint initially opens on South flange Movement of centroid of contact area at joint J2 below bottom prestress bars Figure 11-19. Measured vertical deflec tion near cantilevered end of beam

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151 CHAPTER 12 RESULTS UNIFORM TEMPERATURE CHANGE A uniform temperature change was imposed on segments 2 and 3 of the laboratory beam (Figure 12-1) to investigate the be havior in the absence of self -equilibrating thermally induced stresses. The goal was to determine the maximu m change in prestress that would result from application of thermal loads on the concrete segments while the DYWIDAG post-tensioning bars remained essentially at laborator y temperature. Though the beam wa s statically determinate with respect to the supports, expansion of the concrete segments rela tive to the post-tensioning bars was expected to lead to an increase in prestre ss and the development of net compressive stresses in the concrete. Conversely, contraction (due to cooling) of the concrete segments relative to the post-tensioning bars was expected to lead to a reduction in pres tress and the development of net tensile stresses (i.e. a reduction in compressive stresses) in the conc rete. Understanding how such changes in prestress affected concrete stre sses was important in estimating the effects, if any, of thermally induced changes in prestress on self-equilibrating thermal stresses when the AASHTO nonlinear thermal gradients were later imposed on the beam. The test sequence started with the circulation of tap wate r through segments 2 and 3 for about 24 hours to establish a uniform reference temperature of about 84 oF (low reference temperature). Segments 2 and 3 were then heated to an average temperature of about +41 oF above the low reference temperature us ing the piping configuration shown in Figure 8-6. Forces in the post-tensioning bars and concrete strains at joint J2 were continuou sly recorded during this period, which will subsequently be referred to as the heating phase. Following the heating phase, the temperature of the conc rete segments, which was about 125 oF, was taken as the new reference temperature (high reference). With the data acquisition system still running, the segments were cooled from the high reference te mperature back to the initial (low) reference

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152 temperature using the pipi ng configuration shown in Figure 8-5. This phase of the test will subsequently be referred to as the cooling pha se. Laboratory imposed temperature changes in the heating and cooling phases of the test are shown together with target temperature changes for Segment 2 and Segment 3 in Figure 12-2 and Figure 12-3, respectively. Measured concrete temperatures in Segment 2 and Segment 3 are shown in Figure 12-4 and Figure 12-5, respectively. Temperature changes in the Figure 12-2 and Figure 12-3 are with respect to the low reference temperature (about 84 oF) for the heating phase and th e high reference temperature (about 125 oF) for the cooling phase. The average (uniform) temperature increase during the heating phase of the test was about 40 oF and the average decrease in temperature during the cooling phase was about 38 oF. The difference between the average temperature changes in the heating and cooling phases was due to a slight in crease in tap water temperature during the three day period over which the test was conducted. Th is slight increase cause d segments 2 and 3 to be cooled to a temperature that was higher than the initial temperature from which they were heated. Significant deviation from the target profile occurred at Section A (see Figure 12-1) and Section F (see Figure 12-3). These deviations were due to the fact that sections A and F were adjacent to the ambient segments (segments 1 and 4). These segments (1 and 4) acted as heat sinks because they remained essentially at la boratory temperature during application of the thermal profiles on the heated segments (Segme nts 2 and 3). Additiona lly, the bottom surfaces of segments 2 and 3 could not be adequately heat ed at sections C and D because these locations were close to the mid-support point and could not be adequately insulated with Styrofoam. This issue was resolved in later tests by using flexib le fiberglass to insulate the mid-support area of the beam. Temperature profiles were non uniform not only through the height of the segments

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153 but also across the width. The distribution of temperature cha nge through the height and across the width of the beam at Section C and Sec tion D during the heati ng phase are shown in Figure 12-6 and Figure 12-7, respectively. The color ba r in each figure represents change in temperature (in oF) relative to the low reference temp erature. These figures show that temperatures along the perimeter of each section we re generally slightly lower than temperatures in the interior. This was more pronounced in the web, where the ra tio of concrete area to copper tubes was only about a third of th at in the flange. There were two main reasons for this. First, the segment heating system was designed to e fficiently impose the AASHTO nonlinear gradients while keeping the number of copper tubes embedded in concrete to a minimum. Thus, there was a higher concentration of copper tu bes in the flange (w here the maximum temperature changes in the gradients occur) than in the web (where there was almost no ch ange in temperature). Second, heating the two concrete segments, by approximately 40 oF, uniformly was the most thermally demanding situation imposed on the heating system due to the total volume of concrete and temperature increase involved. Average measured temperature changes in the heated segments were used together with the average measured coefficients of thermal expansion (CTE) in Table 12-1, elastic moduli (MOE) in Table 12-2, and DYWIDAG bar properties to predict anticipated changes in prestress. Concrete elastic moduli in Table 12-2 were obtained by linearl y interpolating between MOEs which were derived from cylinde r test data between test ages of 28 and 360 days. Moments caused by the vertical and horizon tal eccentricities of th e prestress bars and slight curvatures caused by non-uniformity of the imposed temperat ure profiles were neglected in the prediction of prestress change. It was also assumed that fo r the duration of the test the prestress bars and ambient concrete segments did not undergo any ch anges in temperature. Predicted and measured

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154 changes in prestress during the heating and c ooling phases of the test are compared in Table 12-3 and Table 12-4, respectively. Measured total changes in prestress were within 11% of corresponding calculated values. Calculated changes were of hi gher magnitude than measured changes mainly because the ambient segments and prestress bars were subjected to a slight temperature increase due to an increase in laborat ory temperature during the course of the test. It was expected that the steel prestress bars w ould respond to such non-stress-inducing temperature changes more rapidly than the ambient segments because of the relatively high thermal conductivity of steel and the sm all volume of steel compared with concrete (about 1%). Measured total changes in prestress even under this worst case thermal loading condition were less than 6% of the initial total prestress. Measured concrete strains near joint J2 fr om strain gauges located on segments 2 and 3 during the heating and cooling pha ses of the test are shown in Figure 12-8 and Figure 12-9, respectively. Expected (calculated) strain di stributions are also shown in the figures for comparison. Calculated strains were determ ined using measured prestress forces and eccentricities, concrete s ection properties, and the elastic moduli shown in Table 12-2. Concrete strains measured during the heating phase were essentially a mirror image of concrete strains measured during the cooling phase. This showed that strains induced in the heated segments when the beam was heated were relieved when the beam was cooled; evidence that the beam remained elastic under the action of the thermal loads. Because th e strain gauges installed on the concrete segments were self-temperature-compens ating (STC) gauges, it was expected that the measured strains (assuming uniformity of temper ature distributions) woul d arise solely from changes in prestress, and therefore would be compressive during heating and tensile during cooling. It is, however, evident from Figure 12-8 and Figure 12-9 that the opposite was the case.

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155 Measured concrete strains during the heating phase were instead tensile. A similar reversal was observed during the cooling phase. Furthermore, the measured strains were non-uniform through the height of the segments. The observed reve rsals were attributed to the fact that the temperature profiles imposed on the segments were somewhat non-uniform over the cross sectional area of the segments (recall Figure 12-6 and Figure 12-7). Thus, while the total change in prestress was a result of the average (uni form) temperature change imposed on the heated segments, strains measured on the surfaces of the sections were affected by non-uniform temperature changes. Concrete strains measur ed during the heating phase are compared with calculated strains which take in to account both changes in pres tress and the non-uniformity in temperature distributions in Figure 12-10 and Figure 12-11. The calcula ted strains in were determined by superimposing strains caused by th e increase in prestress and stress-inducing strains caused by the non-uniform te mperature distributions shown in Figure 12-6 and Figure 12-7, respectively. Stress-inducing strains cause d by the two-dimensional thermal gradients in the figures were calculated using Eqns. 3-8 thro ugh 3-12 (see Chapter 3) Though the calculated strain magnitudes shown in Figure 12-10 and Figure 12-11 do not exactly match the measured strains they are consistent in sign (i.e. positive, tensile). A possible explanation for the difference in magnitude of meas ured and calculated strains is that precise measurements of temperature at the surface of th e concrete sections, where the st rains were measured, were not available. Instead surface temperatures were ob tained by extrapolating data from thermocouples nearest to, but not exactly at, the surface of th e concrete. Hence the extrapolated surface temperatures may have been less th an the actual surface temperatures.

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156 Table 12-1. Average measured coefficients of thermal expansion (CTE) of concrete segments Segment Average CTE 1 N/A 2 7.7E-6/oF 3 8.0E-6/oF 4 N/A Table 12-2. Calculated m odulus of elasticity (MOE) of concrete segments Segment Age (days) MOE (ksi) 1 268 5231 2 219 4696 3 206 4695 4 257 5101 Table 12-3. Changes in prestress du e to heating of Segments 2 and 3 Bar Designation Measured Initial Prestress (kips) Increase in Measured Prestress (kips) Percentage Increase in Measured Prestress (%) Calculated Increase in Prestress (kips) Difference b/n Measured and Calculated Increase in Prestress (%) P1 94.6 5.6 5.9 5.9 -5.1 P2 87.7 5.2 5.9 5.9 -11.9 P3 90.8 4.5 5.0 5.9 -23.7 P4 89.6 5.8 6.5 5.9 -1.7 Total 362.7 21.1 5.8 23.6 -10.6 Table 12-4. Changes in prestress du e to cooling of Segments 2 and 3 Bar Designation Measured Initial Prestress (kips) Decrease in Measured Prestress (kips) Percentage Decrease in Measured Prestress (%) Calculated Decrease in Prestress (kips) Difference b/n Measured and Calculated Increase in Prestress (%) P1 100.2 -5.5 -5.5 -5.6 -1.8 P2 93.0 -5.2 -5.6 -5.6 -7.1 P3 95.3 -4.1 -4.3 -5.6 -26.8 P4 95.4 -5.3 -5.6 -5.6 -5.4 Total 384.0 -20.0 -5.2 -22.4 -10.7

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157 1.7 ft 2.7 ft 5 ft SEGMENT 1SEGMENT 2 SEGMENT 3 SEGMENT 4 Applied Load (Q) 10.5 ft East West Lab. floor Mid-support End-support Location of interest (Joint J2) 3 ft (AMBIENT) (HEATED) (AMBIENT) (HEATED) A B C D EF 5 ft 5 ft 5 ft P P P: Post-tensioning force Figure 12-1. Laboratory beam Temperature Difference Relative to Reference Condition for each Phase (deg. F)Elevation (in.) -50 -40 -30 -20 -10 0 10 20 30 40 50 0 5 10 15 20 25 30 35 40 Section A (Heating) Section B (Heating) Section C (Heating) Section A (Cooling) Section B (Cooling) Section C (Cooling) Target (Heating) Target (Cooling) Flange Web Figure 12-2. Laboratory imposed te mperature changes on Segment 2

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158 Temperature Difference Relative to Reference Condition for each Phase (deg. F)Elevation (in.) -50 -40 -30 -20 -10 0 10 20 30 40 50 0 5 10 15 20 25 30 35 40 Section D (Heating) Section E (Heating) Section F (Heating) Section D (Cooling) Section E (Cooling) Section F (Cooling) Target (Heating) Target (Cooling) Flange Web Figure 12-3. Laboratory imposed te mperature changes on Segment 3 Temperature (deg. F)Elevation (in.) 80 85 90 95 100 105 110 115 120 125130 0 5 10 15 20 25 30 35 40 Section A (Heating) Section B (Heating) Section C (Heating) Section A (Cooling) Section B (Cooling) Section C (Cooling) Target (Heating) Target (Cooling) Flange Web Figure 12-4. Measured concrete temperatures in Segment 2

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159 Temperature (deg. F)Elevation (in.) 80 85 90 95 100 105 110 115 120 125130 0 5 10 15 20 25 30 35 40 Section D (Heating) Section E (Heating) Section F (Heating) Section D (Cooling) Section E (Cooling) Section F (Cooling) Target (Heating) Target (Cooling) Flange Web Figure 12-5. Measured concrete temperatures in Segment 3 Figure 12-6. Measured temperature ch anges at Section C (Heating phase)

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160 Figure 12-7. Measured temperature ch anges at Section D (Heating phase) Strain (microstrain)Elevation (in.) -400 -350 -300 -250 -200 -150 -100 -50 0 50 100 150 200 0 5 10 15 20 25 30 35 40 Seg. 2, North (Heating) Seg. 2, North (Cooling) Seg. 2, South (Heating) Seg. 2, South (Cooling) Average Calculated (Heating) Average Calculated (Cooling) Flange Web Figure 12-8. Measured strain di stribution on Segment 2 (Section C) due to temperature changes

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161 Strain (microstrain)Elevation (in.) -400 -350 -300 -250 -200 -150 -100 -50 0 50 100 150 200 0 5 10 15 20 25 30 35 40 Seg. 3, North (Heating) Seg. 3, North (Cooling) Seg. 3, South (Heating) Seg. 3, South (Cooling) Average Calculated (Heating) Average Calculated (Cooling) Flange Web Figure 12-9. Measured strain di stribution on Segment 3 (Section D) due to temperature changes Strain (microstrain)Elevation (in.) -400 -350 -300 -250 -200 -150 -100 -50 0 50 100 150 200 0 5 10 15 20 25 30 35 40 Measured (North) Measured (South) Calculated (North) Calculated (South) Flange Web Figure 12-10. Comparison of measur ed and calculated strains at Section C due to moderately nonuniform temperature distribut ion (Segment 2, Heating)

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162 Strain (microstrain)Elevation (in.) -400 -350 -300 -250 -200 -150 -100 -50 0 50 100 150 200 0 5 10 15 20 25 30 35 40 Measured (North) Measured (South) Calculated (North) Calculated (South) Flange Web Figure 12-11. Comparison of measur ed and calculated strains at Section D due to moderately nonuniform temperature distribut ion (Segment 3, Heating)

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163 CHAPTER 13 RESULTS AASHTO POSITIVE THERMAL GRADIENT Results from the application of mechanical loading in combination with the AASHTO positive thermal gradient are presented and discussed in this chapter. The objective of the mechanical-thermal load tests was to experi mentally quantify the self-equilibrating thermal stresses caused by the AASHTO nonlinear positive thermal gradient in the top 4 in. of the combined flanges of segments 2 and 3. Tw o independent methods were used to quantify stresses. The first was to convert measured strains using the elastic modulus, which was determined from tests on cylinders made from the same concrete that was used to construct the beam. Stresses determined using this method will be referred to as elas tic modulus derived stresses (E stresses). This is the method most often used to determine stresses, but may be subject to variation from local strain contributions in the conc rete surrounding the strain gauge, size effect between cylinder and specimen, or creep and shrinkage. The second method was a more direct measure of stress using the known st ress state at incipient joint opening. Stresses determined in this manner will be referred to as joint opening derived stresses (J stresses). In both methods, concrete behavior wa s assumed to be linear elastic. Figure 13-1 illustrates the test sequence that was used. Before mechanical or thermal loads were applied, the forces acting on the beam consisted of prestr ess and self-weight. The test sequence started with partial openi ng and closing of the joint at mi dspan (joint J2) with the beam at a constant referen ce temperature (about 80 oF). As indicated in the figure, strain data from this step were used to establish a reference stre ss state at joint J2. The AASHTO positive thermal gradient was then imposed on segments 2 and 3. After achieving and maintaining the steady state thermal gradient on the heated segments fo r 30 to 45 minutes, joint J2 was again partially opened and closed. Strains at th is stage were used to determin e the thermal stress state. The

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164 heated segments were then cooled to the original reference temper ature at the start of the test, after which joint J2 was again partially opene d and closed, completing the load cycle. Joint-opening loads and contact areas at joint J2, as the joint was gradually opened, which were determined from data collected from step s 1 and 3 of the load sequence, were used to calculate self-equilibrating stresses caused by th e nonlinear gradient (J stresses). Note that neither the elastic moduli nor the coefficients of thermal expansion of segments 2 and 3 were used in the calculation of the J stresses. Elastic modulus derived thermal stresses calculat ed from measured thermal strains close to joint J2 (E stresses) and joint opening derived thermal stresses (J stre sses) are presented and discussed in the following sections. Elastic Modulus Derived Stresses (E stresses) The nonlinear positive thermal gradient imposed on the heated segments of the laboratory beam (see Figure 13-2) in Step 2 of the load sequence is shown in Figure 13-3. For comparison, Figure 13-3 also shows the AASHTO design positiv e gradient. Though it did not exactly match the AASHTO gradient, the shape of the laboratory gradient was more representative of typical field measured gradients (see Figure 13-4). Measured temperatures in the heated segments after the positive thermal gradient was imposed are shown in Figure 13-5. Temperature data for the laboratory-imposed th ermal gradient profile was available up to an elevation of 35.5 in. (0.5 in. below the top su rface of the flange): the elevation of the topmost thermocouples embedded in the heated segments. Thus the concrete temperature at the top surface of the flanges (at an elev ation of 36 in.) was not measured. Because the segments were heated from the inside, rather than externally from solar radiation, it is likely that the top flange surface temperature was equal to or even slightly less than the measured temperature at 35.5 in. For the purpose of calculating theoretical stresse s and strains caused by the laboratory gradient,

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165 the magnitude of the thermal gradient at the top surface of the flange was obtained by extrapolating from measured thermal gradient magnitudes at elevations 32 in. and 35.5 in. Figure 13-6 shows an ideal repr esentation of the components of strains induced in the laboratory beam by the AASHTO design gradient. These strains were calculated according to the procedure outlined in the AASHTO (1989a) guid e specifications and the coefficients of thermal expansion given in Table 12-1 (see Chapter 12) using the equation: SE Tz T ) ( (13-1) where the unrestrained thermal strain profile (T(z)) represents the strains that the section would undergo if the se ction were layered and the la yers were free to deform independently. The total strains (T) are generated when compatib ility between the layers is enforced. Assuming that plane sections remain plane under the action of flexural deformations, this strain distribution is linear. The total strain (T) includes components caused by axial and flexural restraint, which were not present in th e laboratory set-up. The self-equilibrating strains (SE), which are the only strains measurable with temperature compensating strain gauges (see Chapter 3 for a complete discussion), make up the final component of the total strains. The change in strain between the beginning and end of Step 2 at join t J2 are plotted in Figure 13-7 through Figure 13-9. Figure 13-7 and Figure 13-8 show the strain differences along the height of segments 2 and 3, respectively. Figure 13-9 shows a plan view of the strain differences on the top flange near th e same joint. Also shown in the figures are two sets of strain changes predicted using the AASHTO design pro cedure: one using the AASHTO design thermal gradient, and the other using the laboratory-imposed thermal gradient. Because the strain gauges were self-temperature compensating (STC) gauges, and because there was no axial or flexural restraint on the beam, the measured strains consisted only of the self-equilibrati ng component of

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166 the total strains. The average laboratory-imposed thermal gradient profile (average of profiles at Section A through Section F (see Figure 13-3)) was used in calcula ting the laboratory gradient strains in Figure 13-7 through Figure 13-9. No marked difference is apparent between measured and predicted strains below approximately 20 in. elevation. Compressive strain s were present in the bottom of the section up to an elevation of approximately 10 in. Tensile strains arose in the se ction mid-height from about 10 in. to 32 in. elevation. A maximum pr edicted tensile strain (due to the laboratory gradient) of about 52 was predicted at elevation 28 in., whereas a maximum measured tensile strain of about 65 occurred at elevation of 27.5 in. Th e maximum predicted tensile strain due to the AASHTO design gradient, of magnitude about 53 occurred at an el evation of 20 in. The difference between locations of maximum pr edicted tensile strains due to the imposed laboratory gradient and the AASHT O design gradient was due to th e difference in the shape of the laboratory and AASHTO design thermal gradie nts. In each case maximum tensile strain occurred at the location where th e change in slope (in units of oF/in.) of the thermal gradient profile was algebraically at a maximum. This occurred between elevations of 27.5 in. and 28.5 in. for the laboratory gradient and at an elevation of 20 in. for the AASHTO design gradient. Compressive strains also occurred above the mid-thickness of the flange with a gradient steeper than that of the remainder of the profile. Some additional differences between the measur ed and predicted strains are also notable. Measured compressive strains were significantly sm aller in magnitude than predicted at the top of the section in both segments (see Figure 13-9). This was also th e case during prestressing (see Chapter 10) and mechanical load tests (see Chapte r 11). One explanation for the lower measured compressive strains at the top of the section is the shape of the thermal gradient in the top 4 in. of

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167 the flange. The placement of copper tubes in th e flange allowed for a linear gradient between elevations of 32 in. and 35.5 in. The shape and ma gnitude of the thermal gradient in the top 0.5 in. of the flange was, however, not known. To predict top fiber strains, the magnitude of the thermal gradient in the top flange was obtained by extrapolating from the linear thermal gradient between elevations 32 in. and 35.5 in. Another possibility is that diffe rential shrinkage on top of the fl ange at joint J2 contributed to the lower measured strains. Between el evations of 32 in. and 35.5 in., the measured compressive strains more or less followed a linea r distribution as did the predicted strains. The measured strains were, however, generally larger than predicted strains between elevations 32 in. and 34 in. and smaller than predicted strains abov e 34 in. This was attributed to variations between the measured thermal gradients at sect ions A through F, and the average of these gradients (see Figure 13-10), which was used to pred ict strains per the AASHTO design procedure. The uniform and linear sub-components of th e overall nonlinear thermal gradient were expected to lead to additional stresses in the concrete as segm ents 2 and 3 were heated during Step 2. Expansion of the segments relative to the prestressing caused a net increase in prestressing force. However, the measured peak increase was only 0.4% of the initial prestress and was therefore considered negligible. Elastic modulus derived stresses (E stresses) were the self-equilibrating thermal stresses caused by the positive thermal gradient, and we re determined by multiplying the measured strains in Figure 13-7 and Figure 13-8 by the elastic moduli of Segment 2 (4760 ksi) and Segment 3 (4760 ksi), respectively. The elastic moduli were calcu lated by linearly interpolating

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168 cylinder modulus of elastic ity data between test ages of 28 and 360 days. At the time of the test, the ages of segments 2 and 3 were 232 and 219 days, respectively. Figure 13-11 and Figure 13-12 show E stress distributions near joint J2 on Segment 2 and Segment 3, respectively. For comparison, self-e quilibrating thermal stresses were also calculated using the AASHTO recommended procedure disc ussed in Chapter 3, the laboratory thermal gradient, and the AASHTO design gradient. CTEs from Table 12-1 and the segment MOEs noted above were used in these calculations. Table 13-1 compares E stresses computed at the top of the flanges of segments 2 and 3 with similar stresses obtained by extrapolati ng from the linear E stress distributions between elevations 32 in. and 35.5 in. (see Figure 13-11 and Figure 13-12) on the sides of the segment flanges. E stresses in the extreme top flange fibers were significantly lower than stresses extrapolated to the same lo cation. This condition follows from the relatively smaller stress-inducing thermal strains that were measur ed at the top surfaces of the flanges (see Figure 13-9). As discussed previously, the smaller strains were attributed to differential shrinkage at joint J2 and to a lower thermal gradient magnitude than was targeted for the top of the flanges of the segments. At an elevation of 32 in., E stresses in segments 2 and 3 (see Figure 13-11 and Figure 13-12) were compressive whereas predicted st resses were tensile. This was attributed to the difference in magnitude of the laboratory th ermal gradients at sections A through F (from the average thermal gradient used in predicting stre sses) at that elevation; the location of the maximum slope change in the thermal gradients (see Figure 13-13). E stresses and predicted stresses caused by th e laboratory-imposed thermal gradient in the top 4 in. of the flanges of segments 2 and 3 are compared in Table 13-2. Predicted stresses in the extreme top flange fibers (where the maximum co mpressive stresses were expected to occur had

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169 the gradient been linear in the top 4 in. of the flanges) are not shown in the table because the shape and magnitude of the thermal gradient at that location were not measured. E stresses 0.5 in. below the top flange (maximum E stresse s) were approximately 3% and 8% less than corresponding predicted stresses in Segment 2 and Segment 3, respectively. Taking into consideration the possible effects of differential shrinkage at joint J2, these differences were considered to be within the limits of experimental error. Joint Opening Derived Stresses (J Stresses) The known stress state at incipient joint ope ning was used to determine stresses caused by the laboratory positive thermal gradient without c onverting measured strains to stresses using the elastic moduli of the concrete segments. Th e magnitude of stresse s caused by the thermal gradient in the top 4 in. of segments 2 and 3 at joint J2 were quantified using data collected from steps 1 and 3 of the lo ad sequence shown in Figure 13-1. This was accomplished by loading the specimen until joint J2 began to open. At the condition of joint opening, it is known that the normal concrete stress near the joint face is zero ( due to lack of contact). Assuming linear elastic behavior for subsequent short-term loads (thermal or mechanical), it was possible to extrapolate concrete stresses from the known (z ero) stress state. Section pr operties of the contact area at joint J2, after joint opening, were used to calculate these stresses (J stresses). Figure 13-14 and Figure 13-15 illustrate the J st ress calculation procedure using component stress blocks. Stresses at joint J2 prio r to Step 1 of the load sequence consisted of stresses caused by prestress (P) and the self-weight (SW) of the beam. In Step 1, joint J2 was opened and closed at the referen ce temperature of the beam. The state of stress in the contact area at the joint caused by the joint-opening load, QR, will be referred to as the reference stress state (see Figure 13-14). In Step 2 the positive thermal gr adient was applied. Stresses at joint J2 consisted of stresses caused by prestress (P), self-weight (SW), and the nonlinear positive

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170 thermal gradient (PG). In Step 3 of the load sequence, joint J2 was again opened and closed. The state of stress in the contact area at the joint caused by the joint-opening load, QT, will be referred to as the thermal stress state (see Figure 13-15). At incipien t joint opening, flexural stresses caused by QR and QT in the extreme top flange fibers were equal, but opposite, to the existing normal stresses caused by (P + SW) and (P + SW + PG), respectively, at the same location. This condition was us ed to quantify self-equilibratin g thermal stresses caused by the nonlinear positive thermal gradient. Though the con cept of creating a zero stress condition at joint J2 is illustrated for the extreme top flange fi bers, it is generally applicable to any shape of contact area. A general discussion of joint-opening and its uses in quantifying self-equilibrating thermal stresses follows. Figure 13-16 shows uniform opening of joint J2 to a known depth h below the extreme top flange fibers. Because the joint opens uni formly across the width of the section, the boundary (referred to as the cont act boundary in the figure) between open and closed parts of the joint is perpendicular to the sides of the segments The joint opens in this manner when the line of action of the joint-opening lo ad passes through the axis of sy mmetry of the contact area, and normal stresses existing prior to opening the joint are a function of depth only (i.e. uniformly distributed across the width of the section at all depths). If th ese conditions hold true for load cases without the thermal gradient (P + SW) and with the thermal gradient (P + SW + PG), then the contact area at the reference and th ermal stress states is the same (Figure 13-16 (B)). If the distribution of existing normal st resses at the joint caused by (P + SW) and/or (P + SW + PG) varies across the depth and widt h, the depth of joint opening w ould not be uniform across the width of the segments, as was found to be the case for the laboratory beam. As shown in Figure

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171 13-17, the contact areas at the re ference and thermal stress states are in general not the same under these conditions. The zero stress condition created by superi mposing stresses caused by the joint-opening loads QR and QT (see Figure 13-14 and Figure 13-15) on existing normal stresses along corresponding contact boundaries is shown mathematically in the following equations: R z y z y f z y f z y fR SW P ) ( 0 ) ( ) ( ) ( (13-2) T z y z y f z y f z y f z y fT J SW P ) ( 0 ) ( ) ( ) ( ) ( (13-3) Then, T R z y z y f z y f z y fT R J ) ( ), ( ) ( ) ( (13-4) where fP is the concrete stress in the cont act area due to prestressing force, fS is the stress caused by self-weight, fJ is the J stress (self-equilibrati ng concrete stress caused by nonlinear positive thermal gradient), fR is the reference stress state, fT is the thermal stress state, R is the contact boundary at the reference stress state, T is the contact boundary at the thermal stress state, and y and z are vertical and horizontal coordina tes of points on contact boundaries, respectively. These equations are valid only along the c ontact boundary corresponding to each stress state. For example, Equation 13-2 and E quation 13-3 are applicab le along line AB in Figure 13-16. In Figure 13-17, however, Equation 13-2 is applicable along line AB while Equation 13-3 is applicable along line AC. Equation 13-4, whic h is obtained by taking the difference between the reference stress state and ther mal stress state, is valid only at point A in Figure 13-17, where the contact bounda ry at the reference stress state is at the same elevation as the contact boundary at the ther mal stress state. Equation 13-4 shows that self-equilibrating thermal stresses caused by the nonlinear positive ther mal gradient at the poi nts of intersection of the contact boundaries can be dete rmined if stresses caused by QR and QT are known.

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172 The load that caused joint J2 to open at a know n depth h at the reference and final stress states was determined from load vs. strain curves of strain gauges adjacent to the joint. Because the laboratory beam was statically determinate, the bending moment at joint J2 was determined from the joint-opening load without taking the change in stiffness of the beam, caused by opening the joint, into account. Assuming that pl ane sections remained plane under the actions of the forces and moments acting at the join t, stresses caused by join t-opening loads at the reference and final stress stat es along corresponding contact b oundaries were determined with the aid of stress-strain diagrams of the concrete segments and equations of statics. Assuming further that the behavior of the beam was linea r elastic under the action of the applied loads, it became possible to determine stresse s without measuring strain. For stresses due to joint-openi ng loads to be determined without explicitly using the elastic/tangent modulus of concrete (i.e. without the stress-strain cu rve), the material behavior of concrete within the load ranges c onsidered had to be linear elastic. Furthermore, the distribution of strain through the depth of th e contact area at joint J2 (after opening the joint) had to be a linear function of curvature (i.e. pl ane sections remain plane). It was assumed that concrete was homogeneous and isotropic. Line ar elastic material behavior of the beam segments within the range of mechanical loads applied during test ing was supported by data from cylinder tests, which showed that the beam segments were li near elastic up to stresses of about 6000 psi (uniaxial compression). Di stributions of measured concrete st rain through the depth of evolving contact areas near joint J2 were approximately li near as the joint was opened. This was evidence of plane sections remaining plane, within the c ontact area, under flexure. Data collected from in-situ CTE tests conducted on the heated segments showed that, within the temperature ranges to which the segments were subjected during test ing, plane sections remained plane and thermal

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173 strains were a linear function of temperature difference. Based on these observations flexural stresses due to joint-opening lo ads were determined using cla ssical flexural stress formulas. Figure 13-18 and Figure 13-19 show variations of concre te strain with applied load near joint J2 on the North side of Segment 3 at the reference stress state (reference temperature) and thermal stress state (with positive thermal gradient), respectively. Similar plots near the same joint on the South side of Segment 3 are shown in Figure 13-20 and Figure 13-21, respectively. The variation of concrete strain with applied load on top of the fl anges of segments 2 and 3 near joint J2 at the reference and thermal stress states are shown in Figure 13-22 and Figure 13-23, respectively. Data collected from strain gauges near joint J2 on Segment 2 (which were similar to those from Segment 3), LVDT s mounted across joint J2 on top of the flanges of segments 2 and 3, and LVDTs mounted across the same joint on the South side can be found in Appendix D. The variation of measured strains and measured displacements with load near joint J2 on the South side, North side, and on top of the flanges of segments 2 and 3 was discussed in detail in Chapter 11. Two general observations can be made when meas ured concrete strains at the same side of joint J2 and LVDT readings at the reference and thermal stress states are compared. These observations are illustrated in Figure 13-24 with data from the stra in gauges at elevations 33.5 in. and 35.3 in. on the North and South sides of joint J2 respectively. The first is that at the same elevation in the top 4 in. of the flange, the joint opened at higher loads at the thermal stress state than it did at the reference stress state (i.e. QTN > QRN and QTS > QRS). This is also evident in the top flange strains shown in Figure 13-22 and Figure 13-23, and LVDT data (see Figure D-5 through Figure D-8 in Appendix D). Opening of joint J2 at higher loads at the thermal stress

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174 state was consistent with the development of compressive strains in the top concrete fibers caused by the positive thermal gradient. The second observation is that although smaller strains were recorded on the South side of the joint than on the North side (i.e. RS < RN and TS < TN in Figure 13-24), the strain difference between vertical portions of strain diagrams at the reference and thermal stress states (S and N) was independent of the side of the joint on which strain gauges were located. The strain difference was, however, dependent on the distribution of stress-i nducing concrete strains caused by the positive thermal gradient at joint J2 (and therefore the elevation of gauges). In Figure 13-24 the strain difference on th e North side at elevation 33.5 in. (N) was less than the strain difference on the South side of the joint at elevation 35.3 in. (S). This was because the gauge on the South side was at a higher elev ation than the gauge on the North side. Since the strain difference between vertical por tions of strain curves at the reference and thermal stress states represented strains caused by the positive thermal gradient at joint J2, it was evident that within the top 4 in. of the fla nge, these strains (and corresponding stresses) decreased in compression, with the maximum strain s and stresses occurring in the top fibers of the section. This was consistent with the expected distribution of self-equilibrating thermal stresses within the top 4 in. of the flange (see predicted strains and stre sses in the discussion of E stresses) Loads that caused joint J2 to open at the refe rence and thermal stress states were detected using load vs. strain data (detection of jointopening loads using strain gauges was discussed in Chapter 11). LVDT data were mainly used to ch eck joint-opening loads determined with strain gauges, especially on top of the flange, where ve ry low strains were recorded at the reference stress state. Applied loads at the cantilevered-end of the test beam, that caused joint J2 to open at

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175 various depths, are shown in Figure 13-25. Each point in th e figure shows the average load (determined from gauges on segments 2 and 3 on the sa me side (North or Sout h) of the joint) at which the change in strain at that location becam e zero. These points were used to define the boundary of the contact area at varying loads. The sign convention for moments and curvatures is shown in Figure 13-26. Tensile stresses caused by joint-opening loads are positive and compressive stresses are negative. Recall that tensile stresses are actually reductions of the initial compressive stresses caused by prestressing. Figure 13-27 through Figure 13-29 show estimated contact ar eas at joint J2 at the reference and thermal stress states just as opening of the jo int was detected from stra in gauges at elevations of 35.5 in. (South), 33.5 in. (North), and 32.0 in (South), respectively. Contact boundaries are indicated by dashed lines. Contact areas were estimated by interpolat ing between joint-opening loads and the positions of the strain gauges from which the loads were determined (see Figure 13-25). Total stresses caused by moments at joint J2 due to joint-opening loads and changes in prestress were determined using the contact area cross sections a nd Equation 13-5 through Equation 13-11. ) ( ) ( ) ( ) , , (2A p f I I I y I M I M z I M I M A p I I I M M y z fN zy z y zy y y z zy z z y zy y z y z (13-5) v P yM M_ (13-6) h P Q zM M M_ (13-7) A p A p fi i N 4 1) ( (13-8) 4 1 _) ( ) (i y i y h Pei p e p M (13-9) 4 1 _) ( ) (i z i z v Pei p e p M (13-10) Q x MJ Q 2 (13-11)

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176 Where, f is the total stress caused by the joint-opening load (Q), fN is the stress caused by changes in prestress at load Q, MQ is the moment of joint-opening load (Q) at joint J2, p is the change in prestress at load Q, eiy is the vertical eccentricity of post-tensioning bar i, eiz is the horizontal eccentricity of post-tensioning bar i, MP_v is the moment about the vertical axis due to changes in prestress, MP_h is the moment about the horiz ontal axis due to changes in prestress, Iz is the moment of inertia of th e section about the horizontal axis, Iy is the moment of inertia of the section about the vertical axis, Izy is the product of iner tia of the section, z is the horizontal coordinate of the point at which stress is calculated, y is the vertical coordinate of point at which stress is calculated, and xJ2 is the moment arm of the joint-opening load from joint J2. Though data from strain gauges and LVDTs on top of the flanges of segments 2 and 3 were useful in estimating contac t areas, top flange stresses coul d not be determined with these equations. This was because the condition of the joint at the top of the flanges (see Figure 11-6) violated the assumptions under whic h the equations could be used. Table 13-3 shows calculated J stre sses at the locations of strain gauges on the sides of the beam within the top 4 in. of the flange. Though the total stresses (str esses determined from Equation 13-5 are positive, indicating tens ion, they actually re present relief of prestressing-induced compressive stresses at J2 th at were present prior to the application of joint-opening loads. The J stresses were then determined by taking the difference between total stresses at the reference stress state and total stresses at the final stress state. In Equation 13.5, the total stre ss is made of two components; the stress component due to the joint opening load and the st ress component due to changes in prestress. Changes in prestress (determined from meas ured prestress forces and sect ion properties) accounted for less

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177 than 0.5% of total stresses. The calculated tota l stresses were therefor e essentially dependent on the magnitude of joint opening loads. J stresse s, however, were depende nt only on the difference between the joint-opening loads at the referenc e and thermal stress states. For example, the loads initiating opening of joint J2 on the North side at an elevati on of 33.5 in. were greater than on the South side at an elevation of 35.5 in. as can be seen from the magnitudes of the moments in Table 13-3. However, calculated J stresses at an elevation of 33.5 in. were lower than J stresses at an elevation of 35.5 in. This was expected since the distribution of self-equilibrating thermal stresses within the top 4 in. of the flange s of segments 2 and 3 was expected to increase linearly (in compression) from a minimum magnitude at an elev ation of 32 in. to a maximum magnitude at the top flan ge (elevation 36 in.). J stresses and predicted stress es in the top 4 in. of the flange are compared in Table 13-4. J stresses 0.5 in. below the top of the flange (m aximum J stresses) were approximately 10% and 15% less than corresponding predic ted stresses in Segment 2 and Segment 3, respectively. At elevation 32 in., J stresses were about 82% less than predicted st resses. Both predicted and J stresses were, however, tensile. As was the case for E stresses, this was attributed mainly to the difference in magnitude between the measured thermal gradients and the average thermal gradient (with which stresses were predicted). J stresses and E stresses in the top 4 in. of the flange are compared in Table 13-5. Both sets of stresses compared well except at elevati on 32 in. A possible reason for this discrepancy was noted above. Maximum J stresses (at elevati on 35.5 in.) were about 7% and 8% less than maximum E stresses on Segment 2 and Segment 3, respectively.

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178 Table 13-1. Comparison of E stre sses and extrapolated stresses on top of segment flanges near joint J2 (laboratory pos itive thermal gradient) Measured (psi) Extrapolated (psi) Measured/Extrapolated Segment 2, North -307 -786 0.391 Segment 2, South -438 -732 0.598 Segment 3, North -463 -772 0.600 Segment 3, Middle -518 -751 0.690 Segment 3, South -499 -729 0.684 Table 13-2. Comparison of E stre sses and predicted self-equilib rating thermal stresses caused by laboratory positive thermal gradient near joint J2 Segment 2 Elevation (in.) Average E Stress (psi) Average Predicted (psi) E Stress/Predicted 36 -373 N/A N/A 35.5 -671 -693 0.968 33.5 -320 -219 1.461 32 -57 137 -0.416 Segment 3 Elevation (in.) Average E Stress (psi) Average Predicted (psi) E Stress/Predicted 36 -493 N/A N/A 35.5 -674 -729 0.925 33.5 -369 -230 1.604 32 -140 144 -0.972 Table 13-3. J stresses in top 4 in. of flange Moments due to Joint-opening Loads (kip-in.) Total Stresses (psi) Gauge Elevation Reference Thermal Reference Thermal J Stress (psi) 35.5 in. S 1399 2889 366 989 -623 33.5 in. N 2790 4063 801 1124 -323 32.0 in. S 1833 2645 558 533 25 Table 13-4. Comparison of J stresses and predicted stresse s in top 4 in. of flange Segment 2 Gauge Elevation J Stress (psi) Predicted Stress (psi) J Stress/Predicted Stress 35.5 in. S -623 -693 0.899 33.5 in. N -323 -219 1.475 32.0 in. S 25 137 0.182 Segment 3 Gauge Elevation J Stress (psi) Predicted Stress (psi) J Stress/Predicted Stress 35.5 in. S -623 -729 0.855 33.5 in. N -323 -230 1.404 32.0 in. S 25 144 0.174

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179 Table 13-5. Comparison of J stresses a nd E stresses in top 4 in. of flange Segment 2 Gauge Elevation J Stress (psi) E Stress (psi) J Stress/E Stress 35.5 in. S -623 -671 0.928 33.5 in. N -323 -320 1.009 32.0 in. S 25 -57 -0.439 Segment 3 Gauge Elevation J Stress (psi) E Stress (psi) J Stress/E Stress 35.5 in. S -623 -674 0.924 33.5 in. N -323 -369 0.875 32.0 in. S 25 -140 -0.179

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180 Time Step 1Step 2 Step 3 P + SWApplied Loads5 mins9 hrs 5 mins 15 hrs 5 mins Step 5 P + SW: Pretress + Self-weight Step 1: Opening and closing of joint J2 (application and removal of mechanical loads) Step 2: Positive thermal gradient (application of thermal load) Step 3: Opening and closing of joint J2 (application and removal mechanical loads) Step 4: Cooling to reference temperature at start of test (removal of thermal loads) Step 5: Opening and closing of joint J2 (application and removal of mechanical loads) Applied Loads: Step 4 Measured reference strains Measured strains due to mechanical and thermal loading Confirmed reference strains Figure 13-1. Sequence of load app lication (positive gradient test)

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181 1.7 ft 2.7 ft 5 ft SEGMENT 1SEGMENT 2 SEGMENT 3 SEGMENT 4 Applied Load (Q) 10.5 ft East West Lab. floor Mid-support End-support Location of interest (Joint J2) 3 ft (AMBIENT) (HEATED) (AMBIENT) (HEATED) A B C D EF 5 ft 5 ft 5 ft P P P: Post-tensioning force Figure 13-2. Laboratory beam Temperature Difference (deg. F)Elevation (in.) -5 0 5 10 15 20 25 30 35 4045 0 5 10 15 20 25 30 35 40 Section A Section B Section C Section D Section E Section F AASHTO Figure 13-3. Laboratory imposed positive thermal gradient

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182 Figure 13-4. Typical field measured positive ther mal gradient (Roberts, C. L., Breen, J. E., Cawrse J. (2002)., Measurement of Th ermal Gradients and their Effects on Segmental Concrete Bridge, ASCE Journal of Bridge Engineering, Vol. 7, No. 3, Figure 4a, pg. 168) Temperature (deg. F)Elevation (in.) 75 80 85 90 95 100 105 110 115 120125 0 5 10 15 20 25 30 35 40 Section A Section B Section C Section D Section E Section F Target Figure 13-5. Measured temperatures in heated segments (positive thermal gradient)

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183 Strain (microstrain)Elevation (in.) -500 -400 -300 -200 -100 0 100 200 300 400500 0 5 10 15 20 25 30 35 40 Unrestrained thermal strain (T(z)) at elevation z when section fibers are free to deform independently Self-equilibrating strain (SE) arising from enforcement of compatibility between section fibers Total strain (T) (plane section) 1 T = T(z) + SE curvature Figure 13-6. Calculated strain components of the AASHTO positive thermal gradient Strain (microstrain)Elevation (in.) -300 -200 -100 0 100 200 300 400 500 0 5 10 15 20 25 30 35 40 Measured (Seg. 2, North) Measured (Seg. 2, South) Predicted (Laboratory Gradient) Predicted (AASHTO Gradient) Flange Web Figure 13-7. Measured and predicted st rains near joint J2 (Segment 2)

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184 Strain (microstrain)Elevation (in.) -300 -200 -100 0 100 200 300 400 500 0 5 10 15 20 25 30 35 40 Measured (Seg. 3, North) Measured (Seg. 3, South) Predicted (Laboratory Gradient) Predicted (AASHTO Gradient) Flange Web Figure 13-8. Measured and predicted st rains near joint J2 (Segment 3) Strain (microstrain)Elevation (in.) -250 -200 -150 -100 -50 0 50 100 150 200 250 300 350 400450 -12 -10 -8 -6 -4 -2 0 2 4 6 8 10 12 Seg. 2 (Measured) Seg. 2 (Calculated, Lab. Gradient) Seg. 2 (Calculated, AASHTO Gradient) Seg. 3 (Measured) Seg. 3 (Calculated, Lab. Gradient) Seg. 3 (Calculated, AASHTO Gradient) South North Centerline of beam Figure 13-9. Plan view of m easured and predicted strains near joint J2 (Top Flange)

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185 Temperature Difference (deg. F)Elevation (in.) -5 0 5 10 15 20 25 30 35 4045 0 5 10 15 20 25 30 35 40 Section A Section B Section C Section D Section E Section F Average Flange Web Figure 13-10. Comparison of measured thermal gradient profiles with average Stress (psi)Elevation (in.) -2000 -1800 -1600 -1400 -1200 -1000 -800 -600 -400 -200 0 200400 0 5 10 15 20 25 30 35 40 E Stress (Segment 2, North) E Stress (Segment 2, South) Predicted (Laboratory Gradient) Predicted (AASHTO Gradient) Flange Web Figure 13-11. E stresses near joint J2 (Segment 2)

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186 Stress (psi)Elevation (in.) -2000 -1800 -1600 -1400 -1200 -1000 -800 -600 -400 -200 0 200400 0 5 10 15 20 25 30 35 40 E Stress (Segment 3, North) E Stress (Segment 3, South) Predicted (Laboratory Gradient) Predicted (AASHTO Gradient) Flange Web Figure 13-12. E stresses near joint J2 (Segment 3) Temperature Difference (deg. F)Elevation (in.) -5 0 5 10 15 20 25 30 35 4045 0 5 10 15 20 25 30 35 40 Section A Section B Section C Section D Section E Section F Average Difference in magnitude of thermal gradients (from average) at location of maximum slope change leads to measured compressive strains whereas predicted strains are tensile Elevation 32 in. Flange Web Figure 13-13. Difference in magnitude of imposed thermal gradients at location of maximum slope change (elevation 32 in.)

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187 Prestress (P) Self-weight (SW) Joint-opening load (QR) SUM (P + SW + QR)+ + = Apply load QR to create zero stress at top fiber Centroid Tension Compression y z.C.G.(Reference Stress State) Figure 13-14. Superposition of component stress blocks (Mecha nical loads only) (Thermal Stress State) Joint-opening load (QT) Positive gradient (PG) Prestress (P) Self-weight (SW)SUM (P + SW +PG + QT).Apply load QT to create zero stress at top fiber+ + + =Centroid Tension Compression y z.C.G. Figure 13-15. Superposition of co mponent stress blocks (Mechanica l loads with positive thermal gradient)

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188 Joint J2 Segment 2 Segment 3 Strain gauge V M + M contact area contact boundary Beam deformation near joint J2 (Elevation view) Cross section at joint J2 (reference and thermal stress states) Total stress distribution at joint j2 (reference stress state) Total stress distribution at joint J2 (Thermal stress state) h h = depth of joint opening zero stress at depth 'h' from top fiber zero stress at depth 'h' from top fiber V (a) (b)(c)(d) h L L 2Q A B. A P P M + M CompressionTension Figure 13-16. Uniform opening of joint across section width contact boundary contact area hAhBA B. contact boundary hA, hB, hC = depth of joint opening on sides of cross section contact area hAhCA C. Cross section at joint J2 (Reference stress state) Cross section at joint J2 (Thermal stress state) Figure 13-17. Non-uniform opening of joint across section width

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189 Strain (microstrain)Load (kips) -700 -600 -500 -400 -300 -200 -100 0 100 200 300400 0 5 10 15 20 25 30 35 40 45 50 55 60 S3-N-S-02-33.5 S3-N-S-02-30.3 S3-N-S-02-27.4 S3-N-S-3.6-21.3 S3-N-S-02-14.6 S3-N-S-02-7.8 S3-N-S-02-1.1 Figure 13-18. Load vs. strain at refere nce temperature (Segment 3, North) Strain (microstrain)Load (kips) -700 -600 -500 -400 -300 -200 -100 0 100 200 300400 0 5 10 15 20 25 30 35 40 45 50 55 60 S3-N-S-02-33.5 S3-N-S-02-30.3 S3-N-S-02-27.4 S3-N-S-3.6-21.3 S3-N-S-02-14.6 S3-N-S-02-7.8 S3-N-S-02-1.1 Figure 13-19. Load vs. strain with positive thermal gradient (Segment 3, North)

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190 Strain (microstrain)Load (kips) -700 -600 -500 -400 -300 -200 -100 0 100 200 300400 0 5 10 15 20 25 30 35 40 45 50 55 60 S3-S-S-02-35.3 S3-S-S-02-32 S3-S-S-02-28.6 S3-S-S-02-27.5 S3-S-S-3.6-21.3 S3-S-S-02-14.6 S3-S-S-02-7.9 S3-S-S-02-0.9 Figure 13-20. Load vs. strain at refere nce temperature (Segment 3, South) Strain (microstrain)Load (kips) -700 -600 -500 -400 -300 -200 -100 0 100 200 300400 0 5 10 15 20 25 30 35 40 45 50 55 60 S3-S-S-02-35.3 S3-S-S-02-32.0 S3-S-S-02-28.6 S3-S-S-02-27.5 S3-S-S-3.6-21.3 S3-S-S-02-14.6 S3-S-S-02-7.9 S3-S-S-02-0.9 Figure 13-21. Load vs. strain with positiv e thermal gradient (Segment 3, South)

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191 Strain (microstrain)Load (kips) -700 -600 -500 -400 -300 -200 -100 0 100 200 300400 0 5 10 15 20 25 30 35 40 45 50 55 60 S2-TN-S-5.5-7.75 S2-TS-S-5.5-8.25 S3-TN-S-5.5-7.25 S3-T-S-5.5-0.75 S3-TS-S-5.5-7.25 Figure 13-22. Load vs. strain at reference temperature (Top flange) Strain (microstrain)Load (kips) -700 -600 -500 -400 -300 -200 -100 0 100 200 300400 0 5 10 15 20 25 30 35 40 45 50 55 60 S2-TN-S-5.5-7.75 S2-TS-S-5.5-8.25 S3-TN-S-5.5-7.25 S3-T-S-5.5-0.75 S3-TS-S-5.5-7.25 Figure 13-23. Load vs. strain with positive thermal gradient (Top flange)

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192 Strain (microstrain)Load (kips) -700 -600 -500 -400 -300 -200 -100 0 100 200 300400 0 5 10 15 20 25 30 35 40 45 50 55 60 S3-N-S-02-33.5 (Reference) S3-N-S-02-33.5 (Thermal) S3-S-S-02-35.3 (Reference) S3-S-S-02-35.3 (Thermal) QTNQTSQRNQRS RSRNTSTNNS Figure 13-24. Comparison of strain differences on North and South sides of joint J2 (Positive thermal gradient) . .(30.9 kips, 33.5 in.) (41.0 kips, 30.4 in.) (15.5 kips, 35.5 in.) (20.6 kips, 32.0 in.) (22.6 kips, 28.5 in.) (44.2 kips, 27.5 in.)(37.9 kips, 27.5 in.) South North . .(44.6 kips, 33.5 in.) (44.4 kips, 30.4 in.) (32.0 kips, 35.5 in.) (28.9 kips, 32.0 in.) (22.0 kips, 28.5 in.) (47.6 kips, 27.5 in.)(38.0 kips, 27.5 in.) South North Reference stress stateThermal stress state.. .(25.1 kips, 36 in.) (13.0 kips, 36 in.) (15.8 kips, 36 in.). .(30.2 kips, 36 in.) (32.7 kips, 36 in.) (43.3 kips, 36 in.) Figure 13-25. Joint opening loads detected from strain gauge s near joint J2

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193 x y z x Positive curvature yPositive curvature z z y MzC.G. Myx: longitudinal axis of beam (SOUTH) Figure 13-26. Sign convention for moments and curvature South North South North 8 in. 28 in. 7 in. z y MQ MP_h MP_vC.G. 10 in. 8 in. 28 in. 10 in. 7 in. z y MQ MP_h MP_vC.G. Reference stress state Thermal stress stateS-S-S-02-35.5 7.5 in. 14.6 in. 9.4 in. 14.2 in. 2.2 in. 9.8 in. 7.5 in. .. Figure 13-27. Contact areas at joint J2 at incipient opening of jo int on South side at elevation 35.5 in. South North South North 8 in. 28 in. 7 in. z y MQ MP_h MP_vC.G. 10 in. 8 in. 28 in. 10 in. 7 in. 24 in.. z y MQ MP_h MP_vC.G. Reference stress stateThermal stress stateS-S-S-02-32.0 4 in. 10.1 in. 13.9 in. 4 in. 4 in.. Figure 13-28. Contact areas at joint J2 at incipi ent opening of joint on North side at elevation 33.5 in.

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194 South North South North 5.5 in. 28 in. 7 in. z y MQ MP_h MP_vC.G. 10 in. 28 in. 10 in.. z y MQ MP_h MP_vC.G. Reference stress stateThermal stress stateS-N-S-02-33.5 19.6 in. 3 in. 17 in. 5.5 in. 7 in. Figure 13-29. Contact areas at joint J2 at incipi ent opening of joint on South side at elevation 32.0 in.

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195 CHAPTER 14 RESULTS AASHTO NEGATIVE THERMAL GRADIENT Results from the application of mechanical loading in combination with the AASHTO negative thermal gradient are presented and disc ussed in this chapter. The objective of the mechanical-thermal load tests was to experi mentally quantify the self-equilibrating thermal stresses caused by the AASHTO nonlinear negative thermal gradient in the top 4 in. of the flanges of segments 2 and 3. As with the posi tive gradient, two independent methods were used to quantify stresses. Elastic modulus derived st resses (E stresses) were determined by converting measured strains into stresses using the elastic modulus of c oncrete. Independently, joint opening derived stresses (J stresse s) were determined using the known stress state at incipient joint opening. In both methods concrete beha vior was assumed to be linear elastic. The test sequence, illustrated in Figure 14-1, shows that before mechanical or thermal loads were applied, the only forces acting on the beam were prestress and self-weight. The test sequence started with partial openi ng and closing of the joint at mi dspan (joint J2) with the beam at the ambient temperature of the laboratory (about 80 oF). This was followed by application of a uniform temperature increase of about 45 oF on segments 2 and 3 of the beam, after which the top portion of the segments c ould be cooled to impose the negative thermal gradient (see Chapter 8). Joint J2 was partially opened and closed after achieving and maintaining the steady state uniform temperature increase on the heated segments for 30 to 45 minutes. Data from this step of the load sequence were used to establish a zero reference stress state at joint J2. The top of the segments were then cooled to impos e the AASHTO negative thermal gradient. After achieving and maintaining the stea dy state negative thermal gradie nt on the heated segments for 30 to 45 minutes, joint J2 was partially opened and closed to determine the thermal stress state.

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196 The heated segments were then cooled to the re ference temperature (tap water temperature) at the start of the test, after which joint J2 was ag ain opened and closed, completing the load cycle. Data collected from steps 3 and 5 of th e load sequence were used to quantify self-equilibrating thermal stresses caused by the laboratory-imposed negative thermal gradient. Joint-opening loads and contact areas at joint J2, as the joint was gradually opened, were used to calculate self-equilibrating stresses caused by the nonlinear gradient (J stresses). Neither elastic moduli, nor coefficients of ther mal expansion of segments 2 and 3 were used in the calculation of J stresses. Elastic modulus derived thermal stresses calculat ed from measured thermal strains close to joint J2 (E stresses) and joint opening derived thermal stresses (J stre sses) are presented and discussed in the following sections. Elastic Modulus Derived Stresses (E stresses) The nonlinear negative thermal gradient imposed on the heated segments of the laboratory beam (see Figure 14-2) in Step 4 of the load sequence is shown in Figure 14-3. For comparison, Figure 14-3 also shows the AASHT O design negative gradient. Measured temperatures in the heated segments after imposing the ne gative thermal gradient are shown in Figure 14-4. As was done for the positive gradient (describ ed in Chapter 13) temperature on top of the flange was obtained by extrapolati ng the measured temperature data from elevations 32 in. and 35.5 in. The idealized strain components induced by the AASHTO design negative thermal gradient are shown in Figure 14-5 (A detailed description of the strain components is given in Chapter 3 and Chapter 13). The change in measured strain between St ep 3 and 5 at joint J2 are plotted in Figure 14-6 through Figure 14-8. Figure 14-6 and Figure 14-7 show the strain di fference along the height of segments 2 and 3, respectively. Figure 14-8 shows a plan view of the strain differences on the

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197 top flange near the same joint. Also shown in the figures are the two sets of strain changes predicted using the AASHTO design procedur e: one using the AASHTO design thermal gradient, and the other using the laboratory-imposed thermal gradient. Because the strain gauges installed on the beam were self-temperature co mpensating (STC) gauges, and because there was no axial or flexural restraint on the beam, the measured strains consisted only of the self-equilibrating strain component of the total strains. The aver age laboratory-imposed thermal gradient profile (average of prof iles at Section A through Section F (Figure 14-3)) was used in calculating the laboratory gradient strains in Figure 14-6 through Figure 14-8. No marked difference is apparent between measured and predicted strains due to the laboratory gradient below approximately 28 in. elevation. Te nsile strains were present in the bottom of the section up to an el evation of about 10 in. Compressi ve strains arose in the section mid-height from about 10 in. to 32 in. elevati on. A maximum compressive strain (due to the laboratory gradient) of about 21 was predicted at elevation 27.5 in. whereas a maximum measured compressive strain of about 26 occurred at the same elevation. The maximum predicted tensile strain due to the AASH TO design gradient, of magnitude about 15 occurred at an elevation of 20 in. The difference between locations of maximum predicted compressive strains due to the imposed laboratory gradient and the AASHTO design gradient was due to the difference in the shape of the laboratory and AAS HTO design thermal gradients. In each case, the maximum compressive strain occurred at the locati on where the change in slope (in units of oF/in.) of the thermal gradient profile was algebraically at a maximum. This occurred at an elevation of 27.5 in. for the laboratory gradient and at an elevation of 20 in. for the AASHTO design

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198 gradient. Tensile strains also occurred above the mid-thickness of the flange with a steeper gradient than that of the remainder of the profile. Some additional differences between the measur ed and predicted strains are also notable. Measured tensile strains were significantly smaller th an predicted at the top of the section in both segments except for the North top flange of Segment 3 (see Figure 14-8). As with the positive thermal gradient, the smaller measured tensile st rains on top of the sec tion were thought to be caused by a likely discontinuity in the shape of th e thermal gradient in the top 0.5 in. of the flange. Although not measured, it is probable that the temperat ure at the top surface of the flange was less than that of the temperature of the topmost thermocouples (located at an elevation of 35.5 in.). In determining predicte d strains, however, the ma gnitude of the thermal gradient in the top flange wa s obtained by extrapolating the li near thermal gradient between elevations of 32 in. and 35.5 in. The approximate ly 53% difference between strains measured on the North and South top flange of Segment 3 was attributed to the condition at the top surface of the flange at joint J2 shown in Figure 11-6. Measured concrete strains on the North side at midspan (joint J2) and at mid-segment of segments 2 and 3 are compared in Figure 14-9 and Figure 14-10, respectively. The distributions of measured strain on the side of the flange at mid-segment di d not match the predicted strain profile as well as the measured strains at mids pan because only two stra in gauges were located on the side of the flange at mid-segment. Addi tionally, measured tensil e strains on top of the flange at mid-segment were significantly less th an predicted strains at the same locations. Measured strains on top of the flange at midsegment were, however, generally greater than corresponding measured tensile stra ins at joint J2. This observa tion reinforces the possibility that differential shrinkage at joint J2 led to a greater discrepancy between measured and

PAGE 199

199 predicted strains at the joint. Between elevati ons 32 in. and 35.5 in., m easured tensile strains followed a linear distribution as did the predicte d strains. The measured strains were, however, generally larger than predicted strains between elevations 32 in. and 33 in. and smaller than predicted strains above 33 in. As discussed in Chapter 13, a possible reason for the difference between measured and predicted strains in this region of the flange was a variation between measured thermal gradients and th e average thermal gradient (see Figure 14-11), which was used to predict strains per th e AASHTO design procedure. The uniform and linear sub-components of th e overall negative ther mal gradient were expected to lead to additional stresses in the concrete as the top portions of segments 2 and 3 were cooled during Step 4. Cont raction of the segments relative to the prestressing caused a net reduction in prestressing force, however the measured peak reduction was only 0.2% of the initial prestress and was therefore considered negligible. Elastic modulus derived stresses (E stresses) were the self-equilibrating thermal stresses caused by the negative thermal gradient, and were determined by multiplying the measured strains in Figure 14-6 and Figure 14-7 by the elastic moduli of Segment 2 (4850 ksi) and Segment 3 (4850 ksi), respectively. The elastic moduli were calcu lated by linearly interpolating between cylinder modulus of elasticity data between test ages of 28 and 360 days. At the time of the test, the ages of segments 2 and 3 were 251 and 238 days, respectively. Figure 14-12 and Figure 14-13 show E stress distributions near joint J2 on Segment 2 and Segment 3, respectively. E stresses at midspan and mid-segment on the North side of segments 2 and 3 are compared in Figure 14-14 and Figure 14-15, respectively. Also for comparison, self-equilibrating thermal stresses due to the laboratory thermal gradient and the AASHTO design gradient were calculated using the AASHTO recommended procedure discussed in

PAGE 200

200 Chapter 3, and are shown in the figures. CTEs from Table 12-1 and the segment MOEs noted above were used in these calculations. Table 14-1 compares E stresses computed at the top of the flanges of segments 2 and 3 with similar stresses obtained by extrapolati ng from the linear E stress distributions between elevations 32 in. and 35.5 in. (see Figure 14-12 and Figure 14-13) on the sides of the segment flanges. E stresses in the extreme top flange fibers were significantly lower than stresses extrapolated to the same lo cation. This condition follows from the relatively smaller stress-inducing thermal strains that were measur ed at the top surfaces of the flanges (see Figure 14-8). As discussed previously, the smaller strains were attributed to differential shrinkage at joint J2 and to a lower thermal gradient magnitude than was targeted (as prescribed by the AASHTO gradient) for the top of the flanges of the segments. At an elevation of 32 in., the E stress on Segment 2 was about 88% less than the predicted stress. Both stresses were compressive. The E stress on Segment 3 at the sa me elevation, however, was tensile whereas the predicted stress was compressive. As was the case for the positive thermal gradient, this was attributed to the difference in magnitude of th e laboratory thermal gradients at sections A through F (from the average thermal gradient used in predicting stresses) at that elevation; the location of the maximum slope change in the thermal gradients (see Figure 14-16). E stresses and predicted stresses caused by the laboratory-imposed nonlinear negative thermal gradient in the top 4 in. of the fl anges of segments 2 and 3 are compared in Table 14-2. Predicted stresses in the extreme top flange fi bers (where the maximu m tensile stresses were expected to occur, had the gradient been linear in the top 4 in. of the flanges) are not shown in the table because the shape and magnitude of th e thermal gradient in this region were not measured. E stresses 0.5 in. below the top of the flange (maximum E stresses) were

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201 approximately 25% and 14% less than corres ponding predicted stresse s in Segment 2 and Segment 3, respectively. E stresses caused by the positive thermal gradient (see Chapter 13) at the same location were 3% and 8% less than corresponding stresses predicted in Segment 2 and Segment 3, respectively. Beam response was mo re sensitive to small errors in thermocouple readings in the negative thermal gradient case th an in the positive thermal gradient case because of the relatively lesser magnitude (temperature ch ange) of the negative thermal gradient. This was thought to be the reason for the greater discrepancy between maximum E stresses and corresponding predicted stresses due to the nega tive gradient. Taking into consideration the effects of differential shrinkage at joint J2, small errors in measuring strain gauge elevations, and differences between measured thermal gradient s (at sections A through F) and the average thermal gradient within the top 4 in. of the segmen t flanges, these differences were considered to be within the limits of experimental error. Joint Opening Derived Stresses (J Stresses) Joint-opening derived stresses (J stresses) were determined using the procedure outlined in Chapter 13 and data collected from steps 3 and 5 of the load sequence shown in Figure 14-1. For the thermal loading sequence used in the nega tive gradient tests, Eqns. 13-1 and 13-2 were modified as follows: R z y z y f z y f z y f z y fR UT SW P ) ( 0 ) ( ) ( ) ( ) ( (14-1) T z y z y f z y f z y f z y f z y fT J UT SW P ) ( 0 ) ( ) ( ) ( ) ( ) ( (14-2) where, fUT represents stresses caused by the expansi on of the concrete segments (against the restraint of the prestress bars) du e to a uniform temperature increase (see Figure 14-17 and Figure 14-18) and all other quantities ar e as described in Chapter 13. The fUT term was added to account for the fact that the negati ve gradient was imposed by firs t heating the entire section and then cooling the top portion.

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202 Figure 14-19 and Figure 14-20 show variations of concre te strain with applied load near joint J2 on the North side of Segment 3 at the reference stress state (reference temperature) and thermal stress state (with negative thermal gradient ), respectively. Similar plots near the same joint on the South side are shown in Figure 14-21 and Figure 14-22, respectively. The variation of concrete strain with applied load on top of th e flanges of segments 2 and 3 near joint J2 at the reference and thermal stress states are shown in Figure 14-23 and Figure 14-24, respectively. Data collected from strain gauges near joint J2 on Segment 2, LVDTs mounted across joint J2 on top of the flanges of segments 2 and 3, and LVDTs mounted across the same joint on the South side can be found in Appendix E. A comparison of concrete strains at same side of joint J2 at the reference and thermal stress states shows that at identical el evations in the top 4 in. of the flange, the joint opened at lower loads at the thermal stress state than it did at th e reference stress state. This is illustrated in Figure 14-25 with data taken fr om the strain gauges at elev ations 33.5 in. on the North and 35.3 in. on the South side of the joint. The same is true of the top flange strains shown in Figure 14-23 and Figure 14-24. LVDTs on the sides and top of the flange (see Appendix E) also show the joint opening at lower loads at the thermal stress state than at the reference stress state. This was indicative of the development of tensile stresses in the top conc rete fibers at joint J2 due to the negative thermal gradient. It is also evident in Figure 14-25 that, similar to the positive thermal gradient, the strain difference between vertical portions of strain diagrams, at the reference and thermal stress states, was dependent only on the elevation of the gauge and not on the side (North/South) of the joint on which the gauge was located. Loads that caused joint J2 to open at the refe rence and thermal stress states were detected using the strain data shown in Figure 14-19 through Figure 14-24 above, and Figure E-1 through

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203 Figure E-8 in Appendix E. Applie d loads at the cantilevered-end of the test beam, which caused joint J2 to open at various depths, are shown in Figure 14-26. The sign convention for moments and curvatures, which is the same as that used in Chapter 13, is show n (for convenience) in Figure 14-27. Figure 14-28 through Figure 14-30 show estimated contact ar eas at joint J2 at the reference and thermal stress states just as opening of the jo int was detected from stra in gauges at elevations of 35.5 in. (South), 33.5 in. (North), and 32.0 in. (South), respectively. These plots were developed using the same approach detailed in Chapter 13. In Table 14-3 calculated J stresses are presente d for the locations of strain gauges on the sides of the beam within the top 4 in. of the fla nge. As for the positive thermal gradient, the total stresses (stresses determined from Equation 13 -5) though positive, indica ting tension, actually represent relief of existing compressive stresses at J2 prior to the application of joint-opening loads. J stresses were determined by taking the difference between total st resses at the reference stress state and total stresses at the final stress state. Changes in prestress (as the beam was mechani cally loaded and joint J2 opened) accounted for less than 1% of total stresses (see Equation 13 .5). Calculated total stresses were, therefore, essentially dependent on the magnitude of join t-opening loads. J stresses, however, were dependent on the difference between the joint-op ening loads at the reference and thermal stress states. For example, the loads in itiating opening of joint J2 on the North side at an elevation of 33.5 in. were greater than they were on the South si de at an elevation of 35.5 in. as can be seen from the magnitudes of the moments in Table 14-3. However, calculated J stresses at an elevation of 33.5 in. were lower than J stresses at an elevation of 35.5 in. because the difference

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204 in joint-opening moments at elevation 33.5 in. was lower than the difference in moments required to open the joint at elevation 35.5 in. J stresses and stresses predicted with the AASHTO procedure using the laboratory thermal gradient, in the top 4 in. of the flange, are compared in Table 14-4. J stresses 0.5 in. below the top of the flange (maximum J stresses) were approximately 17% and 23% less than corresponding predicted stresses in Segment 2 and Segment 3, respectively. At elevation 32 in., J stresses were about 82% less than predicted stresses. Bo th predicted and J stresses compressive. J stresses and E stresses in the top 4 in. of the flanges are compared in Table 14-5. Maximum J stresses were within 11% of maximum E stresses. J stresses were, in general, higher than E stresses on Segment 2 and lower than E stresses on Segment 3. This could possibly be due to small errors in estimating contact areas and determining joint-opening loads. Another possibility is that J stresses represented the av erage stress between segments 2 and 3 at joint J2 whereas E stresses represented stresses on each segment about 2 in. away from joint J2.

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205 Table 14-1. Comparison of E stre sses and extrapolated stresses on top of segment flanges near joint J2 (laboratory negative thermal gradient) E Stress (psi) Extrapolated (psi) Measured/Extrapolated Segment 2, North 38 252 0.151 Segment 2, South 71 191 0.372 Segment 3, North 255 277 0.921 Segment 3, Middle 69 265 0.260 Segment 3, South 120 252 0.476 Table 14-2. Comparison of E stre sses and predicted self-equilib rating thermal stresses caused by laboratory negative thermal gradient near joint J2 Segment 2 Elevation (in.) Average E Stress (psi) Average Predicted (psi) E Stress/Predicted 36 55 N/A N/A 35.5 193 258 0.748 33.5 79 80 0.994 32 -6 -54 0.116 Segment 3 Elevation (in.) Average E Stress (psi) Average Predicted (psi) E Stress/Predicted 36 148 N/A N/A 35.5 235 272 0.865 33.5 118 84 1.413 32 31 -57 -0.539 Table 14-3. J stresses in top 4 in. of flange Moments due to Joint-opening Loads (kip-in.) Total Stresses (psi) Gauge Elevation Reference Thermal Reference Thermal J Stress (psi) 35.5 in. S 1679 885 443 229 214 33.5 in. N 2961 2510 861 740 121 32.0 in. S 1986 1896 625 635 -10 Table 14-4. Comparison of J stresses and predicted stresse s in top 4 in. of flange Segment 2 Gauge Elevation J Stress (psi) Predicted Stress (psi) J Stress/Predicted Stress 35.5 in. S 214 258 0.829 33.5 in. N 121 80 1.500 32.0 in. S -10 -54 0.185 Segment 3 Gauge Elevation J Stress (psi) Predicted Stress (psi) J Stress/Predicted Stress 35.5 in. S 214 272 0.787 33.5 in. N 121 84 1.440 32.0 in. S -10 -57 0.175

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206 Table 14-5. Comparison of J stresses a nd E stresses in top 4 in. of flange Segment 2 Gauge Elevation J Stress (psi) E Stress (psi) J Stress/E Stress 35.5 in. S 214 193 1.109 33.5 in. N 121 79 1.532 32.0 in. S -10 -6 1.667 Segment 3 Gauge Elevation J Stress (psi) E Stress (psi) J Stress/E Stress 35.5 in. S 214 235 0.911 33.5 in. N 121 118 0.975 32.0 in. S -10 31 -0.323

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207 Time Step 1Step 2Step 3Step 4Step 5 Step 6 P + SW Applied Loads5 mins24 hrs 5 mins6 hrs 5 mins15 hrs5 mins Step 7 P + SW: Pretress + Self-weight Step 1: Opening and closing of joint J2 (application and removal of mechanical loads) Step 2: Uniform temperature change (application of thermal load) Step 3: Opening and closing of joint J2 (application and removal mechanical loads) Step 4: Negative thermal gradient (application of thermal load) Step 5: Opening and closing of joint J2 (application and removal of mechanical loads): Step 6: Cooling to reference temperature at start of test (removal of thermal loads) Step 7: Opening and closing of joint J2 (application and removal of mechanical loads) Applied Loads: Measured reference strains Measured strains due to mechanical loading, uniform temperature change, and AASHTO negative thermal gradient Confirmed reference strains Measured strains due to mechanical loading and uniform temperature change Figure 14-1. Sequence of load app lication (negative gradient test)

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208 1.7 ft 2.7 ft 5 ft SEGMENT 1SEGMENT 2 SEGMENT 3 SEGMENT 4 Applied Load (Q) 10.5 ft East West Lab. floor Mid-support End-support Location of interest (Joint J2) 3 ft (AMBIENT) (HEATED) (AMBIENT) (HEATED) A B C D EF 5 ft 5 ft 5 ft P P P: Post-tensioning force Figure 14-2. Laboratory beam Temperature Difference (deg. F)Elevation (in.) -45 -40 -35 -30 -25 -20 -15 -10 -5 05 0 5 10 15 20 25 30 35 40 Section A Section B Section C Section D Section E Section F AASHTO Figure 14-3. Laboratory imposed negative thermal gradient

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209 Temperature (deg. F)Elevation (in.) 80 85 90 95 100 105 110 115 120 125130 0 5 10 15 20 25 30 35 40 Section A Section B Section C Section D Section E Section F Target Figure 14-4. Measured temperatures in heat ed segments (negativ e thermal gradient) Strain (microstrain)Elevation (in.) -200 -160 -120 -80 -40 0 40 80 120 160200 0 5 10 15 20 25 30 35 40 1Unrestrained thermal strain (T(z)) at elevation z when section fibers are free to deform independently Self-equilibrating strain (SE) arising from enforcement of compatibility between section fibers Total strain (T) (plane section) T = T(z) + SE curvature Figure 14-5. Calculated stra in components of the AASHTO negative thermal gradient

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210 Strain (microstrain)Elevation (in.) -350 -300 -250 -200 -150 -100 -50 0 50 100150 0 5 10 15 20 25 30 35 40 Measured (Seg. 2, North) Measured (Seg. 2, South) Predicted (Laboratory Gradient) Predicted (AASHTO Gradient) Flange Web Figure 14-6. Measured and predicted st rains near joint J2 (Segment 2) Strain (microstrain)Elevation (in.) -350 -300 -250 -200 -150 -100 -50 0 50 100150 0 5 10 15 20 25 30 35 40 Measured (Seg. 3, North) Measured (Seg. 3, South) Predicted (Laboratory Gradient) Predicted (AASHTO Gradient) Flange Web Figure 14-7. Measured and predicted st rains near joint J2 (Segment 3)

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211 Strain (microstrain)Flange Width (in.) -350 -300 -250 -200 -150 -100 -50 0 50 100150 -12 -10 -8 -6 -4 -2 0 2 4 6 8 10 12 Seg. 2 (Measured) Seg. 2 (Predicted, Lab. Gradient) Seg. 2 (Predicted, AASHTO Gradient) Seg. 3 (Measured) Seg. 3 (Predicted, Lab. Gradient) Seg. 3 (Predicted, AASHTO Gradient) South North Figure 14-8. Plan view of m easured and predicted strains near joint J2 (Top Flange) Strain (microstrain)Elevation (in.) -350 -300 -250 -200 -150 -100 -50 0 50 100150 0 5 10 15 20 25 30 35 40 Measured (Mid-segment, Seg. 2) Measured (Midspan, Seg. 2) Predicted (Laboratory Gradient) Predicted (AASHTO Gradient) Flange Web Figure 14-9. Measured and predic ted strains at midspan and midsegment (Segment 2, North)

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212 Strain (microstrain)Elevation (in.) -350 -300 -250 -200 -150 -100 -50 0 50 100150 0 5 10 15 20 25 30 35 40 Measured (Mid-segment, Seg. 3) Measured (Midspan, Seg. 3) Predicted (Laboratory Gradient) Predicted (AASHTO Gradient) Flange Web Figure 14-10. Measured and predicted strains at midspan and mid-segment (Segment 3, North) Temperature Difference (deg. F)Elevation (in.) -45 -40 -35 -30 -25 -20 -15 -10 -5 05 0 5 10 15 20 25 30 35 40 Section A Section B Section C Section D Section E Section F Average Flange Web Figure 14-11. Comparison of measured therma l gradient profiles with average profile

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213 Stress (psi)Elevation (in.) -1000 -800 -600 -400 -200 0 200 400 0 5 10 15 20 25 30 35 40 E Stress (Segment 2, North) E Stress (Segment 2, South) Predicted (Laboratory Gradient) Predicted (AASHTO Gradient) Flange Web Figure 14-12. E stresses near joint J2 (Segment 2) Stress (psi)Elevation (in.) -1000 -800 -600 -400 -200 0 200 400 0 5 10 15 20 25 30 35 40 E Stress (Segment 3, North) E Stress (Segment 3, South) Predicted (Laboratory Gradient) Predicted (AASHTO Gradient) FlangeWeb Figure 14-13. E stresses near joint J2 (Segment 3)

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214 Stress (psi)Elevation (in.) -1000 -800 -600 -400 -200 0 200 400 0 5 10 15 20 25 30 35 40 E Stress (Mid-segment) E Stress (Midspan) Predicted (Laboratory Gradient) Predicted (AASHTO Gradient) Flange Web Figure 14-14. E stresses at mid-segmen t and midspan (Segment 2, North) Stress (psi)Elevation (in.) -1000 -800 -600 -400 -200 0 200 400 0 5 10 15 20 25 30 35 40 E Stress (Mid-segment) E Stress (Midspan) Predicted (Laboratory Gradient) Predicted (AASHTO Gradient) Flange Web Figure 14-15. E stresses at mid-segmen t and midspan (Segment 3, North)

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215 Temperature Difference (deg. F)Elevation (in.) -45 -40 -35 -30 -25 -20 -15 -10 -5 05 0 5 10 15 20 25 30 35 40 Section A Section B Section C Section D Section E Section F Average Elevation 32 in. Flange Web Difference in magnitude of thermal gradients (from average) at location of maximum slope change leads to measured tensile strains whereas predicted strains are compressive Figure 14-16. Difference in magnitude of imposed thermal gradients at location of maximum slope change (elevation 32 in.) Prestress (P) Self-weight (SW) Joint-opening load (QR) SUM (P + SW + QR)+ + = .Apply load QR to create zero stress at top fiber Centroid Tension Compression y z.C.G. +Uniform temperature. increase (UT) (Reference Stress State) Figure 14-17. Superposition of component stress blocks (mechanical with uniform temperature increase)

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216 Prestress (P) Self-weight (SW) Joint-opening load (QT) SUM (P + SW +NG + QT) Negative gradient (NG).Apply load QT to create zero stress at top fiber = + + +Centroid Tension Compression y z.C.G. Uniform temperature. increase (UT)+ (Thermal Stress State) Figure 14-18. Superposition of component stress blocks (mechanical with uniform temperature increase and negative thermal gradient) Strain (microstrain)Load (kips) -700 -600 -500 -400 -300 -200 -100 0 100 200 300400 0 5 10 15 20 25 30 35 40 45 50 55 60 S3-N-S-02-33.5 S3-N-S-02-30.3 S3-N-S-02-27.4 S3-N-S-3.6-21.3 S3-N-S-02-14.6 S3-N-S-02-7.8 S3-N-S-02-1.1 Figure 14-19. Load vs. strain at refere nce temperature (Segment 3, North)

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217 Strain (microstrain)Load (kips) -700 -600 -500 -400 -300 -200 -100 0 100 200 300400 0 5 10 15 20 25 30 35 40 45 50 55 60 S3-N-S-02-33.5 S3-N-S-02-30.3 S3-N-S-02-27.4 S3-N-S-3.6-21.3 S3-N-S-02-14.6 S3-N-S-02-7.8 S3-N-S-02-1.1 Figure 14-20. Load vs. strain with negativ e thermal gradient (S egment 3, North) Strain (microstrain)Load (kips) -700 -600 -500 -400 -300 -200 -100 0 100 200 300400 0 5 10 15 20 25 30 35 40 45 50 55 60 S3-S-S-02-35.3 S3-S-S-02-32.0 S3-S-S-02-28.6 S3-S-S-02-27.5 S3-S-S-3.6-21.3 S3-S-S-02-14.6 S3-S-S-02-7.9 S3-S-S-02-0.9 Figure 14-21. Load vs. strain at refere nce temperature (Segment 3, South)

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218 Strain (microstrain)Load (kips) -700 -600 -500 -400 -300 -200 -100 0 100 200 300400 0 5 10 15 20 25 30 35 40 45 50 55 60 S3-S-S-02-35.3 S3-S-S-02-32.0 S3-S-S-02-28.6 S3-S-S-02-27.5 S3-S-S-3.6-21.3 S3-S-S-02-14.6 S3-S-S-02-7.9 S3-S-S-02-0.9 Figure 14-22. Load vs. strain with negativ e thermal gradient (S egment 3, South) Strain (microstrain)Load (kips) -700 -600 -500 -400 -300 -200 -100 0 100 200 300400 0 5 10 15 20 25 30 35 40 45 50 55 60 S2-TN-S-5.5-7.75 S2-TS-S-5.5-8.25 S3-TN-S-5.5-7.25 S3-T-S-5.5-0.75 S3-TS-S-5.5-7.25 Figure 14-23. Load vs. strain at reference temperature (Top flange)

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219 Strain (microstrain)Load (kips) -700 -600 -500 -400 -300 -200 -100 0 100 200 300400 0 5 10 15 20 25 30 35 40 45 50 55 60 S2-TN-S-5.5-7.75 S2-TS-S-5.5-8.25 S3-TN-S-5.5-7.25 S3-T-S-5.5-0.75 S3-TS-S-5.5-7.25 Figure 14-24. Load vs. strain with ne gative thermal gradient (Top flange) Strain (microstrain)Load (kips) -700 -600 -500 -400 -300 -200 -100 0 100 200 300400 0 5 10 15 20 25 30 35 40 45 50 55 60 S3-N-S-02-33.5 (Reference) S3-N-S-02-33.5 (Thermal) S3-S-S-02-35.3 (Reference) S3-S-S-02-35.3 (Thermal) SNRSRNTSTNQTNQTSQRNQRS Figure 14-25. Comparison of strain differences on North and South sides of joint J2 (Negative thermal gradient)

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220 . .(25.0 kips, 36.0 in.) (32.8 kips, 33.5 in.) (41.2 kips, 30.4 in.) (17.7 kips, 35.5 in.) (22.5 kips, 32.0 in.) (24.1 kips, 28.5 in.) (45.9 kips, 27.5 in.)(38.7 kips, 27.5 in.) South North . .(19.7 kips, 36.0 in.) (27.5 kips, 33.5 in.) (41.5 kips, 30.4 in.) (9.8 kips, 35.5 in.) (21.3 kips, 32.0 in.) (22.6 kips, 28.5 in.) (44.9 kips, 27.5 in.)(38.5 kips, 27.5 in.) South North Reference stress stateThermal stress state. .(15.2 kips, 36.0 in.) (13.5 kips, 36.0 in.). .(9.5 kips, 36.0 in.) (6.0 kips, 36.0 in.) Figure 14-26. Joint opening loads detected from strain gauge s near joint J2 x y z x Positive curvature yPositive curvature z z y MzC.G. Myx: longitudinal axis of beam (SOUTH) Figure 14-27. Sign convention for moments and curvature South North South North 8 in. 28 in. 7 in. z y MQ MP_h MP_vC.G. 10 in. 8 in. 28 in. 10 in. 7 in. z y MQ MP_h MP_vC.G. 7.5 in. Reference stress state Thermal stress stateS-S-S-02-35.5 7.5 in. 11 in. 13 in. 12.6 in. 11.4 in. Figure 14-28. Contact areas at joint J2 at incipi ent opening of joint on South side at elevation 35.5 in.

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221 South North South North 5.5 in. 28 in. 7 in. z y MQ MP_h MP_vC.G. 10 in. 5.5 in. 28 in. 10 in. 7 in. 22.3 in.. z y MQ MP_h MP_vC.G. Reference stress state Thermal stress stateS-N-S-02-33.5 19.9 in. Figure 14-29. Contact areas at joint J2 at incipi ent opening of joint on North side at elevation 33.5 in. South North South North 8 in. 28 in. 7 in. z y MQ MP_h MP_vC.G. 10 in. 8 in. 28 in. 10 in. 7 in. 19.3 in.. z y MQ MP_h MP_vC.G. Reference stress state Thermal stress stateS-S-S-02-32.0 4 in. 4.7 in. 16.1 in. 4.7 in. 4 in. Figure 14-30. Contact areas at joint J2 at incipi ent opening of joint on South side at elevation 32.0 in.

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222 CHAPTER 15 SUMMARY AND CONCLUSIONS Results from a series of tests conducted on a 20 ft-long 3 ft-deep segmental concrete T-beam, aimed at quantifying self-equilibrati ng thermal stresses caused by AASHTO design nonlinear thermal gradients, have be en presented and discussed. Th e beam consisted of four 5 ft long segments that were post-te nsioned together. Layers of copper tubes, which would later carry water, were embedded in the middle tw o segments of the beam (Segments 2 and 3), designated heated segments. Th ermocouples were also cast in to the heated segments to monitor the distribution of temper ature. The two end segments of the beam (Segments 1 and 4), which were designated ambient segments, were strengthened using stee l reinforcing bars to carry loads at the prestress anchorage zones. Th e beam was vertically supported at midspan and at the end of one ambient segment. Mechanical loads were applied at the cantilevered end and thermal profiles were imposed on the heated segments by passing water at specific temperatures through each layer of copper tubes. The region of interest in the experi mental program was the dry joint between the two heated segments of the beam (designated joint J2), which was heavily instrumented with surface strain gauges and L VDTs. Detection of opening of the joint was of primary importance in quantifying stresses cau sed by the application of AASHTO nonlinear thermal gradients. The experimental program consisted of dete rmining the in-situ coefficient of thermal expansion (CTE) of the heated se gments; investigating the behavi or of the beam under the action of mechanical loads; applying a uniform temp erature change on the heated segments to investigate the free expansion behavior of the beam; and imposing the AASHTO design nonlinear thermal gradients in combination with mechanical loads for the purpose of quantifying self-equilibrating thermal stresses du e to the thermal gradients.

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223 In-situ CTEs of Segments 2 and 3 were determined by imposing uniform and linear temperature distributions on each segment. The CTE of Segment 3 was also determined using a procedure specified by AASHTO. Good agre ement was found between the in-situ CTEs determined using uniform and linear thermal pr ofiles for both segments. Good agreement was also found between the CTE determined usi ng the AASHTO method and the average in-situ CTE of Segment 3. AASHTO CTE testing was not conducted for Segment 2 because the cylinders required for the test were not cast for this segment. Mechanical load tests indicated that strain gauges mounted on the side surfaces of the beam close to the joint at midspan (joint J2) we re the most reliable instruments in detecting opening of the joint. However, strain gauges mounted on the top surfaces of the segment flanges near the joint showed little change in strain with increasing applie d load. This was attributed to an imperfect fit (despite match-casting of the segm ents) at the joint, and differential shrinkage in the top flange fibers which were unsealed a nd exposed to the laborat ory environment during curing of the segments. Strain distributions th rough the height of the co ntact area at the joint (before and after the join t opened) were generally found to be linearly dependent on applied load, which allowed for the use of classical flexural st ress formulas in quantifying stresses due to the AASHTO nonlinear thermal gradients. Observati ons and conclusions that were drawn from the directly measured experimental data are as follows: A uniform temperature increase of 41 oF increased the prestress force by about 6% of the initial prestress due to differential movement and heating between the bars and concrete segments. The measured change in prestress compared well with predicted values determined using in-situ CTEs and laborat ory determined concrete elastic moduli. Measured concrete strains caused by the uni form temperature increase were generally tensile, whereas predicted strains (d etermined using the AASHTO recommended procedure) were compressive. The difference was attributed primarily to slight variations in temperature between the inner core and th e outer perimeter of the heated segments.

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224 Measured stress-induced concrete strains caused by the laboratory-imposed nonlinear thermal gradients on top of th e flanges of the heated segments near joint J2 were significantly less than predicted for both positive and negative thermal gradients. For the positive thermal gradient, average measured strains on top of the flanges of segments 2 and 3 were about 56% and 39% less than predicted strains, resp ectively. For the negative thermal gradient, average measured strains at the same locations on segments 2 and 3 were about 81% and 53% less than predicted. The differences were attributed both to differential shrinkage in the t op flange fibers and a probable discontinuity in the thermal gradients (positive and negative) within the top 0.5 in. of the flanges of the heated segments. At elevations below 0.5 in. from the top surface of the segment flanges near joint J2, measured stress-induced concrete strains caused by the laboratory-imposed nonlinear thermal gradients agreed well with strains predicted using the AASHTO recommended method for the analysis of nonlinear thermal gr adients. Maximum meas ured stress-induced concrete strains (which occurred at elevation 35.5 in.) under the action of the positive thermal gradient were about 3% and 7% less than predicted strains on segments 2 and 3, respectively. For the negative thermal gr adient, maximum measured stress-induced concrete strains (at the same location as for the positive thermal gradient) were about 25% and 14% less than predicted strains on segments 2 and 3, respectively. Two independent methods were also used to quantify concrete stresses caused by the laboratory-imposed nonlinear therma l gradients at the joint between the heated segments. The first method involved multiplying measured thermal stress-induced concrete strains by elastic moduli (E stresses) whereas the second method involved determini ng stresses at the joint using the known stress state at incipien t joint opening (J stresses). E stresses were determined throughout the height of the heated segments at a distance of about 2 in. away, the location of strain gauges from joint J2. J st resses were quantified within the top 4 in. of the flanges of the heated segments at joint J2. Conclusions from quantifying the E stresses and J stresses are as follows: J stresses in the extreme top flange fibers at the joint, where the maximum stresses caused by the nonlinear thermal gradients were expected to occur, could not be quantified because of the effects of differential shrinkage and because pieces of concrete had broken off the top surface during transportation and handling of the segments. Though E stresses on top of the flanges of the heated segments near joint J2 were determined, they did not agree well with predicted stresses because of reasons given in the third bul leted paragraph above.

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225 Maximum E stresses caused by the positive thermal gradient, which occurred at elevation 35.5 in. (i.e. 0.5 in. below the top surface of the segment flanges), were about 3% and 8% less than corresponding predicted self-equilibrating thermal stresses in Segment 2 and Segment 3, respectively. Maximum J stresses caused by the positive thermal gradient (also at elevation 35.5 in.) were about 10% and 15% less than the pred icted self-equilibrating thermal stresses in segments 2 and 3, respectively. In the case of the negative thermal gradient, maximum E stresses (which also occurred at elevation 35.5 in.) were about 25% a nd 14% less than corresponding predicted self-equilibrating thermal stresses in segments 2 and 3, respectively. Maximum J stresses (at the same elevation) were about 17% and 23% less than pred icted stresses in segments 2 and 3, respectively. The percentage difference between maximum measured and maximum predicted negative gradient stresses was higher than that for th e positive thermal gradient because the negative thermal gradient was more sensitive to local deviations of temperature from the width-wise average temperatures that were used in predicting the self-equilibrating thermal stresses. The difference in sensitivity was due to the magnitude of the negative thermal gradient being only 30% the magnitude of the positive thermal gradient. E stresses and J stresses in the top few inches of the flanges of segments 2 and 3 were in general lower than stresses predicted using th e AASHTO recommended proce dure. In particular, the maximum quantified stresses due to the negati ve thermal gradient were on the average about 20% less than corresponding pred icted stresses (at the same location). These differences between quantified and AASHTO pred icted stresses could, however, not be attributed to any flaws in the AASHTO method. They were considered to be like ly the result of experimental error. Based on the effects of differential shrinkage at joint J2, and the slight damage to the top flange surfaces of the segments at the joint on the magnitude of quantified stresses, it is possible that self-equilibrating thermal stresses in the top section fibers at dry joints in segmental concrete bridges may be smaller in magnitude than stresses predicted usi ng the AASHTO method. This study focused mainly on quantifying self-equilibrating stresses caused by the AASHTO nonlinear thermal gradients. Some s uggestions on future research are proposed: The current AASHTO nonlinear thermal gradie nts are computationa lly inconvenient and do not work well with most structural analysis software. Furthermore, the stresses of importance in design are the stresses in the top 4 in. of box-girder flanges. A study on

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226 simplifying the nonlinear thermal gradients into a combination of linear gradients, such that stresses of equal magnit ude (especially the maximum st resses) caused by the nonlinear gradients in the top 4 in. ar e generated by the combination of linear gradients, would greatly simplify the computational effort that currently goes into calculating self-equilibrating stresses in complex box-girder sections. The effect on concrete durability of tensile stresses generated by the AASHTO negative thermal gradient in the top few inches of the flanges of segmental concrete bridges needs investigation. Though tensile st resses have been known to cause damage to concrete, this damage has been difficult to quantify. A study into the effect of the relatively steep self-equilibrating stress gradient in the top fe w inches of concrete (compared to typical bending stresses) on the potential for cracking would lead to a better understanding of the level of damage that gradient-induced tensile stresses may cause.

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227 APPENDIX A BEAM SHOP DRAWINGS In this appendix, design plan s for the construction of the laboratory segmental beam are presented. Steel reinforcement in prestress an chorage zones, thermocouple cages, copper tube locations, plans for the loading mechanism, and shear keys are shown.

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228 Figure A-1. Prestress reinforcement details

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229 Figure A-2. Manifold and copper tube details

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230 Figure A-3. Shear key details

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231 APPENDIX B LOADING FRAME DRAWINGS Details of the loading frame which was used to apply mechanical loads at the cantilevered end of the test beam are shown in this appendix.

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232 W16x89 PL 2"x11.25"x17 3 4 11 2" 1 5 BOLT HOLES 1" DIA @ 15" o.c. 4 1 2 1 5 'PL 2"x1'-1"X1'-7" 1'-67 8" MC18x45.8 5 16 11 2" Figure B-1. Loading frame details

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233 MC18x45.8 W16x89 COPE FLANGES @ COLUMN (TYP.) 71 4" 1 13 4" 71 4" 1" DIA BOLT HOLES 1 9 13" 4' STRONG-FLOOR BOLT HOLES LOCATED IN LAB 7 1 2 PL 2"x1'-1"x1'-7" W16x89 4' 1 9 13" W16x89 23 4" 71 2" 23 4" 5 3 4 71 2 53 4 5 16 2" DIA BOLT HOLES Figure B-2. Details of cross channels

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234 10" C15x33.9 JOINT OPENING INTERFACE 3' LOAD CELL 3'-67 8 67 8" 11 2" X 10" X 10" PLATE 10" DRILLED AND TAPPED FOR 0.5" DIA ALLTHREAD 1 2" NUT DRILLED 5 8" DIA 6 7 8 SEGMENT INTERFACE 8 3 4 3 7 8 1 2 3 7 8 Figure B-3. Mid-support details

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235 CHANNELS: C15x33.9 LOAD CELL 11 2" X 9" X 9" PLATE 5'-7 7 8 STACKED NEOPRENE PADS LOAD CELL 3'-6 7 8 6 7 8 1'-81 4 STACKED NEOPRENE PADS Figure B-4. End-support details

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236 APPENDIX C LOAD RESPONSE CURVES AT MID-SEGMENT (MECHANICAL LOADING) In this appendix load versus strain response curves at the middle of Segment 2 and Segment 3 (30 in. away from joint J2) are presented.

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237 Strain (microstrain)Load (kips) -400 -300 -200 -100 0 100 200 300 400 500 600 700 800900 0 5 10 15 20 25 30 35 S2-N-S-30-35.5 S2-N-S-30-28.5 S2-N-S-30-21.2 S2-N-S-30-14.6 S2-N-S-30-7.9 S2-N-S-30-1.0 Figure C-1. Load vs. strain at mi ddle of Segment 2 on North side Strain (microstrain)Load (kips) -400 -300 -200 -100 0 100 200 300 400 500 600 700 800900 0 5 10 15 20 25 30 35 S2-S-S-30-35.5 S2-S-S-30-28.5 S2-S-S-30-21.2 S2-S-S-30-14.6 S2-S-S-30-8.0 S2-S-S-30-0.9 Figure C-2. Load vs. strain at middle of Segment 2 on South side

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238 Strain (microstrain)Elevation (in.) -400 -300 -200 -100 0 100 200 300 400 500 600 700 800900 0 5 10 15 20 25 30 35 40 0 kips 5 kips 10 kips 15 kips 20 kips 25 kips 30 kips Figure C-3. Measured strain distributions at middle of Segment 2 on North side Strain (microstrain)Elevation (in.) -200 -100 0 100 200 300 400 500 600 700 800900 0 5 10 15 20 25 30 35 40 0 kips 5 kips 10 kips 15 kips 20 kips 25 kips 30 kips Figure C-4. Measured strain distributions at middle of Segment 2 on South side

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239 Strain (microstrain)Load (kips) -400 -300 -200 -100 0 100 200 300 400 500 600 700 800900 0 5 10 15 20 25 30 35 S3-N-S-30-35.5 S3-N-S-30-28.5 S3-N-S-30-21.4 S3-N-S-30-14.6 S3-N-S-30-7.7 S3-N-S-30-1.0 Figure C-5. Load vs. strain at middle of Segment 3 on North side Strain (microstrain)Load (kips) -400 -300 -200 -100 0 100 200 300 400 500 600 700 800900 0 5 10 15 20 25 30 35 S3-S-S-30-35.5 S3-S-S-30-28.5 S3-S-S-30-21.2 S3-S-S-30-14.6 S3-S-S-30-8.0 S3-S-S-30-0.9 Figure C-6. Load vs. strain at middle of Segment 3 on South side

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240 Strain (microstrain)Elevation (in.) -400 -300 -200 -100 0 100 200 300 400 500 600 700 800900 0 5 10 15 20 25 30 35 40 0 kips 5 kips 10 kips 15 kips 20 kips 25 kips 30 kips Figure C-7. Measured strain distributions at middle of Segment 3 on North side Strain (microstrain)Elevation (in.) -400 -300 -200 -100 0 100 200 300 400 500 600 700 800900 0 5 10 15 20 25 30 35 40 0 kips 5 kips 10 kips 15 kips 20 kips 25 kips 30 kips Figure C-8. Measured strain distributions at middle of Segment 3 on South side

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241 APPENDIX D LOAD RESPONSE CURVES (POSITIVE THERMAL GRADIENT) Load vs. beam response curves which were de rived from strain gauge and LVDT data are shown here. These curves were used to de termine loads at which the joint at midspan (designated joint J2) opene d. The curves were also used to determine effective concrete contact areas at joint J2, which were then used to quantify J stresses due to the AASHTO nonlinear positive thermal gradient.

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242 Strain (microstrain)Load (kips) -700 -600 -500 -400 -300 -200 -100 0 100 200 300400 0 5 10 15 20 25 30 35 40 45 50 55 60 S2-N-S-02-33.4 S2-N-S-02-30.4 S2-N-S-02-27.5 S2-N-S-3.6-21.3 S2-N-S-02-14.5 S2-N-S-02-7.7 S2-N-S-02-1.0 Figure D-1. Load vs. strain at refere nce temperature (Segment 2, North) Strain (microstrain)Load (kips) -700 -600 -500 -400 -300 -200 -100 0 100 200 300400 0 5 10 15 20 25 30 35 40 45 50 55 60 S2-N-S-02-33.4 S2-N-S-02-30.4 S2-N-S-02-27.5 S2-N-S-3.6-21.3 S2-N-S-02-14.5 S2-N-S-02-7.7 S2-N-S-02-1.0 Figure D-2. Load vs. strain with positive thermal gradient (Segment 2, North)

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243 Strain (microstrain)Load (kips) -700 -600 -500 -400 -300 -200 -100 0 100 200 300400 0 5 10 15 20 25 30 35 40 45 50 55 60 S2-S-S-02-35.5 S2-S-S-02-32.0 S2-S-S-02-28.5 S2-S-S-02-27.3 S2-S-S-3.6-21.2 S2-S-S-02-14.5 S2-S-S-02-7.7 S2-S-S-02-0.9 Figure D-3. Load vs. strain at refere nce temperature (Segment 2, South) Strain (microstrain)Load (kips) -700 -600 -500 -400 -300 -200 -100 0 100 200 300400 0 5 10 15 20 25 30 35 40 45 50 55 60 S2-S-S-02-35.5 S2-S-S-02-32.0 S2-S-S-02-28.5 S2-S-S-02-27.3 S2-S-S-3.6-21.2 S2-S-S-02-14.5 S2-S-S-02-7.7 S2-S-S-02-0.9 Figure D-4. Load vs. strain with positive thermal gradient (Segment 2, South)

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244 Relative Longitudinal Displacement (in.)Load (kips) -0.005 0 0.005 0.01 0.015 0.02 0.025 0.03 0.0350.04 0 5 10 15 20 25 30 35 40 45 50 55 60 J2-TN-D-9.5 J2-T-D J2-TS-D-9.5 Figure D-5. Load vs. joint opening at reference temperature (Top flange) Relative Longitudinal Displacment (in.)Load (kips) -0.005 0 0.005 0.01 0.015 0.02 0.025 0.03 0.0350.04 0 5 10 15 20 25 30 35 40 45 50 55 60 J2-TN-D-9.5 J2-T-D J2-TS-D-9.5 Figure D-6. Load vs. joint opening with positive thermal gradient (Top flange)

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245 Relative Longitudinal Displacement (in.)Load (kips) -0.005 0 0.005 0.01 0.015 0.02 0.025 0.03 0.0350.04 0 5 10 15 20 25 30 35 40 45 50 55 60 J2-S-D-33.75 J2-S-D-30.25 J2-S-D-25.0 J2-S-D-18.25 J2-S-D-11.375 J2-S-D-4.375 Figure D-7. Load vs. joint opening at reference temperature (South side) Relative Longitudinal Displacement (in.)Load (kips) -0.005 0 0.005 0.01 0.015 0.02 0.025 0.03 0.0350.04 0 5 10 15 20 25 30 35 40 45 50 55 60 J2-S-D-33.75 J2-S-D-30.25 J2-S-D-25.0 J2-S-D-18.25 J2-S-D-11.375 J2-S-D-4.375 Figure D-8. Load vs. joint opening with positive thermal grad ient (South side)

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246 APPENDIX E LOAD RESPONSE CURVES (NEGATIVE THERMAL GRADIENT) Load vs. beam response curves which were de rived from strain gauge and LVDT data are shown here. These curves were used to de termine loads at which the joint at midspan (designated joint J2) opene d. The curves were also used to determine effective concrete contact areas at joint J2, which were then used to quantify J stresses due to the AASHTO nonlinear negative thermal gradient.

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247 Strain (microstrain)Load (kips) -700 -600 -500 -400 -300 -200 -100 0 100 200 300400 0 5 10 15 20 25 30 35 40 45 50 55 60 S2-N-S-02-33.4 S2-N-S-02-30.4 S2-N-S-02-27.5 S2-N-S-3.6-21.3 S2-N-S-02-14.5 S2-N-S-02-7.7 S2-N-S-02-1.0 Figure E-1. Load vs. strain at refere nce temperature (Segment 2, North) Strain (microstrain)Load (kips) -700 -600 -500 -400 -300 -200 -100 0 100 200 300400 0 5 10 15 20 25 30 35 40 45 50 55 60 S2-N-S-02-33.4 S2-N-S-02-30.4 S2-N-S-02-27.5 S2-N-S-3.6-21.3 S2-N-S-02-14.5 S2-N-S-02-7.7 S2-N-S-02-1.0 Figure E-2. Load vs. strain with negativ e thermal gradient (Segment 2, North)

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248 Strain (microstrain)Load (kips) -700 -600 -500 -400 -300 -200 -100 0 100 200 300400 0 5 10 15 20 25 30 35 40 45 50 55 60 S2-S-S-02-35.5 S2-S-S-02-32.0 S2-S-S-02-28.5 S2-S-S-02-27.3 S2-S-S-3.6-21.2 S2-S-S-02-14.5 S2-S-S-02-7.7 S2-S-S-02-0.9 Figure E-3. Load vs. strain at refere nce temperature (Segment 2, South) Strain (microstrain)Load (kips) -700 -600 -500 -400 -300 -200 -100 0 100 200 300400 0 5 10 15 20 25 30 35 40 45 50 55 60 S2-S-S-02-35.5 S2-S-S-02-32.0 S2-S-S-02-28.5 S2-S-S-02-27.3 S2-S-S-3.6-21.2 S2-S-S-02-14.5 S2-S-S-02-7.7 S2-S-S-02-0.9 Figure E-4. Load vs. strain with negativ e thermal gradient (Segment 2, South)

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249 Relative Longitudinal Displacement (in.)Load (kips) 0 0.005 0.01 0.015 0.02 0.025 0.03 0.035 0.040.045 0 5 10 15 20 25 30 35 40 45 50 55 60 J2-TN-D-9.5 J2-T-D J2-TS-D-9.5 Figure E-5. Load vs. joint opening at reference temperature (Top flange) Relative Longitudinal Displacement (in.)Load (kips) 0 0.005 0.01 0.015 0.02 0.025 0.03 0.035 0.040.045 0 5 10 15 20 25 30 35 40 45 50 55 60 J2-TN-D-9.5 J2-T-D J2-TS-D-9.5 Figure E-6. Load vs. joint opening with negative thermal gradient (Top flange)

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250 Relative Longitudinal Displacement (in.)Load (kips) -0.005 0 0.005 0.01 0.015 0.02 0.025 0.03 0.0350.04 0 5 10 15 20 25 30 35 40 45 50 55 60 J2-S-D-33.75 J2-S-D-30.25 J2-S-D-25.0 J2-S-D-18.25 J2-S-D-11.375 J2-S-D-4.375 Figure E-7. Load vs. joint opening at reference temperature (South side) Relative Longitudinal Displacement (in.)Load (kips) -0.005 0 0.005 0.01 0.015 0.02 0.025 0.03 0.0350.04 0 5 10 15 20 25 30 35 40 45 50 55 60 J2-S-D-33.75 J2-S-D-30.25 J2-S-D-25.0 J2-S-D-18.25 J2-S-D-11.375 J2-S-D-4.375 Figure E-8. Load vs. joint opening with negative thermal gradient (South side)

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251 LIST OF REFERENCES AASHTO (1989a)., AASHTO Guide Specifications, Thermal Eff ects in Concrete Bridge Superstructures, Washington D.C. AASHTO (1989b)., Guide Specifications for Design and Construction of Segmental Concrete Bridges, 1st Ed., Washington, D.C. AASHTO (1994a)., AASHTO LRFD Bridge Design Specificat ions, Washington, D.C AASHTO (1994b)., Interim Specifications for the Guide Specifications for Design and Construction of Segmental Concrete Bridges, 1st Ed., Washington, D.C. AASHTO (1998a)., AASHTO LRFD Bridge Design Specificati ons, Washington, D.C. AASHTO (1998b)., Guide Specifications for Design and Construction of Segmental Concrete Bridges, Proposed 2nd Ed., Washington, D.C. AASHTO (1999)., Guide Specifications for Desi gn and Construction of Segmental Concrete Bridges, 2nd Ed., Washington, D.C. AASHTO (2004)., AASHTO LRFD Bri dge Design Specifications, 3rd Ed., Washington, D.C. AASHTO TP 60-00. (2004), Standard Method of Te st for Coefficient of Thermal Expansion of Hydraulic Cement Concrete, Washington, D.C. ACI Committee 318 (2002)., Build ing Code Requirements for Stru ctural Concrete (318-02) and Commentary (318R-02). American Concre te Institute, Farmington Hills, Michigan. ASTM C 469-94 (1994), Standard Test Method for Static Modulus of Elasticity and Poissons Ratio of Concrete in Compression, American Society of Testing and Materials, West Conshohocken, PA. ASTM C 39-01 (2001)., Standard Test Method for Compressive St rength of Concrete Cylinders Cast in Place in Cylindrical Molds, Ameri can Society of Testing and Materials, West Conshohocken, PA. Imbsen, R. A., Vandershof, D. E., Schamber, R. A., and Nutt, R.V. (1985)., Thermal Effects in Concrete Bridge Superstructures, NCHR P 276, Transportation Research Board, Washington, D.C. Potgieter, I. C., and Gamble, W. L. (1983)., Response of Highway Bridges to Nonlinear Temperature Distributions, Re p. No. FHWA/IL/UI-201, Univer sity of Illinois at UrbanaChampaign, Urbana-Champaign, Ill. Priestley, M. J. N. (1978)., Design of Concrete Bridges for Thermal Gradients, ACI Journal, 75(5), 209-217.

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252 Roberts, C.L., Breen, J. E., and Kreger, M. E. (1993)., Measurement Based Revisions for Segmental Bridge Design and Construction Cr iteria, Research Rep. 1234-3F, Center for Transportation Research, Univ. of Texas at Austin, Austin, Texas. Roberts, C. L., Breen, J. E., Cawrse J. (2002) ., Measurement of Thermal Gradients and their Effects on Segmental Concrete Bridge, ASCE Journal of Bridge Engineering, Vol. 7, No. 3, 166-174. Shushkewich, K.W. (1998)., Design of Segmental Bridges for Thermal Gradient, PCI Journal, 43(4), 120-137. Steel, Concrete and Composite Bridges, Part I, General Statement. British Standard BS 5400. British Standards Institution. Crowthorne, Berkshire, England (1978). Thompson, M. K., Davis, R. T., Breen, J. E., a nd Kreger, M. E. (1998)., Measured Behavior of a Curved Precast Segmental Concrete Bri dge Erected by Balanced Cantilevering, Research Rep. 1404-2, Center for Transporta tion Research, Univ. of Texas at Austin, Texas.

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253 BIOGRAPHICAL SKETCH The author began his undergraduate educati on in 1997 at Orta Dogu Teknik Universitiesi in Ankara, Turkey. On graduating with a Bachelor of Science degree in ci vil engineering in June 2001, he moved to Ohio where he obtained a Ma ster of Science in ci vil engineering at The University of Akron in August, 2003. Later in August 2003 the author began studying at the University of Florida towards obtaining a Doctor of Philosophy degree in ci vil engineering, with a concentration in structural engineering. Th e author anticipates obtaining this degree in December, 2007. Upon graduating, the author plan s to pursue a career in structural engineering at a design firm.