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Record for a UF thesis. Title & abstract won't display until thesis is accessible after 2010-12-31.

Permanent Link: http://ufdc.ufl.edu/UFE0022760/00001

Material Information

Title: Record for a UF thesis. Title & abstract won't display until thesis is accessible after 2010-12-31.
Physical Description: Book
Language: english
Creator: Llanos, Gustavo
Publisher: University of Florida
Place of Publication: Gainesville, Fla.
Publication Date: 2008

Subjects

Subjects / Keywords: Civil and Coastal Engineering -- Dissertations, Academic -- UF
Genre: Civil Engineering thesis, M.E.
bibliography   ( marcgt )
theses   ( marcgt )
government publication (state, provincial, terriorial, dependent)   ( marcgt )
born-digital   ( sobekcm )
Electronic Thesis or Dissertation

Notes

Statement of Responsibility: by Gustavo Llanos.
Thesis: Thesis (M.E.)--University of Florida, 2008.
Local: Adviser: Hamilton, Homer R.
Electronic Access: INACCESSIBLE UNTIL 2010-12-31

Record Information

Source Institution: UFRGP
Rights Management: Applicable rights reserved.
Classification: lcc - LD1780 2008
System ID: UFE0022760:00001

Permanent Link: http://ufdc.ufl.edu/UFE0022760/00001

Material Information

Title: Record for a UF thesis. Title & abstract won't display until thesis is accessible after 2010-12-31.
Physical Description: Book
Language: english
Creator: Llanos, Gustavo
Publisher: University of Florida
Place of Publication: Gainesville, Fla.
Publication Date: 2008

Subjects

Subjects / Keywords: Civil and Coastal Engineering -- Dissertations, Academic -- UF
Genre: Civil Engineering thesis, M.E.
bibliography   ( marcgt )
theses   ( marcgt )
government publication (state, provincial, terriorial, dependent)   ( marcgt )
born-digital   ( sobekcm )
Electronic Thesis or Dissertation

Notes

Statement of Responsibility: by Gustavo Llanos.
Thesis: Thesis (M.E.)--University of Florida, 2008.
Local: Adviser: Hamilton, Homer R.
Electronic Access: INACCESSIBLE UNTIL 2010-12-31

Record Information

Source Institution: UFRGP
Rights Management: Applicable rights reserved.
Classification: lcc - LD1780 2008
System ID: UFE0022760:00001


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1 SHEAR CAPACITY OF POST-TENSI ONED CONCRETE GIRDERS WITHOUT SHEAR REINFORCEMENT By GUSTAVO ADOLFO LLANOS A THESIS PRESENTED TO THE GRADUATE SCHOOL OF THE UNIVERSITY OF FLOR IDA IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF SCIENCE UNIVERSITY OF FLORIDA 2008

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2 2008 Gustavo Adolfo Llanos

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3 For my father, who was my friend and mentor.

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4 ACKNOWLEDGMENTS I would like to thank the ch air and mem bers of my supervisory committee for their mentoring, and the Florida Department of Trans portation for its generous support. I thank my family and friends for their loving encouragemen t, which motivated me to complete my study.

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5 TABLE OF CONTENTS page ACKNOWLEDGMENTS ............................................................................................................... 4LIST OF TABLES ...........................................................................................................................7LIST OF FIGURES .........................................................................................................................8LIST OF ABBREVIATIONS ........................................................................................................ 11ABSTRACT ...................................................................................................................... .............12 CHAP TER 1 OBJECTIVES .................................................................................................................... .....142 APPROACH ...................................................................................................................... .....153 LITERATURE REVIEW .......................................................................................................164 GIRDER DESIGN ................................................................................................................. .205 BEAM NOMENCLATURE ................................................................................................... 246 GIRDER CONSTRUCTION AND MATERIAL PROPERTIES ..........................................257 PRESTRESSING .................................................................................................................. ..407.1Prestressing Application .............................................................................................. 407.2Instrumentation ............................................................................................................ 407.3Results: Seating Losses ................................................................................................418 MATERIAL PROPERTIES ...................................................................................................559 SHEAR TEST SETUP AND PROCEDURES ....................................................................... 5610 RESULTS AND DISCUSSION: SHEAR TESTS ................................................................. 6110.1Test C1U3 ....................................................................................................................6110.2Test C2U3 ....................................................................................................................6110.3Test C3U2 ....................................................................................................................6211 EFFECT OF SUPPORT CO NDITIONS ON BEHAVIOR ................................................... 7412 STRUT AND TIE ANALYSIS: C3U2 .................................................................................. 86

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6 13 COMPARISON WITH THEORETICAL CAPACITIES ...................................................... 9714 SUMMARY AND CONCLUSIONS ...................................................................................100LIST OF REFERENCES .............................................................................................................102BIOGRAPHICAL SKETCH .......................................................................................................103

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7 LIST OF TABLES Table page 6-1 Dates of C beams ...............................................................................................................397-1 Jacking force measured with load cell ............................................................................... 537-2 Working P-gages for each C beam ....................................................................................537-3 Measured changes in st ress due to seating losses .............................................................. 537-5 Elastic losses for C beams ..................................................................................................537-6 Long term losses in C2 .................................................................................................... ..548-1 Average cylinder strengths ................................................................................................ 558-2 PT-bar strengths .......................................................................................................... .......5513-1 Post-tensioned beam no minal moment capacities ............................................................. 9913-2 Post-tensioned beam shear capacity results .......................................................................99

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8 LIST OF FIGURES Figure page 3-1 Strength of concrete beams failing in shear for various a/d ratios .....................................194-1 Full beam section ......................................................................................................... ......204-2 Girder cross section and post-tensioning tendon details ....................................................214-3 Reinforcement and tendon layout ......................................................................................224-4 Deck configuration and reinforcement .............................................................................. 235-5 Beam nomenclature ......................................................................................................... ..246-1 Pouring of beam .................................................................................................................276-2 End block reinforcement ................................................................................................... .286-4 Strain gages leads exiting duct ........................................................................................... 306-5 Placement of U-bars ....................................................................................................... ....316-6 Formwork of beam and vibrating of concrete ....................................................................326-7 Bottom anchorage with PT duct and grouting tube.. ......................................................... 336-8 Beam being poured ......................................................................................................... ...346-9 Pouring of beam finished .................................................................................................. .356-10 Hand pump for grouting.................................................................................................... .366-11 Deck formwork and mild steel reinforcement ................................................................... 376-12 Finished beam ............................................................................................................ ........387-1 Hydraulic jack used to stress tendons ................................................................................ 447-2 Tendon designation for C beams ....................................................................................... 457-3 Location of gages for C beams .......................................................................................... 467-4 Tendon stress during post-t ensioning of beam C1 .............................................................477-5 Tendon stress during post-t ensioning of beam C2 .............................................................487-6 Example of seati ng and elastic losses ................................................................................ 49

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9 7-7 Summary of seating losses ................................................................................................. 507-8 Summary of elastic losses ................................................................................................. .517-9 Long term strains in beam C2 ............................................................................................ 529-1 Test setup and instrumentation for C beams ...................................................................... 569-2 Support Conditions for C1U3 and C2U3 ........................................................................... 579-3 Test C1U3 ................................................................................................................. .........589-4 Test C2U3 ................................................................................................................. .........599-5 Test C3U2 ................................................................................................................. .........6010-1 Load vs. displacement for C1U3 ....................................................................................... 6310-2 C1U3S14 plot ............................................................................................................. .......6410-3 First and final crack pattern for C1U3 ............................................................................... 6510-4 Load vs. displacement for C2U3 ....................................................................................... 6610-5 C2U3S14 plot ............................................................................................................. .......6710-6 First and final crack pattern for C2U3 ............................................................................... 6810-7 Load vs. displacement for C3U2 ....................................................................................... 6910-8 First and final crack pattern for C3U2 ............................................................................... 7010-9 Strain gages S13, S14, and S15 .........................................................................................7110-10 Crack causing transfer of flexure to strut and tie ............................................................... 7210-11 Cracks around PT anchorage .............................................................................................7311-1 Support condition for C1U3 ............................................................................................... 7711-2 Support condition for C2U3 ............................................................................................... 7811-3 Computer model of beam C at an a/d ratio of 3.0 ..............................................................7911-4 Bearing friction model ................................................................................................... ....8011-5 Definition of transverse support displacement .................................................................. 8111-6 Effect of support restraint on the beam capacity ............................................................... 82

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10 11-7 Load vs. displacement for C1U3 and C2U3 ...................................................................... 8311-8 Plot of C1U3S14, C2U3S14, total botto m displacement for C1U3 and C2U3 ................. 8411-9 Final crack patterns ..................................................................................................... .......8512-1 C3U2 strain gages S13, S14, and S15................................................................................ 8912-2 Crack causing transfer of flexure to strut and tie ............................................................... 9012-3 Change in strain as loading .............................................................................................. ..9112-4 Strut and tie model ...................................................................................................... .......9212-5 Strain gage plot for S5, S6, and S18 .................................................................................. 9312-6 Change in strain as loading .............................................................................................. ..9412-7 Strut and tie model ...................................................................................................... .......9512-8 Strain gage plot for S5, S6, and S18 .................................................................................. 9613-9 Forces in strut-and-tie model .............................................................................................98

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11 LIST OF ABBREVIATIONS a/d shear span to depth fpu specified tensile strength of prestressing steel (ksi) Icr cracked moment of inertia (in.4) LVDT linear variable displacement transducer Mn nominal moment capacity (kip*ft) PT post-tensioning w/c water cement ratio Vc shear contribution of concrete (kip) Vs shear contribution of the steel stirrups (kip) T total lateral displacement (in) strut angle factor relating effect of longitudinal strain on the sh ear capacity of concrete

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12 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 SHEAR CAPACITY OF POST-TENSIONED CONCRETE GIRDER S WITHOUT SHEAR REINFORCEMENT By Gustavo Adolfo Llanos December 2008 Chair: Homer Hamilton Major: Civil Engineering The objective of this study was to evaluate the behavior of post-tensioned I-girders with end blocks. The beams had two pa rabolic tendons and two straight th at were anchored at each of the ends of the beam. Post-tensioning of the b eams was done in the labora tory with the objective of measuring losses due to seati ng, elastic, creep and shrinkage. Outside of the end block, approximately 3 ft from each end, there was no shear reinforcement. U-bars were used in the top fl ange to provide composite action between the deck and girder. Without the presence of shear reinfo rcement loading configurations used short shear span to depth ratios to see if a shear failure would occur. In the field these beams were observed to have no bearing pads and rested directly on concrete. Two post-tensioned beams with the same loading pattern were tested to failure with only the support condition varying, one neoprene and one resting directly on concrete. This was done to see if the stiffness would be affect ed by the support conditions. A third test was conducted for a shorter shear span to observe the type of failure that would occur. Each girder was instrumented to measure strains, vertical de flections and crack initia tion at relevant points.

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13 Finally, capacities were predic ted using three methods, ACI, AASHTO, and Strut-and-Tie. These predicted values were compared to experimental capacities to observe the disparity between the two.

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14 CHAPTER 1 OBJECTIVES One of the early form s of prestressing used in Florida for short span bridges was a precast, post-tensioned I-girder with end blocks. These girders were used in simply supported conditions in which the beam would bear directly on the co ncrete pier cap with only a layer of tar paper separating the two. These beams are particularly interesting because th ey are post-tensioned with both parabolic and straight threadbar tendons and have no shear reinforcement. Mild steel reinforcement is provided only at the end blocks approximately 3 ft from each end, presumably to protect against anchorage failure.

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15 CHAPTER 2 APPROACH Three beam s were constructed using constructio n drawings from actual bridge girders in service as a basis for design. The beams were te sted in three-point bending. Two of the beams have a shear span to depth (a/d ) ratio of 3.0 and the third had an a/d of 2.0. The first two beams were tested with and without neoprene to dete rmine how the behavior might change when the horizontal reaction varies. The third beam evaluated the shear capacity with no mild steel shear reinforcement.

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16 CHAPTER 3 LITERATURE REVIEW Schlaich et al.1 presented the strut-and-tie model. This method is similar to a truss model. Compression is carried by concrete and is represented by struts. Diagonal struts are oriented parallel to the expected axis of cracking. Tension forces are carried by stirr ups, longitudinal reinforcement, or prestressing steel. These te nsion members are called ties. Where the truss members intersect is called nodes. Concrete repr esents the strength in the nodes. The anchorage of the ties is important when considering the nodes strength. The strut-and-tie model allows yielding in the ties before the failure of the c oncrete members such as the nodes and struts. The nodes are classified depending on the forces acting on it. A minimum of three forces need to act on a node to maintain equilibrium. There is also a region called an extended nodal zone which is the intersection of the stru t width and the tie width. To use the strut-and-tie model the member is cl assified in regions, B and D. The B-regions (B for beam or Bernoulli) are based on the Bernou lli hypothesis that strain distribution in a plane remains linear for any loading condition such as bending, shear, axial forces and torsional moments. D-regions (D for discontinuity, disturbance or detail) are the parts of the structure where the strain distribution is nonlinear. Thes e regions are labeled this way because of the changes in geometry or due to changes in loadi ng conditions. Strut-and-Ti e models are best for modeling short shear sp ans like B-regions. The American Concrete Institute (ACI)2 provides examples of se veral different strut and tie models for a variety of structural member s. Guidelines are given when calculating the strength of the struts, tie, and nodes. Reduction factors ar e provided for nodal zones under different loading conditions. Examples are given for idealized prismatic struts and for bottleshaped struts. Bottle-shaped struts are present wh en there is diagonal reinforcement to prevent

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17 splitting of the concre te. ACI reproduces Figure 3-1 from Prestressed Concrete Structures3. The figure represents the shear strength of beam loaded at various a/d ratios. For beams loaded at a/d ratios o f less than 2.5, D -regions control the design of the beam. For a/d ratios greater than 2.5, B-regions are best for modeling the beams strength. Ramirez4 (1994) does a full member strut-tie design of a precast pretensioned beam with depressed strands at midspan. He compares his re sults with the ACI code which uses a sectional approach. At the time the article was presente d there were no requirements considering the interaction of adjacent strands. A strut and tie model is presented which shows the detailing needed to prevent splitting. A stru t and tie model of the forces in the compression flange is also presented. Proper detailing of the web flange conn ection is necessary to in sure that cracking does not occur. This could leave the flange ineff ective in resisting longitudinal stresses. Alshegeir and Ramirez5 (1992) performed testing of three full-scale pretensioned AASHTO type I and II beams. Following testin g an analysis was done. The use of higher strength concrete would improve ultimate capaci ties by strengthening th e nodes and the struts. The size of the bearing plates at the load and support determine one of the dimensions in the nodal zone. The dimensions in the nodal zone dete rmine the stresses in them. The nodes in the support and the load point enc ourage the use of the full uniax ial compressive strength of concrete. This is because of a ll of the framing elements are in compression. When tension ties are present in the node the use of a reduced uni axial compressive strength should be used. MacGregor and Wight6 (2005) explain six methods for sh ear design. The first is a Truss Analogy also known as Strut and Tie model which considers one load case and analyzes the mechanism resisting that load. The second is th e traditional ACI design procedure which uses a Vc, the shear contribution of concrete, term that is factored depending on the type of concrete

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18 and also by an empirical function. ACI uses a Vs, the shear contribution of the stirrups, term which implies that the cracks are forming at an angle close to 45 degrees. The following three methods are variations of the Compression Field Theory (CFT). CFT looks at the web of the beam cracking due to principal tension stresses in the web. Since the web is cracking the web losses ability to transmit tension force. A mechan ism similar to a truss carries tension forces through stirrups and compression forces between the cracks. The first CFT method, CFT-84, did not consider Vc and only considered the stirrups for c ontribution to shear capacity. The second method, MCFT-94, took into account the contribution of concrete similar to ACI but factored Vc by which considers the strut angle, This version uses tables for getting and The latest version, MCFT-04, gives equations for calculating to allow for a simpler approach to getting The last method is the Shear Friction Method. Th is method considers the shear contribution to shear capacity of concrete to be friction be tween sections throughout a beam. These sections represent the inclined cr acks or shear slip planes. Although th ese sections should be considered at an incline for simplicity they are taken to be st raight. This allows us to consider the three main methods for predicting shear capacities and what they consider in analyzing shear capacity. Bakht and Jaeger7 (1988) study the bear ing restraint in slab-on-girder bridges. Models are done for steel on steel and steel on concrete bearings. The presence of horizo ntal restraints at the girder bearings provides stiffness to the beam. Bridges with relatively new bearing pads provide bearing restraint that can reduce the total moment s due to applied loads by 9%. When compared to theoretical deflections, ther e was a 20 to 30% decrease in measured deflections. It is suggested that bearings permitting free movement of the girder not be provided for short spans bridges that can be designed for thermal effects and bearing restraint forc es. Providing bearing restraints can provide a singl e span bridge with a substa ntial increase in capacity.

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19 Figure 3-1. Strength of conc rete beams failing in shear for various a/d ratios

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20 CHAPTER 4 GIRDER DESIGN The constructed girders were m odeled after pos t-tensioned beam conf igurations used in Florida bridge construction in the 1950s. The nearly 47-ft long beams ha d four 1-in. diameter post-tensioning bars., which was a s light alteration from the origin al plans that called for 1 1/8in. diameter ( Figure 4-1). Although the plans called for high strength creepless alloy steel, Grade 150 bars (fpu = 170ksi) were used in the prototype base d on availability. The properties of steel that the plans called for were not know. Two bars were placed in a parabolic conf iguration with the other two bars placed at the bottom of the beam in a straight configuration ( Figure 4-2). Mild steel was placed in the end block for 34 in. at each end of the beam (See Figure 4-3). The longitudinal steel in the end block extended just beyond the last stirrup. T he U-shaped bars located at the top of the beam were intended to ensure composite action and do not extend a sufficient distance into the beam to provide added shear capacity. A 2 ft 4 in. wide by 7 in. thick deck was placed on the girder to imitate actual service conditions ( Figure 4-4). The deck reinf orcement consisted of two ro ws of transverse #5 bars and two rows of longitudinal #4 bars. 46' 10" 10 #6 bars8 #5 bars10 #6 bars 8" 8" Figure 4-1. Full beam section

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21 PARABOLIC BARS STRAIGHT BARS 8"8" 6" 6" 16"6 1/2" 6" 10" Figure 4-2. Girder cross secti on and post-tensioning tendon details

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22 1' 8" 4"4 SP @ 3"3 SP @ 6" 2 7/16"6" 4" 1' 4" 2 1/2" 1" PT BAR Figure 4-3. Reinforcement and tendon layout

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23 2 #4 @ 14" 3 #5 @ 12" #5 bar @ 12" sp. #5 bar @ 6" sp. 2' 4" 7" Figure 4-4. Deck configuration and reinforcement

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24 CHAPTER 5 BEAM NOMENCLATURE The following sections describe testing conducted on several different beam configurations with a number of different load configurations. The beams, tests, and instrumentation will be referred to using the same system. C2U3 is an example of beam 2 with an a/d of approximately 3. C1U3L3 is an example of an LVDT number 3 in beam 1 with an a/d of approximately 3. _ _Beam Test Instrumentation Label Gage Number Sequentially Numbered P Strain Gage on Post-Tensioning Bar R Strain Gage Rosette on Concrete S Single Strain Gage on Concrete L LVDT C1U3 (a/d = 3.0) C2U3 (a/d = 3.0) C3U2 (a/d = 2.0) Figure 5-5. Beam nomenclature

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25 CHAPTER 6 GIRDER CONSTRUCTION AN D MATERIAL PROPERTIES Construction was perform ed at the Florida Department of Trans portation Structures laboratory in Tallahassee, Florida. Formwork was constructed of welded steel panels that were assembled to provide a single form for the full length of the beam. Steel reinforcement was fastened to the formwork and rested on chairs in order to keep them in place while concrete was poured (See Figure 6-2 and Figure 6-3). 40 mm galvanized steel duct was used to hold a single post-tensioning bar. The duct was fastened to fo rmwork and strapped to chairs at increm ental points along the beam length to maintain the para bolic or straight conf iguration during casting. Assembly started with placing the bottom form s on the top flange of a steel I-beam, which was placed on the strong floor. One side of the formwork was erected. Mild steel cages were assembled and placed at each end. Plywood bulkheads were fabricated that enclosed the ends of the beam form. Anchorages were 1-3/4 in. x 6 in. x 10 in. steel plates with countersunk holes. The holes were conical in shape. The anchorages are fitted with 1 in. anchor nuts. The anchorages were dome shaped so that when fitting against the bear ing plate there is one line of contact surface. The anchorages were fastened to the plywood bul khead in the proper configuration and angle. The duct was then formed and installed from anc horage to anchorage alo ng with tubes and vents necessary to facilitate grouting. Strain gages were applied to the prestressing bars as detailed in the instrumentation section. A hole was cut in to the duct surrounding theses gages to pass the wires connecting to these gages. The bars were then carefully inse rted into the duct with anchor nuts installed. The hole was sealed and the wires were lead out of the beam (See Figure 6-4). Ubars were held in place b y tying them to a l ongitudinal bar running along the top of the beam

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26 (See Figure 6-5). The opposite form was then installe d with all-thread rod used as form ties. Final ad justments in duct and reinforcement were made after the form ties were in place. The beams were cast using ready mix concrete that was bucketed to the form with the laboratory crane ( Figure 6-8). The water cement ratio was 0.41 and the aggregate size and type was in. Florida Lim estone. One concrete truck was needed for the entire beam. The concrete was vibrated using both internal and external vibration. Twelve cylinders were taken to test compressive strength of the concrete. When cylinder strengths tested at or above 3600psi the beam was stressed as detailed in the following section. Immediately after stressing the PT ducts we re grouted. The grou ting procedure was as follows. The grout used was a Portland cement and water mixture mixed to w/c=0.45. Several batches of grout were mixed in a 5-gallon bucket single batch and used to fill the ducts with the hand pump shown in Figure 6-10. The grout was injected from one end of the beam and was continuous ly pumped until it ran out of the vent pipe at the opposite anchorage. The grouting proceeded from bar 1 duct to bar 4 duct. After grouting, the deck formwork and m ild steel reinforcement were placed ( Figure 6-11). The deck was poured using the sam e method as the beam. The finished beam is shown in Figure 6-12.

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27 Figure 6-1. Pouring of beam

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28 Figure 6-2. End block reinforcement

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29 Figure 6-3. End block reinforcement resting against a chair Chair

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30 Figure 6-4. Strain ga ges leads exiting duct

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31 Figure 6-5. Placement of U-bars

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32 Figure 6-6. Formwork of beam and vibrating of concrete

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33 A B Figure 6-7. Bottom anchorage with PT duct and gr outing tube. A) inside view, B) outside view.

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34 Figure 6-8. Beam being poured

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35 Figure 6-9. Pouring of beam finished

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36 Figure 6-10. Hand pump for grouting

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37 Figure 6-11. Deck formwork and mild steel reinforcement

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38 Figure 6-12. Finished beam

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39 Table 6-1. Dates of C beams Beam Casting of Beam Casting of Deck PostTensioning Grouting Testing C1 12-5-07 1-15-08 1210-07 12-10-07 2-20-08 C2 1-30-08 3-26-08 25-08 2-5-08 4-30-08 C3 4-11-08 6-2-08 416-08 4-16-08 7-25-08

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40 CHAPTER 7 PRESTRESSING 7.1 Prestressing Application A 60 Mp Series 04 jack was used to stress the PT bars. The jack is a 80 ton hydraulic actuator designed to stress a single threadbar tendon. The jack is f itted with a socket at the nose that fits the PT bar nut and can tighten just prior to release. The target prestress for each tendon was 93 kips Prestress was measured with load cells placed between the anchor plate and the jack. As each bar was being stressed the nut needed to be tightened with a wrench that was attached to the jack. The jack was placed on the anchorages at the North end of the beam (as it wa s oriented during stressing). Refer to Figure 7for a picture of the jack. To avoid exceeding allowable concrete stresses, the bars were stressed in two stages in the following order: 2,3,1,4 (Figure 7-2). The first stage consiste d of stressing each tendon to 50% of the desired final stress in the order indicated. T he stressing sequence was then repeated to reach the final desired stress. Table 7-1 shows the jacking force at each stage for each beam. 7.2 Instrumentation Strain gages were applied to the bars to al low m easurement of prestress losses and tendon stresses during load testing. Tandem gages were placed on the bars near each end of the beam ( Figure 7-3). Using the measured strains, stress es were calculated by factoring them by Youngs modulus. Some of the gages were damaged duri ng installation and prestr essing of the tendons. Table 7-2 shows the surviving strain gages for C1 and C2. None of the gages in C3 survived or provided data that coul d be used to measure stresses.

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41 7.3 Results: Seating Losses Measurem ents were taken during post-tension ing to determine seating losses, elastic losses, friction losses and early creep losses. Se ating losses in prestressi ng bar anchorages occur when the bar is released and the an chor nut is allowed to settle against the an chor plate. As the bar is being prestressed, the anchor nut is tighten ed with a wrench to minimize the seating losses when the tendon is released. Wh en the bar is released the remaining space is closed, which is termed take up Seating losses can be measured by observing the change in strain that occurs when the jack is released. This is best done when using the strain data fr om the gages locat ed nearest the stressing end of the beam. Strain gages at the dead end will be affected by friction losses from wobble or drape. Figure 7-4 and Figure 7-5 show a time trace of th e stress in each tend on. The stress was calculated from strain data using a Youngs modulus of 28,500 ksi. The plots display only the data from strain gages that were ope rating properly and includ e the average of each tandem pair of strain gages when both were ope rating correctly and sing le readings when only one of the gages was working properly. The pl ots illustrate the staging used to stress the tendons. Each was initially stressed to approximately half of the target prestress, followed by another round of prestressing to reach the target prestress. Figure 7-6 illustrates how elastic losses a nd seating losses were determ ined from the strains measured in the bars during post-tensi oning. The graph shows the plots of two tandem strain gages converted to stress. As noted on the plot, seating loss was the immediate reduction in stress as the jack was released. The maximum strain of the averaged tandem pair of strain gages was used. The three subsequent sharp dr ops in stress are the elastic losses caused by stressing each of the adjacent tendons.

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42 The jacking stresses and loss in stress due to seating are summarized in Table 7-3. The seating losses for beam C1 bars 3 and 4 and beam C2 bar 1 were measured using strain gages at the stressing end of the beam. Seating losses for bars 3 and 4 in beam C2 were measured using the strain gages at the dead end. In addition, the prestress loss as a percentage of the jacking stress is shown for both stages. Seating lo sses for the straight tendons (3 and 4) were consistently in the range of 2% regardless of the jacking stress. The parabolic tendon, however, was 2 to 3 times this value. This could have be en due to the anchor plate not being perpendicular to the post-tensioning bar. This could have caused the bar to sit lo wer on the countersunk hole while stressing. When the bar is released the bar w ould pull up higher and sit tighter into the anchor plate. The take up at the stressing end anchorage was calculated using this sudden change in strain and multiplying it by the length of the tendons, 46ft 10in. and are presented in Table 7-4. Typical set can be about 0.03 in. but varies depending on the type of anchorage (L in and Burns 1981). Table 7-5 shows the elastic losses due to st ressin g of adjacent tendons. The change in strain for each tendon was measured as each of the following bars in the sequence were stressed. For example, during stage 1 stressi ng of tendon 4 in beam C1, the m easured decrease in stress of tendon 3 was 1.8 ksi. The attendant loss of pr estress was 3.9% based on the stress in tendon 3 just prior to stressing tendon 4. In general, the highest lo sses were caused by immediately adjacent tendons. For instance, the maximu m loss in tendon 1 (3.0%) was caused by the adjacent tendon 2.

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43 Using the AASHTO8 method for calculating losses due to elastic shortening the first and second stage of stressing was calculated to be 2.6 ksi. A comparison could not be done due to a lack of data. A wobble coefficient was calculated for Bar 4 beam C1. This was done by taking the maximum stress in the bar, measured by the stra in gage, at the jacki ng end and comparing the stress at the same point in time at the dead e nd of the beam. Using these two stresses a wobble coefficient of 0.0007 per ft was measured. The Amer ican Concrete Institut e, ACI, gives a range for the wobble coefficient of 0.0001 to 0.0006 for high-strength bars grouted in metal sheathing (ACI 2005). To observe long-term losses, tendon stresses in C2 were measured for approximately 2.5 days after stressing ( Figure 7-9). The percentage of losses due to short-term creep and shrinkage effects were 6.3 and 5.6 percent (See Table 7-6) A loss of 1.6 ksi is calculated using the AASHTO method. Equation 5.9.5.4.2a-1 and 5.9 .5.4.2b-1, from AASHTO 2007, were used for calculating shrinkage and creep, resp ectively. Using our initial prestr ess force this yields a loss of approximately 1.7%.

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44 Figure 7-1. Hydraulic jack used to stress tendons

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45 Bar 1 Bar 2 Bar 4 Bar 3 Figure 7-2. Tendon designation for C beams

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46 P13 & P14 P9 & P10 P5 & P6 P1 & P2 P15 & P16 P11 & P12 P7 & P8 P3 & P4 BACK BAR FRONT BAR1' 0" + -1' 0" + Figure 7-3. Location of gages for C beams

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47 Time (seconds)Stress (ksi) Stress (MPa) 0 500 1000 1500 20002500 0 20 40 60 80 100 120 0 150 300 450 600 750 C1U3P11 C1U3P12 C1U3P14 C1U3P15 C1U3P16 Figure 7-4. Tendon stress during po st-tensioning of beam C1

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48 Time (seconds)Stress (ksi) Stress (MPa) 0 500 1000 1500 2000 25003000 0 20 40 60 80 100 120 0 150 300 450 600 750 C2U3P3 C2U3P9 C2U3P10 C2U3P13 C2U3P14 Figure 7-5. Tendon stress during po st-tensioning of beam C2

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49 Time (seconds)Stress (ksi) 0 500 1000 15002000 40 42 44 46 48 50 Average Stress in C1 Bar 3 Seating Loss Elastic Loss Creep Figure 7-6. Example of s eating and elastic losses

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50 1234 TendonsPrestress Loss (%) 0 1 2 3 4 5 6 7 8 9 10 C1 Stage 1 C2 Stage 1 C1 Stage 2 C2 Stage 2 Figure 7-7. Summary of seating losses

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51 Prestress Loss (%) 0 2 4 6 8 10 12 14 C1 C21234 Tendons Figure 7-8. Summary of elastic losses

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52 Time (seconds)Stress (ksi) Stress (MPa) 0 50000 100000 150000 200000250000 0 20 40 60 80 100 120 0 150 300 450 600 750 C2U3P3 C2U3P13 C2U3P14 Figure 7-9. Long term strains in beam C2

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53 Table 7-1. Jacking force measured with load cell Stage Jacking Force (kip) C1 C2 C3 1 46.7 45.7 46.7 2 94.5 93.4 93.5 Table 7-2. Working P-gages for each C beam C1 C2 P11 P3 P12 P9 P14 P10 P15 P13 P16 P14 Table 7-3. Measured changes in stress due to seating losses Bar Stage Jacking Stress (ksi) Seating Loss (ksi) Prestress Loss (%) C1 C2 C1 C2 C1 C2 1 1 --42.8 --3.13 --7.3 2 --99.7 --4.46 --4.5 3 1 48.6 49.9 1.0 0.74 2.1 1.5 2 100 99.2 1.3 0.47 1.3 0.5 4 1 48.0 53.5 1.4 1.50 2.4 2.8 2 103 103 2.2 2.46 2.1 2.4 Table 7-4. Measured take-up Tendon Stage 1 (in.) Stage 2 (in.) C1 C2 C1 C2 1 --0.06 --0.09 3 0.02 0.02 0.02 0.01 4 0.03 0.03 0.04 0.05 Table 7-5. Elastic losses for C beams Tendon Jacking Tendon Stage 1 Stage 2 C1 C2 C1 C2 f (ksi) %loss f (ksi) %loss f (ksi) %loss f (ksi) %loss 1 4 ----0.51 1.3 ----0.46 0.5 3 1 0.9 2.0 0.81 1.7 1.1 1.1 1.21 1.2 3 4 1.8 3.9 1.75 3.4 2.4 2.4 1.91 2.0

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54 Table 7-6. Long term losses in C2 Tendon f (ksi) %loss 1 5.99 6.3 4 5.52 5.6

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55 CHAPTER 8 MATERIAL PROPERTIES For each beam tested cy linder strength were te sted for the beam itself and the deck. The average strengths for the beam and the deck are presented in Table 8-1. Samples of the posttensioning bars were also taken and tested, their average m ateri al properties are presented in Table 8-2. Table 8-1. Average cylinder strengths Beam Beam Cylinder Strengths (ksi ) Deck Cylinder Strengths (ksi) C1 7.96 3.34 C2 8.64 5.47 C3 8.64 4.89 Table 8-2. PT-bar strengths EUL @ 0.50% Stress (ksi) 140.2 Tensile Strength (ksi) 169.9 Elongation (%) 7.8 Youngs Modulus (ksi) 30152.5

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56 CHAPTER 9 SHEAR TEST SETUP AND PROCEDURES Three tests were conducted using a th ree point loading schem e shown in Figure 9-1. Two tests were conducted using a shear span to depth (a/d) ratio of 3.0. One of these tests (C1U3) was set up with the beam bearing direct ly on the concrete pedestal support ( Figure 9-2). The second test (C2U3) was set up with the beam b earing on a neoprene pad (2 in. thick). This was done to observe the effect of the support conditions on the beam behavior. The third test (C3U2) was loaded at a/d = 2.0 and was be aring on a neoprene pad. This te st was intended to evaluate the shear behavior of the short shea r span and no shear reinforcement. The load was applied through a 1-in. thick re inforced neoprene bear ing pad at a loading rate of 0.25 kips/second. Displacements were m easured at the load point and each of the supports. Beam end movement was measured at the top and bottom. A load cell was used to measure load under the actuator. The detailed instrumentation for each test is shown in Figure 93 through Figure 9-5. Strain was measured with 60 mm strain rosettes and strain gages. For test C2U3 five 30 mm strain gages were used in the deck and top flange of the beam in addition to the 60 mm gages. Test C3U2 used sixteen 30 mm strain gages in the top flange and deck of the beam in addition to the 60 mm gages. 4" 4" 9 2' 9" 9" 2' 9"46' 10" a LVD T LVDT LVDT LVDT Load Cell Figure 9-1. Test setup and instrumentation for C beams

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57 A B Figure 9-2. Support Conditions for A) C1U3 and B) C2U3

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58 4" 4" 9" 2' 9" 9" 2' 9"46' 10" 12' 1" L1 L2 L3 L4 L5 L8 L6 and L7 on each side of load plate A 1" 6" 4" 10" 2' 8" 1' 7" 3' 10"1' 10" 1' 1" 2' 7" 7' 10" 10' 1" 11' 1" 12' 1"S14 S13 S12 S10 S11 S9 R7 R6 R5 R4 S16 S15 S8 S7 S6 R3 R2 R1 S5 S4 S3S1 S2 Top View at Load Point 1' 1" 1' 2" DECK/GIRDER INTERFACE B Figure 9-3. Test C1U3 A) setup B) instrumentation

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59 4" 9" 2' 9" 9" 2' 9"46' 10" 12' 1" L1 L2 L3 L4 L5L6 L10 L7 and L8 on each side of load plate L910' 7" 13' 7" 4" A 10' 1" 11' 1" 12' 1" 13' 1" 14' 1" 15' 1"1' 10"9' 1" 20' 0" S15 S14 S13 R2 R1 R3 S6S5S4 S1 S2S3S29 S31 S30 S26 Top View at Load Point S28 S27 S20 S19 S 1 7 S 1 8 2 6 "6" 6 S21 S22 S23 S24 S25 2 2 2 2 2 DECKNOTE NOTES10 S12 S11 S9 S7 S8 1' 2" 2' 2" 3' 2" 10" 1' 10" 2' 10" 1' 1" 1' 2" S 1 6 DECK/GIRDER INTERFACE B Figure 9-4. Test C2U3 A) setup B) instrumentation

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60 4" 9" 2' 9" 9" 2' 9"46' 10" 8' 0" L1 L2 L3 L4 L5 L6 L10 L7 and L8 on each side of load plate L96' 6" 9 6" 4" A 6' 0" 7' 0" 8' 0" 9' 3" 10' 0" 11' 0"1' 10"5' 0"S15 S14 S13 R2 R1S 1 7 S8 S7S2S1 S9S3 S10S4 S11S5 S12S6 S20 S19 Top View at Load Point 5 5 "S 1 8 S 1 62 0 S29 S30 S31 S32 S33 2" 2" 2" 2" 2" DECKNOTE NOTE 1' 1" 1' 2" DECK/GIRDER INTERFACE S21 S22 S23 S24 S25 4" 2" 2"S26 S27 S28 S34 S35 S36 B Figure 9-5. Test C3U2 A) setup B) instrumentation

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61 CHAPTER10 RESULTS AND DISCUSSION: SHEAR TESTS 10.1 Test C1U3 Figure 10-1 showed linear-elastic behavior for te st C1U3 up to a load of 74 kips where the first flexural crack occurred. The crack was detected by gage S14, which was located on the beam bottom under the load point ( Figure 10-2). Gage S14 showed that the flexural crack for med at a tensile strain of nearly 400 microstrain. Figure 10-3 showed the loca tion of the first crack. As loading continued, furt her flexure cracks formed under th e load point as the stiffness decreased. The beam reached its maximum capacity at a shear of 135 kips where a flexurecompression failure occurred in th e deck under the load point. Figure 10-3 showed the final crack pattern. 10.2 Test C2U3 The initial behavior of C2U3 was sim ila r to C2U3 up to and including cracking. Figure 10-4 showed linear elastic behavior up to a load of 74 kips where the first flexural crack occurred. The crack was detected by gage S 14, which was located on the beam bottom under the load point ( Figure 10-5). Although the initial strain beha vior was linear, the behavior appeared to soften as the crack ing load of 74 kips was reached the strain spiked. Figure 10-6 showed the location of the first crack. At a load of appr oxim ately 92 kips the beams began to soften. Softening in the beam was shown by the change of slope in the load displacement curve. Beyond this point the beam was cracking more fr equently. The load-displacement eventually plateaus, indicating that the tendons have yielded. The beam reached its maximum capacity at a shear of 127 kips where a flexurecompression failure occurred in the deck under the load point. Figure 10-6 showed the final crack pattern.

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62 10.3 Test C3U2 Figure 10-7 is the load displacement plot for test C3U2. The beam showed linear-elastic behavior until a load of 86 kips. A crack wa s also heard and observed at this load. Figure 10-8 showed where the first crack in itiated. As load ing continued cracks were observed. Strain gages S13, S14, and S15 showed when so me of these cracks occurred (See Figure 10-9). S14 showed a constan t growth in strain until a load of 92 kips where the strain immediately changed slope and began to lose tensile strain. Th e strain measured at 92 kips was 386 microstrain. Cracks also formed at 109 kips and at 155 kips. The load displacement curve shows that the beam was cracking a significant amount during this range of lo ads. At a load of 156 kips a large crack was observed running through the web and into the transition zone between the web and the end block (See Figure 10-10). At a load of approximately 179 kips the load displacement curve began to flatten with little incr ease in capacity relative to disp lacement indicating that the bar were yielding. At a load of 187 kips cracks were observed around the anchor plate for the parabolic PT bars (See Figure 10-11). The test was terminated at this p oint to avoid an explosive failure. The final crack pattern can be seen in Figure 10-8. The peak load measured during testing was 187 kips. This widespre ad cracking and large deflection indicate that the prestressing bars had reached yield. The fina l failure m ode, however, was not determined because the test was terminated prior to r eaching the peak capacity.

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63 Displacement (inches)Superimposed Shear (kip) 0 0.5 1 1.5 2 2.53 0 25 50 75 100 125 150 Figure 10-1. Load vs. displacement for C1U3

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64 Superimposed Shear (kip)Strain (microstrain) 0 25 50 75 100 125150 -500 -400 -300 -200 -100 0 100 200 300 400 500 S14 Figure 10-2. C1U3S14 plot

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65 Figure 10-3. First and final crack pattern for C1U3

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66 Displacement (inches)Superimposed Shear (kip) 0 1 2 3 4 56 0 25 50 75 100 125 150 Figure 10-4. Load vs. displacement for C2U3

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67 Superimposed Shear (kip)Strain (microstrain) 0 50 100 150 -1000 -750 -500 -250 0 250 500 750 1000 S14 Figure 10-5. C2U3S14 plot

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68 Figure 10-6. First and final crack pattern for C2U3

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69 Displacement (in.)Superimposed Shear (kip) 0 0.5 1 1.5 2 2.53 0 50 100 150 200 Figure 10-7. Load vs. displacement for C3U2

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70 Figure 10-8. First and final crack pattern for C3U2

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71 Superimposed Shear (kip)Strain (microstrain) 0 50 100 150200 -100 0 100 200 300 400 500 S15S14S13 S13 S14 S15 Figure 10-9. Strain gages S13, S14, and S15

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72 Figure 10-10. Crack causing transf er of flexure to strut and tie

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73 Figure 10-11. Cracks around PT anchorage

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74 CHAPTER 11 EFFECT OF SUPPORT CONDITIONS ON BEHAVIOR C1U3 and C2U3 were conducted with a shear sp an to depth ratio (a/d) of 3.0. The first test, C1U3, used support conditions shown in Figure 11-1 in which the beam was bearing directly on concrete. The second test, C2U3, used neoprene pads under each of the supports ( Figure 11-2). Both tests had the same loadi ng schem e and loading rate, the support conditions were the only variable between th e two tests. The intent of the test was to explore the difference in behavior between the two support conditions. This information will be used to guide the interpretation of data on future load tests. Typically, beams are modeled assuming the b eam is supported by a pin and roller, which offers no resistance to transverse movement. Conversely, arches are modeled with pinned supports, which provide and infi nitely stiff support and ensure pure arching action. These modeling choices are made with the understanding that the ac tual conditions are situated somewhere between these bounds. Shallow arches re quire very stiff support conditions to ensure pure compression. Furthermore, very small tran sverse movements allowed at the reaction will shift the behavior from arching to flexure. To estimate the magnitude of load that must be resisted by the suppor ts in the laboratory, the beam specimen was modeled using membrane elements as shown in Figure 11-3. A rectangular cross-section was used with a thickness of 17 in., wh ich is the average thickness of the specim en. The element was 5.8-ft long by 3.92-ft deep, and a modulus of elasticity of 4030 ksi was used, which corresponds to a compressive strength of 5 ksi. The transverse and vertical reactions for a unit load required to maintain pure arching are shown in the figure. While pure arching was not expected to occu r using the tested support conditions, some effect was anticipated. Figure 11-4 shows the expected restra int provided by the supports used in

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75 the testing. For the direct bearing testing, the tran sverse reaction is expect ed to be a function of the frictional force generated by th e direct concrete contact. For the neoprene bearing pad test, the reaction is expected to be a function of the shear stiffness a nd the transverse displacement of the bottom of the beam. Figure 11-5 defines the transv erse support displacem ent. Figure 11-6 shows the effect of the transverse reactions on the internal forces. As the HL reaction increases, then the tension force required to maintain equilibrium is reduced. If the horizontal reaction is sufficient, then T will go to zero. The overall behavior of the two tests is illu strated in the load vs. displacement curves shown in Figure 11-7. As discussed previously, th e shear at which crack ing occurred was approximately 74 kips for both tests. Furtherm ore, the behavior up to cracking appears very similar between the two beams, indicating that th e different support conditi ons had little effect before the beam cracked. This lack of differen ce is likely due to the relatively small amount of support movement needed to relieve ar ching action before cracking occurs. Figure 11-8 shows the flexural tensile strain under the load point and the total lateral displacem ent of the beam bearing ( T) defined as: RLT (10-1) where the variables are defined in Figure 11-5. The total transverse movement of the bearings on both beam s is nearly identical up to cracking. The total movement measured for C1U3 and C2U3 at a superimposed shear of 70 ki ps was 0.080 and 0.085 inches respectively. For comparison, one of the transverse support restraints was removed from the model shown in Figure 11-3 to determine the total transverse m ovement expected. The resulting total movement was 0.108 in., which is comparable with the observed values. Fo r the direct concrete bearing condition, it is suspected that support blocks settled as lo ad was applied, which relieved the arching action prior to cracki ng. Furthermore, the movement was so small that the neoprene

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76 bearing pad generated little tran sverse reaction. In conclusion, the bearing conditions used in these tests appeared to have litt le effect on the early behavior of the beams. If similar bearing conditions are encountered in the field, then it is expected that little difference might be seen in the field under load test conditions. After first crack the beam behavior began to diverge ( Figure 11-7). The di rect bearing test showed a higher post-cracking stiffness with a 6. 8% higher capacity than that of the neoprene bearing tes t. The ultimate displacement, how ever, was approximately 59.0% of the neoprene bearing test. Further evidence of post-cracking b earing restraint is seen in the divergence of T as ultimate capacity is approached ( Figure 11-8). After cracking, the total outward support move ment of C2U3 was greater th an that of C1U3 indicating that the transverse force generated at the support for C1U3 was beginning to effect the behavior. This diffe rence is an indication that the frictional force generate d was greater than that provided by the neoprene bearing pads. In conclusion, the direct cont act bearing provided more restra int than that of the neoprene bearing pad, thus resulting in higher capacity and less ductility. The two final crack patterns can be seen in Figure 11-9. For C1U3 cracks were not observed to spread into the top flange as they were in C2U3. Since th e cracks are sm aller in C1U3 its cracked moment of inertia, Icr, is larger than that of C2U3. The stiffness of a member is dependant on its moment of inertia, the higher the Icr, the smaller the deflection. This behavior is observed while comparing the two load vs. displacement plots in Figure 11-7. Both C1U3 and C2U3 displayed the sam e be havior until cracking occurred. Once cracking becomes present the two tests begin to react in different ways because of the support conditions. The inability of C1U3s ends to slide freely cau se a marginal increase in capacity, 8 kips, but lead to a sudden failure, C2U3 had a ducti le failure which is more desirable.

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77 Concrete Block Floor Ties for Concrete Blocks A B Figure 11-1. Support condition for C1U3

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78 Concrete Block Floor Neoprene Pad A B Figure 11-2. Support condition for C2U3

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79 1 0.25 0.75 1.67 1.67 Figure 11-3. Computer model of beam C at an a/d ratio of 3.0

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80 P HL= m RLor HL= DLKNEOPRENERL HR= m RRor HR= DRKNEOPRENERR Figure 11-4. Bearing friction model

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81 DRDL Figure 11-5. Definition of tr ansverse support displacement

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82 RLHLT C + HLPA B Figure 11-6. Effect of support restraint on the beam capacity

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83 Displacement (inches)Superimposed Shear (kip) 0 1 2 3 4 56 0 50 100 150 C1U3 C2U3 Figure 11-7. Load vs. displacement for C1U3 and C2U3

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84 Superimposed Shear (kip)Strain (microstrain) DT (inches) 0 50 100 150 -1000 -2 -500 -1 0 0 500 1 1000 2 S14 for both C1 and C2 Strain C1U3 Strain C2U3 DT C2U3 DT C1U3 Figure 11-8. Plot of C1U3S14, C2U3S14, to tal bottom displacement for C1U3 and C2U3

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85 A B Figure 11-9. Final crack pattern s for A) C1U3 and B) C2U3

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86 CHAPTER 12 STRUT AND TIE ANALYSIS: C3U2 Figure 10-7 is the load displacement plot for test C3U2. The beam shows linea r-elastic behavior until a load of 86 kips. As loading continued flexure cracks were observed. Strain gages S13, S14, and S15 are located at the bottom of the beam a nd measure the initial flexure cracks. At a load of 153 kips a large crack wa s observed running through the web and into the transition zone between the web and the end block ( Figure 12-2). When this crack occurs the beam stops behaving as a flexural member and be gins to behave as a strut and tie model. Figure 12-3 shows the strain through the height of the beam as load ing continues. The strain distribution is linear unti l a load of 153 kips where the strain is no longer linear due to cracking. Evidence of this change in behavior can be observed in Figure 12-4. Figure 12-5 shows that the gages on the top of the deck, S5 and S6, grow constantly in com pression until 153 kips where the strain suddenly drops. Corresponding to the sudden drop in strain for gages S5 and S6 th ere is a jump in compressive strain in gage S18. This shows that when this crack occurs the compressive strain is transferred from the deck and into the compression strut. As loading increases the parabolic bars begin to carry load. When this happens a node is created at the junction between the original strut and the parabolic ba rs, or tie. As the second tie carries additional force the node tr avels towards the anchorage. The compression forces begin to change direction at the node to wards the support. At a load of approximately 179 kips the load displacement curve begins to flatte n with little increase in capacity relative to displacement. The flattening of the load displacement curve shows that the PT bars are beginning to yield. At a load of 188 kips cracks were observed around th e anchor plate for the parabolic PT bars. Cracking around the anchor plate confirm that the parabolic tendons were ca rrying all the tensile

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87 force in the strut and tie model. The PT bars, or the tie, is what caused the beam to fail. The bars could no longer carry any additional force. Figure 10-7 is the load displacement plot for test C3U2. The beam shows linea r-elastic behavior until a load of 86 kips. As loading continued flexure cracks were observed. Strain gages S13, S14, and S15 are located at the bottom of the beam a nd measure the initial flexure cracks. At a load of 153 kips a large crack wa s observed running through the web and into the transition zone between the web and the end block ( Figure 10-10). When this crack occurs the beam stops behaving as a flexural member and be gins to behave as a strut and tie model. Figure 12-3 shows the strain through the height of the beam as load ing continues. The strain distribution is linear unti l a load of 153 kips where the strain is no longer linear due to cracking. Cracking in the beam has occurred before 153 kips as shown by gages S13 and S14 yet the progression of strain is still li near that load. This is confirmation that the beam has full composite action between the deck and beam, beam theory applies, and the section is behaving as a B-region. B-regions typically begin at a distance of one member-depth away from a discontinuity. This distance is used as a guideline and is not precise. The load point for this test lies at approximately one member depth away from the transition between the end block and the I-shape in the section. Evidence of this change in behavior can be observed in Figure 12-4. Figure 12-5 shows that the gages on the top of the deck, S5 and S6, grow constantly in com pression until 153 kips where the strain suddenly dropped. Corresponding to the sudden drop in strain for gages S5 and S6 there was jump in compressive strain in gage S18. This showed that when this crack ( Figure 10-10) occurred the compressive strain was transferred from the deck and into the compression strut ( Figure 12-4).

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88 As loading increased the parabolic bars begin to carry load. When this happened a node is created at the junction between the original strut and the parabolic ba rs, or tie. As the second tie carried additional force the node traveled toward s the anchorage. The compression forces began to change direction at the node towards the supp ort. At a load of approximately 179 kips the load displacement curve began to flatten with litt le increase in capacity relative to displacement. The flattening of the load displacement curve showed that the PT bars are beginning to yield. At a load of 188 kips cracks were observed around th e anchor plate for the parabolic PT bars. Cracking around the anchor plate confirm that the parabolic tendons were ca rrying all the tensile force in the strut and tie model. The PT bars, or the tie, is what caused the beam to fail. The bars could no longer carry any additional force.

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89 Superimposed Shear (kip)Strain (microstrain) 0 50 100 150200 -100 0 100 200 300 400 500 S15S14 S13 S13 S14 S15 Figure 12-1. C3U2 strain gages S13, S14, and S15

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90 Figure 12-2. Crack causing transfer of flexure to strut and tie

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91 Strain (microstrain)Height from Bottom of Beam (in) -300 -200 -100 0 100 200300 0 10 20 30 40 50 153 kip 120 kip 80 kip 0 kip Figure 12-3. Change in strain as loading

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92 Parabolic Bar Figure 12-4. Strut and tie model

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93 Superimposed Shear (kip)S5 and S6 Strain (microstrain) S18 Strain (microstrain) 0 50 100 150200 -400 -100 -300 -75 -200 -50 -100 -25 0 0 100 25 200 50 300 75 400 100 S5S6S 1 8 S5 S6 S18 Figure 12-5. Strain gage plot for S5, S6, and S18

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94 Strain (microstrain)Height from Bottom of Beam (in) -300 -200 -100 0 100 200300 0 10 20 30 40 50 153 kip 120 kip 80 kip 0 kip Strain Plot Figure 12-6. Change in strain as loading

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95 Figure 12-7. Strut and tie model

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96 Superimposed Shear (kip)S5 and S6 Strain (microstrain) S18 Strain (microstrain) 0 50 100 150200 -400 -100 -300 -75 -200 -50 -100 -25 0 0 100 25 200 50 300 75 400 100 S5S6S 1 8 S5 S6 S18 Figure 12-8. Strain gage plot for S5, S6, and S18

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97 CHAPTER 13 COMPARISON WITH THEORETICAL CAPACITIES It is g enerally accepted that when the shear span to depth ratio (a/d) is less than about 2.5, then the behavior is better modeled by strut and tie method. When a/d greater than 2.5, then semi-empirical sectional models are usually em ployed to determine capacity. This section provides a comparison of the calcu lated capacity of the beam and the experimentally measured capacity. When the shear span ratio is in the range used for these tests (2.0 and 3.0) the failure mode can vary widely depending on the beam conf iguration, detailing, and material properties. These failure modes can be flexural, shear-compression, web-shear, or anchorage, or a combination thereof. Consequently, the calculate d values presented in this section cover the range of possibilities to determin e those that best fit the actual measured capacity and behavior. Nominal moment capacity, Mn, was calculated using strain compatibility (See Table 13-1). The stres s strain curve generated from the average yield and ultimate strengths from bar tension tests was used to calculate moment capacity. Th e material properties used to calculate moment capacity were: the compressive strength of concre te was 7.98 ksi, the prestress in the bars was 109 ksi, the yield stress for the bars was 140 ksi, and Youngs modulus for the bars was 28500 ksi. Shear capacity was calculated using the methods prescribed in AASHT O LRFD and ACI. Using the ACI method gave the most conservativ e results compared to the two other methods. With an a/d of 2 the experimental capacity was 3 67% of the theoretical result. The experimental results for the a/d ratios of 3 were 318% and 291 % of the theoretical result. MCFT was more accurate as you increased the distance of the load ing point from the support. The second a/d of 3 test yielded the most accurate result being within 58% of the th eoretical result (See Table 13-2).

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98 A strut-and-tie model was performed for an a/d ra tio of 2. From testing it can be seen that the PT bars were yielding. Since the bars we re yielding, the forces in them were found by multiplying the area of the bars, 0.85 sq in., by thei r yielding stress. Each tie had two PT bars and their yielding stress was 140 ksi, which was f ound from testing data. By making a cut at the load point and summing the moments about the node just below the load point, the force at the reaction can be found. With the forces in the bars and at the reaction known the forces in the struts were found by nodal analysis. The calculated forces in each of the members can be seen in Figure 13-9. Com paring the experimental to predicted capaci ties for shear or flexure it could be seen that flexure provided the best re presentation of the beams capacity. This was due to the beams unusual configuration. 172 kip 211 kip2 9 9 k i p5 0 1 k i p238 kip @ 6 deg. 238 kip(-) Compression 479 kip @ 8 deg. Figure 13-9. Forces in strut-and-tie model

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99 Table 13-1. Post-tensioned b eam nominal moment capacities a/d Mex p Mn Mex p / Mn (kip*ft) (kip*ft) (kip*ft) 2 1507 1428 1.06 3 1685 1519 1.11 3 (2n d Test) 1587 1519 1.05 Table 13-2. Post-tensioned beam shear capacity results a/d ACI Strut & Tie MCFT VEXP Vn VEXP / Vn Vn VEXP / Vn Vn VEXP / Vn (kip) (kip) (kip) (kip) 2 196 42 4.67 172 1.14 84 2.33 3 142 34 4.18 ----84 1.69 3 (2n d Test) 133 34 3.91 ----84 1.58

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100 CHAPTER 14 SUMMARY AND CONCLUSIONS Post-tensioned beam s were c onstructed and post-tensioned. Th is set of testing conducted destructive load tests to post-tensioned beams which had no shear reinforcement outside of the end block, approximately 3 ft from each end of the beam. The beams had two straight bars and two parabolic bars. The bars were anchored us ing 1 in. thick steel plates. Post-tensioning stresses were monitored and recorded. Losses were calculated using measured strains during stressing. Seating, Elastic, short-te rm Creep and Shrinkage losses were able to be measured. The short-term creep and shrinkage losses were measured for approximately 2.5 days. Losses due to creep and shrinkage were higher than calcu lated values from AAS HTO 2007. Creep and shrinkage are measured over longer periods of time than the period which was measured during our tests which may have altered the comparison. Tests were done to observe the effect of support conditions on the behavior of the beam. The support conditions were of interest because of the variability of them in the field. The beams were observed to be resting on tar paper and steel plates. A test was done with a shorter shear span to see if the beam would fail in shear. Shear was of interest because of the lack of reinforcement in the beams. This lack of reinforcement has produced low bridge ratings fo r the beams. The following conclusions were made: The measured take-up was in the range recommended by Lins and Burns (1981) for straight bars. Parabolic bars had slightly higher take up valu es due to their alignment with the anchor plate. A concrete on concrete bearing surface behaved the same as a beam with neoprene bearing pads up until cracking occurred. Once cracking occurred the stiffnesses of the beams differed resulting in a more ductile failur e mode for the neoprene bearing pads. Bearing surfaces did not change the failure mode, which was a flexural failure.

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101 The concrete surface only provided a slight incr ease in capacity over the neoprene pad but led to a non-duc tile failure. Loading the beam at an a/d ratio of 2 did not cause the beam to fail in shear even with the absence of shear reinforcement. The failure at an a/d 2 was due to the PT bars yielding which was best represented by a strut-and-tie model or its moment capacity. The moment capacity for each of the tests, a/d of 2 and 3, provided the most accurate representation of the beams capacity.

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102 LIST OF REFERENCES 1. Schlaich, J.; Schfer, K.; and Jennewein, M. Toward a Consistent Design of Structural Concrete, PCI Journal V. 32(3), No. 3, 1987, pp. 74-151. 2. ACI Comm ittee 318 (ACI), Building Code Requirements for Structural Concrete and Commentary (ACI 318-05/ACI 318R-05), Amer ican Concrete Inst itute, Detroit, 2005. 3. Collins, M.P., Mitchell, D., Prestressed Concrete Structures. Prentice Hall Inc., Englewood Cliffs, 1991, 766 pp. 4. Ramirez, J.A., Strut-Tie Design of Pretensioned Concrete Members. ACI Structural Journal V. 91, No. 4, Sept.-Oct. 1994, pp. 572-578. 5. Alshegeir, A. and Ramirez, J.A., Strut-T ie Approach in Pretensioned Deep Beams. ACI Structural Journal V. 89, No. 3, May-June 1992, pp. 296-304. 6. MacGregor, J. and Wight, J., Reinforced C oncrete: Mechanics and Design. Pearson Preston Hall, Upper Saddle River, N.J. 7. Bakht, B. and Jaeger, L.G., Bearing Re straint in Slab-on-Girder Bridges. Journal of Structural Engineering V. 114, No. 12, December 1988, pp. 2724-2740. 8. American Association of State and Highw ay Officials (AASHTO), AASHTO LRFD Bridge Specifications. Washington, DC. 2007.

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103 BIOGRAPHICAL SKETCH Gustavo Adolfo Llanos was bor n in 1984. He was born and raised in Miam i, Florida, and is the youngest of two brothers. He graduate d from Miami Killian High School in 2002. He earned his B.S. in civil engineering from Florida State University (FSU) in 2006. He is pursuing his M.E. in structural engineering from the Un iversity of Florida (UF). Upon completion of his masters degree, Gustavo will be working with BCC Engineering in Miami, Florida.