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Field Verification of Camber Estimates for Prestressed Concrete Bridge Girders


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FIELD VERIFICATION OF CAMBER ESTIMATES FOR PRESTRESSED CONCRETE BRIDGE GIRDERS by JONATHAN E. SANEK 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 ENGINEERING UNIVERSITY OF FLORIDA 2005

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ii ACKNOWLEDGMENTS Completion of this thesis and the research associated with it would not have been successful without the help a nd guidance of a number of indi viduals. The author would like to thank Dr. Ronald A. Cook for the gui dance and support he provided throughout the duration of the project. He was a f ountainhead of knowledge who, because of his sincerity and contribution to the project, could not have been a more valuable asset toward the completion of this research endeavor. The author would also like to thank Dr. David Bloomquist whose counsel and expertis e in the instrumentation employed on this project and, to a broader extent, the myri ad of technical subjects pertaining to development and completion of this rese arch were very much appreciated. Many others imparted their own indi vidual efforts toward the successful conclusion of this project. The author w ould like to thank Isaac Canner, Xiaoming Wen, Michael Reponen, and Joe Liberman for the help they provided in the field. Also, I thank George Lopp for the guidance and help he offered in the operation of the MTS concrete cylinder testing apparatus; Chuck Broward and Danny Brown for their help with the fabrication of the instrumentation used on th is project; Richard DeLorenzo for his help testing the 6-inch x 12-inc h cylinder specimens; and Dr Bon Dewitt for his help operating the surveying instrume ntation implemented on this project. The author would like to thank Marc Ansley from the Flor ida Department of Transportation. His knowledge, resources and financ ial support were greatly appr eciated. The author would also like to offer his gratitude to John Jarrett and all those individuals at the Durastress

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iii Inc. precast facility. Without th eir cooperation, this project c ould not have taken place. Lastly, the author would like to thank his frie nds and family for the help and support they offered throughout his educational career.

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iv TABLE OF CONTENTS page ACKNOWLEDGMENTS..................................................................................................ii LIST OF TABLES.............................................................................................................vi LIST OF FIGURES..........................................................................................................vii ABSTRACT....................................................................................................................... ..x 1 INTRODUCTION........................................................................................................1 2 PRESTRESSED BEAM CAMBER.............................................................................3 2.1 Introduction...........................................................................................................3 2.2 Construction Problems..........................................................................................3 2.3 Time Dependent Effects........................................................................................4 2.4 Calculation of Camber...........................................................................................9 2.5 LRFD Prestress Loss...........................................................................................10 2.6 LRFD Creep Coefficient.....................................................................................14 2.7 Thermal Effects...................................................................................................15 2.8 Effect of Coarse Aggregate.................................................................................17 2.8.1 Introduction.............................................................................................17 2.8.2 Mechanical Properties.............................................................................17 2.8.3 Physical Properties..................................................................................18 2.8.4 Effects of Coarse Aggregate on Differential Shrinkage..........................19 3 METHODOLOGY.....................................................................................................21 3.1 Camber Measurement..........................................................................................21 3.2 Thermal Gradient Measurement and Camber Correction...................................25 3.3 Supplemental Material Testing............................................................................29 4 SUMMARY OF RESULTS.......................................................................................32 4.1 Camber Measurement at Release........................................................................32 4.2 Camber Measurement Summary.........................................................................35 4.3 Supplemental Material Testing Summary...........................................................45

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v 4.4 Florida Limerock Specimens...............................................................................53 4.4.1 Camber Measurement at Release............................................................53 4.4.2 Camber Measurement Summary.............................................................55 5 CONCLUSIONS AND RECCOMENDATIONS......................................................58 APPENDIX A CAMBER AT RELEASE MEASUREMENTS.........................................................60 B FIELD CAMBER MEASUREMENTS.....................................................................61 C EMPIRICAL THERMAL ANALYSIS......................................................................66 D ANALYTICAL THERMAL ANALYSIS.................................................................73 E TABULATED AMBIENT DATA.............................................................................89 F MIX DESIGNS.........................................................................................................102 G TABULATED MATERIAL TESTING DATA.......................................................107 H RECOMMENDED 78 BULB-TEE CAMBER CALCULATION.........................111 I DOCUMENTED LIMERO CK SPECIMEN DATA................................................118 REFERENCES................................................................................................................120 BIOGRAPHICAL SKETCH...........................................................................................123

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vi LIST OF TABLES Table page 1 Angular measurement technique accuracy...............................................................23 2 Pro-LevelTM measurement technique accuracy........................................................25 3 Example of field measurements and thermally corrected cambers..........................28 4 Comparison of field measured camber to predicted camber....................................36 5 Girder pour identification summary.........................................................................46 6 Tabular comparison of predicted and actual camber values for Limerock and granite specimens of the AASHTO Type IV girder.................................................56 7 Comparison of field measured camber to predicted camber at 240 days for BulbTee girders................................................................................................................57

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vii LIST OF FIGURES Figure page 1 Drying shrinkage vs. time..........................................................................................7 2 Concrete creep vs. time after loading.........................................................................7 3 Camber at midspan vs. time.......................................................................................8 4 Effect of relative aggregate and ceme nt stiffness on concrete stiffness...................18 5 Optical target mounted on fixed ceramic magnet....................................................21 6 Isometric view of a thre e-point resection analysis...................................................22 7 Pro-LevelTM water manometer schematic................................................................24 8 Pro-LevelTM water manometer measurement technique..........................................25 9 Infrared temperature sensor......................................................................................26 10 Example single day temperature pr ofile of Bulb-Tee girder 3.................................27 11 Field cured 4x 8 c oncrete test cylinders...............................................................29 12 Computerized MTS concrete cylinder testing apparatus........................................30 13 Bar chart of 78 Bulb-Tee camber at re lease, after moving, and FDOT predicted values........................................................................................................................3 3 14 Bar chart of AASHTO Type IV camber at release, after moving, and FDOT predicted values........................................................................................................34 15 Bar chart of AASHTO Type IV camber at release, after moving, and FDOT predicted values........................................................................................................34 16 AASHTO Type IV girder in storage........................................................................37 17 Field camber measurements for 78 Bulb-Tee girder 1...........................................37 18 Field camber measurements for 78 Bulb-Tee girder 2...........................................38

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viii 19 Field camber measurements for 78 Bulb-Tee girder 3...........................................38 20 Field camber measurements for 78 Bulb-Tee girder 4...........................................39 21 Field camber measurements for 78 Bulb-Tee girder 5...........................................39 22 Field camber measurements for 78 Bulb-Tee girder 6...........................................40 23 Summary of field camber measurements for all 78 Bulb-Tee girders...................40 24 Field camber measurements for AASHTO Type IV girder 1..................................41 25 Field camber measurements for AASHTO Type IV girder 2..................................41 26 Field camber measurements for AASHTO Type IV girder 3..................................42 27 Summary of field camber measurements for all AASHTO Type IV girders...........42 28 Field camber measurements for AASHTO Type V girder 1....................................43 29 Field camber measurements for AASHTO Type V girder 2....................................44 30 Field camber measurements for AASHTO Type V girder 3....................................44 31 Field camber measurements for AASHTO Type V girder 4....................................45 32 Summary of field camber measuremen ts for all AASHTO Type V girders............45 33 78 Bulb-Tee pour A comp ressive strength vs. time............................................47 34 78 Bulb-Tee pour A elastic modulus vs. time.....................................................48 35 78 Bulb-Tee pour B comp ressive strength vs. time............................................48 36 78 Bulb-Tee pour B elastic modulus vs. time.....................................................49 37 AASHTO Type IV pour A comp ressive strength vs. time...................................49 38 AASHTO Type IV A elastic modulus vs. time....................................................50 39 AASHTO Type V pour A compressive strength vs. time....................................50 40 AASHTO Type V A elastic modulus vs. time.....................................................51 41 AASHTO Type V pour B compressive strength vs. time....................................51 42 AASHTO Type V B elastic modulus vs. time......................................................52 43 Limerock 72" Bulb-Tee and AASHTO Type IV camber at release........................54

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ix 44 72" Bulb-Tee (Limerock) girder camber growth summary.....................................55 45 AASHTO Type IV (Limerock) girder camber growth summary............................56 46 Comparison of predicted camber to actual field camber for granite and limerock specimens of AASHTO Type IV girder...................................................................57

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x Abstract of Thesis Presen ted to the Graduate School of the University of Florida in Partial Fulfillment of the Requirements for the Degree of Master of Engineering FIELD VERIFICATION OF CAMBER ESTIMATES FOR PRESTRESSED CONCRETE BRIDGE GIRDERS by Jonathan Edward Sanek May 2005 Chair: Ronald A. Cook Cochair: David Bloomquist Major Department: Civil and Coastal Engineering Prestressed concrete girders are used on ma ny of Floridas bridges. These girders are subject to camber, the upward deflection of the girder due to the eccentricity of the prestressing force. Over time, the girders experience camber growth as a result of growing compressive strain in the pre-compress ed tensile zone. This compressive strain causes a reduction in the prestressing force, or what is referred to as a prestress loss. These strains are due to time-dependent pheno mena, specifically creep and shrinkage of the concrete. It is necessary to accurately pr edict the camber of a girder in order to avoid problems and delays during construction due to build-up or bearings. Differences have been found between camber predicted by th e design program employed by the FDOT and the measured field camber for prestressed Bulb-Tee girders. The focus of this investigation was to develop a realistic time-dependent camber growth model using periodic field measurements ta ken on a variety of different prestressed concrete bridge girders. Specifically, the types of girders m onitored for this projec t were 1) the 78-inch

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xi Florida Bulb-Tee girder, 2) the AASHTO Type IV girder, and 3) the AASHTO Type V girder.

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1 CHAPTER 1 INTRODUCTION Prestressing of concrete, in general, is the introduction of an internal loading condition such that the perfor mance of the structural member is improved in several ways. Specifically, a prestressing force is used in flexural members to lessen the concrete tensile stresses. This is done in order to prevent or reduce concrete cracking in the tensile zone due to tensile stresses exceeding the rupture strength of the concrete. The prestressing force is typically applied to a c oncrete beam section such that it creates an eccentric, axial loading condition resulting in an upward deflection or camber. Also, as a result of preventing cracking, this “preloading” reduces the amount the flexural member will deflect under service loads, thus improving the serviceability of the member. The prestressing force, however, does not increas e the flexural strength of an element. The prestressed beam design program currently implemented by the Florida Department of Transportation, Eng LFRD PSBeam v.1.85 includes calculations for the prediction of time-dependent camber growth th at have not been field verified. This camber growth is obtained by calculating the elastic camber at the release of the prestressed girder (i.e., a pplication of the prestressing force) and applying a timedependent multiplication factor. The focus of this investigation was to obtain field camber measurements on different types of bri dge girders with the goal of verifying or improving the present design methodology used by the FDOT for time-dependent camber estimation.

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2 Periodic field camber measurements from initi al prestress transfer to as much as six months after transf er were performed on: Six (6) Florida 78-inch Bulb-Tee were 162feet in length with fifty-three (53) 0.60”-diameter, 270-ksi, “Lo-Lax” prestres sing strands, and used FDOT Class VI coarse granite aggregate concrete with a specified 28-day compressive strength of 8,500-psi. Three (3) AASHTO Type IV girders were 91-feet in length with thirty (30) ”diameter, 270-ksi, “Lo-Lax” prestressing strands, and used FDOT Class IV coarse granite aggregate concrete with a spec ified 28-day compressi ve strength of 5,500psi. Four (4) AASHTO Type V girders were 81-f eet in length with twenty-eight (28) ”-diameter, 270-ksi, “Lo-Lax” prestres sing strands, and used a FDOT Class IV coarse granite aggregate concrete with a specified 28-day compressive strength of 5,500-psi.

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3 CHAPTER 2 PRESTRESSED BEAM CAMBER 2.1 Introduction Camber is the upward deflec tion of a flexural member due the eccentricity of the prestressing force. The prestressing for ce is placed eccentrical ly to counteract the downward deflection of the flexural member caused by gravity loads and service loads. The amount of camber is dependent upon se veral factors: the tendon profile, the prestress magnitude, the span, the section pr operties, and the elas tic modulus of the concrete (Nawy 2003). 2.2 Problems with Construction The need for accurate predictions of estim ated camber in prestressed structural members can not be overstated. However, even in controlled conditions, predictions of element deflections to a high degree of accur acy are difficult (Tadros, Ghali, and Meyer 1985). Discrepancies between the predicted and the actual measured field camber can cause delays in construction because of corr ections to build-up and/or bearings of the prestressed structure. In the FDOT struct ural design guidelines, the haunch between the slab and the girder can be adjusted in or der to compensate for variation between the required and provided deck pr ofile and maintain a consta nt slab thickness (Yazdani, Mtenga, and Richardson 1999). These solutions cause construction delays which can be costly and cause additional problems throughout later construction stages.

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4 2.3 Time-Dependent Effects One important characteristic of camber is that it increases with time. This camber growth begins immediately following the appl ication of the prestressing force to the flexural element. This is known as the pres tress “transfer” or “release.” The element first deflects upward due to the elastic strain in the pre-compressed tensile zone. Strains due to concrete creep and shrinkage then begi n to grow with time (at a higher rate in the pre-compressed tensile zone than in th e compressive zone), thus creating a timedependent relationship of camber growth (Sinno and Furr 1970). These strains bring about losses in the prestressing force, or what are referred to as “prestress losses.” These prestress losses cause a reduction in the pr estressing force which leads to an overall reduction in the amount of camber a prestressed element will exhibit. These prestress losses can be calculated one of several ways: lump sum estimates of the total prestress loss, refined estimates of each contributing fa ctor (as outlined by ACI 209R Committee Report and AASHTO LRFD Bridge Design Specification ), or a rigorous analysis using the “time-step pro cedure” (Naaman and Hamza 1993). The timestep procedure is the most accurate method for determining long-term prestress losses when the material properties and environmenta l conditions are wellknown. This method takes into account the interd ependent effects of the longterm prestress losses upon one another. For example, the relaxation of the prestressing steel reduces the amount of stress applied to the pre-compressed tensile zone of the flexural element. This reduced stress then affects the amount that th e concrete will creep and shri nk. The time-st ep procedure descretizes these effects into time increments, at the end of which a prestress loss is then calculated and accumulated (Naaman and Ha mza 1993). Prestress losses to be

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5 considered in an analysis of a pre-tensioned flexural member are loss due to; anchorage of prestressing steel ( ANC ), deflecting device for draped strands in pre-tensioned construction ( DEF ), elastic shortening ( ES ), creep of concrete ( CR ), shrinkage of concrete ( SH ), and relaxation of th e prestressing steel ( RET ) (Preston 1975). The total prestress loss ( TL ) is defined by the equation: tiRET SH CR ES DEF ANC TL ) ( (1) For analysis of a post-tensioned flexural member, loss due to friction of the prestressing tendon ( FR ) would be included in the total prestress loss calculation (Naaman and Hamza 1993). In this equati on, time-dependent losses from creep, shrinkage, and steel relaxation are lumped toge ther because they are interdependent upon one another. Although long-term prestress lo sses include the effect due to relaxation of the prestressing steel, the more dominant factors are those due to creep and shrinkage of the concrete. The bulk of the prestr ess loss due to relaxation occurs before the transfer of the prestressing force. Thus, there are few pr ovisions made to include the effects of the prestress loss due to relaxation for calculati ons of the long-term prestress loss and camber because they are relatively small (Magura, Sozen, and Sie ss 1964). Generally, 30-40% of the steel relaxation takes place within the firs t two days following the application of the prestressing force. Therefore, prestress losse s due to creep and shri nkage of the concrete are overwhelmingly the more in fluential factors in affectin g the long-term behavior of prestressed elements. Creep is an increase in strain with ti me under a sustained stress condition (Neville 1971). The amount of creep a concrete struct ural element will undergo depends primarily

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6 on the magnitude of the applied load, the tim e for which the load is applied, and the strength of the concrete at which the load is first introduced (Kostmatka and Panarese 1988). Additional factors affecting the creep of a concrete specimen are the curing history of the concrete; type, amount and ma ximum size of aggregate; type of cement; amount of cement paste; size and shape of concrete specimen; volume to surface area ratio; amount of non-prestressed steel reinfo rcement; and the temper ature and humidity at which the concrete specimen is stored (Kostmatka and Panarese 1988). Shrinkage is the volumetric deformation of a concrete specimen with time in an unstressed condition (Illston and England 1970). Shrinkage is caused by ambient relative humidity that is below the point of satura tion of the concrete (i .e., relative humidity < 100%). Both creep and shrinkage of concrete resu lt mainly from the removal of absorbed water from the calcium-silicate-hydrate (CSH) portion of the cement matrix. This causes a strain in the concrete which, in turn, resu lts in a volumetric deformation (Mehta 1986). The difference between these two is that creep is stress induced while shrinkage is induced by ambient conditions. Because these phenomena are based on a common origin, it is stated that they are interrel ated to one another and occur simultaneously (Mindness, Young, and Darwin 2003). Also, becau se concrete creep and shrinkage occur simultaneously, it is impossible to test fo r each of them independently. Instead, shrinkage strain must be tested for alone a nd then subtracted from the strain resulting from the combined effect of creep and shrinkage (Lybas 1990). A strong validation of concrete creep a nd shrinkage’s interd ependence upon one another is the evidence that the time-dependent be havior of creep is very similar to that of

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7 shrinkage. Both shrinkage and creep curves grow logarithmically with time with some portion of the resultant strain being irreversible or plastic due to rewetting or unloading, respectively. Fig. 1 below shows the time-de pendent behavior of shrinkage and Fig. 2 shows the time-dependent behavior of creep. 0 100 200 300 400 500 600 700 05101520253035404550Time (Days)Microstrain Total Shrinkage Figure 1. Drying shrinkage vs. time. 0 100 200 300 400 500 600 700 800 900 1000 01020304050607080Time After Loading (Days)Microstrain Creep Strain Elastic Strain Figure 2. Concrete creep vs. time after loading.

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8 It is also interesting to note that the camber growth curve also follows a similar trend (see Fig. 3). 0 0.2 0.4 0.6 0.8 1 1.2 020406080100120140Time After Transfer (days)Total Midspan Camber (in.) Camber at Release Figure 3. Camber at midspan vs. time. These figures help substantiate the importan ce of concrete creep a nd shrinkage effects on the time-dependent behavior of prestressed flexural elements. Another consideration is differential shri nkage. Differential shrinkage is solely influenced by the geometry of the prestresse d element’s cross-section. Because it is caused by the rate of wa ter loss from the CSH portion of th e cement matrix, it is apparent that the rate at which water is transported from the interior of the concrete section to the atmosphere would be controlled by the length of the diffusion path traveled by the water (Mehta 1986). This factor is taken in to account when calculating the amount of shrinkage that will occur using the ACI 209R correction factors based on either the average-thickness method or the volume-to-surface area ratio ( V/S ) method. Typically, the average-thickness method tends to compute correction factors that are greater than those calculated using the volume-to-surface area method ( ACI 209R ).

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9 These numerical representations of the ge ometry of a section appear to have a linear relationship with the l ogarithm of shrinkage (Nevil le 1971). Generally, a higher volume-to-surface area ratio or theoretical-thickness will produce less ultimate shrinkage in concrete. However, considering the geomet ry of some AASHTO girders, specifically the Florida Bulb-Tee girder, shrinkage may occur at different rates between the top flange, which has a “T-shape,” and the bo ttom bulb. Evidence has shown that members with small cross-sections result, initially, in faster rates of shrinkage, but lower ultimate shrinkage values, and vise-versa for member s with large cross-sections (Mindness, Young, and Darwin 2003). A “T-shaped” sec tion, with a lower V/S ratio, will dry and shrink more rapidly than a square-shape d section (Mindness, Young, and Darwin 2003), such as the bulb portion of the Florida Bulb-T ee, but have less ultimate shrinkage. This is known as differential shrinkage and could ac count for errors in the calculation of the long-term camber growth of Florida Bulb-Tee girder. Also, uneven drying conditions due to poorly ventilated areas of the girder during storage could al so cause differential shrinkage. When the concrete section of a prestressed element dries asymmetrically, warping can occur (Nev ille 1971), thus altering the camber. 2.4 Calculation of Camber Nilson suggests that the effects of creep and shrinkage should not only affect the long-term loading due to the prestress force but it should also affect that due to the selfweight of the member (Nilson 1987). Taking th is into account, the calculation of camber is given by Equation 2 below. i o i pe pi pet t t t 1 2 (2)

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10 where: pi = Camber due to initial prestress force after steel relaxationand elastic shorteningrelated losses (in.) pe = Camber due to effective pres tress force after all prestress losses, (in.) o = Deflection due to self -weight of member (in.) (t,ti) = LRFD time-dependent creep coefficient. The calculation of the initial prestress fo rce, effective prestress force, and the creep coefficient, as outlined by the AASHTO LRFD Bridge Design Specification are discussed in the sections below. 2.5 LRFD Prestress Loss Calculations The Florida Department of Transporta tion’s prestressed be am design program, Eng LFRD PSBeam v.1.85 uses refined estimates of time -dependent prestress losses as outlined by the AASHTO LRFD Bridge Design Specification in section 5.9.5.4. These estimates provide a more accurate representation of creep-, shrinkage-, and steel relaxation-related losses than those obtained using the lump-sum estimate approach. These prestress losses for pretensioned memb ers are calculated usi ng the equations listed below. Elastic Shortening ( ES ): cgp ci p pESf E E f (3) where: fcgp = sum of concrete stresses at center of gravity of the prestressing tendons due to the prestress force at transfer and the self-weight of the member at

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11 the sections of maximum moment (ksi) Ep = elastic modulus of prestressing tendons (ksi) Eci = elastic modulus of conc rete at transfer (ksi) p ci g g g m g ps g g m g m g pbt ps pESE E I A A e I A A M e A e I f A f 2 2 (4)pu pbtf f 75 0 for low relaxation strands (5)pu pbtf f 70 0 for stress-relieved strands (6) where: Aps = area of prestressing steel (in2) Ag = gross area of section (in2) Eci = elastic modulus of conc rete at transfer (ksi) Ep = elastic modulus of pr estressing tendons (ksi) em = average eccentricity of prestressing tendons at midspan (in) fpbt = stress in prestressing tendons immediately prior to transfer (ksi) fpu = ultimate tensile stress of prestressing tendons (ksi) Ig = moment of inertia of th e gross concrete section (in4) Mg = moment at midspan due to member self-weight (kipin) Relaxation of the Prestre ssing Tendon at Transfer ( RET ):

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12 pj py pj pRf f f t f 55 0 0 40 0 24 log1 for low-relaxation strands (7) pj py pj pRf f f t f 55 0 0 10 0 24 log1 for stress-relieved strands (8) where: t = estimated time from jacking to transfer (days) fpj = jacking stress of the tendon (ksi) fpy = specified yield strength of prestressing steel (ksi) Drying Shrinkage ( SR ): H fpSR 150 0 0 17 (9) where: H = average annual ambient relative humidity (%) Concrete Creep ( CR ): 0 0 7 0 12 cdp cgp pCRf f f (10) where: fcgp = concrete stress at center of gravity of prestressing steel at transfer (ksi) fcdp = change in concrete stre ss at center of gravity of prestressing steel due to permanent loads except load from prestressing force (i.e., gravity loads) calculated at same section as fcgp (ksi) Relaxation of the Prestressi ng Tendon after Transfer ( RET ):

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13 30 0 2 0 4 0 0 202 pCR pSR pES pRf f f f for low relaxation strands (11) pCR pSR pES pRf f f f 2 0 4 0 0 202 for stress relieved strands (12) The Eng LFRD PSBeam v.1.85 program first calculates the prestress loss due to the relaxation in the prestressing steel using either Equation 7 or 8, depending on the type of prestressing strands used (i.e., low-relaxatio n strands or stress-relieved strands). Then, assuming an initial value of 5% for the pres tress loss due to elas tic shortening of the concrete and considering the initial prestr ess loss due to relaxation, it calculates an estimated value of the prestress at transfer (i.e., 105 0R pj pj pef f f f ). Using this estimated prestress, a second value for the pr estress loss due to el astic shortening is calculated using Equation 3. This procedure is then repeated, iteratively, once more to determine the final prestress loss due to elastic shortening. The program then calculates the prestress losses due to shrinkage and creep of the concrete using Equations 9 and 10. A final value of the prestress loss due to the relaxation of the prestressing steel is then calculated using Equation 11 or 12, depending on the type of prestressing strands used, using the values calculated in the previous steps. Using th ese calculated prestress losses, the initial prestress force, Pi, can be obtained by subtracti ng the steel re laxation loss ( R1 ) and the elastic shortening loss from the jacking force. This is used to determine the camber immediately after transfer, or pi. The effective prestress force, Pe, is the force in the tendons after all of the pres tress losses. It is calculate d by subtracting time-dependent losses due to creep, shrinka ge, and steel relaxation ( R2 ) from the initial prestress force. The effective prestress force is used to cal culate the reduced cambe r after the long-term

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14 prestress losses, or pe. Example calculations of this method can be found in Appendix H. 2.6 LRFD Creep Coefficient Section 5.4.2.3.2 of the 1998 AASHTO LRFD Bridge Design Specification uses equations from the ACI 209R Committee Report and empirical data as the basis for the calculation of what is known as the “creep coe fficient.” The creep coefficient is the ratio of creep strain to elastic strain at some ti me after loading. The time-dependent equation given below was introduced by Collins and Mitchell (1991) and adopted by the AASHTO LRFD Bridge Design Specification 6 0 6 0 118 010 120 58 1 5 3 ,i i i f c it t t t t H k k t t (13) where: t = time, in days, after loading ti = time, in days, time at which load is applied after casting kc = correction factor for V/S ratio kf = correction factor that accounts for lower creep of highstrength concrete H = relative humidity, in percent Correction Factors: 9000 ` 67 0 1c ff k (14) where: f`c = 28-day compressive strength of the concrete (psi)

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15 587 2 77 1 80 1 45 2654 0 36 0S V S V ce t t t e t k (15) where: V/S = volume to surface area ratio (in.) The correction factor, kf, (Equation 14) accounts for the in fluence of concrete strength (Collins and Mitchell, 1991). Ngab, Nils on, and Slate found in a 1981 study that concrete with a compressive strength in the range of 9,000 to 12,000 psi (i.e., highstrength concrete) tended to ex hibit a creep coefficient of ab out 50 to 75 pe rcent that of normal-strength concrete under normal drying conditions. The correction factor, kc, (Equation 15) accounts for the effects of th e volume-to-surface ratio and is based on empirical data given in the PCI Design Handbook and the CPCI Metric Design Manual The design program, Eng LFRD PSBeam v.1.85, used by the Florida Department of Transportation uses magnifi cation factors in order to obt ain a time-dependent camber estimate. The values listed in the program are an average of the creep coefficients calculated using the LRFD method specified above and values taken from an older program once used by the FDOT. These factors are multiplied by the elastic camber, or camber immediately after transfer, to obtain a time-dependent value of the camber at 30-, 60-, 120-, and 240-days. 2.7 Thermal Effects The prestressed beam camber can be significantly influenced by ambient conditions experienced during st orage and at the time of meas urement. Conditions such as ambient temperature, wind speed, relative humidity, solar radiation, as well as the composite material and section properties of the girder can infl uence how the beam’s

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16 internal temperature changes. Generally, if a structural member undergoes a uniform temperature increase, that member will experi ence a thermally induced strain and expand uniformly. However, due to the restraint pr ovided by the prestress force, this movement is inhibited in the pre-compre ssed tensile zone in the base of the beam and not in the compressive zone in the flange of the beam thus producing an incr ease in the girder’s curvature. Also, from the field observat ions made, it is known that the temperature increase is not uniform. The girders often e xperienced higher internal temperatures in the top flange than in the bottom flange, creating a thermal gradient. This thermal gradient adds to the effect of an increase in beam curvature. In a University of Texas study, this thermal effect was accounted for using an empirical analysis in which the beam’s temperature gradient and camber were measured several times throughout the day in order to obtain a relationship between the two. The first camber reading was taken as the baseline reading, and an increase in camber was calculated by subtracting the subsequent readin gs from this initial value. A relationship between the increase in camber and thermal grad ient was then used to correct these field measured values for thermally induced effects (Byle, Burns, and Carrasquillo 1997). This empirical method and an analytical me thod are used to account for any thermally induced changes in camber inhere nt in the field measurements. The analytical method is outlined by the NCHRP Report 276 which investigates thermal effects in concrete superstructures. This report organizes the United States into maximum solar radiation zones from which the predicted positive thermal gradient profile for a given concrete section can be determined using the tables provided. The actual thermal gradient profile obtained from the field measurements was used to account for thermal effects on pres tressed beam camber.

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172.8 Effects of Coarse Aggregate 2.8.1 Introduction It is not unexpected that the physical properties of th e coarse aggregate strongly influence the behavior of concrete since co arse aggregate makes up nearly three quarters of concrete by volume (Sengul, Tasdemir and Tasdemir 2002). Aggregate was originally considered an inert material added to the concrete mixture as a space filler for economical purposes (Neville 1963). However, the material properties of the coarse aggregate can strongly influence the physical be havior of concrete. Generally, aggregate properties are separated into three categories; physical prop erties, chemical properties, and mechanical properties. Concerning aggr egates effect on creep and shrinkage of concrete, the mechanical and physical properties of coarse aggregate are of the most interest. 2.8.2 Mechanical Properties Specifically, the most important mechanical property that affects the behavior of creep and shrinkage in concrete is the elas tic modulus of the coarse aggregate (Mehta 1986). The elastic modulus of a ma terial is defined as the change in stress with respect to elastic strain and is a measur e of a materials resistance to deformation. Elastic modulus of concrete is of particular concern in pr estressed and reinforced flexural elements (Baalbaki, Aicin, and Ballivy 1992). Concrete with a high modulus of elasticity will offer a higher degree of resi stance against volumetric deforma tion. This results not only in a lower elastic strain, but also lower long-term strains due to creep and shrinkage, and hence causing lower long-term prestress losses. The influence of th e aggregate properties increase as the strength of th e cement paste matrix grows cl ose to that of the coarse

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18 aggregate, causing the concrete to act more monolithically (Giaccio and Zerbino 1998). This effect will be significant for the case of prestressed structural elements where highstrength concrete is used. C oncordantly, a decrease in aggr egate stiffness corresponds to a decrease in aggregate strength thus causing th e strength of the aggregate to be closer to that of the high-strength cement matrix. The co ncrete stress-strain be havior acts linearly over a broader range, creating a concrete w ith a higher stiffne ss (Neville 1997) than expected using empirical relationships (see Fi g. 4). However, a de crease in aggregate stiffness will, over all, lead to a total decrease in the stiffness of the concrete. For aggregates with a higher elastic modulus, this effect will not be as pronounced. Figure 4. Effect of relative aggregate and ceme nt stiffness on concrete stiffness (Neville 97) 2.8.3 Physical Properties Of the physical properties of the coarse aggregate that influence the elastic modulus of the aggregate, porosity is the mo st significant (Mehta 1986). In a physical sense, an aggregate with a higher porosity, su ch as limestone, will have a lower density, therefore causing the aggregate to have a lowe r modulus of elastici ty and thus, have a lower stiffness. The result of this effect is a lower degree of restraint against

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19 deformation, and therefore, creep and shrinkage will have a more significant effect on the time-dependant deformation of concrete. C onversely, an increase in porosity of the aggregate actually increases its bond strength along the interfacial zone, thus increasing the concrete’s compressive stre ngth (Atcin and Mehta 1990). Other factors affecting the elastic modulus of the concrete are the maxi mum size, shape, surface texture, grading, and volume fraction of the aggregate; the por osity and water/cement ratio of the cementpaste matrix; the moisture state of the speci men at loading (Mehta 1986); age and curing conditions of the concrete specimen (Troxell Davis, and Kelly 1968). Specimens tested in wet conditions had a tendency to present high er elastic moduli values than those tested in dry conditions. Also, the effect of age on the elastic modulus resu lts in a rapid growth within the first few months a nd then begins to taper off. The elastic modulus may still continue to grow even after 3 y ears (Troxell, Davis, and Kelly 1968). In particular, creep is influenced by the amount of aggregate th e concrete contains and stiffness of the aggregate. Aggregate size, grading, and surf ace texture have little effect on creep (Mindness, Young, and Darwin 2003). Shrinkage is also influenced by the amount and stiffness of the coarse aggreg ate. In contrast, maximum aggregate size does have a significant effect on drying shrinkage in concrete (Mindn ess, Young, and Darwin 2003. 2.8.4 Effect of Aggregate on Differential Shrinkage The effect of aggregate on differential sh rinkage, aside from its direct influence on drying shrinkage, is the degree of restra int against volumetric deformation provided by the amount of coarse aggregate. Obvious ly an increase in aggregate content would significantly increase the concrete’s ability to restrain any volumetric change due to drying shrinkage (Neville 1971) thus differen tial shrinkage, overall, would become less

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20 of a factor. Another effect that the aggregate could have on differential shrinkage could be due to the asymmetric segregation of coar se aggregate during the casting process. A higher concentration of coarse aggregate at the bottom of a flexural element would cause a higher degree of restraint in the bottom than in the top, therefore creating the conditions of differential shrinkage.

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21 CHAPTER 3 METHODOLOGY 3.1 Camber Measurement The initial field measurements of th e camber were made using a surveying theodolite and three optical targ ets. Three ceramic magnets were mounted to the top of each beam at the endpoints and midpoint to which the optical targets were temporarily affixed for each field measurement as seen in Fig. 5. Figure 5. Optical target m ounted on fixed ceramic magnet The targets were always mounted in the same orientation to ensure consistency between readings and validate the zero reading for each girder. Vertical and horizontal angular readings from the theodolite were made and r ecorded a total of four times for each of the three targets (twice direct and twice reverse). This ensured that the angular readings were accurate and allowed for corrections to th e zenith readings due to possible circle graduation errors inherent to the theodolite.

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22 Using these angular readings and th e known distances between the endpoint targets and the target at mids pan, the field camber could be calculated using a three-point resection analysis (see Fig. 6). Figure 6. Isometric view of a three-point resection analysis The resection procedure simply consists of a special case of triangulation. Using the measured distances, “A” and “C”, along with the measured angles; zeniths “A”, “B” and “C”, and horizontal angles “X” and “Y”, th e relative vertical he ight of each target (relative to the instrument) can be triangulated By subtracting the average relative height of the two endpoint targets from the relative height of the midspan target, we obtain the camber of the beam. Before the prestressing tendons were cut, a zero reading was made on each girder to eliminate any systematic error inherent in the measuring process due to any surface irregularities or differential target heights. Immediately after the release of the prestressing force, measurements using the su rveying technique where compared to those

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23 measured directly off of the bed liner using a vernier caliper. The measurements using the vernier caliper were taken as the actual va lues for the percent difference calculations. The results are summarized in Table 1. Table 1. Angular measurement technique accuracy Beam No. Surveying Technique (in) Direct Measurement (in) Difference (in) Percent Difference (%) FLBT 1 1.84 1.82 0.02 1.21% FLBT 2 1.47 1.43 0.04 2.95% FLBT 3 1.63 1.61 0.02 1.68% FLBT 4 2.05 2.05 0.00 0.20% FLBT 5 2.02 2.00 0.02 1.00% FLBT 6 1.81 1.82 -0.01 -0.60% TYPE IV 1 0.65 0.68 -0.03 -4.71% TYPE IV 2 0.61 0.62 0.00 -0.65% TYPE IV 3 0.67 0.64 0.03 3.91% Although the accuracy of this method was accepta ble, the actual field measurements were time consuming and the process of calculating the camber from angular measurements was very indirect. This method was used for th e first four months of field measurements after which it was determined that a quick er, more direct method could be employed using a Pro-LevelTM water manometer. The Pro-LevelTM water manometer is a surveying instrument which operates under the principle that water in a U-shaped tube will equalize to the same relative elevation due to the constant atmos pheric pressure. The instru ment’s effective measuring resolution is 0.05-inches, which makes the accuracy of the measurements within the deliverable accuracy of 0.10-inches. The meas uring system consists of an adjustable water reservoir, a 100-ft vinyl hose, and a gr aduated measuring rod or stadia with an adjustable length (see Fig. 7). The reservoir is placed in a fixed location and the height is adjusted such that the meniscus reads somewhere near the middle of the stadia graduations. The stadia is then positioned at each target and the relative height is

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24 recorded to the nearest 0.05-inches. The ca mber is calculated by subtracting the average relative height of the endpoint readings from the relative he ight of the midspan reading (see Fig. 8). This instrument was used for the final three months of observations and was the only method of measurement used on th e AASHTO Type V prestressed girders. Similarly, the measurements taken at release of these specimens using the Pro-LevelTM water manometer were compared to those meas ured directly off of the bed liner using a vernier caliper to de termine the accuracy. Figure 7. Pro-LevelTM water manometer schematic (Source: http://prolevel.com/operation.htm Last accessed November 30, 2004).

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25 The measurements using the vernier caliper were taken as the actual values for the percent difference calculations. Thes e results are summarized in Table 2. Table 2. Pro-LevelTM measurement technique accuracy Beam No. Pro-LevelTM (in) Direct Measurement (in) Difference (in) Percent Difference (%) TYPE V 1 0.85 0.82 0.03 3.66% TYPE V 2 0.90 0.85 0.05 5.88% TYPE V 3 0.85 0.85 0.00 0.00% TYPE V 4 0.70 0.65 0.05 7.69% Figure 8. Pro-LevelTM water manometer measurement technique (Source: http://prolevel.com/operation.htm Last accessed November 30, 2004) 3.2 Thermal Gradient Measurement and Camber Correction To account for the influence of the therma l gradient on the camber measurements, an infrared temperature sensor was used to measure the surface temperature of each girder (Fig. 9). As shown in the example provi ded in Fig. 10 and in detail in Appendix B, this was done at several points along the profile of the section at the midspan of the girder coinciding with the time of the camber measurements.

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26 Figure 9. Infrared temperature sensor In order to properly account for the effect of the th ermal gradient, the surface temperature profile and camber were measured three times on single days (i.e.,, the effect of camber change relative to time since st rand release was eliminated). This was done twice for the first three 78-inch Florida Bulb-Tee girders and one time each for the second three 78-inch Florida Bulb-Tee, AASHTO Type IV, and AASHTO Type V girders. A sample of the single day thermal gradient readings for a 78-inch Florida BulbTee girder is shown in Fig. 10. The corre sponding camber measurements for this girder were 2.99 in. at 7:30 AM, 3.13 in. at 9:30 AM and 3.65 in. at 12:30 PM. This clearly indicates that the thermal gradient has a signi ficant influence on cambe r. As discussed in Section 2.7, an empirical method and an analytical method were investigated for correcting the camber measurements to account for the thermal gradient. The empirical method was based on approxi mating a linear thermal gradient over the depth of the beam. The linear differential temperature used in the empirical method is indicated by “ Temperature” shown in Fig. 10. Th is was calculated by subtracting the average temperature of the bottom bulb from th e average temperature of the top flange.

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27 E D C B A By determining the linear relationship between the change in thermal gradient and the change in camber, a correction factor was esta blished to account for the thermal gradient. Details of the empirical method for correcti on of camber are presented in Appendix C. Cambers were also corrected using the analytical thermal analysis. Using the thermal coefficient of the concrete provided in Table 5 of NCHRP Report 276 the mechanical properties of the concrete, and th e section properties, the thermally induced internal stresses due to the gradient can be determined. Assuming the thermal gradient does not change along the length of the girder, a resistin g internal moment can be calculated by integrating these stresses over th e depth of the girder. Then, the deflection due to this moment can then be calculated using Equation 16 below. g c thermI E L M 82 int (16) where: Mint = internal moment due to thermally induced stresses (kip*in) L = length of girder (in) Figure 10: Example single day temperat ure profile of Bulb-Tee girder 3. -78 -68 -58 -48 -38 -28 -18 -8 707580859095100105110115120Surface Temperature (deg F)Dsitance from Top Flange (in) 7:30 AM 9:30 AM 12:30 PM T A =118 oF TB=103 oF TC=84 oF TD=85 oF TE=85 oF Temperature

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28 Ec = elastic modulus of concrete (ksi) Ig = gross moment of inertia of girder (in4) A MathCAD worksheet was developed for the analytical method and is presented in Appendix D. Table 3 presents the actual field measurements and the corrected cambers resulting from both the empirical and analyti cal methods for the example shown in Fig. 10. Appendix B provides full information on all field measurements and the resulting correction for both the empirical and analyt ical methods to account for the thermal gradient. Table 3. Example of tabularized field m easurements and thermally corrected cambers. 0.0090 1/oF Date Time Time After Release (Days) Field Camber (in) Top Flange Temp (oF) Bottom Flange Temp (oF) Web Temp (oF) Top Bulb Temp (oF) Bottom Bulb Temp (oF) T (oF) Empirical Corrected Camber (in) Analytical Corrected Camber (in) 6/7/20047:30 AM58.982.99787375747512.962.97 6/7/20049:30 AM59.063.13917574767862.962.98 6/7/200412:30 PM59.193.6511810384858525.52.812.79 78" Florida Bulb-Tee 3 CFtherm = As indicated by the example shown in Ta ble 4 and by Appendix B, there is an insignificant difference between the corrected cambers for thermal gradient using the empirical method and the analytical method. Since the analytical method, based on NCHRP Report 276 better represents the actual cam ber changes caused by the thermal gradient, the corrections resu lting from this method were used for developing camber versus time relationships. The empirical me thod would appear to be appropriate for future use in field applications where the de tailed analytical met hod is not available. In addition to measuring the surface temper ature of the girder at the time of each camber reading, data regarding ambient cond itions was also collected from a nearby weather station operated by the University of Florida Institute of Food and Agricultural

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29 Sciences, or IFAS. The data collected incl uded the ambient temperature at 60-cm and at 200-cm, the relative humidity, a nd the solar radiation all colle cted in one hour intervals throughout the day. The weather station data was taken from a unit located in Tavares, Florida (approximately 5 miles from the storage facility). This data is presented in Appendix E. 3.3 Supplemental Material Testing The field camber measurements were suppl emented with periodic material testing in order to obtain a time relationship with both the actual compressi ve strength and the elastic modulus of the concrete used in the girders. These cy linders were stripped of their molds once the forms were removed from the gi rders. They were then stored near the girders and “field cured” under the same conditions as the girders (see Fig. 11). Figure 11. Field cured 4"x 8" concrete test cylinders. This ensured that when the cylinders were te sted, the results would provide an accurate representation of the actual conc rete material properties of the girders. A series of three 4-inch x 8-inch cylinders were used for each test. The cylinders were tested in a computerized MTS testing apparatus in accordance with ASTM C39-96 and ASTM

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30 C469-94 The elastic modulus was obtained usi ng the strain measurements from two MTS extensometers connected to a computeriz ed data acquisition system in conjunction with the load data from the load cell (see Fig. 12). The tests were made approximately every seve n days until 28-days after the prestressing tendons were cut. Subsequently, the cylinders were tested more sparsely to show the long-term behavior of the concrete compressi ve strength and elastic modulus. The elastic modulus was obtained four different ways: 1. A linear regression of th e stress-strain data. 2. The outlined procedure in ASTM C469-94 (Equation 17). 1 2 1 2 cE (17) where: 1 = stress at 500-microstrain (psi) 2 = 40% of f`c (psi) 1 = 500-microstrain ( ) Figure 12. Computerized MTS concrete cylinder testing apparatus.

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31 2 = strain at 40% of f`c ( ) 3. The empirical relationship given by ACI 318 02 section 8.5.1 (Equation 18); c cf w Ec` 33 *5 1 (18) where: wc = unit weight of the concrete (pcf) f`c = compressive strength of the concrete (psi). 4. The empirical relationship given by AASHTO LRFD Bridge Design Specification in section C5.4.2.4 (Equation 19). cf Ec` 1820 (19) where: f`c = compressive strength of the concrete (ksi). The results of those four met hods for determining the modulus of elasticity are presented in Appendix G.

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32 CHAPTER 4 SUMMARY OF RESULTS 4.1 Camber Measurement at Release The camber measurements taken after th e girders had been relocated to the storage area of the precast yard were genera lly larger that those measurements taken immediately after the release of the prestress force. The in crease in camber from release to relocation for the each prestressed girder is illustrated in Figs. 13 through 15. The camber values shown in these figures have been analytically corrected for thermal gradient effects as discussed Section 3.2. The increase in camber after removal from the casting beds is most likely due to the horizon tal restraint at the e ndpoints of the girder provided by the frictional force between the girder and the bed liner at transfer. One would surmise this effect to be more pronounc ed in heavier beams with larger span-todepth ratios. This is clearly shown in Fi g. 13 for the 162 ft. 78-inch Florida Bulb-Tee girders. Fig. 14 also indicates a very substa ntial change for the 91 ft Type IV girders. The substantial increase in camber from transfer to relocation for the AASHTO Type IV girders could have been affected by the procedure used for relocation of these girders. A permanent storage location was unavailable after the prestressing tendons had been cut so the girders were temporarily stored upon dunnage next to the casting bed until some space could be freed. As indicate d in Appendix B, two hours elapsed from the camber measurement at the time of transfer and the camber measur ement after the beams were stored. This is comparable to the thre e hours for 78-inch Bulb -Tee girders 1-3, two

PAGE 44

33 and one-half hours for 78-inch Bulb-Tees 46, and one hour for the AAHSTO Type V girders. A comparison of the span-to-depth ratio of the AASHTO Type IV girders versus that of the 78-inch Bulb-Tee girders indicates that these values are close suggesting that perhaps the AASHTO Type IV girders are subj ect to a frictional restraining force at transfer as well. For tabulated values of the camber at release versus the camber after moving including percent increase calc ulations, refer to Appendix A. 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 123456 Beam IDCamber (in) After Moving At Release FDOT Predicted Camber FDOT Predicted Camber Figure 13. Bar chart of 78” Bulb-Tee cam ber at release, after moving, and FDOT predicted values.

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34 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 123 Beam IDCamber (in) After Moving At Release FDOT Predicted Camber Figure 14. Bar chart of AASHTO Type IV camber at release, after moving, and FDOT predicted values. 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 1234 Beam IDCamber (in) After Moving At Release FDOT Predicted Camber Figure 15. Bar chart of AASHTO Type V camber at release, after moving, and FDOT predicted values.

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354.2 Camber Measurement Summary The field camber measurements made on the 78-inch Bulb-Tee girders were on the order of 55-percent that of the predicted values--obtained from the Eng LFRD PSBeam v.1.85 program--within the first few weeks of measurements to about 35-percent of the predicted values near the end of data collection. The program generally overestimated the time-dependent camber gr owth. The field camber measurements for each 78-inch Bulb-Tee girder and the predicted values using the Eng LFRD PSBeam v.1.85 design program are presented below in Fig. 17 through Fig. 23. The estimated camber values for each girder obtained using the design program were calculated using: 1. The specified 28-day compressive strength and the AASHTO empirically calculated elastic moduli (at rele ase and at 28-days). 2. The measured 28-day compressive stre ngth and the measured elastic moduli (at release and at 28-days). The temperature corrected camber values we re calculated using th e analytical thermal analysis. The method employed by the Eng LFRD PSBeam v.1. 85 design program produced camber estimates that exceeded the 78-inch Bulb-Tee girder field measurements by as much as 180-percent. For this reason, it is suggested that the method described in section 2.4 for the time-dependent camber estimate be used in place of the current method. A MathCAD worksheet, inco rporating the use of the LRFD refined prestress loss calculation me thod described in section 2.5, the LRFD creep coefficient calculation described in secti on 2.6, and Nilson’s camber cal culation method described in section 2.4, can be found in Appendix H. A comparison between the mean interpolated field measurements, the predicted values taken from Eng LFRD PSBeam v.1.85 and the

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36 predicted values using this recommended me thod for the 78-inch Bulb-Tee girder using the actual tested material properties is gi ven in Table 4. For the percent difference calculation, the field camber was taken as the actual value. Table 4. Comparison of field measured camber to predicted camber. Time After Transfer Mean Interpolated Field Camber Mean FDOT Predicted Camber % Difference Recommended Method % Difference (day) (in) (in) (%) (in) (%) 0 1.80 3.4490.7% 1.92 6.65% 30 3.00 5.9598.6% 2.95 -1.47% 60 3.04 6.88126% 3.35 9.99% 120 3.07 8.02161 % 3.83 24.8% 200 3.10 8.66179% 4.34 39.8% The field camber measurements made on the AASHTO Type IV girders were very close to the predicte d values--obtained from the Eng LFRD PSBeam v.1.85 program--within the first few weeks of measurements. Then, the field measured values began to diverge from the pr edicted values, becoming about 50-percent of the predicted values near the end of data collection. These girders were properly stored upon dunnage, but were left with little cl earance between the ground and the bottom flange unlike the other types of girders which were stored w ith about 18-inches of clearance between the ground and the bottom flange. In addition, vegetation growth surrounded the bottom flange and the girders were stored with litt le space in-between. Th e lack of ventilation surrounding the bottom flange could have caused more water to be trapped, thus creating a condition of differential shri nkage, and causing long-term effects (such as creep and shrinkage) to be less pronounced resulting in lower camber. Figure 16 shows the storage of the AASHTO Type IV girders. The fi eld camber measurements for each AAHSTO Type IV girder and the predicted values using the Eng LFRD PSBeam v.1.85 design program are presented in Fig. 24 through Fig. 27.

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37 Figure 16. AASHTO Type IV girder in storage. 0.0 1.0 2.0 3.0 4.0 5.0 6.0 7.0 8.0 9.00 7 14 21 28 35 42 49 56 63 70 77 84 91 98 105 112 119 126 133 140 147 154 161 168 175 182 189 196Time (Days)Camber (in) Field Data Temperature Corrected FDOT Spec. f`c & Comp E FDOT Actual f`c & Actual E Figure 17. Field camber measuremen ts for 78" Bulb-Tee girder 1.

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38 0.0 1.0 2.0 3.0 4.0 5.0 6.0 7.0 8.0 9.00 7 14 21 28 35 42 49 56 63 70 77 84 91 98 105 112 119 126 133 140 147 154 161 168 175 182 189 196Time (Days)Camber (in) Field Data Temperature Corrected FDOT Spec. f`c & Comp E FDOT Actual f`c & Actual E Figure 18. Field camber measuremen ts for 78" Bulb-Tee girder 2. 0.0 1.0 2.0 3.0 4.0 5.0 6.0 7.0 8.0 9.00 7 14 21 28 35 42 49 56 63 70 77 84 91 98 105 112 119 126 133 140 147 154 161 168 175 182 189 196Time (Days)Camber (in) Field Data Temperature Corrected FDOT Spec. f`c & Comp E FDOT Actual f`c & Actual E Figure 19. Field camber measuremen ts for 78" Bulb-Tee girder 3.

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39 0.0 1.0 2.0 3.0 4.0 5.0 6.0 7.0 8.0 9.0 0714212835424956637077849198105112119 Time (Days)Camber (in) Field Data Temperature Corrected FDOT Spec. f`c & Comp E FDOT Actual f`c & Actual E Figure 20. Field camber measuremen ts for 78" Bulb-Tee girder 4. 0.0 1.0 2.0 3.0 4.0 5.0 6.0 7.0 8.0 9.0 0714212835424956637077849198105112119 Time (Days)Camber (in) Field Data Temperature Corrected FDOT Spec. f`c & Comp E FDOT Actual f`c & Actual E Figure 21. Field camber measuremen ts for 78" Bulb-Tee girder 5.

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40 0.0 1.0 2.0 3.0 4.0 5.0 6.0 7.0 8.0 9.0 0714212835424956637077849198105112119 Time (Days)Camber (in) Field Data Temperature Corrected FDOT Spec. f`c & Comp E FDOT Actual f`c & Actual E Figure 22. Field camber measuremen ts for 78" Bulb-Tee girder 6. 0.0 1.0 2.0 3.0 4.0 5.0 6.0 7.0 8.0 9.00 7 14 21 28 35 42 49 56 63 70 77 84 91 98 105 112 119 126 133 140 147 154 161 168 175 182 189 196Time (Days)Camber (in) Corrected Camber FDOT Spec. f`c & Comp E FDOT Actual f`c & Actual E Figure 23. Summary of field camber measur ements for all 78" Bulb-Tee girders.

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41 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 0714212835424956637077849198105112Time (Days)Camber (in) Field Data Temperature Corrected FDOT Spec. f`c & Calculated E FDOT Actual f`c & Actual E Figure 24. Field camber measurements for AASHTO Type IV girder 1. 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 0714212835424956637077849198105112Time (Days)Camber (in) Field Data Temperature Corrected FDOT Spec. f`c & Calculated E FDOT Actual f`c & Actual E Figure 25. Field camber measurements for AASHTO Type IV girder 2.

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42 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 0714212835424956637077849198105112Time (Days)Camber (in) Field Data Temperature Corrected FDOT Spec. f`c & Calculated E FDOT Actual f`c & Actual E Figure 26. Field camber measurements for AASHTO Type IV girder 3. 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 0714212835424956637077849198105112Time (Days)Camber (in) Corrected Camber FDOT Spec. f`c & Calculated E FDOT Actual f`c & Actual E Figure 27. Summary of field camber measur ements for all AASHTO Type IV girders. The AASHTO Type V girders observed for this investigation were monitored for 28-days past the release of th e prestress force. During th is period, the field camber measurements adhered very closely to th e predicted values obtained from the Eng LFRD PSBeam v.1.85 program. The 30-day predicted cam ber from the design program was

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43 essentially the same as that measured in th e field. The field camber measurements for each AAHSTO Type IV girder and the predicted values using the Eng LFRD PSBeam v.1.85 design program are presented in Fig. 28 through Fig. 32. For a tabular summary of the field camber measurements including empiri cally and analytically corrected values as well as surface temperature values, refer to Appendix B. 0.0 0.5 1.0 1.5 2.0 2.5 07142128 Time (Days)Camber (in) Field Data Temperature Corrected FDOT "Spec f`c & Comp E" FDOT "Act f`c & Act E" Figure 28. Field camber measuremen ts for AASHTO Type V girder 1.

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44 0.0 0.5 1.0 1.5 2.0 2.5 07142128 Time (Days)Camber (in) Field Data Temperature Corrected FDOT "Spec f`c & Comp E" FDOT "Act f`c & Act E" Figure 29. Field camber measuremen ts for AASHTO Type V girder 2. 0.0 0.5 1.0 1.5 2.0 2.5 07142128 Time (Days)Camber (in) Field Data Temperature Corrected FDOT "Spec f`c & Calc E" FDOT "Act f`c & Act E" Figure 30. Field camber measuremen ts for AASHTO Type V girder 3.

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45 0.0 0.5 1.0 1.5 2.0 2.5 07142128 Time (Days)Camber (in) Field Data Temperature Corrected FDOT "Spec f`c & Calc E" FDOT "Act f`c & Act E" Figure 31. Field camber measuremen ts for AASHTO Type V girder 4. 0.0 0.5 1.0 1.5 2.0 2.5 07142128 Time (Days)Camber (in) Corrected Camber FDOT "Spec f`c & Calc E" FDOT "Act f`c & Act E" Figure 32. Summary of field camber measur ements for all AASHTO Type V girders. 4.3 Supplemental Material Testing Summary The supplemental material testing was pe rformed periodically in conjunction with the field camber measurements in order to observe the relationship between the actual material properties and the time-dependent camber growth. Cylinders were made for

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46 each pour of the girders being observed for this investigation. The six 78-inch Bulb-Tee girders were produced in two pours, the th ree AASHTO Type IV girders were produced in one, and the four AASHTO Type V girders were produced in two. Each series of test cylinders is identified by the type of girder and a letter representing which pour they were made from. For example, the test cylinders made from the first pour of 78-inch Bulb-Tee girders is identified with the letter “A.” A table summarizing which pours represent which girders is given in Table 5. The mate rial tests were performed each week for the first 28-days and were then tested more sparsely thereafter in order to obtain a long-term model of the compressive strength and elastic modulus growth. Table 5. Girder pour identification summary. Pour A Pour B 78" Florida Bulb-Tee Girders 1-3 Girders 4-6 AASHTO Type IV Girders 1-3 — AASHTO Type V Girders 1-2 Girders 3-4 In addition to the three 4-inch x 8-inch cylinders used for each test, a series of three 6inch x 12-inch cylinders were also tested on a few occasions for comparison. The compressive strength and elastic modulus test s for the 6-inch x 12-inch cylinders were performed by the Florida Department of Tran sportation Materials office in Gainesville, Florida. Material data from the 6-inch x 12-inch cylinders was obtained for the 78-inch Bulb-Tee girders and the AASHTO Type IV gird ers. Because there was little discernable difference between the results of the 4-inch x 8-inch cylinder test s and the 6-inch x 12inch cylinder tests, it was decided that testing of only the 4-in ch x 8-inch cylinder specimens for the AASHTO Type V girders woul d be adequate. Graphic representations of the compressive strength and the elastic modulus, obtaine d using the linear regression

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47 analysis, are presented in the figures below. For the tabularized version of the materials testing summary refer to Appendix G. Fo r the mix design of each pour, refer to Appendix F. Graphical repres entations of the results of the supplemental materials testing are as follows: The results of the material tests for pour s “A” and “B” of the 78-inch Bulb-Tee girders for both the 4-inch x 8-inch cyli nder specimens and the 6-inch x 12-inch cylinder specimens are summarized in Fig. 33 through Fig. 36. The results of the material tests for pour “A” of the AASHTO Type IV girders for both the 4-inch x 8-inch cylinder specime ns and the 6-inch x 12-inch cylinder specimens are summarized in Fig. 37 and Fig. 38. The results of the material tests for pours “A” and “B” of the AASHTO Type V girders for the 4-inch x 8-inch cylinde r specimens are summarized in Fig. 39 through Fig. 42. 0 2000 4000 6000 8000 10000 120000 7 14 21 28 35 42 49 56 63 70 77 84 91 98 105 112 119 126 133 140 147 154 161 168 175 182 189 196 203Time After Casting (days)Compressive Strength (psi) 4-inch x 8-inch Cylinder 6-inch x 12-inch Cylinder Figure 33. 78" Bulb-Tee pour "A compressive strength vs. time.

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48 0 1000 2000 3000 4000 5000 6000 70000 7 14 21 28 35 42 49 56 63 70 77 84 91 98 105 112 119 126 133 140 147 154 161 168 175 182 189 196 203Time After Casting (days)Elastic Modulus (ksi ) 4-inch x 8-inch Cylinder 6-inch x 12-inch Cylinder Figure 34. 78" Bulb-Tee pour "A" elastic modulus vs. time. 0 1000 2000 3000 4000 5000 6000 7000 8000 9000 10000 0714212835424956637077849198105112119126Time (days)Compressive Strength (psi) 4-inch x 8-inch Cylinder 6-inch x 12-inch Cylinder Figure 35. 78" Bulb-Tee pour "B compressive strength vs. time.

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49 0 1000 2000 3000 4000 5000 6000 0714212835424956637077849198105112119126Time (days)Elastic Modulus (ksi ) 4-inch x 8-inch Cylinder 6-inch x 12-inch Cylinder Figure 36. 78" Bulb-Tee pour "B" elastic modulus vs. time. 0 1000 2000 3000 4000 5000 6000 7000 8000 9000 10000 0714212835424956637077849198105112119126133140Time After Casting (days)Compressive Strength (psi) 4-inch x 8-inch Cylinder 6-inch x 12-inch Cylinder Figure 37. AASHTO Type IV pour "A" compressive strength vs. time.

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50 0 1000 2000 3000 4000 5000 6000 7000 0714212835424956637077849198105112119126133140Time After Casting (days)Elastic Modulus (ksi ) 4-inch x 8-inch Cylinder 6-inch x 12-inch Cylinder Figure 38. AASHTO Type IV pour "A" elastic modulus vs. time. 0 1000 2000 3000 4000 5000 6000 7000 8000 9000 10000 0714212835Time After Casting (days)Compressive Strength (psi) Figure 39. AASHTO Type V pour "A" compressive strength vs. time.

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51 0 1000 2000 3000 4000 5000 6000 0714212835Time After Casting (days)Elastic Modulus (ksi ) Figure 40. AASHTO T ype V pour "A" elastic modulus vs. time. 0 1000 2000 3000 4000 5000 6000 7000 8000 9000 0714212835Time After Casting (days)Compressive Strength (psi) Figure 41. AASHTO Type V pour "B" compressive strength vs. time.

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52 0 1000 2000 3000 4000 5000 6000 0714212835Time After Casting (days)Elastic Modulus (ksi ) Figure 42. AASHTO T ype V pour "B" elastic modulus vs. time.

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534.4 Florida Limerock Specimens In addition to the specimens using gr anite as a coarse aggregate, several specimens using Florida Limerock as a coarse aggregate were also investigated to determine the effects of the type of co arse aggregate content on long-term camber growth. The camber for these specimens was obtained from the prestressing yard inspection records and not from actual meas urements performed using the procedures discussed in Chapter 3. These documente d measurements were obtained for for: Ten (10) AASHTO Type IV girders were 95feet in length with thirty-seven (37) 0.6”-diameter, 270-ksi, “Lo-Lax” prestr essing strands, and used FDOT Class VI coarse limerock aggregate concrete with a specified 28-day co mpressive strength of 8,500-psi. Eight (8) 72-inch Florida Bulb-Tee girder s were 129-feet in length with fourty (40) 0.6”-diameter, 270-ksi, “Lo-Lax” pr estressing strands, and used FDOT Class VI coarse limerock aggregate concrete with a specified 28-day compressive strength of 8,500-psi. The measured field cambers for these specimens were compared to the predicted values obtained using the Eng LFRD PSBeam v.1.85 design program. Detailed information on the data obtained from the prestressing ya rd records is provided in Appendix I. 4.4.1 Camber Measurement at Release The average initial camber measuremen t for the ten AASHTO Type IV girders and the eight 72-inch Florida Bulb-Tee girders fabricated using Florida Limerock as the coarse aggregate are shown in Fig. 43. It should be noted that the initial camber measurements where performed while the girders were in the forms and that no camber measurement was made after moving the girders to their storage location. As shown in Fig. 13 and Fig. 43 the initial camber for the Florida Bulb-Tee sections was much closer to that expected when using Florida Limerock as the coarse aggregate.

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54 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5Beam IDCamber (in) AASHTO Type IV 72" Bulb-Tee FDOT Predicted Camber FDOT Predicted Camber Figure 43. Limerock 72" Bulb-Tee a nd AASHTO Type IV camber at release.

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554.4.2 Camber Measurement Summary The time-dependent camber growth for the 72-inch Bulb-Tee girders and the AASHTO Type IV girders, both using Florida Limerock as a coarse aggregate, can be seen in Fig. 44 and Fig 45, re spectfully. The predicted values from the design program were produced using the actual tested material properties given in Appendix I. 0.00 1.00 2.00 3.00 4.00 5.00 6.00 7.00 8.00 9.000 14 28 42 56 70 84 98 112 126 140 154 168 182 196 210 224 238 252 266 280 294 308 322 336 350 364Time after Transfer (days)Camber (in) Field Camber FDOT Figure 44. 72" Bulb-Tee (Limerock) girder camber growth summary.

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56 0.00 1.00 2.00 3.00 4.00 5.00 6.00 7.00 8.00 014284256Time after Transfer (days)Camber (in) Field Camber FDOT Figure 45. AASHTO Type IV (Limeroc k) girder camber growth summary. This comparison is illustrated graphical ly for the AASHTO Type IV girders in Fig 46 and presented in tabular form in Table 6. From this figure, it can be stated that the type of coarse aggregate has an effect on the long-term behavior of these prestressed girders. The design program overestimates the long-term camber by as much as 70% for the girders using granite as a coarse aggregat e, but only 20% for the girders using Florida Limerock as a coarse aggregate. Table 6. Tabular comparison of predicted and actual camber values for Limerock and granite specimens of the AASHTO Type IV girder. (A)(B)(A)(B) Field Camber (in) FDOT Predicted Camber (in) Field Camber (in) FDOT Predicted Camber (in) 02.352.701.1500.641.131.77 303.9764.671.1701.021.131.10 604.2575.391.27301.1471.961.71 601.342.271.69 Limerock SpecimensGranite Specimens Time After Transfer (days) Time After Transfer (days) Difference (B/A) Difference (B/A)

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57 0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0 01428425670Time After Casting (days)Difference Limerock Specimens Granite Specimens FDOTFigure 46. Comparison of predicted camber to actual field camber for granite and limerock specimens of AASHTO Type IV girder. For the 72-inch Florida Bulb-Tee girders, comparisons were made to the predicted values from the Eng LFRD PSBeam v.1.85 design program and the recommended approach given by Equation 2 at 240-days after the transfer. Table 7. Comparison of field measured camber to predicted camber at 240 days for Bulb-Tee girders. Mean Interpolated Field Camber (in) Mean FDOT Camber (in) % Difference (%) Recommended Method (in) % Difference (%) Granite 3.109.29199%4.34 40.0% Limerock 4.887.8159.9%3.48 -29.7%

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58 CHAPTER 5 CONCLUSIONS AND RECCOMENDATIONS The conclusions and recommendations pres ented in this thes is are based upon the data collected during this projec t, analysis of this data, and previous research literature a propos this project. The camber increase with time was less th an what was estimated for the 162 ft. 78-inch Florida Bulb-Tees and the 91 ft. AASHTO Type IV girders. It is suggested that the FDOT LFRD PSBeam v.1.85 design program be modified to account for this. One possible approach would be the use of the time-dependent creep coefficient given by Section 5.4.2.3.2 of the AASHTO LRFD Bridge Design Specification This creep coefficient should not only be applied to the camber due to the long-term loading of to the prestre ss force, but it should also be applied to the deflection associated with the long-term loading due to the self-weight of the member. This can be done using the relationship propos ed by Nilson in Eq. 2. Refer to Appendix H for example cal culations showing this method. For the influence of the thermal gradient on camber, there was little difference between the empirically corrected cambe r measurements and the analytically corrected camber measurements in the majority of cases. Either method is suitable for the correction of camber due to thermal gradient effects. Both the AASHTO and the ACI methods fo r calculating the el astic modulus were fairly accurate for the 78-inch Bulb-Tee specimens for which an FDOT Class VI concrete was used, and also for th e AASHTO Type IV and AASHTO Type V specimens for which an FDOT Class IV concrete was used. Guidelines for storage of the girders w ith instruction of th e amount of clearance necessary between the ground and bottom fl ange should be implemented in order to reduce the effect of differe ntial shrinkage in the field. Further investigation should be done with reference to the increase in camber from immediately after transfer to when the girders have been relocated to storage. This effect was consistently th e most pronounced in heavy girders with a large span to depth ratio.

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59 Further investigation should be done on the eff ect of aggregate type on the longterm camber growth in prestressed girder s to determine whether it is one of the possible causes for the discrepancy be tween the predicted and actual camber values.

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60 APPENDIX A CAMBER AT RELEASE Beam ID FDOT Predicted Camber* (in) Camber At Transfer (in) Camber After Moving (in) Camber Increase (in) Percent Increase (%) 13.571.842.300.4624.77% 23.571.472.030.5638.07% 33.571.632.130.5030.81% 43.312.052.570.5124.98% 53.312.022.370.3517.23% 63.311.812.250.4424.49% Beam ID FDOT Predicted Camber* (in) Camber At Transfer (in) Camber After Moving (in) Camber Increase (in) Percent Increase (%) 11.130.651.180.5381.94% 21.130.610.900.2946.64% 31.130.671.000.3349.77% Beam ID FDOT Predicted Camber* (in) Camber At Transfer (in) Camber After Moving (in) Camber Increase (in) Percent Increase (%) 10.650.850.880.034.00% 20.650.900.87-0.04-3.89% 30.670.850.980.1315.65% 40.670.700.67-0.03-4.00% AASHTO Type IV Girders AASHTO Type V Girders 78" Bulb-Tee Girders *FDOT predicted camber values based on actual tested material properties. 1 1 Note: Cambers are analytically corrected for thermal effects.

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61 APPENDIX B FIELD CAMBER MEASUREMENTS 0.0055 1/oF Date Time Time After Release (Days) Field Camber (in) Top Flange Temp (oF) Bottom Flange Temp (oF) Web Temp (oF) Top Bulb Temp (oF) Bottom Bulb Temp (oF) T (oF) Empirical Corrected Camber (in) Analytical Corrected Camber (in) 4/9/20048:00 AM0.001.8401.841.84 4/9/200411:00 AM0.132.43102.302.30 4/16/200412:00 PM7.173.66153.363.36 4/23/200410:00 AM14.083.3383.183.18 4/23/200412:00 PM14.173.61153.313.31 4/23/20042:00 PM14.253.87203.443.44 4/29/200411:00 AM20.133.51917874747410.53.303.18 5/7/200411:00 AM28.133.64937874747411.53.413.29 5/21/200411:00 AM42.133.7393807777779.53.533.44 6/7/20047:30 AM58.983.57757378747503.573.57 6/7/20049:30 AM59.063.68947978859003.683.68 6/7/200412:30 PM59.193.9811799838686223.503.26 6/17/200411:00 AM69.133.839986838382103.623.52 7/2/200411:00 AM84.1253.811049086868511.53.573.45 7/14/200411:00 AM96.1253.711049487898611.53.483.34 7/21/200412:00 PM103.166673.891009082848112.53.623.62 7/28/20049:00 AM110.041673.33979086888573.203.11 8/11/20047:00 AM123.963.25817982838103.253.25 8/11/200410:00 AM124.083.481008885868493.303.20 8/11/200412:00 PM124.173.901109788878716.53.553.36 8/24/200410:00 AM137.083333.50978684848383.353.26 9/9/200410:00 AM153.083333.3888828282813.53.313.28 9/21/200410:00 AM165.083333.28727374747503.283.28 10/5/20049:00 AM179.041673.2582798181790.53.243.25 10/26/20049:00 AM200.041673.18706974736903.183.18 78" Florida Bulb-Tee 1 CFtherm =

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62 0.0088 1/oF Date Time Time After Release (Days) Field Camber (in) Top Flange Temp (oF) Bottom Flange Temp (oF) Web Temp (oF) Top Bulb Temp (oF) Bottom Bulb Temp (oF) T (oF) Empirical Corrected Camber (in) Analytical Corrected Camber (in) 4/9/20048:00 AM0.001.4701.471.47 4/9/200411:00 AM0.132.22102.032.03 4/16/200412:00 PM7.173.62153.143.14 4/23/200410:00 AM14.083.0582.842.84 4/23/200412:00 PM14.173.46153.013.01 4/23/20042:00 PM14.253.81203.143.14 4/29/200411:00 AM20.133.38977975747314.52.952.93 5/7/200411:00 AM28.133.631008579787814.53.173.16 5/21/200411:00 AM42.133.74928076757411.53.363.37 6/7/20047:30 AM58.983.44757275747703.443.44 6/7/20049:30 AM59.063.7394807980778.53.453.48 6/7/200412:30 PM59.194.06119104888986243.203.26 6/17/200411:00 AM69.133.4910694908886133.093.07 7/2/200411:00 AM84.1253.9210995899086143.443.48 7/14/200411:00 AM96.1253.931089289898612.53.503.55 7/28/20049:00 AM110.041673.6398908688857.53.393.39 8/11/20047:00 AM123.963.35817982838103.353.35 8/11/200410:00 AM124.083.631018985858410.53.293.30 8/11/200412:00 PM124.173.9811095888786163.423.46 8/24/200410:00 AM137.083333.7010086828282113.343.36 9/9/200410:00 AM153.083333.63898282818243.503.51 9/21/200410:00 AM165.083333.40727374747503.403.40 10/5/20049:00 AM179.041673.35807881807903.353.35 10/26/20049:00 AM200.041673.28706973726903.283.28 0.0090 1/oF Date Time Time After Release (Days) Field Camber (in) Top Flange Temp (oF) Bottom Flange Temp (oF) Web Temp (oF) Top Bulb Temp (oF) Bottom Bulb Temp (oF) T (oF) Empirical Corrected Camber (in) Analytical Corrected Camber (in) 4/9/20048:00 AM0.001.6301.631.63 4/9/200411:00 AM0.132.35102.132.13 4/16/200412:00 PM7.173.25152.812.81 4/23/200410:00 AM14.083.0582.832.83 4/23/200412:00 PM14.173.26152.822.82 4/23/20042:00 PM14.253.52202.882.88 4/29/200411:00 AM20.133.28948076757412.52.912.88 5/7/200411:00 AM28.133.451028980787817.52.902.87 5/21/200411:00 AM42.133.821018780777617.53.223.24 6/7/20047:30 AM58.982.99787375747512.962.97 6/7/20049:30 AM59.063.13917574767862.962.98 6/7/200412:30 PM59.193.6511810384858525.52.812.79 6/17/200411:00 AM69.133.7810695878687143.303.31 7/2/200411:00 AM84.1253.561129687888517.53.003.00 7/14/200411:00 AM96.1253.4510695878786143.012.98 7/28/20049:00 AM110.041673.2597908687895.53.093.08 8/11/20047:00 AM123.962.98827982828102.982.98 8/11/200410:00 AM124.083.1810188858584102.892.87 8/11/200412:00 PM124.173.5311197888787172.992.97 8/24/200410:00 AM137.083333.209886838282102.912.89 9/9/200410:00 AM153.083333.1088828383822.53.033.04 9/21/200410:00 AM165.083333.03727374747503.033.03 10/5/20049:00 AM179.041672.9882808282790.52.962.97 10/26/20049:00 AM200.041672.85717075746902.852.85 78" Florida Bulb-Tee 2 78" Florida Bulb-Tee 3 CFtherm = CFtherm =

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63 0.0129 1/oF Date Time Time After Release (Days) Field Camber (in) Top Flange Temp (oF) Bottom Flange Temp (oF) Web Temp (oF) Top Bulb Temp (oF) Bottom Bulb Temp (oF) T (oF) Empirical Corrected Camber (in) Analytical Corrected Camber (in) 6/28/20046:30 AM0.002.05757981808002.052.05 6/28/20049:00 AM0.102.57797982818102.572.57 7/2/200412:00 PM4.232.89110104969391152.332.37 7/14/200412:00 PM16.233.2510410193929210.52.812.88 7/21/200412:00 PM23.233.2610294878785122.762.86 7/28/20049:00 AM30.102.9795888687855.52.762.80 8/11/20047:00 AM44.022.77817982828102.772.77 8/11/200410:00 AM44.152.9999928990867.52.702.75 8/11/200412:00 PM44.233.341099992908715.52.672.82 8/24/200410:00 AM57.153.1998868483829.52.802.89 9/9/200410:00 AM73.152.97888182828132.852.89 9/21/200410:00 AM85.152.84727374747402.842.84 10/5/20049:00 AM99.103.02807880807903.023.02 10/26/20049:00 AM120.103.02696972716903.023.02 0.0106 1/oF Date Time Time After Release (Days) Field Camber (in) Top Flange Temp (oF) Bottom Flange Temp (oF) Web Temp (oF) Top Bulb Temp (oF) Bottom Bulb Temp (oF) T (oF) Empirical Corrected Camber (in) Analytical Corrected Camber (in) 6/28/20046:30 AM0.002.02757881808002.022.02 6/28/20049:00 AM0.102.37798082828102.372.37 7/2/200412:00 PM4.233.26114103949289182.642.66 7/14/200412:00 PM16.233.321119591908913.52.852.90 7/21/200412:00 PM23.233.391008984848410.53.023.06 7/28/20049:00 AM30.103.13948986878652.962.97 8/11/20047:00 AM44.023.068079852838203.063.06 8/11/200410:00 AM44.153.2398878484848.52.942.97 8/11/200412:00 PM44.233.561079488878713.53.053.12 8/24/200410:00 AM57.153.38958483828373.133.17 9/9/200410:00 AM73.152.98858384868302.982.98 9/21/200410:00 AM85.153.11727374747503.113.11 10/5/20049:00 AM99.102.96817981827902.962.96 10/26/20049:00 AM120.102.98716974746902.982.98 0.0131 1/oF Date Time Time After Release (Days) Field Camber (in) Top Flange Temp (oF) Bottom Flange Temp (oF) Web Temp (oF) Top Bulb Temp (oF) Bottom Bulb Temp (oF) T (oF) Empirical Corrected Camber (in) Analytical Corrected Camber (in) 6/28/20046:30 AM0.001.81777982818001.811.81 6/28/20049:00 AM0.102.25817981828102.252.25 7/2/200412:00 PM4.233.44112105969491162.722.89 7/14/200412:00 PM16.233.31113104969392162.612.76 7/21/200412:00 PM23.233.3810894868884152.712.90 7/28/20049:00 AM30.103.02958886858472.742.79 8/11/20047:00 AM44.022.84837982828202.842.84 8/11/200410:00 AM44.153.0994878585836.52.832.89 8/11/200412:00 PM44.233.421099890898715.52.722.90 8/24/200410:00 AM57.153.241028885848311.52.752.88 9/9/200410:00 AM73.152.99928788888532.872.90 9/21/200410:00 AM85.152.82737374747502.822.82 10/5/20049:00 AM99.102.9283808181791.52.862.87 10/26/20049:00 AM120.102.8471697271680.52.822.83 CFtherm = CFtherm = CFtherm = 78" Florida Bulb-Tee 4 78" Florida Bulb-Tee 5 78" Florida Bulb-Tee 6

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64 0.0132 1/oF Date Time Time After Release (Days) Field Camber (in) Top Flange Temp (oF) Bottom Flange Temp (oF) Web Temp (oF) Top Bulb Temp (oF) Bottom Bulb Temp (oF) T (oF) Empirical Corrected Camber (in) Analytical Corrected Camber (in) 6/10/20049:30 AM0.000.65838385888500.650.65 6/10/200411:30 AM0.081.181048887989211.171.18 6/17/20049:00 AM6.981.29878585848231.241.23 6/24/20043:00 PM14.231.47117100959695131.221.25 7/2/20049:00 AM21.981.2898888786857.51.151.15 7/14/200410:00 AM34.021.201019090898871.091.08 7/21/20049:00 AM40.981.16928586868531.121.11 7/28/20049:00 AM47.981.5092858687871.51.471.48 8/11/20047:00 AM61.901.33798283827901.331.32 8/11/200410:00 AM62.021.4595878788892.51.401.41 8/11/200412:00 PM62.101.45107919090918.51.291.31 8/24/200410:00 AM75.021.50938687878441.421.43 9/9/200410:00 AM91.021.58948686868641.491.51 9/21/200410:00 AM103.021.58757475757501.581.58 10/5/20049:00 AM116.981.63888485848041.541.55 10/26/20049:00 AM137.981.75817474737061.611.64 0.0276 1/oF Date Time Time After Release (Days) Field Camber (in) Top Flange Temp (oF) Bottom Flange Temp (oF) Web Temp (oF) Top Bulb Temp (oF) Bottom Bulb Temp (oF) T (oF) Empirical Corrected Camber (in) Analytical Corrected Camber (in) 6/10/20049:30 AM0.000.61878588938700.610.61 6/10/200411:30 AM0.081.05105878586879.50.780.90 6/17/20049:00 AM6.981.2492848489841.51.191.22 6/24/20043:00 PM14.231.53120999610396101.111.36 7/2/20049:00 AM21.981.2893888886845.51.091.18 7/14/200410:00 AM34.021.22101939289888.50.941.07 7/21/20049:00 AM40.981.2487828282803.51.121.17 7/28/20049:00 AM47.981.51938586878721.431.48 8/11/20047:00 AM61.901.06798283827901.061.05 8/11/200410:00 AM62.021.29938485858631.181.24 8/11/200412:00 PM62.101.26107918990918.50.961.12 8/24/200410:00 AM75.021.31948686868451.131.22 9/9/200410:00 AM91.021.64928686868631.501.59 9/21/200410:00 AM103.021.71757475757501.711.71 10/5/20043:36 AM116.751.6489848484804.51.431.55 10/26/20049:00 AM137.981.7478767675704.51.521.65 0.0123 1/oF Date Time Time After Release (Days) Field Camber (in) Top Flange Temp (oF) Bottom Flange Temp (oF) Web Temp (oF) Top Bulb Temp (oF) Bottom Bulb Temp (oF) T (oF) Empirical Corrected Camber (in) Analytical Corrected Camber (in) 6/10/20049:30 AM0.000.67868487958900.670.67 6/10/200411:30 AM0.081.171048885848710.51.021.00 6/17/20049:00 AM6.981.25958786848471.141.12 6/24/20043:00 PM14.231.471161039910510071.351.36 7/2/20049:00 AM21.981.2895898987846.51.181.16 7/14/200410:00 AM34.021.39101888888886.51.281.28 7/21/20049:00 AM40.981.3790818080805.51.271.27 7/28/20049:00 AM47.981.49928686878721.451.46 8/11/20047:00 AM61.901.59788283827901.591.59 8/11/200410:00 AM62.021.9196868584856.51.761.80 8/11/200412:00 PM62.101.64109918990919.51.451.48 8/24/200410:00 AM75.021.7196878686846.51.581.60 9/9/200410:00 AM91.021.69938685858641.601.62 9/21/200410:00 AM103.021.71757474757501.711.71 10/5/20043:36 AM116.751.76888284828041.681.69 10/26/20049:00 AM137.981.76777272717041.681.69 AASHTO Type IV 1 AASHTO Type IV 2 AASHTO Type IV 3 CFtherm = CFtherm = CFtherm =

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65 0.0037 1/oF Date Time Time After Release (Days) Field Camber (in) Top Flange Temp (oF) Bottom Flange Temp (oF) Web Temp (oF) Top Bulb Temp (oF) Bottom Bulb Temp (oF) T (oF) Empirical Corrected Camber (in) Analytical Corrected Camber (in) 9/28/20049:00 AM0.000.9081787979790.50.900.90 9/28/200410:00 AM0.040.90898282828330.890.87 10/5/20049:00 AM7.001.2889828585831.51.271.26 10/12/20049:00 AM14.001.30747374747401.301.30 10/19/20049:00 AM21.001.30797779817501.301.30 10/19/200411:00 AM21.081.35898282817861.321.28 10/19/20041:00 PM21.171.351008682818012.51.291.20 10/26/20049:00 AM28.001.28717173757101.281.28 0.0061 1/oF Date Time Time After Release (Days) Field Camber (in) Top Flange Temp (oF) Bottom Flange Temp (oF) Web Temp (oF) Top Bulb Temp (oF) Bottom Bulb Temp (oF) T (oF) Empirical Corrected Camber (in) Analytical Corrected Camber (in) 9/28/20049:00 AM0.000.85788080808000.850.85 9/28/200410:00 AM0.041.0087828383831.50.990.98 10/5/20049:00 AM7.001.25878284848311.241.24 10/12/20049:00 AM14.001.28747373747401.281.28 10/19/20049:00 AM21.001.3381767877752.51.301.30 10/19/200411:00 AM21.081.4091828080787.51.341.31 10/19/20041:00 PM21.171.4310286838280131.311.27 10/26/20049:00 AM28.001.3376717473711.51.311.31 0.0075 1/oF Date Time Time After Release (Days) Field Camber (in) Top Flange Temp (oF) Bottom Flange Temp (oF) Web Temp (oF) Top Bulb Temp (oF) Bottom Bulb Temp (oF) T (oF) Empirical Corrected Camber (in) Analytical Corrected Camber (in) 9/28/20049:00 AM0.000.70797880797900.700.70 9/28/200410:00 AM0.040.7390828382814.50.700.67 10/5/20049:00 AM7.001.20888285848221.181.18 10/12/20049:00 AM14.001.25747273747401.251.25 10/19/20049:00 AM21.001.1080767776752.51.081.07 10/19/200411:00 AM21.081.15878079797851.111.09 10/19/20041:00 PM21.171.209986828180121.091.06 10/26/20049:00 AM28.001.15717174747101.151.15 AASHTO Type V 4 CFtherm = AASHTO Type V 2 AASHTO Type V 3 CFtherm = CFtherm =

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66 APPENDIX C EMPIRICAL THERMAL ANALYSIS For the empirical thermal gradient camb er correction method, a linear thermal gradient approximation was made. This was calculated by subtracting the average temperature of the bottom bulb from the aver age temperature of the top flange (Equation C-1). 2 2E D B AT T T T T (C-1) where: Ti = temperature at location A B D or E along the cross section (oF) In order to correct for the effect of the th ermal gradient on the prestressed beam camber, a thermal correction factor needed to be de termined. This factor was obtained by first determining the percent camber change relative to the early morning camber measurement ( C %) where there was essentially no gradient (Equation C-2). %io oCC C C (C-2) where: Co = morning field measured camber reading (in.) Ci = subsequent field measured camber reading (in.)

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67 The thermal gradient versus normalized camber reading was plotted and a linear regression of the data produced a thermal correction factor (Equation C-3) for the adjustment of the field measur ed camber values (Equation C-4). %/100thermC CF T (C-3) ) ( T CF C C Ctherm field field corr (C-4) where: Cfield = field measured camber reading (in.) Assumptions made to obtain this thermal correct ion factor were that a thermal gradient of zero yielded no change in camber (i.e., the linear regression was forced through the origin) and that negative thermal gradients did not produce negative camber effects (i.e., an increase in camber). Temperature field measurements were not made for the first three camber readings of the 78inch Bulb-Tee girders (girders 1, 2, and 3). The thermal gradients were estimated for these readings based on the time of reading and ambient temperature.

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68Date Time Field Measured Camber (in) C% (%) Top Flange Temp (oF) Bottom Flange Temp (oF) Web Temp (oF) Top Bulb Temp (oF) Bottom Bulb Temp (oF) T (oF) CFtherm (1/oF) 6/7/20047:30 AM3.570.00%75737874750 6/7/20049:30 AM3.682.91%94797885900 6/7/200412:30 PM3.9811.31%1179983868622 8/11/20047:00 AM3.250.00%81798283810 8/11/200410:00 AM3.486.92%100888586849 8/11/200412:00 PM3.9019.99%1109788878716.5 Date Time Field Measured Camber (in) C% (%) Top Flange Temp (oF) Bottom Flange Temp (oF) Web Temp (oF) Top Bulb Temp (oF) Bottom Bulb Temp (oF) T (oF) CFtherm (1/oF) 6/7/20047:30 AM3.440.00%75727574770 6/7/20049:30 AM3.738.53%94807980778.5 6/7/200412:30 PM4.0618.17%11910488898624 8/11/20047:00 AM3.350.00%81798283810 8/11/200410:00 AM3.638.20%1018985858410.5 8/11/200412:00 PM3.9818.65%1109588878616 Date Time Field Measured Camber (in) C% (%) Top Flange Temp (oF) Bottom Flange Temp (oF) Web Temp (oF) Top Bulb Temp (oF) Bottom Bulb Temp (oF) T (oF) CFtherm (1/oF) 6/7/20047:30 AM2.990.00%78737574751 6/7/20049:30 AM3.134.68%91757476786 6/7/200412:30 PM3.6521.95%11810384858525.5 8/11/20047:00 AM2.980.00%82798282810 8/11/200410:00 AM3.186.72%1018885858410 8/11/200412:00 PM3.5318.47%1119788878717 78" Bulb-Tee 1 78" Bulb-Tee 3 0.0055 0.0088 0.009 78" Bulb-Tee 2 0.00% 5.00% 10.00% 15.00% 20.00% 25.00% 051015202530Temperature Gradient (oF)Camber Increase (%) FLBT (1) FLBT (2) FLBT (3) Linear (FLBT (1)) Linear (FLBT (2)) Linear (FLBT (3))

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69 Date Time Field Measured Camber (in) C% (%) Top Flange Temp (oF) Bottom Flange Temp (oF) Web Temp (oF) Top Bulb Temp (oF) Bottom Bulb Temp (oF) T (oF) CFtherm (1/oF) 8/11/20047:00 AM2.770.00%81798282810 8/11/200410:00 AM2.998.14%99928990867.5 8/11/200412:00 PM3.3420.79%1099992908715.5 Date Time Field Measured Camber (in) C% (%) Top Flange Temp (oF) Bottom Flange Temp (oF) Web Temp (oF) Top Bulb Temp (oF) Bottom Bulb Temp (oF) T (oF) CFtherm (1/oF) 8/11/20047:00 AM3.060.00%807985283820 8/11/200410:00 AM3.235.73%98878484848.5 8/11/200412:00 PM3.5616.36%1079488878713.5 Date Time Field Measured Camber (in) C% (%) Top Flange Temp (oF) Bottom Flange Temp (oF) Web Temp (oF) Top Bulb Temp (oF) Bottom Bulb Temp (oF) T (oF) CFtherm (1/oF) 8/11/20047:00 AM2.840.00%83798282820 8/11/200410:00 AM3.098.80%94878585836.5 8/11/200412:00 PM3.4220.24%1099890898715.5 0.0129 0.0106 0.0131 78" Bulb-Tee 4 78" Bulb-Tee 5 78" Bulb-Tee 6 0.00% 5.00% 10.00% 15.00% 20.00% 25.00% 051015202530Temperature Gradient (oF)Camber Increase (%) FLBT (4) FLBT (5) FLBT (6) Linear (FLBT (4)) Linear (FLBT (5)) Linear (FLBT (6))

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70Date Time Field Measured Camber (in) C% (%) Top Flange Temp (oF) Bottom Flange Temp (oF) Web Temp (oF) Top Bulb Temp (oF) Bottom Bulb Temp (oF) T (oF) CFtherm (1/oF) 8/11/20047:00 AM1.330.00%79828382790 8/11/200410:00 AM1.459.43%95878788892.5 8/11/200412:00 PM1.459.43%107919090918.5 Date Time Field Measured Camber (in) C% (%) Top Flange Temp (oF) Bottom Flange Temp (oF) Web Temp (oF) Top Bulb Temp (oF) Bottom Bulb Temp (oF) T (oF) CFtherm (1/oF) 8/11/20047:00 AM1.060.00%79828382790 8/11/200410:00 AM1.2921.23%93848585863 8/11/200412:00 PM1.2618.87%107918990918.5 Date Time Field Measured Camber (in) C% (%) Top Flange Temp (oF) Bottom Flange Temp (oF) Web Temp (oF) Top Bulb Temp (oF) Bottom Bulb Temp (oF) T (oF) CFtherm (1/oF) 8/11/20047:00 AM1.590.00%78828382790 8/11/200410:00 AM1.9120.47%96868584856.5 8/11/200412:00 PM1.643.15%109918990919.5 AASHTO Type IV 1 0.0132 0.0276 0.0123 AASHTO Type IV 2 AASHTO Type IV 3 0.00% 5.00% 10.00% 15.00% 20.00% 25.00% 051015202530Temperature Gradient (oF)Camber Increase (%) Type IV 1 Type IV 2 Type IV 3 Linear (Type IV 1) Linear (Type IV 2) Linear (Type IV 3)

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71Date Time Field Measured Camber (in) C% (%) Top Flange Temp (oF) Bottom Flange Temp (oF) Web Temp (oF) Top Bulb Temp (oF) Bottom Bulb Temp (oF) T (oF) CFtherm (1/oF) 10/19/20049:00 AM1.180.00%81777878752.5 10/19/200411:00 AM1.256.38%91828080787.5 10/19/20041:00 PM1.256.38%1038882818015 Date Time Field Measured Camber (in) C% (%) Top Flange Temp (oF) Bottom Flange Temp (oF) Web Temp (oF) Top Bulb Temp (oF) Bottom Bulb Temp (oF) T (oF) CFtherm (1/oF) 10/19/20049:00 AM1.300.00%79777981750 10/19/200411:00 AM1.353.85%89828281786 10/19/20041:00 PM1.353.85%1008682818012.5 Date Time Field Measured Camber (in) C% (%) Top Flange Temp (oF) Bottom Flange Temp (oF) Web Temp (oF) Top Bulb Temp (oF) Bottom Bulb Temp (oF) T (oF) CFtherm (1/oF) 10/19/20049:00 AM1.330.00%81767877752.5 10/19/200411:00 AM1.405.66%91828080787.5 10/19/20041:00 PM1.437.55%1028683828013 Date Time Field Measured Camber (in) C% (%) Top Flange Temp (oF) Bottom Flange Temp (oF) Web Temp (oF) Top Bulb Temp (oF) Bottom Bulb Temp (oF) T (oF) CFtherm (1/oF) 10/19/20049:00 AM1.100.00%80767776752.5 10/19/200411:00 AM1.154.55%87807979785 10/19/20041:00 PM1.209.09%998682818012 AASHTO Type V 1 0.005 0.0037 0.0061 0.0075 AASHTO Type V 2 AASHTO Type V 3 AASHTO Type V 4

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72 0.00% 5.00% 10.00% 15.00% 20.00% 25.00% 051015202530Temperature Gradient (oF)Camber Increase (%) Type VA (1) Type VA (2) Type VB (3) Type VB (4) Linear (Type VA (1)) Linear (Type VA (2)) Linear (Type VB (3)) Linear (Type VB (4))

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73 APPENDIX D ANALYTICAL THERMAL ANALYSIS A nalytical Thermal Analysis--written by Jonathan Sanek, Universtiy of Florida Department of Civil and Coastal Engineering78" Bulb-Tee Girder, Pour AORIGIN1 ORIGIN Input Field Temperature Measurments t camber 0.00 0.13 7.17 14.08 14.17 14.25 20.13 28.13 42.13 58.98 59.06 59.19 69.13 84.125 96.125 110.0416667 123.96 124.08 124.17 137.0833333 153.0833333 165.0833333 179.0416667 200.0416667 FLBT1 0 0 0 0 0 0 91 93 93 75 94 117 99 104 104 97 81 100 110 97 88 72 82 70 0 0 0 0 0 0 78 78 80 73 79 99 86 90 94 90 79 88 97 86 82 73 79 69 0 0 0 0 0 0 74 74 77 78 78 83 83 86 87 86 82 85 88 84 82 74 81 74 0 0 0 0 0 0 74 74 77 74 85 86 83 86 89 88 83 86 87 84 82 74 81 73 0 0 0 0 0 0 74 74 77 75 90 86 82 85 86 85 81 84 87 83 81 75 79 69 FLBT2 0 0 0 0 0 0 97 100 92 75 94 119 106 109 108 98 81 101 110 100 89 72 80 70 0 0 0 0 0 0 79 85 80 72 80 104 94 95 92 90 79 89 95 86 82 73 78 69 0 0 0 0 0 0 75 79 76 75 79 88 90 89 89 86 82 85 88 82 82 74 81 73 0 0 0 0 0 0 74 78 75 74 80 89 88 90 89 88 83 85 87 82 81 74 80 72 0 0 0 0 0 0 73 78 74 77 77 86 86 86 86 85 81 84 86 82 82 75 79 69

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74 Input Field Temperature Measurments (cont...) Height vector corresponding to temperature readings H vec 0 5 35 65 78 (in) FLBT3 0 0 0 0 0 0 94 102 101 78 91 118 106 112 106 97 82 101 111 98 88 72 82 71 0 0 0 0 0 0 80 89 87 73 75 103 95 96 95 90 79 88 97 86 82 73 80 70 0 0 0 0 0 0 76 80 80 75 74 84 87 87 87 86 82 85 88 83 83 74 82 75 0 0 0 0 0 0 75 78 77 74 76 85 86 88 87 87 82 85 87 82 83 74 82 74 0 0 0 0 0 0 74 78 76 75 78 85 87 85 86 89 81 84 87 82 82 75 79 69

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75Gross Moment of Inertia (in^4) I g 935547.485 I g0 Hz zc ()2bz () d Location of Neutral Axis from top of member (in) c37.613 c Q y A First Moment Area (in^3) Q y 41563.094 Q y0 Hz zbz () d Cross-Sectional Area (in^2) A1105.007 A0 Hz bz () d Input Material Testing Data 5.3106 taken from Table 5 of NCHRP Report 276 t emod 0 7 14 21 28 42 84 109 136 200 (days) E c 4309 5228 5304 5336 5444 5588 6005 6070 6126 6017 (ksi) Et () outilinterpt emod E c ti i lastt () for out Section Properties H78 (in) L1942.625 (in) Section Shape bz ()600z 3 if 6011.75z3 () []3z 7 if 132z7 () []7z 10 if 710z 60 if 72.1z60 () []60z 70 if 2870z H if

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76(in) corr 0.37 corr M int L2 8Et cambertime I g (kip*in) M int 4.429103 M int0 Hz T z ()bz () zc () d (ksi) T z ()Et cambertime Tz () (deg F) Tz ()T grad Beamz ()time BeamFLBT1 time15 Example Calculation of Internal Moment Due to Positive Thermal Gradient T grad Beamz () outilinterpH vec T vec Beam ()i z i rowsBeam () for out Linear Interpolation of Thermal Gradient for variable, z... T vec Beam () miniminsubmatrixBeami i colsBeam () T gij Beamij mini T gij T gij T gij 0 if T gij 0 otherwise j colsBeam () for outisubmatrixT g i i colsT g T i rowsBeam () for out Extract Thermal Gradient and Normalized based on Minimum Measured Temperature Along Profile... Calculations

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77 A nalytical Thermal Analysis--written by Jonathan Sanek, Universtiy of Florida Department of Civil and Coastal Engineering78" Bulb-Tee Girder, Pour BORIGIN1 ORIGIN Input Field Temperature Measurments t camber 0.00 0.10 4.23 16.23 23.23 30.10 44.02 44.15 44.23 57.15 73.15 85.15 99.10 120.10 FLBT4 75 79 110 104 102 95 81 99 109 98 88 72 80 69 79 79 104 101 94 88 79 92 99 86 81 73 78 69 81 82 96 93 87 86 82 89 92 84 82 74 80 72 80 81 93 92 87 87 82 90 90 83 82 74 80 71 80 81 91 92 85 85 81 86 87 82 81 74 79 69 FLBT5 75 79 114 111 100 94 80 98 107 95 85 72 81 71 78 80 103 95 89 89 79 87 94 84 83 73 79 69 81 82 94 91 84 86 85 84 88 83 84 74 81 74 80 82 92 90 84 87 83 84 87 82 86 74 82 74 80 81 89 89 84 86 82 84 87 83 83 75 79 69 Height vector corresponding to temperature readings H vec 0 5 35 65 78 (in) FLBT6 77 81 112 113 108 95 83 94 109 102 92 73 83 71 79 79 105 104 94 88 79 87 98 88 87 73 80 69 82 81 96 96 86 86 82 85 90 85 88 74 81 72 81 82 94 93 88 85 82 85 89 84 88 74 81 71 80 81 91 92 84 84 82 83 87 83 85 75 79 68

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78Gross Moment of Inertia (in^4) I g 935547.485 I g0 Hz zc ()2bz () d Location of Neutral Axis from top of member (in) c37.613 c Q y A First Moment Area (in^3) Q y 41563.094 Q y0 Hz zbz () d Cross-Sectional Area (in^2) A1105.007 A0 Hz bz () d Input Material Testing Data 5.3106 taken from Table 5 of NCHRP Report 276 t emod 0 4 16 22 34 43 56 72 84 120 (days) E c 4759 4677 4813 5099 4932 5133 5222 5370 5365 5160 (ksi) Et () outilinterpt emod E c ti i lastt () for out Section Properties H78 (in) L1942.625 (in) Section Shape bz ()600z 3 if 6011.75z3 () []3z 7 if 132z7 () []7z 10 if 710z 60 if 72.1z60 () []60z 70 if 2870z H if

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79(in) corr 0.238 corr M int L2 8Et cambertime I g (kip*in) M int 2.431103 M int0 Hz T z ()bz () zc () d (ksi) T z ()Et cambertime Tz () (deg F) Tz ()T grad Beamz ()time BeamFLBT4 time8 Example Calculation of Internal Moment Due to Positive Thermal Gradient T grad Beamz () outilinterpH vec T vec Beam ()i z i rowsBeam () for out Linear Interpolation of Thermal Gradient for variable, z... T vec Beam () miniminsubmatrixBeami i colsBeam () T gij Beamij mini T gij T gij T gij 0 if T gij 0 otherwise j colsBeam () for outisubmatrixT g i i colsT g T i rowsBeam () for out Extract Thermal Gradient and Normalized based on Minimum Measured Temperature Along Profile... Calculations

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80 A nalytical Thermal Analysis--written by Jonathan Sanek, Universtiy of Florida Department of Civil and Coastal EngineeringAASHTO Type IV Girder, Pour AORIGIN1 ORIGIN Input Field Temperature Measurments t camber 0.00 0.08 6.98 14.23 21.98 34.02 40.98 47.98 61.90 62.02 62.10 75.02 91.02 103.02 116.98 137.98 TYPEIV1 83 104 87 117 98 101 92 92 79 95 107 93 94 75 88 81 83 88 85 100 88 90 85 85 82 87 91 86 86 74 84 74 85 87 85 95 87 90 86 86 83 87 90 87 86 75 85 74 88 98 84 96 86 89 86 87 82 88 90 87 86 75 84 73 85 92 82 95 85 88 85 87 79 89 91 84 86 75 80 70 TYPEIV2 87 105 92 120 93 101 87 93 79 93 107 94 92 75 89 78 85 87 84 99 88 93 82 85 82 84 91 86 86 74 84 76 88 85 84 96 88 92 82 86 83 85 89 86 86 75 84 76 93 86 89 103 86 89 82 87 82 85 90 86 86 75 84 75 87 87 84 96 84 88 80 87 79 86 91 84 86 75 80 70 Height vector corresponding to temperature readings H vec 0 11.02 25.51 41.5 54.02 (in) TYPEIV3 86 104 95 116 95 101 90 92 78 96 109 96 93 75 88 77 84 88 87 103 89 88 81 86 82 86 91 87 86 74 82 72 87 85 86 99 89 88 80 86 83 85 89 86 85 74 84 72 95 84 84 105 87 88 80 87 82 84 90 86 85 75 82 71 89 87 84 100 84 88 80 87 79 85 91 84 86 75 80 70

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81Gross Moment of Inertia (in^4) I g 268621.613 I g0 Hz zc ()2bz () d Location of Neutral Axis from top of member (in) c29.663 c Q y A First Moment Area (in^3) Q y 23960.324 Q y0 Hz zbz () d Cross-Sectional Area (in^2) A807.739 A0 Hz bz () d Input Material Testing Data 5.3106 taken from Table 5 of NCHRP Report 276 t emod 0 7 14 21 34 40 61 74 102 138 (days) E c 4506 4911 5390 5191 5456 5830 5886 5672 5853 5887 (ksi) Et () outilinterpt emod E c ti i lastt () for out Section Properties H54.02 (in) L1092.32 (in) Section Shape bz ()20.080z 8.03 if 20.082.015z8.03 () []8.03z 14.01 if 8.0314.01z 37 if 8.032z37 () []37z 45.98 if 2845.98z H if

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82(in) corr 0.072 corr M int L2 8Et cambertime I g (kip*in) M int 732.438 M int0 Hz T z ()bz () zc () d (ksi) T z ()Et cambertime Tz () (deg F) Tz ()T grad Beamz ()time BeamTYPEIV1 time12 Example Calculation of Internal Moment Due to Positive Thermal Gradient T grad Beamz () outilinterpH vec T vec Beam ()i z i rowsBeam () for out Linear Interpolation of Thermal Gradient for variable, z... T vec Beam () miniminsubmatrixBeami i colsBeam () T gij Beamij mini T gij T gij T gij 0 if T gij 0 otherwise j colsBeam () for outisubmatrixT g i i colsT g T i rowsBeam () for out Extract Thermal Gradient and Normalized based on Minimum Measured Temperature Along Profile...Calculations

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83Et () outilinterpt emod E c ti i lastt () for out (ksi) E c 4909 5130 5361 5419 5323 (days) t emod 0 7 14 22 28 taken from Table 5 of NCHRP Report 276 5.3106 Input Material Testing Data TYPEV4 79 90 88 74 80 87 99 71 78 82 82 72 76 80 86 71 80 83 85 73 77 79 82 74 79 82 84 74 76 79 81 74 79 81 82 74 75 78 80 71 TYPEV3 78 87 87 74 81 91 102 76 80 82 82 73 76 82 86 71 80 83 84 73 78 80 83 74 80 83 84 74 77 80 82 73 80 83 83 74 75 78 80 71 (in) H vec 0 8.5 28.5 50 63 Height vector corresponding to temperature readings TYPEV2 81 89 89 74 79 89 100 71 78 82 82 73 77 82 86 71 79 82 85 74 79 82 82 73 79 82 85 74 81 81 81 75 79 83 83 74 75 78 80 71 TYPEV1 82 89 88 74 81 91 103 76 79 82 83 73 77 82 88 72 80 82 85 74 78 80 82 73 79 82 86 74 78 80 81 72 79 82 83 74 75 78 80 71 t camber 0.00 0.04 7.00 14.00 21.00 21.08 21.17 28.00 Input Field Temperature Measurments ORIGIN ORIGIN1 AASHTO Type V Girder, Pour A--written by Jonathan Sanek, Universtiy of Florida Department of Civil and Coastal Engineering A nalytical Thermal Analysis

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84Gross Moment of Inertia (in^4) I g 521157.365 I g0 Hz zc ()2bz () d Location of Neutral Axis from top of member (in) c31.04 c Q y A First Moment Area (in^3) Q y 31446.978 Q y0 Hz zbz () d Cross-Sectional Area (in^2) A1013.107 A0 Hz bz () d bz ()420z 5 if 428.667z5 () []5z 8 if 162z8 () []8z 12 if 812z 45 if 82z45 () []45z 55 if 2855z H if Section Shape (in) L972.625 (in) H63 Section Properties

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85(in) corr 0.088 corr M int L2 8Et cambertime I g (kip*in) M int 2.103103 M int0 Hz T z ()bz () zc () d (ksi) T z ()Et cambertime Tz () (deg F) Tz ()T grad Beamz ()time BeamTYPEV1 time6 Example Calculation of Internal Moment Due to Positive Thermal Gradient T grad Beamz () outilinterpH vec T vec Beam ()i z i rowsBeam () for out Linear Interpolation of Thermal Gradient for variable, z... T vec Beam () miniminsubmatrixBeami i colsBeam () T gij Beamij mini T gij T gij T gij 0 if T gij 0 otherwise j colsBeam () for outisubmatrixT g i i colsT g T i rowsBeam () for out Extract Thermal Gradient and Normalized based on Minimum Measured Temperature Along Profile...Calculations

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86Et () outilinterpt emod E c ti i lastt () for out (ksi) E c 4796 5164 5331 5466 5313 (days) t emod 0 7 14 22 28 taken from Table 5 of NCHRP Report 276 5.3106 Input Material Testing Data TYPEV4 79 90 88 74 80 87 99 71 78 82 82 72 76 80 86 71 80 83 85 73 77 79 82 74 79 82 84 74 76 79 81 74 79 81 82 74 75 78 80 71 TYPEV3 78 87 87 74 81 91 102 76 80 82 82 73 76 82 86 71 80 83 84 73 78 80 83 74 80 83 84 74 77 80 82 73 80 83 83 74 75 78 80 71 (in) H vec 0 8.5 28.5 50 63 Height vector corresponding to temperature readings TYPEV2 81 89 89 74 79 89 100 71 78 82 82 73 77 82 86 71 79 82 85 74 79 82 82 73 79 82 85 74 81 81 81 75 79 83 83 74 75 78 80 71 TYPEV1 82 89 88 74 81 91 103 76 79 82 83 73 77 82 88 72 80 82 85 74 78 80 82 73 79 82 86 74 78 80 81 72 79 82 83 74 75 78 80 71 t camber 0.00 0.04 7.00 14.00 21.00 21.08 21.17 28.00 Input Field Temperature Measurments ORIGIN ORIGIN1 AASHTO Type V Girder, Pour B--written by Jonathan Sanek, Universtiy of Florida Department of Civil and Coastal Engineering A nalytical Thermal Analysis

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87Gross Moment of Inertia (in^4) I g 521157.365 I g0 Hz zc ()2bz () d Location of Neutral Axis from top of member (in) c31.04 c Q y A First Moment Area (in^3) Q y 31446.978 Q y0 Hz zbz () d Cross-Sectional Area (in^2) A1013.107 A0 Hz bz () d bz ()420z 5 if 428.667z5 () []5z 8 if 162z8 () []8z 12 if 812z 45 if 82z45 () []45z 55 if 2855z H if Section Shape (in) L972.625 (in) H63 Section Properties

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88(in) corr 0.059 corr M int L2 8Et cambertime I g (kip*in) M int 1.41103 M int0 Hz T z ()bz () zc () d (ksi) T z ()Et cambertime Tz () (deg F) Tz ()T grad Beamz ()time BeamTYPEV4 time6 Example Calculation of Internal Moment Due to Positive Thermal Gradient T grad Beamz () outilinterpH vec T vec Beam ()i z i rowsBeam () for out Linear Interpolation of Thermal Gradient for variable, z... T vec Beam () miniminsubmatrixBeami i colsBeam () T gij Beamij mini T gij T gij T gij 0 if T gij 0 otherwise j colsBeam () for outisubmatrixT g i i colsT g T i rowsBeam () for out Extract Thermal Gradient and Normalized based on Minimum Measured Temperature Along Profile...Calculations

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89 APPENDIX E TABULATED AMBIENT DATA 2 YearMonthDayHour Temp (oC)Temp (oF)Temp (oC)Temp (oF) RHSOLRD (60 cm)(60 cm)(200 cm)(200 cm)(%)(W/m2) 200449019.0766.3319.4767.05950 200449118.9666.1319.3266.78960 200449218.9466.0919.2366.61960 200449319.1566.4719.3666.85960 200449419.1466.4519.3266.78960 200449519.0966.3619.3266.78950 200449619.1766.5119.3766.879512 200449719.5767.2319.7067.469377 200449821.0169.8220.8869.5887288 200449922.1171.8021.7871.2081329 2004491023.7474.7323.1473.6574622 2004491125.7078.2624.8176.6665760 2004491226.5779.8325.8478.5161825 2004491326.8280.2826.6079.8855577 2004491427.8982.2027.5081.5051637 2004491528.9984.1828.6883.6243685 2004491628.9384.0729.2084.5639490 2004491728.7583.7529.1284.4235286 2004491826.5079.7027.1080.784282 2004491923.2573.8524.0775.33590 2004492021.5470.7722.4672.43710 2004492119.8067.6420.7169.28760 2004492218.7365.7119.5567.19840 2004492317.8264.0818.4565.21900Bulb-Tee A At Release 2 Highlighted entries are when fi eld measurements were made ( 78” Bulb-Tee A, 78” Bulb-Tee B, AASHTO Type IV A, AASHTO V A and B, and All Girders)

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90 3 YearMonthDayHour Temp (oC)Temp (oF)Temp (oC)Temp (oF) RHSOLRD (60 cm)(60 cm)(200 cm)(200 cm)(%)(W/m2) 200441609.7049.4610.1050.18830 200441618.3847.088.7147.68890 200441627.6845.828.0646.51910 200441637.2345.017.4845.46920 200441646.9344.477.1544.87920 200441656.8244.287.0744.73930 200441667.3145.167.3745.279435 2004416713.2755.8912.4454.3985222 2004416818.2364.8117.5763.6359447 2004416920.8669.5519.9767.9548649 20044161021.8271.2820.9469.6946747 20044161122.7472.9322.0071.6045874 20044161223.8574.9323.0273.4444945 20044161324.7276.5023.9475.0942950 20044161425.2077.3624.5976.2639903 20044161524.7876.6024.4475.9940659 20044161624.2475.6324.2675.6740530 20044161723.5974.4623.6674.5940299 20044161822.1471.8522.4572.414684 20044161920.3868.6820.8469.51531 20044162019.1866.5219.6867.42590 20044162118.1264.6218.6265.52660 20044162217.1662.8917.6663.79700 20044162316.9562.5117.4363.37720 2004423018.3665.0518.9966.18850 2004423117.0762.7317.6463.75900 2004423216.9062.4217.3663.25920 2004423317.7063.8618.2864.90920 2004423417.8564.1318.3264.98920 2004423517.7163.8818.2264.80930 2004423617.1962.9417.4863.469439 2004423720.7869.4020.4068.7288210 2004423823.7974.8223.3073.9476438 2004423925.9778.7525.3577.6364634 20044231027.5081.5026.7580.1553845 20044231128.3583.0327.4481.3946945 20044231229.0684.3128.1282.6241833 20044231329.9085.8228.7783.7939899 20044231429.9185.8428.9884.1639821 20044231529.6185.3029.0484.2741687 20044231629.2184.5829.0784.3340461 20044231729.0984.3628.9784.1540312 20044231827.8782.1728.1782.7143101 20044231925.4277.7625.9878.76482 20044232023.7274.7024.2575.65540 20044232122.1871.9222.7772.99620 20044232220.7269.3021.3570.43700 20044232319.8667.7520.4868.86780Bulb-Tee A 7-Day ReadingBulb-Tee A 14-Day Reading 3Highlighted entries are when field measurements were made ( 78” Bulb-Tee A, 78” BulbTee B, AASHTO Type IV A, AASHTO V A and B, and All Girders)

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914 YearMonthDayHour Temp (oC)Temp (oF)Temp (oC)Temp (oF) RHSOLRD (60 cm)(60 cm)(200 cm)(200 cm)(%)(W/m2) 2004429019.8167.6620.2668.47720 2004429119.7167.4820.1468.25710 2004429219.3866.8819.8867.78760 2004429319.3666.8519.8167.66770 2004429419.7167.4820.1068.18740 2004429519.8967.8020.2868.50750 2004429619.9167.8420.2368.417652 2004429720.8769.5720.9069.6275223 2004429823.1573.6722.9773.3567459 2004429925.0177.0224.7976.6259596 20044291026.7080.0626.2479.2356766 20044291127.5881.6427.1680.8954644 20044291227.2581.0527.0680.7154395 20044291327.5381.5527.3281.1853431 20044291426.7780.1926.7480.1356313 20044291526.2479.2326.2679.2760255 20044291626.1779.1126.1679.0962312 20044291725.2577.4525.4477.7967128 20044291824.0975.3624.3675.857346 20044291923.3373.9923.6974.64761 20044292022.8873.1823.2273.80790 20044292122.9073.2223.1873.72810 20044292222.5872.6422.8973.20850 20044292322.3172.1622.6072.68870 2004430022.1271.8222.4072.32880 200457018.6065.4819.3166.76840 200457118.0364.4518.5865.44880 200457217.6863.8218.2064.76910 200457317.2162.9817.7363.91920 200457416.5961.8616.9762.55940 200457516.2861.3016.6661.99950 200457616.8462.3117.0062.609553 200457720.9069.6220.6869.2288200 200457823.7574.7523.4574.2173470 200457926.3679.4525.7978.4260648 2004571027.5481.5726.9580.5152799 2004571128.7783.7928.0682.5147904 2004571229.4384.9728.7083.6641942 2004571329.8985.8029.1584.4740912 2004571430.5386.9529.8985.8038829 2004571530.5286.9430.2186.3838688 2004571630.8587.5330.6487.1535539 2004571730.8087.4430.8287.4834336 2004571830.0986.1630.4786.8538128 2004571927.1780.9127.8882.18473 2004572024.9376.8725.6078.08530 2004572123.5474.3724.1775.51580 2004572221.8871.3822.7372.91630 2004572320.1868.3220.9969.78740 200458019.8367.6920.6669.19740Bulb-Tee A 20-Day ReadingBulb-Tee A 28-Day Reading 4Highlighted entries are when field measurements were made ( 78” Bulb-Tee A, 78” BulbTee B, AASHTO Type IV A, AASHTO V A and B, and All Girders)

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925 YearMonthDayHour Temp (oC)Temp (oF)Temp (oC)Temp (oF) RHSOLRD (60 cm)(60 cm)(200 cm)(200 cm)(%)(W/m2) 2004521020.8769.5721.5870.84820 2004521119.0066.2019.5167.12890 2004521218.6065.4819.0766.33910 2004521317.9764.3518.4565.21920 2004521417.3063.1417.6963.84930 2004521516.9762.5517.3463.21941 2004521618.3565.0318.3565.039368 2004521723.6374.5323.3674.0583251 2004521825.1877.3224.9176.8476467 2004521926.4979.6826.1078.9866556 20045211028.1382.6327.4281.3656829 20045211129.7485.5328.6783.6144952 20045211230.3286.5829.3384.7944923 20045211331.2688.2730.1386.2340970 20045211431.6488.9530.7887.4036764 20045211531.8189.2631.3488.4137731 20045211631.9189.4431.5688.8137567 20045211731.2388.2131.1788.1142332 20045211828.9184.0429.3084.745081 20045211927.0380.6527.6181.70579 20045212025.2077.3625.7878.40650 20045212124.0075.2024.5676.21710 20045212223.1673.6923.6774.61770 20045212322.2572.0522.8973.20810 2004522021.7271.1022.4572.41840 200467021.771.0622.3272.18890 200467120.9869.7621.5370.75920 200467220.5769.0321.0769.93940 200467320.3668.6520.8569.53950 200467420.3968.7020.9169.64960 200467520.1868.3220.7269.30962 200467621.5670.8121.7471.139692 200467724.4776.0524.1775.5185242 200467826.6679.9926.3279.3873466 200467928.1182.6027.7381.9165642 2004671029.6685.3929.1184.4060784 2004671130.8287.4830.0386.0557899 2004671231.889.2431.0487.8753728 2004671332.3490.2131.7789.1950266 2004671432.790.8632.3290.1846582 2004671531.2288.2031.5288.7448163 2004671628.683.4829.0684.3158106 2004671727.4381.3727.5481.5765181 2004671824.7876.6025.0777.137897 2004671922.0971.7622.4372.37894 2004672021.8271.2822.1671.89920 2004672121.8771.3722.3172.16890 2004672221.7871.2022.2972.12900 2004672321.5570.7922.0171.62920 200468021.4470.5921.9271.46920Bulb-Tee A 59-Day Reading Bulb-Tee A 42-Day Reading 5Highlighted entries are when field measurements were made ( 78” Bulb-Tee A, 78” BulbTee B, AASHTO Type IV A, AASHTO V A and B, and All Girders)

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936 YearMonthDayHour Temp (oC)Temp (oF)Temp (oC)Temp (oF) RHSOLRD (60 cm)(60 cm)(200 cm)(200 cm)(%)(W/m2) 2004610022.7472.9323.0673.51970 2004610122.3672.2522.7472.93970 2004610222.472.3222.7472.93980 2004610322.4272.3622.7772.99980 2004610422.4272.3622.7873.00980 2004610522.2472.0322.6372.73981 2004610623.1973.7423.3273.989893 2004610725.7678.3724.7876.6092312 2004610827.5281.5427.0980.7674493 2004610928.7183.6828.3382.9971668 20046101029.5685.2129.2484.6366787 20046101130.4186.7430.0286.0462690 20046101230.5687.0130.2686.4760499 20046101332.0489.6731.4588.6155237 20046101432.9191.2432.3890.2851736 20046101527.7681.9728.382.946786 20046101625.477.7225.7278.307837 20046101725.6578.1725.9678.737545 20046101824.9276.8625.2677.478236 20046101924.1875.5224.5276.14838 20046102023.3574.0323.7274.70870 20046102123.0773.5323.4374.17880 20046102222.5772.6323.0173.42890 20046102322.0971.7622.5172.52910 2004611021.8371.2922.2372.01930 2004617024.6876.4225.2177.38830 2004617124.2475.6324.7476.53850 2004617223.6174.5024.1875.52880 2004617322.7572.9523.3173.96910 2004617422.8173.0623.474.12930 2004617523.3874.0823.9275.06913 2004617624.4175.9424.6576.378977 2004617726.3579.4326.379.3481268 2004617827.5781.6327.4881.4674464 2004617928.4583.2128.2782.8968707 20046171029.1884.5229.0184.2262624 20046171130.3386.5930.0186.0256734 20046171231.2788.2930.9387.6751705 20046171331.5888.8431.4988.6848219 20046171431.7389.1131.7189.0848657 20046171531.9189.4431.9989.5848603 20046171631.488.5231.4988.6853538 20046171730.186.1830.5186.9255175 20046171829.2484.6329.6485.3559122 20046171928.1282.6228.7183.686219 20046172026.9180.4427.5481.57670 20046172125.9678.7326.5779.83740 20046172225.377.5425.9278.66790 20046172324.6576.3725.2277.40830 2004618024.1175.4024.6776.41860Bulb-Tee A 69-Day Reading Type IV 7-Day Reading Type IV Release 6Highlighted entries are when field measurements were made ( 78” Bulb-Tee A, 78” BulbTee B, AASHTO Type IV A, AASHTO V A and B, and All Girders)

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947 YearMonthDayHour Temp (oC)Temp (oF)Temp (oC)Temp (oF) RHSOLRD (60 cm)(60 cm)(200 cm)(200 cm)(%)(W/m2) 2004624025.4577.8126.3379.39810 2004624125.4677.8326.279.16800 2004624224.1875.5224.9376.87860 2004624323.5474.3724.0875.34900 2004624423.4274.1623.975.02900 2004624523.1673.6923.6874.62912 2004624624.2475.6324.4175.949173 2004624728.0782.5327.982.2278266 2004624829.585.1029.3784.8770436 2004624930.9587.7130.6487.1565642 20046241032.2189.9831.7889.2057790 20046241133.4192.1432.9291.2641889 20046241234.293.5633.7392.7137740 20046241334.9794.9534.594.1032248 20046241434.8494.7134.4193.9439837 20046241534.7594.5534.4994.0840688 20046241634.4393.9734.493.9238539 20046241734.0393.2534.1593.4741350 20046241833.0991.5633.592.3042155 20046241931.2388.2131.9589.515221 20046242029.5485.1730.1986.34580 20046242125.7278.3026.3679.45650 20046242224.9676.9325.6478.15730 20046242324.3375.7925.0777.13750 2004625024.0975.3624.8376.69760 2004628024.3875.8824.8876.78840 2004628124.2275.6024.8476.71830 2004628224.0475.2724.5876.24850 2004628324.1475.4524.6276.32860 2004628424.4976.0825.0277.04860 2004628523.8574.9324.3475.81880 2004628624.3375.7924.6676.398748 2004628725.2677.4725.5177.928187 2004628825.7778.3926.178.987797 2004628926.5479.7726.8680.3569130 20046281027.9282.2627.9782.3565265 20046281129.0184.2228.8683.9567379 20046281229.9285.8629.7585.5563414 20046281329.7585.5529.8585.7364331 20046281429.5185.1229.6585.3765346 20046281531.3588.4330.9887.7662800 20046281630.0986.1630.1186.2059417 20046281724.5176.1224.9476.897325 20046281822.9473.2923.4274.16774 20046281921.8471.3122.2572.05892 20046282022.0471.6722.3372.19940 20046282122.7472.9323.0573.49950 20046282223.0573.4923.3874.08950 20046282323.1973.7423.5674.41950 2004629023.0673.5123.4674.23960Type IV 14-Day Reading Bulb-Tee B Release 7Highlighted entries are when field measurements were made ( 78” Bulb-Tee A, 78” BulbTee B, AASHTO Type IV A, AASHTO V A and B, and All Girders)

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958 YearMonthDayHour Temp (oC)Temp (oF)Temp (oC)Temp (oF) RHSOLRD (60 cm)(60 cm)(200 cm)(200 cm)(%)(W/m2) 200472024.9776.9525.5377.95850 200472124.1275.4224.776.46890 200472223.5574.3924.1175.40910 200472323.2773.8923.7974.82930 200472423.1573.6723.5974.46940 200472522.8373.0923.2573.85951 200472623.4674.2323.774.669547 200472727.3681.2526.8680.3583276 20047282984.2028.6183.5074455 200472930.386.5429.6885.4271589 2004721031.9389.4731.0987.9661862 2004721132.390.1431.5188.7260822 2004721232.690.6831.9689.5358524 2004721332.9291.2632.3690.2554292 2004721433.5292.3433.0491.4751803 2004721528.0582.4928.2982.9267167 2004721624.5376.1524.9176.847918 2004721723.3774.0723.4874.269311 2004721823.7774.7923.9575.11936 2004721923.5474.3723.7974.82931 2004722023.3674.0523.5974.46940 2004722123.4574.2123.7174.68930 2004722223.1173.6023.4874.26930 2004722322.7172.8823.0773.53950 200473022.6872.8223.0473.47960 2004714026.0878.9426.6880.02820 2004714125.7478.3326.2779.29860 2004714225.3877.6825.8978.60880 2004714325.277.3625.778.26880 2004714425.0977.1625.6178.10890 2004714524.9976.9825.5678.01890 2004714625.0177.0225.4677.838923 2004714726.3679.4526.4779.658699 2004714828.1482.6528.0582.4979322 2004714930.2486.4329.9485.8969588 20047141031.0787.9330.8287.4865585 20047141132.4990.4832.0189.6258767 20047141234.1393.4333.592.3051871 20047141334.4994.0833.8592.9349184 20047141434.4594.0133.9693.1351819 20047141532.7390.9132.5990.6657460 20047141633.7592.7533.6192.5051547 20047141732.9591.3133.0491.4753338 20047141831.6388.9331.9789.5557155 20047141929.8385.6930.4386.776316 20047142028.8883.9829.4885.06700 20047142128.1982.7428.7983.82740 20047142227.3381.1927.9782.35780 20047142326.8580.3327.4181.34800 2004715026.679.8827.1980.94810Bulb-Tee B 4-Day ReadingBulb-Tee B 16-Day Reading Type IV 34-Day Reading Type IV 21-Day Reading Bulb-Tee A 96-Day Reading Bulb-Tee A 84-Day Reading 8Highlighted entries are when fi eld measurements were made ( 78” Bulb-Tee A 78” BulbTee B, AASHTO Type IV A, AASHTO V A and B, and All Girders)

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969 YearMonthDayHour Temp (oC)Temp (oF)Temp (oC)Temp (oF) RHSOLRD (60 cm)(60 cm)(200 cm)(200 cm)(%)(W/m2) 2004721023.1673.6923.5874.44950 2004721122.8673.1523.2373.81960 2004721223.574.3023.7874.80970 2004721323.6574.5723.8975.00970 2004721423.2473.8323.4474.19970 2004721523.2873.9023.574.30970 2004721623.3774.0723.5774.439822 2004721723.774.6623.7874.809894 2004721825.0477.0724.5776.2397359 2004721927.5881.6426.9580.5184581 20047211029.5385.1529.0384.2574781 20047211130.687.0830.1886.3267766 20047211232.2390.0131.7689.1754781 20047211332.7790.9932.4390.3747879 20047211433.1791.7132.9491.2945754 20047211532.6690.7932.6990.8447406 20047211632.7690.9732.8591.1345355 20047211732.2990.1232.5190.5249297 20047211830.6687.1931.187.9852108 20047211929.0884.3429.7285.505713 20047212027.5881.6428.3983.10640 20047212126.7380.1127.4881.46700 20047212225.3677.6526.1179.00790 20047212323.6774.6124.3875.88860 2004722022.8673.1523.3874.08910 2004728024.375.7424.7276.50870 2004728123.8574.9324.2575.65900 2004728223.6774.6124.0475.27920 2004728323.3273.9823.7474.73940 2004728423.2673.8723.6874.62940 2004728523.1673.6923.5774.43940 2004728623.5874.4423.8274.889439 200472872678.8025.6978.2485157 2004728828.0482.4727.5981.6677414 2004728930.2186.3829.4384.9770530 20047281029.7685.5729.4885.0669399 20047281131.989.4230.8687.5561713 20047281230.8587.5330.7687.3761185 20047281329.8785.7729.885.6469367 2004728143289.6031.2688.2760634 20047281529.7885.6029.4585.0171493 20047281629.9385.8729.985.8269278 20047281729.0484.2729.2484.6372105 20047281827.681.6827.9882.367817 20047281925.1577.2725.4277.76900 20047282024.1875.5224.4475.99920 20047282123.9475.0924.2475.63940 20047282223.8574.9324.2375.61940 20047282323.6274.522475.20950 2004729023.4474.1923.7474.73950Bulb-Tee B 23-Day ReadingBulb-Tee B 29-Day Reading Type IV 47-Day Reading Type IV 40-Day Reading Bulb-Tee A 109-Day Reading 9Highlighted entries are when field measurements were made ( 78” Bulb-Tee A, 78” BulbTee B, AASHTO Type IV A, AASHTO V A and B, and All Girders)

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9710 YearMonthDayHour Temp (oC)Temp (oF)Temp (oC)Temp (oF) RHSOLRD (60 cm)(60 cm)(200 cm)(200 cm)(%)(W/m2) 2004811024.5776.2324.9076.82890 2004811124.5876.2424.8876.78900 2004811224.2175.5824.4375.97920 2004811324.4776.0524.7676.57910 2004811424.3375.7924.6076.28910 2004811523.9775.1524.2275.60920 2004811624.2075.5624.2775.699242 2004811725.8678.5525.5577.9987163 2004811827.0680.7126.7080.0683322 2004811928.0082.4027.6781.8179344 20048111030.3686.6529.6385.3372772 20048111132.0289.6431.3588.4362797 20048111232.6290.7232.1289.8258790 20048111333.8892.9833.1291.6255874 20048111433.1391.6333.0791.5353431 20048111527.9382.2728.3683.057380 20048111629.2684.6728.8683.9572470 20048111728.0282.4428.2082.7677118 20048111828.3282.9828.3883.0876153 20048111926.2879.3026.6379.93803 20048112025.1877.3225.4577.81850 20048112124.6076.2824.9476.89820 20048112224.1075.3824.4576.01850 20048112324.2475.6324.5476.17880 2004812024.6076.2825.0277.04850 2004824024.1675.4924.4075.92910 2004824123.5574.3923.8174.86920 2004824223.3073.9423.5674.41920 2004824323.0773.5323.3273.98930 2004824422.8573.1323.0773.53940 2004824522.8573.1323.0173.42950 2004824623.1173.6023.1673.699511 2004824724.6376.3324.3575.8392128 2004824827.4681.4327.0980.7681370 2004824929.0784.3328.6283.5273569 20048241030.0186.0229.6285.3269546 20048241130.4286.7630.0586.0965578 20048241231.2188.1830.8587.5362583 20048241332.2590.0531.6388.9357816 20048241432.9191.2432.4390.3753763 20048241531.2888.3031.4388.5757273 20048241628.1882.7228.3082.9473256 20048241726.9580.5127.1780.917895 20048241824.1275.4224.3475.81892 20048241923.7274.7023.6474.55950 20048242024.0875.3424.0375.25960 20048242124.2875.7024.2175.58960 20048242224.5476.1724.4976.08960 20048242324.2675.6724.2175.58960 2004825024.3375.7924.3075.74960Bulb-Tee A 137-Day Reading Type IV 75-Day Reading Bulb-Tee B 57-Day Reading Bulb-Tee B 44-Day Reading Type IV 61-Day Reading Bulb-Tee A 123-Day Reading 10Highlighted entries are when field measurements were made ( 78” Bulb-Tee A, 78” Bulb-Tee B, AASHTO Type IV A, AASHTO V A and B, and All Girders)

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9811 YearMonthDayHour Temp (oC)Temp (oF)Temp (oC)Temp (oF) RHSOLRD (60 cm)(60 cm)(200 cm)(200 cm)(%)(W/m2) 200499024.5376.1524.6976.44910 200499124.1375.4324.1475.45930 200499224.2775.6924.0775.33940 200499324.6276.3224.0675.31950 200499424.5976.2623.9175.04960 200499524.5376.1523.7374.71960 200499624.5876.2423.7274.70964 200499725.0177.0223.9275.069531 200499826.0578.8925.0277.0489253 200499927.3581.2326.5979.8685392 2004991029.8285.6828.9284.0674740 2004991130.5386.9530.0086.0069415 2004991231.4188.5430.7887.4064731 2004991329.7485.5329.6385.3366352 2004991427.8582.1328.1382.6374100 2004991526.5379.7526.4679.6387127 2004991627.0080.6026.9480.498681 2004991724.7576.5524.6476.359311 2004991824.5976.2624.1575.47953 2004991924.6876.4224.1375.43960 2004992024.5176.1223.7974.82960 2004992124.2275.6023.4174.14960 2004992223.9975.1823.1273.62970 2004992323.9875.1623.0173.42970 2004910023.8574.9322.8173.06970 2004921023.5074.3023.4174.14860 2004921123.8374.8924.0575.29780 2004921223.6074.4823.9275.06760 2004921323.4974.2823.8274.88760 2004921423.2773.8923.5274.34790 2004921523.4374.1723.6474.55790 2004921623.4774.2523.8174.86784 2004921723.7874.8023.9975.187965 2004921824.7376.5124.8976.8074155 2004921927.1780.9127.0880.7464555 20049211027.6981.8427.8282.0859427 20049211127.7381.9127.9182.2458418 20049211228.3082.9428.4083.1257529 20049211327.5281.5427.8282.0861269 20049211427.1480.8527.3781.2764280 20049211526.5579.7926.7280.1070266 20049211626.3879.4826.5579.7971225 20049211726.0578.8926.3979.5069139 20049211824.7876.6025.1677.297312 20049211924.6876.4225.1577.27720 20049212024.7776.5925.2577.45730 20049212124.7676.5725.2277.40730 20049212224.5776.2325.0377.05750 20049212324.3475.8124.7876.60760 2004922024.6176.3025.0777.13750Type IV 91-Day Reading Bulb-Tee B 73-Day Reading Bulb-Tee A 165-Day Reading Bulb-Tee A 153-Day Reading Type IV 103-Day Reading Bulb-Tee B 85-Day Reading 11Highlighted entries are when field measurements were made ( 78” Bulb-Tee A, 78” Bulb-Tee B, AASHTO Type IV A, AASHTO V A and B, and All Girders)

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9912 YearMonthDayHour Temp (oC)Temp (oF)Temp (oC)Temp (oF) RHSOLRD (60 cm)(60 cm)(200 cm)(200 cm)(%)(W/m2) 2004928024.1575.4723.9775.15920 2004928123.7974.8223.4374.17930 2004928223.5074.3022.8973.20940 2004928323.4474.1922.4872.46950 2004928423.2573.8522.1671.89960 2004928523.0573.4921.8771.37960 2004928622.8973.2021.6871.02967 2004928724.0875.3422.4472.3994134 2004928826.1379.0324.8776.7787347 2004928927.7381.9127.2080.9678535 20049281028.7583.7528.4983.2870710 20049281129.9485.8929.6585.3765788 20049281230.4186.7430.2386.4162739 20049281331.0887.9430.9287.6659762 20049281431.5288.7431.4888.6655713 20049281531.3288.3831.4788.6554560 20049281630.5586.9930.9787.7556371 20049281729.2884.7029.8585.7362162 20049281827.1380.8327.8182.067014 20049281925.5177.9226.2179.18780 20049282024.5276.1425.0577.09840 20049282123.7374.7124.1075.38880 20049282223.1373.6323.3474.01910 20049282323.0073.4022.9973.38930 2004929022.8273.0822.6172.70940 2004105023.3674.0523.2973.92910 2004105123.3474.0122.9573.31930 2004105222.9973.3822.5772.63930 2004105322.4572.4121.9271.46940 2004105421.7771.1921.1270.02950 2004105522.0371.6521.0069.80960 2004105621.8671.3520.7369.31967 2004105723.9275.0622.3972.3091117 2004105826.1279.0225.3877.6882264 2004105927.6881.8227.0780.7376464 20041051028.0282.4427.6881.8271376 20041051129.7185.4829.0884.3464775 20041051229.7185.4829.4785.0562494 20041051329.9785.9529.8985.8058518 20041051429.3084.7429.4585.0160283 20041051529.1684.4929.1484.4561406 20041051628.3282.9828.6283.5263186 20041051725.0777.1325.4277.767839 20041051825.1077.1825.5477.97742 20041051924.8876.7825.1677.29800 20041052024.5476.1724.7776.59810 20041052123.8374.8924.0575.29840 20041052223.4574.2123.5674.41860 20041052323.2173.7823.1373.63880 2004106023.1773.7123.0473.47890Type V Release Bulb-Tee A 179-Day Reading Type IV 116-Day Reading Bulb-Tee B 99-Day Reading Type V 7-Day Reading 12Highlighted entries are when field measurements were made ( 78” Bulb-Tee A, 78” Bulb-Tee B, AASHTO Type IV A, AASHTO V A and B, and All Girders)

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10013 YearMonthDayHour Temp (oC)Temp (oF)Temp (oC)Temp (oF) RHSOLRD (60 cm)(60 cm)(200 cm)(200 cm)(%)(W/m2) 20041012021.5070.7020.3168.56910 20041012121.6270.9220.6269.12900 20041012221.8471.3121.0569.89890 20041012321.7771.1921.2270.20880 20041012421.7671.1721.2270.20890 20041012521.9571.5121.3370.39900 20041012622.2772.0921.6971.04881 20041012722.6972.8422.1771.918629 20041012823.3974.1022.8973.208588 20041012923.5274.3423.1273.6284111 200410121023.1473.6522.1871.9291226 200410121123.7974.8223.0773.5386241 200410121224.8876.7824.1675.4983315 200410121326.3179.3625.7678.3777390 200410121426.4379.5726.1179.0077314 200410121527.4181.3427.0080.6073417 200410121627.2881.1027.1980.9472303 200410121726.7880.2026.9480.497497 200410121825.2077.3625.3777.67812 200410121924.2575.6524.1075.38870 200410122023.5674.4123.0773.53900 200410122123.5274.3422.8773.17910 200410122222.7072.8622.0671.71930 200410122321.8271.2820.9169.64950 20041013021.5370.7520.5268.94960 20041019022.1271.81622.2672.068860 20041019122.3572.2322.3672.248870 20041019222.171.7822.0771.726870 20041019321.4170.53821.370.34910 20041019420.9869.76420.5869.044930 20041019520.8869.58420.2668.468940 20041019621.3570.4320.4168.738941 20041019721.7571.1520.5268.9369449 20041019824.5876.24423.1273.61688248 20041019926.8680.34825.8778.56680449 200410191028.9384.07428.382.9471596 200410191129.8985.80229.2984.72266603 200410191230.3586.6329.8385.69462592 200410191330.3886.68430.1486.25260484 200410191430.5987.06230.4786.84658498 200410191530.1286.21630.2686.46859277 200410191628.5383.35429.184.386344 200410191722.6272.71622.2972.122911 200410191821.8771.36620.9669.728931 200410191921.7871.20420.9669.728930 200410192021.8371.29420.7269.296950 200410192121.7171.07820.4368.774950 200410192221.6570.9720.3268.576950 200410192322.0571.6920.7569.35920 20041020021.7971.22220.4868.864940Type V 21-Day Reading Type V 14-Day Reading 13Highlighted entries are when field measurements were made ( 78” Bulb-Tee A, 78” Bulb-Tee B, AASHTO Type IV A, AASHTO V A and B, and All Girders)

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10114 YearMonthDayHour Temp (oC)Temp (oF)Temp (oC)Temp (oF) RHSOLRD (60 cm)(60 cm)(200 cm)(200 cm)(%)(W/m2) 20041026017.3463.21217.0662.708920 20041026116.7962.22216.3661.448930 20041026216.1961.14215.6260.116940 20041026315.7860.40415.159.18950 20041026415.760.2614.8858.784960 20041026516.0160.81815.2359.414970 20041026616.3361.39415.5259.936972 20041026718.2364.81416.9262.4569783 20041026820.9469.69219.4567.0189265 20041026923.1473.65222.4172.33876457 200410261025.2177.37824.5376.15468611 200410261126.679.8826.0178.81860723 200410261227.581.526.9880.56454666 200410261327.4481.39227.1580.8753546 200410261427.3481.21227.2681.06852487 200410261527.2681.06827.2781.08654355 200410261625.8378.49425.9778.74660199 200410261724.3675.84824.7676.5686453 200410261822.9973.38223.474.12690 200410261921.8571.3322.2872.104740 200410262021.1270.01621.5370.754770 200410262120.969.6221.1970.142800 200410262220.6169.09820.8169.458820 200410262320.2968.52220.3368.594850 20041027019.9867.96419.9467.892870Bulb-Tee A 200-Day Reading Type IV 131-Day Reading Bulb-Tee B 120-Day Reading Type V 28-Day Reading Highlighted entries are when field measurements were made ( 78” Bulb-Tee A, 78” BulbTee B, AASHTO Type IV A, AASHTO V A and B, and All Girders)

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102 APPENDIX F MIX DESIGNS CLASS CONCRETE:VIDATE:4/1/2004 SPECIFIED 28-DAY COMP STRENGTH:8500 PSI COURSE AGGREGATE:ANDERSON COLUMBIAGRADE:67S.G. (SSD):2.720 FINE AGGREGATE:FLORIDA ROCKF.M.:2.11S.G. (SSD):2.630 PIT NO. (COURSE):GA-553TYPE:CRUSHED GRANITE PIT NO. (FINE):36-491TYPE:SILICA SAND CEMENT:SUANEE AMERICAN (BRANFORD)SPEC:AASHTO M-85 TYPE II AIR ENTR. ADMIX:DARAVAIR 1000W.R. GRACESPEC:AASHTO M-154 1st ADMIX:WRDA 60W.R. GRACESPEC:AASHTO M-194 TYPE D 2nd ADMIX:ADVA 540W.R. GRACESPEC:ASTM C-494 TYPE F 3rd ADMIX:N/ASPEC:N/A FLY ASH:ISGFERNANDIA BEACHSPEC:ASTM C-618 CLASS F HOT WEATHER DESIGN MIX4 X 8 COMPRESSIVE STRENGTH 10050 PSI : CEMENT (Kg) LBS:775SLUMP RANGE: COURSE AGG (Kg) LBS:1800AIR CONTENT: FINE AGG (Kg) LBS:855UNIT WEIGHT (WET):145.4(Kg/m3)PCF AIR ENT ADMX (mL) OZ:3.0W/C RATIO (PLANT):0.35(Kg/Kg)LBS/LB 1st ADMIX (mL) OZ:23.3W/C RATIO (FIELD):0.35(Kg/Kg)LBS/LB 2nd ADMIX (mL) OZ:46.5THEO. YIELD:27.00(m3)CU FT 3rd ADMIX (mL) OZ:0.0 WATER (mL) GAL:39.30 WATER (Kg) LBS:327.4 FLY ASH (Kg) LBS:170 CHLORIDE CONTENT:0.277(Kg/m3)LB/CY SLUMP:8.25(mm) IN AIR CONTENT:2.90% CONC. TEMPERATURE:74DEG (C) F AMB. TEMPERATURE:55DEG (C) F CALC W/B RATIO:0.35(Kg/Kg)LBS/LB< 0.40HIGH STRENGTH CONCRETE78" Bulb-Tee Girder Pour ASOURCE OF MATERIALSConcrete Mix DesignPRODUCER TEST DATA 5.50 TO 8.50 (mm) IN 1.0% TO 5.0%

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103 CLASS CONCRETE:VIDATE:6/17/2004 SPECIFIED 28-DAY COMP STRENGTH: 8500 PSI COURSE AGGREGATE:ANDERSON COLUMBIAGRADE:67S.G. (SSD):2.720 FINE AGGREGATE:FLORIDA ROCKF.M.:2.11S.G. (SSD):2.630 PIT NO. (COURSE):GA-553TYPE:CRUSHED GRANITE PIT NO. (FINE):36-491TYPE:SILICA SAND CEMENT:SUANEE AMERICAN (BRANFORD)SPEC:AASHTO M-85 TYPE II AIR ENTR. ADMIX:DARAVAIR 1000W.R. GRACESPEC:AASHTO M-154 1st ADMIX:WRDA 60W.R. GRACESPEC:AASHTO M-194 TYPE D 2nd ADMIX:ADVA 540W.R. GRACESPEC:ASTM C-494 TYPE F 3rd ADMIX:N/ASPEC:N/A FLY ASH:ISGFERNANDIA BEACHSPEC:ASTM C-618 CLASS F HOT WEATHER DESIGN MIX4 X 8 COMPRESSIVE STRENGTH 10050 PSI : CEMENT (Kg) LBS:775SLUMP RANGE: COURSE AGG (Kg) LBS:1800AIR CONTENT: FINE AGG (Kg) LBS:855UNIT WEIGHT (WET):145.4(Kg/m3)PCF AIR ENT ADMX (mL) OZ:3.0W/C RATIO (PLANT):0.35Kg/Kg)LBS/LB 1st ADMIX (mL) OZ:23.3W/C RATIO (FIELD):0.35Kg/Kg)LBS/LB 2nd ADMIX (mL) OZ:46.5THEO. YIELD:27.00(m3)CU FT 3rd ADMIX (mL) OZ:0.0 WATER (mL) GAL:39.30 WATER (Kg) LBS:327.4 FLY ASH (Kg) LBS:170 CHLORIDE CONTENT:0.277(Kg/m3)LB/CY SLUMP:6.75(mm) IN AIR CONTENT:3.00% CONC. TEMPERATURE:88DEG (C) F AMB. TEMPERATURE:74DEG (C) F CALC W/B RATIO:0.35(Kg/Kg)LBS/LB< 0.40HIGH STRENGTH CONCRETE78" Bulb-Tee Girder Pour BSOURCE OF MATERIALSConcrete Mix DesignPRODUCER TEST DATA 5.50 TO 8.50 (mm) IN 1.0% TO 5.0%

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104CLASS CONCRETE:IVDATE:6/7/2004 SPECIFIED 28-DAY COMPRESSIVE STREN G :38 MPA COURSE AGGREGATE:ANDERSON COLUMBIAGRADE:57S.G. (SSD):2.720 FINE AGGREGATE:FLORIDA ROCKF.M.:2.11S.G. (SSD):2.630 PIT NO. (COURSE):GA-553TYPE:CRUSHED GRANITE PIT NO. (FINE):36-491TYPE:SILICA SAND CEMENT:SUANEE AMERICANSPEC:AASHTO M-85 TYPE II AIR ENTR. ADMIX:DARAVAIR 1000W.R. GRACESPEC:AASHTO M-154 1st ADMIX:WRDA 60W.R. GRACESPEC:AASHTO M-194 TYPE D 2nd ADMIX:ADVA 540W.R. GRACESPEC:ASTM C-494 TYPE F 3rd ADMIX:N/ASPEC:N/A FLY ASH:ISGSPEC:ASTM C-618 CLASS F HOT WEATHER METRIC DESIGN MIX4 X 8 COMPRESSIVE STRENGTH @ 28 DAYS = 59.0 MPA : CEMENT (Kg):430.00SLUMP RANGE: COURSE AGG (Kg):1800.00AIR CONTENT: FINE AGG (Kg):544.00UNIT WEIGHT (WET):2337.00(Kg/m3) AIR ENT ADMX (mL):116.00W/C RATIO (PLANT):0.36(Kg/Kg) 1st ADMIX (mL):843.00W/C RATIO (FIELD):0.36(Kg/Kg) 2nd ADMIX (mL):1682.00THEO. YIELD:1.01(m3) 3rd ADMIX (mL):0.00 WATER (L):188.00 WATER (Kg):188.00 FLY ASH (Kg):95.00 CHLORIDE CONTENT:0.18(Kg/m3) SLUMP:170.00(mm) AIR CONTENT:1.90% CONC. TEMPERATURE:34.00DEG C AMB. TEMPERATURE:31.00DEG C CALC W/B RATIO:0.36(Kg/Kg)< 0.40HIGH STRENGTH CONCRETEAASHTO Type IV Girder Pour ASOURCE OF MATERIALSConcrete Mix DesignPRODUCER TEST DATA 140 TO 220 (mm) 1.00% TO 5.00%

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105CLASS CONCRETE:IVDATE:9/17/2004 SPECIFIED 28-DAY COMP. STRENGTH:5500 PSI COURSE AGGREGATE:ANDERSON COLUMBIAGRADE:67S.G. (SSD):2.720 FINE AGGREGATE:FLORIDA ROCKF.M.:2.11S.G. (SSD):2.630 PIT NO. (COURSE):GA-553TYPE:CRUSHED GRANITE PIT NO. (FINE):36-491TYPE:SILICA SAND CEMENT:SUANEE AMERICAN (BRANFORD)SPEC:AASHTO M-85 TYPE II AIR ENTR. ADMIX:DARAVAIR 1000W.R. GRACESPEC:AASHTO M-154 1st ADMIX:WRDA 60W.R. GRACESPEC:AASHTO M-194 TYPE D 2nd ADMIX:ADVA 540W.R. GRACESPEC:ASTM C-494 TYPE F 3rd ADMIX:N/ASPEC:N/A FLY ASH:ISGFERNANDIA BEACHSPEC:ASTM C-618 CLASS F HOT WEATHER DESIGN MIX4 X 8 COMPRESSIVE STRENGTH 10050 PSI : CEMENT (Kg) LBS:725SLUMP RANGE: COURSE AGG (Kg) LBS:1820AIR CONTENT: FINE AGG (Kg) LBS:917UNIT WEIGHT (WET):145.9(Kg/m3)PCF AIR ENT ADMX (mL) OZ:3.0W/C RATIO (PLANT):0.36(Kg/Kg)LBS/LB 1st ADMIX (mL) OZ:21.8W/C RATIO (FIELD):0.32(Kg/Kg)LBS/LB 2nd ADMIX (mL) OZ:43.5THEO. YIELD:27.00(m3)CU FT 3rd ADMIX (mL) OZ:0.0 WATER (mL) GAL:38.00 WATER (Kg) LBS:316.5 FLY ASH (Kg) LBS:160 CHLORIDE CONTENT:0.296(Kg/m3)LB/CY SLUMP:7.25(mm) IN AIR CONTENT:2.70% CONC. TEMPERATURE:91DEG (C) F AMB. TEMPERATURE:85DEG (C) F CALC W/B RATIO:0.36(Kg/Kg)LBS/LB< 0.40HIGH STRENGTH CONCRETEAASHTO Type V Girder Pour ASOURCE OF MATERIALSConcrete Mix DesignPRODUCER TEST DATA 5.50 TO 8.50 (mm) IN 1.0% TO 6.0%

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106CLASS CONCRETE:IVDATE:9/21/2004 SPECIFIED 28-DAY COMP. STRENGTH:5500 PSI COURSE AGGREGATE:ANDERSON COLUMBIAGRADE:67S.G. (SSD):2.720 FINE AGGREGATE:FLORIDA ROCKF.M.:2.11S.G. (SSD):2.630 PIT NO. (COURSE):GA-553TYPE:CRUSHED GRANITE PIT NO. (FINE):36-491TYPE:SILICA SAND CEMENT:SUANEE AMERICAN (BRANFORD)SPEC:AASHTO M-85 TYPE II AIR ENTR. ADMIX:DARAVAIR 1000W.R. GRACESPEC:AASHTO M-154 1st ADMIX:WRDA 60W.R. GRACESPEC:AASHTO M-194 TYPE D 2nd ADMIX:ADVA 540W.R. GRACESPEC:ASTM C-494 TYPE F 3rd ADMIX:N/ASPEC:N/A FLY ASH:ISGFERNANDIA BEACHSPEC:ASTM C-618 CLASS F HOT WEATHER DESIGN MIX4 X 8 COMPRESSIVE STRENGTH 10050 PSI : CEMENT (Kg) LBS:725SLUMP RANGE: COURSE AGG (Kg) LBS:1820AIR CONTENT: FINE AGG (Kg) LBS:917UNIT WEIGHT (WET):145.9(Kg/m3)PCF AIR ENT ADMX (mL) OZ:3.0W/C RATIO (PLANT):0.36(Kg/Kg)LBS/LB 1st ADMIX (mL) OZ:21.8W/C RATIO (FIELD):0.31(Kg/Kg)LBS/LB 2nd ADMIX (mL) OZ:43.5THEO. YIELD:27.00(m3)CU FT 3rd ADMIX (mL) OZ:0.0 WATER (mL) GAL:38.00 WATER (Kg) LBS:316.5 FLY ASH (Kg) LBS:160 CHLORIDE CONTENT:0.296(Kg/m3)LB/CY SLUMP:7.75(mm) IN AIR CONTENT:4.50% CONC. TEMPERATURE:83DEG (C) F AMB. TEMPERATURE:73DEG (C) F CALC W/B RATIO:0.36(Kg/Kg)LBS/LB< 0.40HIGH STRENGTH CONCRETEAASHTO Type V Girder Pour BSOURCE OF MATERIALSConcrete Mix DesignPRODUCER TEST DATA 5.50 TO 8.50 (mm) IN 1.0% TO 6.0%

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107 APPENDIX G TABULATED MATERIAL TESTING DATA Time After Release Time After Casting Average Compressive Strength Elastic Modulus (Linear Regression) Elastic Modulus (ASTM) Elastic Modulus (ACI) Elastic Modulus (AASHTO) (day)(day) (psi) (ksi)(ksi)(ksi)(ksi) 0 0 0000 0769034309434148074782 71481175228467052135185 142186805304471853905362 212888275336472254365407 283593265444484355875558 424997665588494957185687 8491101076005600258175786 109116105756070608259505919 136143105096126622659315900 200207105386017596959395908 Time After Release Time After Casting Average Compressive Strength Elastic Modulus (Linear Regression) Elastic Modulus (ASTM) Elastic Modulus (ACI) Elastic Modulus (AASHTO) (day)(day) (psi) (ksi)(ksi)(ksi)(ksi) 0 0 0000 0772304924494249204894 182587605442532054155387 233093775348534556035573 313894075575557756115582 20020700 tj = 7days after casting to release 6" x 12" Cylinder Specimens 4" x 8" Cylinder Specimens78" Bulb-Tee Pour "A"

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108 Time After Release Time After Casting Average Compressive Strength Elastic Modulus (Linear Regression) Elastic Modulus (ASTM) Elastic Modulus (ACI) Elastic Modulus (AASHTO) (day)(day) (psi) (ksi)(ksi)(ksi)(ksi) 0 0 0000 0970144759470948454820 41375784677466650375010 162580534813477351925165 223183445099508552855257 344386784932491753905362 435286245133513153735345 566588995222519554585429 728190925370534455175488 849391155365537455245495 12012990935160516055175488 Time After Release Time After Casting Average Compressive Strength Elastic Modulus (Linear Regression) Elastic Modulus (ASTM) Elastic Modulus (ACI) Elastic Modulus (AASHTO) (day)(day) (psi) (ksi)(ksi)(ksi)(ksi) 0 0 0000 0966534806476647194695 tj = 9days after casting to release78" Bulb-Tee Pour "B"4" x 8" Cylinder Specimens 6" x 12" Cylinder Specimens

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109Time After Release Time After Casting Average Compressive Strength Elastic Modulus (Linear Regression) Elastic Modulus (ASTM) Elastic Modulus (ACI) Elastic Modulus (AASHTO) (day)(day) (psi) (ksi)(ksi)(ksi)(ksi) -0 0 0000 0354104506443842794233 71067934911484747954744 141783055390538553025245 212482815191519652955237 343784405456544753455288 404384405830578153455287 616491355886585555615501 747788805672563454835423 10210590695853581355415481 13814193995887588756415580 Time After Release Time After Casting Average Compressive Strength Elastic Modulus (Linear Regression) Elastic Modulus (ASTM) Elastic Modulus (ACI) Elastic Modulus (AASHTO) (day)(day) (psi) (ksi)(ksi)(ksi)(ksi) 0 0 0000 4759104726472944734425 343785405481555153775319 13814100 tj = 3days after casting to releaseAASHTO Type IV Pour "A"4" x 8" Cylinder Specimens 6" x 12" Cylinder Specimens Time After Release Time After Casting Average Compressive Strength Elastic Modulus (Linear Regression) Elastic Modulus (ASTM) Elastic Modulus (ACI) Elastic Modulus (AASHTO) (day)(day) (psi) (ksi)(ksi)(ksi)(ksi) 0 0 0000 01063364909485446294581 71772895130510549654914 142478625361532751575103 223286165419541253985342 283884785323531053555299 tj = 10days after casting to releaseAASHTO Type V Pour "A"4" x 8" Cylinder Specimens

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110Time After Release Time After Casting Average Compressive Strength Elastic Modulus (Linear Regression) Elastic Modulus (ASTM) Elastic Modulus (ACI) Elastic Modulus (AASHTO) (day)(day) (psi) (ksi)(ksi)(ksi)(ksi) 0 0 0000 0756834796475143844339 71470455164513748814831 142175105331532650404988 222981885466533652625208 283581725313531352575203 tj = 7days after casting to releaseAASHTO Type V Pour "B"4" x 8" Cylinder Specimens

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111 APPENDIX H RECOMMENDED 78” BULB-TEE CAMB ER PREDICTION METHOD Mean tested value I top 2496944 (in^4) moment of inertia about top of section B top 41566 (in^3) first moment area about top of section Bulb-Tee Tendon Properties PrestressType"Low Relaxation" y cgt 70.7 (in) y NA 37.6 (in) e cgt y cgt y NA (in) (straight tendon configuration) A ps 11.5 (in^2) f pu 270 (ksi) f py 0.9f pu PrestressType"Low Relaxation" if 0.85f pu PrestressType"Stress Relieved" if f pj 0.75f pu PrestressType"Low Relaxation" if 0.70f pu PrestressType"Stress Relieved" if E p 28500 (ksi) Recommended Camber Growth Model Using LRFD Creep Coefficient for 78" Florida Bulb-Tee Girder--written by Jonathan Sanek, University of Florida Department of Civil and Coastal Engineering Given Structural Parameters 78-inch Bulb-Tee Properites Bulb-Tee Section PropertiesBulb-Tee Material Properties Perim295 (in) c 145 (pcf) Area1105 (in^2) f'c8.5 (ksi) Mean tested value I935544 (in^4) E c 5146 (ksi) Mean tested value L1942.625 (in) E ci 4534 (ksi)

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112 y cgp distance from top flange to c.g. of prestressing steel I moment of inertia about top Iteration 1 f pES 0.05f pj f pES 10.125 (ksi) f pe.ES f pj f pES f pR1 f pe.ES 189.1 (ksi) M g w sw L2 8 M g 43740 (kip*in) P e f pe.ES A ps P e 2174.649 (kip) M pe.top P e y cgt M pe.top 153748 (kip*in) f cgp I top P e B top M g M pe.top AreaM g M pe.top B top P e y cgt AreaI top B top2 f cgp 4.831 (ksi) f pES E p E ci f cgp f pES 30.365 (ksi) Bulb-Tee Calculated Properties w sw Area 1728 c 1000 w sw 0.093 (kip/in) VS Area Perim VS3.746 (in) Assumed Conditions H65 Relative Humidity t j 8 (days from jacking to transfer) FDOT/LFRD Prestress Loss Calculation (Section 5.9.5.4) i. Prestress Loss due to Initial Relaxation of the Prestressing Steel f pR1 log24.0t j 40.0 f pj f py 0.55 f pj PrestressType"Low Relaxation" if log24.0t j 10.0 f pj f py 0.55 f pj PrestressType"Stress Relieved" if f pR1 3.275 (ksi) f pR1.% f pR1 f pj 100 f pR1.% 1.6 (%) ii. Prestress Loss due to Elastic Shotening (assume initially 5% due to elastic shorting) P e effective prestress force after elastic shortening and relaxation losses B first moment area about top

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113(%) f pES.% 12.9 f pES.% f pES f pj 100 (ksi) f pES 26.072 f pES E p E ci f cgp (ksi) f cgp 4.148 f cgp I top P e B top M g M pe.top AreaM g M pe.top B top P e y cgt AreaI top B top2 (kip*in) M pe.top 137292 M pe.top P e y cgt (kip) P e 1941.89 P e f pe.ES A ps (kip*in) M g 43740 M g w sw L2 8 (ksi) f pe.ES 168.86 f pe.ES f pj f pES f pR1 Iteration 2 ii. Prestress Loss due to Elastic Shotening (continued)

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114(ksi) f cdp M g e cgt I f cdp 1.548 (ksi) f pCR out12.0f cgp 7.0 f cdp outout out0 if out0 otherwise f pCR 17.151 (ksi) f pCR.% f pCR f pj 100 f pCR.% 8.5 (%) v. Prestress Loss due to Relaxation of the Prestressing Steel After Transfer f pR2 R220.00.4 f pES 0.2 f pSR f pCR R2R20.30 PrestressType"Low Relaxation" if R2R2 PrestressType"Stress Relieved" if f pR2 1.407 (ksi) f pR2.% f pR2 f pj 100 f pR2.% 0.695 (%) iii. Prestress Loss due Shrinkage of Concrete f pSR 17.00.150H f pSR 7.25 (ksi) f pSR.% f pSR f pj 100 f pSR.% 3.6 (%) iv. Prestress Loss due Creep of Concrete f pe f pj f pR1 f pES f pe 173.153 (ksi) M pe f pe A ps e cgt M pe 65911 (kip*in) f cgp M pe e cgt I f cgp 2.332

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115f pe 147.345 (ksi) vii. Creep Coefficient Cacluation (LRFD 5.4.2.3.2-1, Collins and Mitchell, 1991) LRFD C5.4.2.3.2-1 k c t () 45t 26e0.36VS t 1.801.77e0.54 VS 2.587 k f f'c () 1 0.67 f'c 9 LRFD 5.4.2.3.2-2 t j t f'c 3.5k c t () k f f'c () 1.58 H 120 t j0.118 tt j 0.610.0tt j 0.6 LRFD 5.4.2.3.2-1 C release t j 0t j f'c C release 0 C 30day t j 30t j f'c C 30day 0.362 C 60day t j 60t j f'c C 60day 0.501 C 120day t j 120t j f'c C 120day 0.671 C 240day t j 240t j f'c C 240day 0.849 v. Effective Prestress After Initial Effects f pi f pR1 f pES f pi 29.347 (ksi) f pi.% f pi f pj 100 f pi.% 14.5 (%) f pi f pj f pi f pi 173.153 (ksi) vi. Effective Prestress After Initial and Time-Dependent Effects f pTOT f pR1 f pES f pSR f pCR f pR2 f pTOT 55.155 (ksi) f pTOT.% f pTOT f pj 100 f pTOT.% 27.2 (%) f pe f pj f pTOT

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116(in) 240day 4.336 240day pe pi pe 2 C 240day sw 1C 240day (in) 120day 3.83 120day pe pi pe 2 C 120day sw 1C 120day (in) 60day 3.348 60day pe pi pe 2 C 60day sw 1C 60day (in) 30day 2.952 30day pe pi pe 2 C 30day sw 1C 30day (in) release 1.924 release pe pi pe 2 C release sw 1C release Application of calculated creep coefficients to camber and dead-load deflection (Deflection due to beam self-weight) (in) sw 3.571 sw 5w sw L4 384E c I (Camber due to effective prestressing force, i.e. after prestress losses) (in) pe 5.496 pe f pe A ps e cgt L2 8E c I (Camber due to applied prestressing force) (in) pi 7.33 pi f pi A ps e cgt L2 8E ci I Camber Calculations

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117Time-Dependent Camber Growth Model camber t j t f'c pe pi pe 2 t j tt j f'c sw 1 t j tt j f'c Field Camber Measurements FDOT Curve Fit 020406080100120140160180200 0 2 4 6 8 10 Recommended Bulb-Tee Camber Growth ModelTime after Transfer (days)Camber (in) 15 15 Note: Dashed line represents curve fit of FDOT produced values, the solid line represents recommended camber growth model, and the “X’s” represent the field measured values.

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118 APPENDIX I DOCUMENTED LIMROCK SPECIMEN DATA Date Time After Release (Days) Field Camber (in) Date Time After Release (Days) Field Camber (in) Date Time After Release (Days) Field Camber (in) 8/26/200402.388/26/200402.388/26/200402.38 9/18/2004234.009/18/2004233.759/18/2004234.00 10/20/2004554.1910/20/2004554.3110/20/2004554.25 Date Time After Release (Days) Field Camber (in) Date Time After Release (Days) Field Camber (in) Date Time After Release (Days) Field Camber (in) 8/26/200402.258/26/200402.388/26/200402.38 9/18/2004233.889/18/2004239/18/200423 10/20/2004554.2510/20/2004554.1310/20/2004554.13 Date Time After Release (Days) Field Camber (in) Date Time After Release (Days) Field Camber (in) Date Time After Release (Days) Field Camber (in) 8/26/200402.388/26/200402.508/26/200402.38 9/18/2004239/18/2004239/18/200423 10/20/2004554.1310/20/2004554.2510/20/2004554.19 Date Time After Release (Days) Field Camber (in) 8/26/200402.25 9/18/200423 10/20/2004554.25 AASHTO Type IV 1 (Limerock) AASHTO Type IV 7 (Limerock)AASHTO Type IV 8 (Limerock)AASHTO Type IV 9 (Limerock) AASHTO Type IV 10 (Limerock) AASHTO Type IV 3 (Limerock) AASHTO Type IV 4 (Limerock) A ASHTO Type IV 5 (Limerock) A ASHTO Type IV 6 (Limerock) AASHTO Type IV 2 (Limerock)

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119 Date Time After Release (Days) Field Camber (in) Date Time After Release (Days) Field Camber (in) Date Time After Release (Days) Field Camber (in) 11/4/200302.5011/4/200302.5011/4/200302.50 7/9/20042484.137/9/20042484.137/9/20042484.25 8/19/20042894.508/19/20042894.258/19/20042894.25 9/18/20043194.509/18/20043194.259/18/20043194.25 10/20/20043514.5010/20/20043514.5010/20/20043514.50 11/19/20043814.6311/19/20043814.3811/19/20043814.50 Date Time After Release (Days) Field Camber (in) Date Time After Release (Days) Field Camber (in) Date Time After Release (Days) Field Camber (in) 11/4/200302.5011/18/200302.6311/18/200302.50 7/9/20042484.387/9/20042345.007/9/20042345.25 8/19/20042894.508/19/20042755.508/19/20042755.50 9/18/20043194.259/18/20043055.259/18/20043055.50 10/20/20043514.3810/20/20043375.7510/20/20043375.75 11/19/20043814.3811/19/20043675.2511/19/20043675.25 Date Time After Release (Days) Field Camber (in) Date Time After Release (Days) Field Camber (in) 11/18/200302.5011/18/200302.50 7/9/20042345.257/9/20042345.25 8/19/20042755.508/19/20042755.75 9/18/20043055.509/18/20043055.50 10/20/20043375.1310/20/20043375.75 11/19/20043675.2511/19/20043675.13 72" Bulb-Tee 7 (Limerock)72" Bulb-Tee 8 (Limerock) 72" Bulb-Tee 3 (Limerock) 72" Bulb-Tee 6 (Limerock) 72" Bulb-Tee 1 (Limerock)72" Bulb-Tee 2 (Limerock) 72" Bulb-Tee 4 (Limerock)72" Bulb-Tee 5 (Limerock) Time After Transfer (days) Average Compressive Strength (psi) Time After Transfer (days) Average Compressive Strength (psi) 0673007063 2894072810068 AASHTO Type IV (Limerock)72" Bulb-Tee (Limerock)

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120 REFERENCES Referenced Standards and Reports ASTM C 157-93 C 512-87 ACI 318-02 Building Code and Commentary Section 8.5.1 AASHTO LRFD Bridge Design Specification, 1998 ed. Section 5.9.5.4 AASHTO Guide Specifications 1989, “Thermal Effects in Concrete Bridge Superstructures (NCHRP R-276),” Ameri can Association of State Highway and Transportation Officials, Washington, D.C., 52 pp. ACI Committee 209R 1997, “Prediction of Creep, Shri nkage, and Temperature Effects in Concrete Structures (ACI 209R-92),” Am erican Concrete Institute, Farmington Hills, MI, 47 pp. Cited References Atcin, P. C. and Mehta P. K., 1990, “Effect of Coarse Aggregate Characteristics on Mechanical Properties of High-Strength C oncrete,” American Concrete Institute Materials Journal, v. 87, is. 2, American Concrete Institute, Farmington Hills, MI, pp. 103-107. Baalbaki, Walid; Aicin, Pierre-Claude; and Ballivy, Gerard, 1992, “On Predicting Modulus of Elasticity in High-Strength C oncrete,” American Concrete Institute Materials Journal, v. 89, is. 5, American Concrete Institute, Farmington Hills, MI, pp. 517-520. Branson, Dan E., 1977, Deformation of Concrete Structures McGraw Hill, Inc., New York, NY, pp. 1-40.

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121 Byle, K.A.; Burns, Ned H.; Carrasquillo, Ramn L.; 1997. “Time-Dependent Deformation Behavior of Prestressed Hi gh Performance Concrete Bridge Beams,” Center for Transportation Research, Bur eau of Engineering Research, University of Texas, Austin, TX. Canadian Prestressed Concrete Institute, Metric Design Manual Precast and Prestressed Concrete 3rd ed., CPCI, Ottawa, 1996. Giaccio, G. and Zerbino, R., 1998, “Failure Mechanism of Concrete, Combined Effects of Coarse Aggregate and Strength Level,” El sevier Science, Elsevier Science Ltd., New York, NY, 8 pp. Illston, J.M. and England, L., 1970, “Cr eep and Shrinkage of Concrete and Their Influence on Structural Behavior—A Review of Methods of Analysis,” Structural Engineer, Institution of Structural Engineers, London, UK, pp. 283-292. Kostmatka, Steven H. and Panarese, William C., 1988, Design and Control of Concrete Mixtures 13th Ed., Portland Cement Associat ion, Skokie, IL, pp. 153-159. Lybas, John M., 1990, “Reconciliation Study of Creep in Florida Concrete,” Structures and Material Research Repor t, No. 90-1, University of Florida Department of Civil and Coastal Engineering, Gainesville, FL, 115 pp. Magura, Donald D.; Sozen, Mete A.; and Si ess, Chester P., 1964, “A Study of Stress Relaxation in Prestressing Reinforcement, ” Precast/Prestressed Concrete Institute Journal, v. 9, is. 2, Precast/Prestressed Concrete Institute, Chicago, IL, pp. 13-57. Mehta, Kumar P., 1986, Concrete: Structure, Properties, and Materials Prentice Hall, Inc., Englewood Cliffs, NJ. Mindness, Sidney; Young, J. Fran cis; and Darwin, David, 2003, Concrete 2nd Ed., Pearson Education, Inc., Upper Saddle River, NJ, pp. 417-456. Naaman, A. E. and Hamza, A. M., 1993, “Pre stress Losses in Partia lly Prestressed High Strength Concrete Beams,” Precast/Prestressed Concrete Institute Journal, v. 38, is. 3, Precast/Prestressed Concrete Institute, Chicago, IL, pp. 98-114. Nawy, Edward G., 2003, Prestressed Concrete, A Fundamental Approach 4th Ed., Pearson Education, Inc., pp. 403-480. Neville, Adam M., 1997, “Aggregate Bond and Modulus of Elasticity of Concrete,” American Concrete Institute Materials Jour nal, v. 94, is. 1, American Concrete Institute, Farmington Hills, MI, pp. 71-74.

PAGE 133

122 Neville, Adam M., 1971, Hardened Concrete: Physical and Mechanical Aspects American Concrete Institute monograph, No. 6, American Concrete Institute, Detroit, MI, pp. 142-159, 359-433. Neville, A. M., 1963, Properties of Concrete Sir Isaac Pitman & Sons Ltd., London, UK, pp. 95-170. Nilson, Arthur H., 1987, Design of Prestressed Concrete 2nd Ed., John Wiley & Sons, Inc., New York, NY, pp. 33-36. Preston, H.K., 1975, “Recommendations for Estim ating Prestress Losses ,” Journal of the Prestressed Concrete Institute, Prestresse d Concrete Institute, Chicago, IL, pp. 4375. Prestressed Concrete Institute, PCI Design Handbook: Precast and Prestressed Concrete 5th ed., PCI, Chicago, 1999. R&A Products, January 20, 1996 The Pro-LevelTM Water Manometer “The Pro-LevelTM Manometer Overview – Functions, Uses, Advantages, Accuracy: Operation” R&A Products, San Diego, CA, < http://prolevel.com/operation.htm > November 20, 2004. Sengul, zkan; Tasdemir, Canan; and Tasdem ir, Mehmet Ali, 2002, “Influence of Aggregate Type on Mechanical Behavi or of Normala nd High-Strength Concretes,” American Concrete Institute Ma terials Journal, v. 99, is. 6, American Concrete Institute, Farmingt on Hills, MI, pp. 528-533. Sinno, R. and Furr, H. L., 1970, “Hyperbolic Functions for Prestre ss Loss and Camber,” ASCE Journal of the Structural Division, v. 96, no. ST4, American Society of Civil Engineers Publications Reston, VA, pp. 803-821. Tadros, M. K.; Ghali, A.; and Meyer, A. W., 1985, “Prestress Loss and Deflection of Precast Concrete Members,” Precast/Prestressed Concrete Institute Journal, v. 30, is. 1, Precast/Prestressed Concrete Institute, Chicago, IL, pp. 114-141. Troxell, George Earl; Davis, Harmer E.; and Kelly, Joe W., 1968, Composition and Properties of Concrete 2nd Ed. McGraw Hill, Inc., New York, NY, pp. 290-351. Yazdani, N.; Mtenga, P.; and Richardson, N., 1999, “Camber Variation in Precast Girders,” Concrete International, Ameri can Concrete Institute, Farmington Hills, MI, pp. 45-49.

PAGE 134

123 BIOGRAPHICAL SKETCH The author was born on January 17, 1980, in Menominee Falls, Wisconsin. He began attending the University of Florid a in August 1998 after gr aduating from high school in Bradenton, Florida. After receiving the degree of Bachelor of Science in Civil Engineering with highest honors from the Univ ersity of Florida in December 2003, he began graduate school in the Department of Civil and Coastal Engineering. After receiving his Master of Engi neering degree in December 2004, with a concentration in civil engineering structures, he will pursue a career in structural bridge design. The author has been a member of American Soci ety of Civil Engineers since 1998, Tau Beta Pi and Chi Epsilon since 2000.


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FIELD VERIFICATION OF CAMBER ESTIMATES FOR PRESTRESSED
CONCRETE BRIDGE GIRDERS














by


JONATHAN E. SANEK


A THESIS PRESENTED TO THE GRADUATE SCHOOL
OF THE UNIVERSITY OF FLORIDA IN PARTIAL FULFILLMENT
OF THE REQUIREMENTS FOR THE DEGREE OF
MASTER OF ENGINEERING

UNIVERSITY OF FLORIDA


2005















ACKNOWLEDGMENTS

Completion of this thesis and the research associated with it would not have been

successful without the help and guidance of a number of individuals. The author would

like to thank Dr. Ronald A. Cook for the guidance and support he provided throughout

the duration of the project. He was a fountainhead of knowledge who, because of his

sincerity and contribution to the project, could not have been a more valuable asset

toward the completion of this research endeavor. The author would also like to thank Dr.

David Bloomquist whose counsel and expertise in the instrumentation employed on this

project and, to a broader extent, the myriad of technical subjects pertaining to

development and completion of this research were very much appreciated.

Many others imparted their own individual efforts toward the successful

conclusion of this project. The author would like to thank Isaac Canner, Xiaoming Wen,

Michael Reponen, and Joe Liberman for the help they provided in the field. Also, I thank

George Lopp for the guidance and help he offered in the operation of the MTS concrete

cylinder testing apparatus; Chuck Broward and Danny Brown for their help with the

fabrication of the instrumentation used on this project; Richard DeLorenzo for his help

testing the 6-inch x 12-inch cylinder specimens; and Dr. Bon Dewitt for his help

operating the surveying instrumentation implemented on this project. The author would

like to thank Marc Ansley from the Florida Department of Transportation. His

knowledge, resources and financial support were greatly appreciated. The author would

also like to offer his gratitude to John Jarrett and all those individuals at the Durastress









Inc. precast facility. Without their cooperation, this project could not have taken place.

Lastly, the author would like to thank his friends and family for the help and support they

offered throughout his educational career.
















TABLE OF CONTENTS


page

A C K N O W L E D G M E N T S .................................................................................................. ii

LIST OF TABLES ............ ........................ ..... ........................ vi

L IST O F F IG U R E S .... ......................................................... .. .......... .............. vii

A B STR A C T ................................................. ..................................... .. x

1 IN TRODU CTION ................................................. ...... .................

2 PRESTRESSED BEAM CAMBER....................................................................... 3

2 .1 Introdu action ............................................... .......................... 3
2.2 C construction P problem s ........................................ .......................................3
2.3 Tim e D dependent Effects .............................................................. ....... ......4
2.4 C alculation of C am ber.......................................... .......................................9
2.5 L R FD Prestress L oss ......... ................... ......... .................................. 10
2.6 LRFD Creep Coefficient .................................. .....................................14
2.7 Thermal Effects ........................................................ 15
2.8 E effect of C oarse A ggregate ..................................................................... ... ... 17
2 .8 .1 Intro du action ............................................... ................ 17
2.8.2 M echanical Properties ........................................ .......... ..............17
2 .8.3 P hy sical P properties ........................ .... ................ ............... .. 18
2.8.4 Effects of Coarse Aggregate on Differential Shrinkage..........................19

3 M E T H O D O L O G Y ............................................................................ ................... 2 1

3.1 C am ber M easurem ent................ .... ..... ......... .............................. ................2 1
3.2 Thermal Gradient Measurement and Camber Correction .................................25
3.3 Supplem ental M material Testing................................................................ .. .... 29

4 SUM M ARY OF RESULTS ............................................... ............................ 32

4.1 Camber M easurem ent at Release ............................................. ............... 32
4.2 Camber M easurem ent Sum m ary .............................................. .............. 35
4.3 Supplem ental M material Testing Sum m ary .............................................................45









4.4 Florida Lim erock Specim ens......................................... .......................... 53
4.4.1 Camber M easurem ent at Release .................................. ............... 53
4.4.2 Camber M easurement Summary ........................................ ......... 55

5 CONCLUSIONS AND RECCOMENDATIONS........................................................58

APPENDIX

A CAMBER AT RELEASE MEASUREMENTS................................... ...................60

B FIELD CAMBER MEASUREMENTS ........................................ ............... 61

C EMPIRICAL THERMAL ANALYSIS....................... ....... ...............66

D ANALYTICAL THERMAL ANALYSIS ...................................... ...............73

E TABULATED AM BIEN T DATA .................................................................. ......89

F M IX DESIGNS .................. .................. ................... .......... ........ ..... 102

G TABULATED MATERIAL TESTING DATA ................................................ 107

H RECOMMENDED 78" BULB-TEE CAMBER CALCULATION.................111

I DOCUMENTED LIMEROCK SPECIMEN DATA ................................................118

R E F E R E N C E S ........................................ .......................................... ............... .... 12 0

BIOGRAPHICAL SKETCH .................... ..................................... ............... 123
















LIST OF TABLES


Table page

1 Angular measurement technique accuracy................. .. .......... ..... .......... 23

2 Pro-LevelTM measurement technique accuracy ...................................................25

3 Example of field measurements and thermally corrected cambers........................28

4 Comparison of field measured camber to predicted camber................ ......... 36

5 Girder pour identification summary ..................... ....................... ............... 46

6 Tabular comparison of predicted and actual camber values for Limerock and
granite specimens of the AASHTO Type IV girder.................... ................56

7 Comparison of field measured camber to predicted camber at 240 days for Bulb-
Tee girders ................ ......... .... ............................................ 57















LIST OF FIGURES


Figure p

1 D trying shrinkage vs. tim e ........................................ ................................. 7

2 Concrete creep vs. tim e after loading................................ ................................. 7

3 C am ber at m idspan vs. tim e ............................................................ .....................8

4 Effect of relative aggregate and cement stiffness on concrete stiffness ................. 18

5 Optical target mounted on fixed ceramic magnet ......................................... 21

6 Isometric view of a three-point resection analysis................................................ 22

7 Pro-LevelTM water manometer schematic.............................................................24

8 Pro-LevelTM water manometer measurement technique .......................................25

9 Infrared tem perature sensor........................................................... ............... 26

10 Example single day temperature profile of Bulb-Tee girder 3..............................27

11 Field cured 4"x 8" concrete test cylinders .................................... ............... 29

12 Computerized MTS concrete cylinder testing apparatus ............. ..............30

13 Bar chart of 78" Bulb-Tee camber at release, after moving, and FDOT predicted
values ................... .................................................... ......... 33

14 Bar chart of AASHTO Type IV camber at release, after moving, and FDOT
predicted values ............... ... ....... .............. ... ........................ 34

15 Bar chart of AASHTO Type IV camber at release, after moving, and FDOT
predicted values ............ .. ... ....... .......... ..... .. .......... ........... 34

16 AASHTO Type IV girder in storage................ ............ ................ ................. 37

17 Field camber measurements for 78" Bulb-Tee girder 1 .......................................37

18 Field camber measurements for 78" Bulb-Tee girder 2 ..................................38









19 Field camber measurements for 78" Bulb-Tee girder 3 .......................................38

20 Field camber measurements for 78" Bulb-Tee girder 4..................................39

21 Field camber measurements for 78" Bulb-Tee girder 5 .......................................39

22 Field camber measurements for 78" Bulb-Tee girder 6.............. ...................40

23 Summary of field camber measurements for all 78" Bulb-Tee girders ................40

24 Field camber measurements for AASHTO Type IV girder 1 ................................41

25 Field camber measurements for AASHTO Type IV girder 2 ................................41

26 Field camber measurements for AASHTO Type IV girder 3 ................................42

27 Summary of field camber measurements for all AASHTO Type IV girders...........42

28 Field camber measurements for AASHTO Type V girder 1..................................43

29 Field camber measurements for AASHTO Type V girder 2....................................44

30 Field camber measurements for AASHTO Type V girder 3....................................44

31 Field camber measurements for AASHTO Type V girder 4...................................45

32 Summary of field camber measurements for all AASHTO Type V girders............45

33 78" Bulb-Tee pour "A" compressive strength vs. time................ .............. ....47

34 78" Bulb-Tee pour "A" elastic modulus vs. time.................. .................. ..............48

35 78" Bulb-Tee pour "B" compressive strength vs. time.......................................48

36 78" Bulb-Tee pour "B" elastic modulus vs. time.................................. ..............49

37 AASHTO Type IV pour "A" compressive strength vs. time...............................49

38 AASHTO Type IV "A" elastic modulus vs. time ......................................... 50

39 AASHTO Type V pour "A" compressive strength vs. time ..................................50

40 AASHTO Type V "A" elastic modulus vs. time ........................................... 51

41 AASHTO Type V pour "B" compressive strength vs. time ..................................51

42 AASHTO Type V "B" elastic modulus vs. time................................................52

43 Limerock 72" Bulb-Tee and AASHTO Type IV camber at release ......................54









44 72" Bulb-Tee (Limerock) girder camber growth summary ...................................55

45 AASHTO Type IV (Limerock) girder camber growth summary ..........................56

46 Comparison of predicted camber to actual field camber for granite and limerock
specimens of AASHTO Type IV girder...........................................57















Abstract of Thesis Presented to the Graduate School
of the University of Florida in Partial Fulfillment of the
Requirements for the Degree of Master of Engineering

FIELD VERIFICATION OF CAMBER ESTIMATES FOR PRESTRESSED
CONCRETE BRIDGE GIRDERS

by

Jonathan Edward Sanek

May 2005

Chair: Ronald A. Cook
Cochair: David Bloomquist
Major Department: Civil and Coastal Engineering

Prestressed concrete girders are used on many of Florida's bridges. These girders

are subject to camber, the upward deflection of the girder due to the eccentricity of the

prestressing force. Over time, the girders experience camber growth as a result of

growing compressive strain in the pre-compressed tensile zone. This compressive strain

causes a reduction in the prestressing force, or what is referred to as a "prestress loss."

These strains are due to time-dependent phenomena, specifically creep and shrinkage of

the concrete. It is necessary to accurately predict the camber of a girder in order to avoid

problems and delays during construction due to build-up or bearings. Differences have

been found between camber predicted by the design program employed by the FDOT and

the measured field camber for prestressed "Bulb-Tee" girders. The focus of this

investigation was to develop a realistic time-dependent camber growth model using

periodic field measurements taken on a variety of different prestressed concrete bridge

girders. Specifically, the types of girders monitored for this project were 1) the 78-inch









Florida Bulb-Tee girder, 2) the AASHTO Type IV girder, and 3) the AASHTO Type V

girder.















CHAPTER 1
INTRODUCTION

Prestressing of concrete, in general, is the introduction of an internal loading

condition such that the performance of the structural member is improved in several

ways. Specifically, a prestressing force is used in flexural members to lessen the concrete

tensile stresses. This is done in order to prevent or reduce concrete cracking in the tensile

zone due to tensile stresses exceeding the rupture strength of the concrete. The

prestressing force is typically applied to a concrete beam section such that it creates an

eccentric, axial loading condition resulting in an upward deflection or camber. Also, as a

result of preventing cracking, this "preloading" reduces the amount the flexural member

will deflect under service loads, thus improving the serviceability of the member. The

prestressing force, however, does not increase the flexural strength of an element.

The prestressed beam design program currently implemented by the Florida

Department of Transportation, Eng LFRD PSBeam v.1.85, includes calculations for the

prediction of time-dependent camber growth that have not been field verified. This

camber growth is obtained by calculating the elastic camber at the release of the

prestressed girder (i.e., application of the prestressing force) and applying a time-

dependent multiplication factor. The focus of this investigation was to obtain field

camber measurements on different types of bridge girders with the goal of verifying or

improving the present design methodology used by the FDOT for time-dependent camber

estimation.









Periodic field camber measurements from initial prestress transfer to as much as

six months after transfer were performed on:

Six (6) Florida 78-inch Bulb-Tee were 162-feet in length with fifty-three (53)
0.60"-diameter, 270-ksi, "Lo-Lax" prestressing strands, and used FDOT Class VI
coarse granite aggregate concrete with a specified 28-day compressive strength of
8,500-psi.

Three (3) AASHTO Type IV girders were 91-feet in length with thirty (30) 12"-
diameter, 270-ksi, "Lo-Lax" prestressing strands, and used FDOT Class IV coarse
granite aggregate concrete with a specified 28-day compressive strength of 5,500-
psi.

Four (4) AASHTO Type V girders were 81-feet in length with twenty-eight (28)
1/"-diameter, 270-ksi, "Lo-Lax" prestressing strands, and used a FDOT Class IV
coarse granite aggregate concrete with a specified 28-day compressive strength of
5,500-psi.















CHAPTER 2
PRESTRESSED BEAM CAMBER

2.1 Introduction

Camber is the upward deflection of a flexural member due the eccentricity of the

prestressing force. The prestressing force is placed eccentrically to counteract the

downward deflection of the flexural member caused by gravity loads and service loads.

The amount of camber is dependent upon several factors: the tendon profile, the

prestress magnitude, the span, the section properties, and the elastic modulus of the

concrete (Nawy 2003).

2.2 Problems with Construction

The need for accurate predictions of estimated camber in prestressed structural

members can not be overstated. However, even in controlled conditions, predictions of

element deflections to a high degree of accuracy are difficult (Tadros, Ghali, and Meyer

1985). Discrepancies between the predicted and the actual measured field camber can

cause delays in construction because of corrections to build-up and/or bearings of the

prestressed structure. In the FDOT structural design guidelines, the haunch between the

slab and the girder can be adjusted in order to compensate for variation between the

required and provided deck profile and maintain a constant slab thickness (Yazdani,

Mtenga, and Richardson 1999). These solutions cause construction delays which can be

costly and cause additional problems throughout later construction stages.









2.3 Time-Dependent Effects

One important characteristic of camber is that it increases with time. This camber

growth begins immediately following the application of the prestressing force to the

flexural element. This is known as the prestress "transfer" or "release." The element

first deflects upward due to the elastic strain in the pre-compressed tensile zone. Strains

due to concrete creep and shrinkage then begin to grow with time (at a higher rate in the

pre-compressed tensile zone than in the compressive zone), thus creating a time-

dependent relationship of camber growth (Sinno and Furr 1970). These strains bring

about losses in the prestressing force, or what are referred to as "prestress losses." These

prestress losses cause a reduction in the prestressing force which leads to an overall

reduction in the amount of camber a prestressed element will exhibit.

These prestress losses can be calculated one of several ways: lump sum estimates

of the total prestress loss, refined estimates of each contributing factor (as outlined by

ACI 209R Committee Report and AASHTO LRFD Bridge Design Specification), or a

rigorous analysis using the "time-step procedure" (Naaman and Hamza 1993). The time-

step procedure is the most accurate method for determining long-term prestress losses

when the material properties and environmental conditions are well-known. This method

takes into account the interdependent effects of the long-term prestress losses upon one

another. For example, the relaxation of the prestressing steel reduces the amount of stress

applied to the pre-compressed tensile zone of the flexural element. This reduced stress

then affects the amount that the concrete will creep and shrink. The time-step procedure

descretizes these effects into time increments, at the end of which a prestress loss is then

calculated and accumulated (Naaman and Hamza 1993). Prestress losses to be









considered in an analysis of a pre-tensioned flexural member are loss due to; anchorage

of prestressing steel (ANC), deflecting device for draped strands in pre-tensioned

construction (DEF), elastic shortening (ES), creep of concrete (CR), shrinkage of

concrete (SH), and relaxation of the prestressing steel (RET) (Preston 1975). The total

prestress loss (TL) is defined by the equation:

TL = ANC +DEF +ES + (CR + SH +RET)


For analysis of a post-tensioned flexural member, loss due to friction of the

prestressing tendon (FR) would be included in the total prestress loss calculation

(Naaman and Hamza 1993). In this equation, time-dependent losses from creep,

shrinkage, and steel relaxation are lumped together because they are interdependent upon

one another.

Although long-term prestress losses include the effect due to relaxation of the

prestressing steel, the more dominant factors are those due to creep and shrinkage of the

concrete. The bulk of the prestress loss due to relaxation occurs before the transfer of the

prestressing force. Thus, there are few provisions made to include the effects of the

prestress loss due to relaxation for calculations of the long-term prestress loss and camber

because they are relatively small (Magura, Sozen, and Siess 1964). Generally, 30-40% of

the steel relaxation takes place within the first two days following the application of the

prestressing force. Therefore, prestress losses due to creep and shrinkage of the concrete

are overwhelmingly the more influential factors in affecting the long-term behavior of

prestressed elements.

Creep is an increase in strain with time under a sustained stress condition (Neville

1971). The amount of creep a concrete structural element will undergo depends primarily









on the magnitude of the applied load, the time for which the load is applied, and the

strength of the concrete at which the load is first introduced (Kostmatka and Panarese

1988). Additional factors affecting the creep of a concrete specimen are the curing

history of the concrete; type, amount and maximum size of aggregate; type of cement;

amount of cement paste; size and shape of concrete specimen; volume to surface area

ratio; amount of non-prestressed steel reinforcement; and the temperature and humidity at

which the concrete specimen is stored (Kostmatka and Panarese 1988).

Shrinkage is the volumetric deformation of a concrete specimen with time in an

unstressed condition (Illston and England 1970). Shrinkage is caused by ambient relative

humidity that is below the point of saturation of the concrete (i.e., relative humidity <

100%).

Both creep and shrinkage of concrete result mainly from the removal of absorbed

water from the calcium-silicate-hydrate (CSH) portion of the cement matrix. This causes

a strain in the concrete which, in turn, results in a volumetric deformation (Mehta 1986).

The difference between these two is that creep is stress induced while shrinkage is

induced by ambient conditions. Because these phenomena are based on a common

origin, it is stated that they are interrelated to one another and occur simultaneously

(Mindness, Young, and Darwin 2003). Also, because concrete creep and shrinkage occur

simultaneously, it is impossible to test for each of them independently. Instead,

shrinkage strain must be tested for alone and then subtracted from the strain resulting

from the combined effect of creep and shrinkage (Lybas 1990).

A strong validation of concrete creep and shrinkage's interdependence upon one

another is the evidence that the time-dependent behavior of creep is very similar to that of












shrinkage. Both shrinkage and creep curves grow logarithmically with time with some


portion of the resultant strain being irreversible or plastic due to rewetting or unloading,


respectively. Fig. 1 below shows the time-dependent behavior of shrinkage and Fig. 2


shows the time-dependent behavior of creep.


700
7 0 0 I----------------------------- - - - ----------

600


500


400

2 Total
300 Shrinkage


200


100


0
0 5 10 15 20 25 30 35 40 45 50
Time (Days)


Figure 1. Drying shrinkage vs. time.


1000
9000 ------------------------------------------------
900 .........-

800

700

.* 600 Creep
T Strain
500

2 400

300

200-
Elastic
100
10 Strain

0


10 20 30 40 50 60
Time After Loading (Days)


Figure 2. Concrete creep vs. time after loading.


70 80










It is also interesting to note that the camber growth curve also follows a similar trend (see

Fig. 3).


1.2





0.8
E

S0.6
S-------------------- --
0.4

I- Camber at
0.2 Release


0
0 20 40 60 80 100 120 140
Time After Transfer (days)

Figure 3. Camber at midspan vs. time.


These figures help substantiate the importance of concrete creep and shrinkage effects on

the time-dependent behavior of prestressed flexural elements.

Another consideration is differential shrinkage. Differential shrinkage is solely

influenced by the geometry of the prestressed element's cross-section. Because it is

caused by the rate of water loss from the CSH portion of the cement matrix, it is apparent

that the rate at which water is transported from the interior of the concrete section to the

atmosphere would be controlled by the length of the diffusion path traveled by the water

(Mehta 1986). This factor is taken into account when calculating the amount of

shrinkage that will occur using the ACI 209R correction factors based on either the

average-thickness method or the volume-to-surface area ratio (V/S) method. Typically,

the average-thickness method tends to compute correction factors that are greater than

those calculated using the volume-to-surface area method (ACI 209R).









These numerical representations of the geometry of a section appear to have a

linear relationship with the logarithm of shrinkage (Neville 1971). Generally, a higher

volume-to-surface area ratio or theoretical-thickness will produce less ultimate shrinkage

in concrete. However, considering the geometry of some AASHTO girders, specifically

the Florida Bulb-Tee girder, shrinkage may occur at different rates between the top

flange, which has a "T-shape," and the bottom bulb. Evidence has shown that members

with small cross-sections result, initially, in faster rates of shrinkage, but lower ultimate

shrinkage values, and vise-versa for members with large cross-sections (Mindness,

Young, and Darwin 2003). A "T-shaped" section, with a lower V/S ratio, will dry and

shrink more rapidly than a square-shaped section (Mindness, Young, and Darwin 2003),

such as the bulb portion of the Florida Bulb-Tee, but have less ultimate shrinkage. This

is known as differential shrinkage and could account for errors in the calculation of the

long-term camber growth of Florida Bulb-Tee girder. Also, uneven drying conditions due

to poorly ventilated areas of the girder during storage could also cause differential

shrinkage. When the concrete section of a prestressed element dries asymmetrically,

warping can occur (Neville 1971), thus altering the camber.

2.4 Calculation of Camber

Nilson suggests that the effects of creep and shrinkage should not only affect the

long-term loading due to the prestress force but it should also affect that due to the self-

weight of the member (Nilson 1987). Taking this into account, the calculation of camber

is given by Equation 2 below.

A pe )A + )] (2)
A=A p+ .2(t t,)- Ao [l+ 0(t, t) (2)









where:

Ap, = Camber due to initial prestress force after steel relaxation-
and elastic shortening-related losses (in.)

Ape = Camber due to effective prestress force after all prestress
losses, (in.)

Ao = Deflection due to self-weight of member (in.)

q(t,t,) = LRFD time-dependent creep coefficient.

The calculation of the initial prestress force, effective prestress force, and the

creep coefficient, as outlined by the AASHTO LRFD Bridge Design Specification, are

discussed in the sections below.

2.5 LRFD Prestress Loss Calculations

The Florida Department of Transportation's prestressed beam design program,

Eng LFRD PSBeam v.1.85, uses refined estimates of time-dependent prestress losses as

outlined by the AASHTO LRFD Bridge Design Specification in section 5.9.5.4. These

estimates provide a more accurate representation of creep-, shrinkage-, and steel

relaxation-related losses than those obtained using the lump-sum estimate approach.

These prestress losses for pretensioned members are calculated using the equations listed

below.

Elastic Shortening (ES):

E
AfpE =E fcgp (3)
Ec,

where:

fcgp = sum of concrete stresses at center of gravity of
the prestressing tendons due to the prestress force
at transfer and the self-weight of the member at









the sections of maximum moment (ksi)

Ep = elastic modulus of prestressing tendons (ksi)

Ec, = elastic modulus of concrete at transfer (ksi)

A s Ap fpb .(lg +e 2 -Ag)-e *Mg *A
Af ps p=

A .(I +e2 .A)-+A, g, Ec, (4)
ps g m E


fpbt = 0.75 fp, for low relaxation strands (5)

fpbt = 0.70 fp, for stress-relieved strands (6)

where:

Aps = area of prestressing steel (in2)

Ag = gross area of section (in2)

Ec, = elastic modulus of concrete at transfer (ksi)

Ep= elastic modulus of prestressing tendons (ksi)

e, = average eccentricity of prestressing tendons at
midspan (in)

fpbt = stress in prestressing tendons immediately prior
to transfer (ksi)

fp, = ultimate tensile stress of prestressing tendons (ksi)

Ig= moment of inertia of the gross concrete section
(in4)

Mg = moment at midspan due to member self-weight
(kip-in)

Relaxation of the Prestressing Tendon at Transfer (RET):









Af l log(24.0 't) fP- f
40.0 _f 1 (7)


for low-relaxation strands

Af pl log(24.0. t) fPJ -.55. f
AfpR1 10
10.0 fpy (8)

for stress-relieved strands

where:

t = estimated time from jacking to transfer (days)

fp = jacking stress of the tendon (ksi)

fp = specified yield strength of prestressing steel (ksi)

Drying Shrinkage (SR):

Afs =(17.0- 0.150.H) (9)

where:

H = average annual ambient relative humidity (%)

Concrete Creep (CR):

AfpR = 12.0 fgp- 7.0. Afcd >0 (10)

where:

fgp = concrete stress at center of gravity of prestressing
steel at transfer (ksi)

Afcdp = change in concrete stress at center of gravity of
prestressing steel due to permanent loads
except load from prestressing force (i.e.,
gravity loads) calculated at same section asfgp
(ksi)


Relaxation of the Prestressing Tendon after Transfer (RET):









Afp2 = [20.0 0.4. Afp 0.2. (Afp + Afp )]. 0.30
(11)
for low relaxation strands

AfR2 = 20.0- 0.4. Afp, 0.2. (Af SR AJP )
(12)
for stress relieved strands


The Eng LFRD PSBeam v.1.85 program first calculates the prestress loss due to

the relaxation in the prestressing steel using either Equation 7 or 8, depending on the type

of prestressing strands used (i.e., low-relaxation strands or stress-relieved strands). Then,

assuming an initial value of 5% for the prestress loss due to elastic shortening of the

concrete and considering the initial prestress loss due to relaxation, it calculates an

estimated value of the prestress at transfer (i.e., fpe = fp (0.05 f + AfR,)). Using this

estimated prestress, a second value for the prestress loss due to elastic shortening is

calculated using Equation 3. This procedure is then repeated, iteratively, once more to

determine the final prestress loss due to elastic shortening. The program then calculates

the prestress losses due to shrinkage and creep of the concrete using Equations 9 and 10.

A final value of the prestress loss due to the relaxation of the prestressing steel is then

calculated using Equation 11 or 12, depending on the type of prestressing strands used,

using the values calculated in the previous steps. Using these calculated prestress losses,

the initial prestress force, P,, can be obtained by subtracting the steel relaxation loss (R1)

and the elastic shortening loss from the jacking force. This is used to determine the

camber immediately after transfer, or Ap,. The effective prestress force, Pe, is the force in

the tendons after all of the prestress losses. It is calculated by subtracting time-dependent

losses due to creep, shrinkage, and steel relaxation (R2) from the initial prestress force.

The effective prestress force is used to calculate the reduced camber after the long-term









prestress losses, or Ape. Example calculations of this method can be found in Appendix

H.

2.6 LRFD Creep Coefficient

Section 5.4.2.3.2 of the 1998 AASHTO LRFD Bridge Design Specification uses

equations from the ACI 209R Committee Report and empirical data as the basis for the

calculation of what is known as the "creep coefficient." The creep coefficient is the ratio

of creep strain to elastic strain at some time after loading. The time-dependent equation

given below was introduced by Collins and Mitchell (1991) and adopted by the AASHTO

LRFD Bridge Design Specification.


(tt=3.5-kc-k-1.58- H ito + (t-t (13)
120 10 + (t )06

where:

t = time, in days, after loading

t,= time, in days, time at which load is applied after casting

kc = correction factor for V/S ratio

kf = correction factor that accounts for lower creep of high-
strength concrete

H = relative humidity, in percent

Correction Factors:

kf -1
S= 067+(f/ (14)
(f/+ 19000)

where:

fc = 28-day compressive strength of the concrete (psi)









t
26-e 0S36- !1.80+1.77.e (15)
k =
t 2.587 (15)

45 +t

where:

V/S = volume to surface area ratio (in.)

The correction factor, kf, (Equation 14) accounts for the influence of concrete strength

(Collins and Mitchell, 1991). Ngab, Nilson, and Slate found in a 1981 study that

concrete with a compressive strength in the range of 9,000 to 12,000 psi (i.e., high-

strength concrete) tended to exhibit a creep coefficient of about 50 to 75 percent that of

normal-strength concrete under normal drying conditions. The correction factor, kc,

(Equation 15) accounts for the effects of the volume-to-surface ratio and is based on

empirical data given in the PCI Design Handbook and the CPCIMetric Design Manual.

The design program, Eng LFRD PSBeam v.1.85, used by the Florida Department

of Transportation uses magnification factors in order to obtain a time-dependent camber

estimate. The values listed in the program are an average of the creep coefficients

calculated using the LRFD method specified above and values taken from an older

program once used by the FDOT. These factors are multiplied by the elastic camber, or

camber immediately after transfer, to obtain a time-dependent value of the camber at 30-,

60-, 120-, and 240-days.

2.7 Thermal Effects

The prestressed beam camber can be significantly influenced by ambient

conditions experienced during storage and at the time of measurement. Conditions such

as ambient temperature, wind speed, relative humidity, solar radiation, as well as the

composite material and section properties of the girder can influence how the beam's









internal temperature changes. Generally, if a structural member undergoes a uniform

temperature increase, that member will experience a thermally induced strain and expand

uniformly. However, due to the restraint provided by the prestress force, this movement

is inhibited in the pre-compressed tensile zone in the base of the beam and not in the

compressive zone in the flange of the beam, thus producing an increase in the girder's

curvature. Also, from the field observations made, it is known that the temperature

increase is not uniform. The girders often experienced higher internal temperatures in the

top flange than in the bottom flange, creating a thermal gradient. This thermal gradient

adds to the effect of an increase in beam curvature.

In a University of Texas study, this thermal effect was accounted for using an

empirical analysis in which the beam's temperature gradient and camber were measured

several times throughout the day in order to obtain a relationship between the two. The

first camber reading was taken as the baseline reading, and an increase in camber was

calculated by subtracting the subsequent readings from this initial value. A relationship

between the increase in camber and thermal gradient was then used to correct these field

measured values for thermally induced effects (Byle, Burns, and Carrasquillo 1997).

This empirical method and an analytical method are used to account for any thermally

induced changes in camber inherent in the field measurements.

The analytical method is outlined by the NCHRP Report 276 which investigates

thermal effects in concrete superstructures. This report organizes the United States into

maximum solar radiation zones from which the predicted positive thermal gradient

profile for a given concrete section can be determined using the tables provided. The

actual thermal gradient profile obtained from the field measurements was used to account

for thermal effects on prestressed beam camber.









2.8 Effects of Coarse Aggregate

2.8.1 Introduction

It is not unexpected that the physical properties of the coarse aggregate strongly

influence the behavior of concrete since coarse aggregate makes up nearly three quarters

of concrete by volume (Sengul, Tasdemir, and Tasdemir 2002). Aggregate was

originally considered an inert material added to the concrete mixture as a space filler for

economical purposes (Neville 1963). However, the material properties of the coarse

aggregate can strongly influence the physical behavior of concrete. Generally, aggregate

properties are separated into three categories; physical properties, chemical properties,

and mechanical properties. Concerning aggregates effect on creep and shrinkage of

concrete, the mechanical and physical properties of coarse aggregate are of the most

interest.

2.8.2 Mechanical Properties

Specifically, the most important mechanical property that affects the behavior of

creep and shrinkage in concrete is the elastic modulus of the coarse aggregate (Mehta

1986). The elastic modulus of a material is defined as the change in stress with respect to

elastic strain and is a measure of a materials resistance to deformation. Elastic modulus

of concrete is of particular concern in prestressed and reinforced flexural elements

(Baalbaki, Aicin, and Ballivy 1992). Concrete with a high modulus of elasticity will

offer a higher degree of resistance against volumetric deformation. This results not only

in a lower elastic strain, but also lower long-term strains due to creep and shrinkage, and

hence causing lower long-term prestress losses. The influence of the aggregate properties

increase as the strength of the cement paste matrix grows close to that of the coarse







18


aggregate, causing the concrete to act more monolithically (Giaccio and Zerbino 1998).

This effect will be significant for the case of prestressed structural elements where high-

strength concrete is used. Concordantly, a decrease in aggregate stiffness corresponds to

a decrease in aggregate strength thus causing the strength of the aggregate to be closer to

that of the high-strength cement matrix. The concrete stress-strain behavior acts linearly

over a broader range, creating a concrete with a higher stiffness (Neville 1997) than

expected using empirical relationships (see Fig. 4). However, a decrease in aggregate

stiffness will, over all, lead to a total decrease in the stiffness of the concrete. For

aggregates with a higher elastic modulus, this effect will not be as pronounced.




45 60 G 1
40 -0 A rebate g b
'0 o // -" c'm nt

30 ." -n ,men 40 _-m 0nt
Scment Pail
modulusoft ero ms s c ( 1 ) I a p
S /
i 0s / / / 20

5 "
0 0
0 1000 2000 3000 0 1000 2000 3000
MI crc lraIn Mcro itaIn


Figure 4. Effect of relative aggregate and cement stiffness on concrete stiffness (Neville
97)

2.8.3 Physical Properties

Of the physical properties of the coarse aggregate that influence the elastic

modulus of the aggregate, porosity is the most significant (Mehta 1986). In a physical

sense, an aggregate with a higher porosity, such as limestone, will have a lower density,

therefore causing the aggregate to have a lower modulus of elasticity and thus, have a

lower stiffness. The result of this effect is a lower degree of restraint against







19

deformation, and therefore, creep and shrinkage will have a more significant effect on the

time-dependant deformation of concrete. Conversely, an increase in porosity of the

aggregate actually increases its bond strength along the interfacial zone, thus increasing

the concrete's compressive strength (Aitcin and Mehta 1990). Other factors affecting the

elastic modulus of the concrete are the maximum size, shape, surface texture, grading,

and volume fraction of the aggregate; the porosity and water/cement ratio of the cement-

paste matrix; the moisture state of the specimen at loading (Mehta 1986); age and curing

conditions of the concrete specimen (Troxell, Davis, and Kelly 1968). Specimens tested

in wet conditions had a tendency to present higher elastic moduli values than those tested

in dry conditions. Also, the effect of age on the elastic modulus results in a rapid growth

within the first few months and then begins to taper off. The elastic modulus may still

continue to grow even after 3 years (Troxell, Davis, and Kelly 1968).

In particular, creep is influenced by the amount of aggregate the concrete contains

and stiffness of the aggregate. Aggregate size, grading, and surface texture have little

effect on creep (Mindness, Young, and Darwin 2003). Shrinkage is also influenced by

the amount and stiffness of the coarse aggregate. In contrast, maximum aggregate size

does have a significant effect on drying shrinkage in concrete (Mindness, Young, and

Darwin 2003.

2.8.4 Effect of Aggregate on Differential Shrinkage

The effect of aggregate on differential shrinkage, aside from its direct influence

on drying shrinkage, is the degree of restraint against volumetric deformation provided

by the amount of coarse aggregate. Obviously an increase in aggregate content would

significantly increase the concrete's ability to restrain any volumetric change due to

drying shrinkage (Neville 1971) thus differential shrinkage, overall, would become less







20

of a factor. Another effect that the aggregate could have on differential shrinkage could

be due to the asymmetric segregation of coarse aggregate during the casting process. A

higher concentration of coarse aggregate at the bottom of a flexural element would cause

a higher degree of restraint in the bottom than in the top, therefore creating the conditions

of differential shrinkage.















CHAPTER 3
METHODOLOGY

3.1 Camber Measurement

The initial field measurements of the camber were made using a surveying

theodolite and three optical targets. Three ceramic magnets were mounted to the top of

each beam at the endpoints and midpoint to which the optical targets were temporarily

affixed for each field measurement as seen in Fig. 5.

















Figure 5. Optical target mounted on fixed ceramic magnet

The targets were always mounted in the same orientation to ensure consistency between

readings and validate the zero reading for each girder. Vertical and horizontal angular

readings from the theodolite were made and recorded a total of four times for each of the

three targets (twice direct and twice reverse). This ensured that the angular readings were

accurate and allowed for corrections to the zenith readings due to possible circle

graduation errors inherent to the theodolite.







22

Using these angular readings and the known distances between the endpoint

targets and the target at midspan, the field camber could be calculated using a three-point

resection analysis (see Fig. 6).






















Figure 6. Isometric view of a three-point resection analysis

The resection procedure simply consists of a special case of triangulation. Using the

measured distances, "A" and "C", along with the measured angles; zeniths "A", "B" and

"C", and horizontal angles "X" and "Y", the relative vertical height of each target

(relative to the instrument) can be triangulated. By subtracting the average relative height

of the two endpoint targets from the relative height of the midspan target, we obtain the

camber of the beam.

Before the prestressing tendons were cut, a zero reading was made on each girder

to eliminate any systematic error inherent in the measuring process due to any surface

irregularities or differential target heights. Immediately after the release of the

prestressing force, measurements using the surveying technique where compared to those










measured directly off of the bed liner using a vernier caliper. The measurements using

the vernier caliper were taken as the actual values for the percent difference calculations.

The results are summarized in Table 1.

Table 1. Angular measurement technique accuracy
Surveying Direct Percent
Technique Measurement Difference Difference
Beam No. (in) (in) (in) (%)
FLBT 1 1.84 1.82 0.02 1.21%
FLBT 2 1.47 1.43 0.04 2.95%
FLBT 3 1.63 1.61 0.02 1.68%
FLBT 4 2.05 2.05 0.00 0.20%
FLBT 5 2.02 2.00 0.02 1.00%
FLBT 6 1.81 1.82 -0.01 -0.60%
TYPE IV 1 0.65 0.68 -0.03 -4.71%
TYPE IV 2 0.61 0.62 0.00 -0.65%
TYPE IV 3 0.67 0.64 0.03 3.91%

Although the accuracy of this method was acceptable, the actual field measurements were

time consuming and the process of calculating the camber from angular measurements

was very indirect. This method was used for the first four months of field measurements

after which it was determined that a quicker, more direct method could be employed

using a Pro-Level" water manometer.

The Pro-Level" water manometer is a surveying instrument which operates under

the principle that water in a U-shaped tube will equalize to the same relative elevation

due to the constant atmospheric pressure. The instrument's effective measuring

resolution is 0.05-inches, which makes the accuracy of the measurements within the

deliverable accuracy of 0.10-inches. The measuring system consists of an adjustable

water reservoir, a 100-ft vinyl hose, and a graduated measuring rod or stadia with an

adjustable length (see Fig. 7). The reservoir is placed in a fixed location and the height is

adjusted such that the meniscus reads somewhere near the middle of the stadia

graduations. The stadia is then positioned at each target and the relative height is











recorded to the nearest 0.05-inches. The camber is calculated by subtracting the average


relative height of the endpoint readings from the relative height of the midspan reading


(see Fig. 8). This instrument was used for the final three months of observations and was


the only method of measurement used on the AASHTO Type V prestressed girders.


Similarly, the measurements taken at release of these specimens using the Pro-Levelm


water manometer were compared to those measured directly off of the bed liner using a


vernier caliper to determine the accuracy.


Setuflrc Hdc_

U$pa Tnurrcb
Sciewv


Lowe Thrmb


COn-rd Stand
72" Tube


Ern COD


Pe,


Components of the PRO-LEVEL


Wit C Ccp "-'-=|
Veri t CdP TrMcspenird o

T | Ajustc


Cc* n.4ins >Ac4u



./Leg_ ii I ,kI I
Oil







/Leg Viny lHcc


Leg Thumb Screw





erv.:il STand Measuring Rod


2uttcn

-2A PCIl


Figure 7. Pro-LevelTM water manometer schematic (Source:
http://prolevel.com/operation.htm, Last accessed November 30, 2004).


1 I' :,i l







25


The measurements using the vernier caliper were taken as the actual values for the

percent difference calculations. These results are summarized in Table 2.

Table 2. Pro-LevelTM measurement technique accuracy

Direct Percent
Pro-LevelTM Measurement Difference Difference
Beam No. (in) (in) (in) (%)
TYPE V 1 0.85 0.82 0.03 3.66%
TYPE V 2 0.90 0.85 0.05 5.88%
TYPE V 3 0.85 0.85 0.00 0.00%
TYPE V 4 0.70 0.65 0.05 7.69%


tt/t t t Lve





















3.2 Thermal Gradient Measurement and Camber Correction
an infrared temperature sensor was used to measure the surface temperature of each
ABe *ReadinhgNin

Pecoc A21 A ittdna g

BeBteionDHefnBhen |









.nNO 2
Figure 8. Pro-LevelTM water manometer measurement technique (Source:
http://prolevel.com/operation.htm, Last accessed November 30, 2004)

3.2 Thermal Gradient Measurement and Camber Correction

To account for the influence of the thermal gradient on the camber measurements,

an infrared temperature sensor was used to measure the surface temperature of each

girder (Fig. 9). As shown in the example provided in Fig. 10 and in detail in Appendix B,

this was done at several points along the profile of the section at the midspan of the girder

coinciding with the time of the camber measurements.









S


i/ ~-











Figure 9. Infrared temperature sensor


In order to properly account for the effect of the thermal gradient, the surface

temperature profile and camber were measured three times on single days (i.e.,, the effect

of camber change relative to time since strand release was eliminated). This was done

twice for the first three 78-inch Florida Bulb-Tee girders and one time each for the

second three 78-inch Florida Bulb-Tee, AASHTO Type IV, and AASHTO Type V

girders. A sample of the single day thermal gradient readings for a 78-inch Florida Bulb-

Tee girder is shown in Fig. 10. The corresponding camber measurements for this girder

were 2.99 in. at 7:30 AM, 3.13 in. at 9:30 AM, and 3.65 in. at 12:30 PM. This clearly

indicates that the thermal gradient has a significant influence on camber. As discussed in

Section 2.7, an empirical method and an analytical method were investigated for

correcting the camber measurements to account for the thermal gradient.

The empirical method was based on approximating a linear thermal gradient over

the depth of the beam. The linear differential temperature used in the empirical method is

indicated by "A Temperature" shown in Fig. 10. This was calculated by subtracting the

average temperature of the bottom bulb from the average temperature of the top flange.












B 8 t T.. 13'- TA=1189 F
S-218 -

g T,. .. T 8
-38 - -
w T =84T=8
E Surface Temperature (deg F



















Cambers were also corrected using the analytical thermal analysis. Using the
II-48 - I---- I- I- L- 7

13, k --0--7:30 AM
-68 o 'D 85 F -- 9:30 AM
\ -A- 12:30 PM
)S( \ TE=85 'F --I -----
g -78 ,E-I (16)
70 75 80 85 90 95 100 105 110 115 120
Surface Temperature (deg F)

Figure 10: Example single day temperature profile of Bulb-Tee girder 3.

By determining the linear relationship between the change in thermal gradient and the

change in camber, a correction factor was established to account for the thermal gradient.

Details of the empirical method for correction of camber are presented in Appendix C.

Cambers were also corrected using the analytical thermal analysis. Using the

thermal coefficient of the concrete provided in Table 5 of NCHRP Report 276, the

mechanical properties of the concrete, and the section properties, the thermally induced

internal stresses due to the gradient can be determined. Assuming the thermal gradient

does not change alonngth th of the girder, a resisting internal moment can be

calculated by integrating these stresses over the depth of the girder. Then, the deflection

due to this moment can then be calculated using Equation 16 below.

Min L2
A therm ~ A. (16)


where:

Mnt = internal moment due to thermally induced
stresses (kip*in)

L = length of girder (in)










Ec = elastic modulus of concrete (ksi)

Ig = gross moment of inertia of girder (in4)

A MathCAD worksheet was developed for the analytical method and is presented in

Appendix D.

Table 3 presents the actual field measurements and the corrected cambers

resulting from both the empirical and analytical methods for the example shown in Fig.

10. Appendix B provides full information on all field measurements and the resulting

correction for both the empirical and analytical methods to account for the thermal

gradient.


Table 3. Example of tabularized field measurements and thermally corrected cambers.
78" Florida Bulb-Tee 3
CFthen = 0.0090 1/F
Top Bottom Bottom Empirical Analytical
Time After Field Flange Flange Web Top Bulb Bulb Corrected Corrected
Release Camber Temp Temp Temp Temp Temp AT Camber Camber
Date Time (Days) (in) (oF) (oF) (oF) (oF) (oF) (oF) (in) (in)
6/7/2004 7:30 AM 58.98 2.99 78 73 75 74 75 1 2.96 2.97
6/7/2004 9:30AM 59.06 3.13 91 75 74 76 78 6 2.96 2.98
6/7/2004 12:30 PM 59.19 3.65 118 103 84 85 85 25.5 2.81 2.79

As indicated by the example shown in Table 4 and by Appendix B, there is an

insignificant difference between the corrected cambers for thermal gradient using the

empirical method and the analytical method. Since the analytical method, based on

NCHRP Report 276, better represents the actual camber changes caused by the thermal

gradient, the corrections resulting from this method were used for developing camber

versus time relationships. The empirical method would appear to be appropriate for

future use in field applications where the detailed analytical method is not available.

In addition to measuring the surface temperature of the girder at the time of each

camber reading, data regarding ambient conditions was also collected from a nearby

weather station operated by the University of Florida Institute of Food and Agricultural









Sciences, or IFAS. The data collected included the ambient temperature at 60-cm and at

200-cm, the relative humidity, and the solar radiation all collected in one hour intervals

throughout the day. The weather station data was taken from a unit located in Tavares,

Florida (approximately 5 miles from the storage facility). This data is presented in

Appendix E.

3.3 Supplemental Material Testing

The field camber measurements were supplemented with periodic material testing

in order to obtain a time relationship with both the actual compressive strength and the

elastic modulus of the concrete used in the girders. These cylinders were stripped of their

molds once the forms were removed from the girders. They were then stored near the

girders and "field cured" under the same conditions as the girders (see Fig. 11).

















Figure 11. Field cured 4"x 8" concrete test cylinders.

This ensured that when the cylinders were tested, the results would provide an accurate

representation of the actual concrete material properties of the girders. A series of three

4-inch x 8-inch cylinders were used for each test. The cylinders were tested in a

computerized MTS testing apparatus in accordance with ASTM C39-96 and ASTM









C469-94. The elastic modulus was obtained using the strain measurements from two

MTS extensometers connected to a computerized data acquisition system in conjunction

with the load data from the load cell (see Fig. 12).

















Figure 12. Computerized MTS concrete cylinder testing apparatus.

The tests were made approximately every seven days until 28-days after the prestressing

tendons were cut. Subsequently, the cylinders were tested more sparsely to show the

long-term behavior of the concrete compressive strength and elastic modulus. The elastic

modulus was obtained four different ways:

1. A linear regression of the stress-strain data.

2. The outlined procedure in ASTM C469-94 (Equation 17).


E- 2 (17)
2 1

where:

ao = stress at 500-microstrain (psi)

o2 = 40% off'c (psi)

e1 = 500-microstrain (E)









E2 = strain at 40% off' (8)


3. The empirical relationship given by ACI318 02, section 8.5.1 (Equation 18);

Ec =w 5* 331f-C (18)

where:

wc = unit weight of the concrete (pcf)

fc = compressive strength of the concrete (psi).


4. The empirical relationship given by AASHTO LRFD Bridge Design Specification
in section C5.4.2.4 (Equation 19).

E =1820. -f (19)

where:

fc = compressive strength of the concrete (ksi).

The results of those four methods for determining the modulus of elasticity are presented

in Appendix G.















CHAPTER 4
SUMMARY OF RESULTS

4.1 Camber Measurement at Release

The camber measurements taken after the girders had been relocated to the

storage area of the precast yard were generally larger that those measurements taken

immediately after the release of the prestress force. The increase in camber from release

to relocation for the each prestressed girder is illustrated in Figs. 13 through 15. The

camber values shown in these figures have been analytically corrected for thermal

gradient effects as discussed Section 3.2. The increase in camber after removal from the

casting beds is most likely due to the horizontal restraint at the endpoints of the girder

provided by the frictional force between the girder and the bed liner at transfer. One

would surmise this effect to be more pronounced in heavier beams with larger span-to-

depth ratios. This is clearly shown in Fig. 13 for the 162 ft. 78-inch Florida Bulb-Tee

girders. Fig. 14 also indicates a very substantial change for the 91 ft. Type IV girders.

The substantial increase in camber from transfer to relocation for the AASHTO

Type IV girders could have been affected by the procedure used for relocation of these

girders. A permanent storage location was unavailable after the prestressing tendons had

been cut so the girders were temporarily stored upon dunnage next to the casting bed

until some space could be freed. As indicated in Appendix B, two hours elapsed from the

camber measurement at the time of transfer and the camber measurement after the beams

were stored. This is comparable to the three hours for 78-inch Bulb-Tee girders 1-3, two











and one-half hours for 78-inch Bulb-Tees 4-6, and one hour for the AAHSTO Type V


girders. A comparison of the span-to-depth ratio of the AASHTO Type IV girders versus


that of the 78-inch Bulb-Tee girders indicates that these values are close suggesting that


perhaps the AASHTO Type IV girders are subject to a frictional restraining force at


transfer as well. For tabulated values of the camber at release versus the camber after


moving including percent increase calculations, refer to Appendix A.


4.0
FDOT Predicted Camber
3.5 FDOT Predicted Camber
3-. ---- - -----------------
3.0

2.5

2.0
E
O 1.5

1.0

0.5

0.0
1 2 3 4 5 6
Beam ID

After Moving E At Release

Figure 13. Bar chart of 78" Bulb-Tee camber at release, after moving, and FDOT
predicted values.












4.0

3.5

3.0

2.5

. 2.0
E FDOT Predicted Camber
O 1.5

1.0 -

0.5

0.0
1 2 3
Beam ID

After Moving At Release

Figure 14. Bar chart of AASHTO Type IV camber at release, after moving, and
FDOT predicted values.

4.0

3.5

3.0

2.5

. 2.0
E FDOT Predicted Camber
0 1.5

1.0

0.5

0.0
1 2 3 4
Beam ID

After Moving At Release

Figure 15. Bar chart of AASHTO Type V camber at release, after moving, and
FDOT predicted values.









4.2 Camber Measurement Summary

The field camber measurements made on the 78-inch Bulb-Tee girders were on

the order of 55-percent that of the predicted values--obtained from the Eng LFRD

PSBeam v.1.85 program--within the first few weeks of measurements to about 35-percent

of the predicted values near the end of data collection. The program generally

overestimated the time-dependent camber growth. The field camber measurements for

each 78-inch Bulb-Tee girder and the predicted values using the Eng LFRD PSBeam

v.1.85 design program are presented below in Fig. 17 through Fig. 23. The estimated

camber values for each girder obtained using the design program were calculated using:

1. The specified 28-day compressive strength and the AASHTO empirically
calculated elastic moduli (at release and at 28-days).

2. The measured 28-day compressive strength and the measured elastic moduli (at
release and at 28-days).

The temperature corrected camber values were calculated using the analytical thermal

analysis.

The method employed by the Eng LFRD PSBeam v.1.85 design program

produced camber estimates that exceeded the 78-inch Bulb-Tee girder field

measurements by as much as 180-percent. For this reason, it is suggested that the method

described in section 2.4 for the time-dependent camber estimate be used in place of the

current method. A MathCAD worksheet, incorporating the use of the LRFD refined

prestress loss calculation method described in section 2.5, the LRFD creep coefficient

calculation described in section 2.6, and Nilson's camber calculation method described in

section 2.4, can be found in Appendix H. A comparison between the mean interpolated

field measurements, the predicted values taken from Eng LFRD PSBeam v.1.85, and the









predicted values using this recommended method for the 78-inch Bulb-Tee girder using

the actual tested material properties is given in Table 4. For the percent difference

calculation, the field camber was taken as the actual value.

Table 4. Comparison of field measured camber to predicted camber.

Mean Mean
Time Interpolated FDOT
After Field Predicted % Recommended %
Transfer Camber Camber Difference Method Difference
(day) (in) (in) (%) (in) (%)
0 1.80 3.44 90.7% 1.92 6.65%
30 3.00 5.95 98.6% 2.95 -1.47%
60 3.04 6.88 126% 3.35 9.99%
120 3.07 8.02 161 % 3.83 24.8%
200 3.10 8.66 179% 4.34 39.8%

The field camber measurements made on the AASHTO Type IV girders were

very close to the predicted values--obtained from the Eng LFRD PSBeam v.1.85

program--within the first few weeks of measurements. Then, the field measured values

began to diverge from the predicted values, becoming about 50-percent of the predicted

values near the end of data collection. These girders were properly stored upon dunnage,

but were left with little clearance between the ground and the bottom flange unlike the

other types of girders which were stored with about 18-inches of clearance between the

ground and the bottom flange. In addition, vegetation growth surrounded the bottom

flange and the girders were stored with little space in-between. The lack of ventilation

surrounding the bottom flange could have caused more water to be trapped, thus creating

a condition of differential shrinkage, and causing long-term effects (such as creep and

shrinkage) to be less pronounced resulting in lower camber. Figure 16 shows the storage

of the AASHTO Type IV girders. The field camber measurements for each AAHSTO

Type IV girder and the predicted values using the Eng LFRD PSBeam v.1.85 design

program are presented in Fig. 24 through Fig. 27.







































Figure 16. AASHTO Type IV girder in storage.


9.0
-----------------------------------------------------------------------------------------------






6.0-



4 .0 --- 1^ -1 L I- 1- L -I L I -- L --- L -- -- -- --- -- -- 1 -1
.0 I I I
8.0





o I It I^ I I l 1 I) C )l i i A i i i

S.0 i i --- --- --- -- i i -
2.0 r-- - A Temperature Corrected

1.0 ____ -+-FDOTSpec.fc&CompE
-x- FDOT Actual fc & Actual E
0.0

T i me(Da Os) ) 0 J i i O
Time (Days)


Figure 17. Field camber measurements for 78" Bulb-Tee girder 1.
















9.0


8.0


7.0


6.0


5.0


E 4.0


3.0


1.0


Time (Days)


Figure 18. Field camber measurements for 78" Bulb-Tee girder 2.






---------
- - - --- - - I- - -- - -
I I I I I I I I I I I I I I I I I
l l l l l l l l l l l l l l l l l l l


A I I I 4
I I I --I-
Ai~


S I I


Field Data

A Temperature Corrected

S---- FDOT Spec. fc & Comp E

-x- FDOT Actual fc & Actual E


~ Cl I' ( 0 (4 0 J 0 (- 0) -J (0

Time (Days)


Figure 19. Field camber measurements for 78" Bulb-Tee girder 3.


---



-,-r
S- I - --- -------








-- t


+ Field Data

A Temperature Corrected

i FDOT Spec. f c & Comp E
-- FDOT Actual fc & Actual E-
FDOT Actual fc & Actual E
i r i i i i i i i i















!l---- FDOT Actual f'c & Actual E


9.0


8.0


7.0


6.0


5.0
a) -


. 4.0


3.0


2.0


1.0


00nn


S// I i i


.~















9.0


8.0


7.0


6.0


5.0


S4.0


3.0


2.0


1.0


0.0


0 7 14 21 28 35 42 49 56 63 70 77 84 91 98 105 112 119
Time (Days)


Figure 20. Field camber measurements for 78" Bulb-Tee girder 4.


9.0


8.0


7.0


6.0


5.0


S4.0


3.0


2.0


1.0


nn


0 7 14 21 28 35 42 49 56 63 70 77 84 91 98 105 112 119
Time (Days)


Figure 21. Field camber measurements for 78" Bulb-Tee girder 5.


I -- t I I





-- ---- ---------







A \* Field Data

A Temperature Corrected

S-+- FDOT Spec.fc& Comp E

-x- FDOT Actual fc & Actual E
I

I










t IDO Icua c I I I


-A -- -

Field Data

A Temperature Corrected

-- FDOT Spec. fc & Comp E

FDOT Actual fc & Actual E
I I I '" II I


0.

























6.0


5.0


E 4.0


3.0


2.0


1.0


0.0


0 7 14 21 28 35 42 49 56 63 70 77
Time (Days)


84 91 98 105 112 119


Figure 22. Field camber measurements for 78" Bulb-Tee girder 6.


8.0


7.0


6.0


5.0


4.0
0.


o 4 -. ) ) ~ A Ci 0 4 C


Time (Days)


A Corrected Camber

-+- FDOT Spec. fc& Comp E

-- FDOT Actual fc & Actual E


ID 0I I O I A -I CO CI N) (0 0)


Figure 23. Summary of field camber measurements for all 78" Bulb-Tee girders.


I-- ------ ---- -




-


-r
I I

I I -. L I ---II- L -- ----




Field Data

a Temperature Corrected

-I+- FDOT Spec. fc & Comp E

-x- FDOT Actual fc & Actual E


Aa
A ~ A A. A- -


I I-


-1----
i-
----r-




























2.0
E

1.5


1.0


0.5


0.0


0 7 14 21 28 35 42 49 56 63 70 77 84 91 98 105 112
Time (Days)


Figure 24. Field camber measurements for AASHTO Type IV girder 1.


0 7 14 21 28 35 42 49 56 63 70 77 84 91 98 105 112
Time (Days)


Figure 25. Field camber measurements for AASHTO Type IV girder 2.


* Field Data

A Temperature Corrected

-- FDOT Spec. fc & Calculated E __ __
-0--FDOActal-c-&ctu---a-l-
--FDOT Actual fc & Actual E -
L___ L L---x- _-1--- -






1t I I4 1 I I
I I A I 0 1 II I
L I I I I I


3.5 1


* Field Data

A Temperature Corrected

- FDOT Spec. fc & Calculated E -

- FDOT Actual fc & Actual E -x
L L --- -- ;s -- L -


4x I II I I


2.0
E

1.5


1.0














4.0


3.5


3.0


2.5


S2.0
E

1.5


1.0


0.5


0.0








4.0


3.5


3.0


2.5


S 2.0
E

1.5


1.0


0.5


0.0


0 7 14 21 28 35 42 49 56 63 70 77 84 91 98 105 112
Time (Days)


Figure 26. Field camber measurements for AASHTO Type IV girder 3.


0 7 14 21 28 35 42 49 56 63 70 77 84 91 98 105 112
Time (Days)



Figure 27. Summary of field camber measurements for all AASHTO Type IV girders.



The AASHTO Type V girders observed for this investigation were monitored for



28-days past the release of the prestress force. During this period, the field camber



measurements adhered very closely to the predicted values obtained from the Eng LFRD



PSBeam v.1.85 program. The 30-day predicted camber from the design program was


* Field Data

A Temperature Corrected

--- FDOT Spec.fc& Calculated E -- -_.--
-0-- T Actal-fc -Actu---a-l-
-*-FDOT Actual fc & Actual E -x----- -
I --.--. -,




-- I I I
a --

t t^ t t A
r r r r rr


A Corrected Camber

-x- FDOT Spec. fc & Calculated E

--- FDOT Actual fc & Actual E E _-- --

I- - -I-I-I-I- I
^ "r""'^ ^ ^ ------- '




I I A I IA I I I
A AlI I I I I I I

/ *F F F l F r
^< I :; I *
L L__ _ _ _ _ _ _ _ _ ^ ^ ^ ^ ^ _








43


essentially the same as that measured in the field. The field camber measurements for


each AAHSTO Type IV girder and the predicted values using the Eng LFRD PSBeam


v.1.85 design program are presented in Fig. 28 through Fig. 32. For a tabular summary of


the field camber measurements including empirically and analytically corrected values as


well as surface temperature values, refer to Appendix B.


2.0



1.5


0.5 +


Time (Days)

Figure 28. Field camber measurements for AASHTO Type V girder 1.


* Field Data

A Temperature Corrected

- FDOT "Spec fc & Comp E"

SFDOT "Act fc & Act E"
S- ------


I -------"'-- a -------------









44



2.5

Field Data

A Temperature Corrected
2.0
FDOT "Spec fc & Comp E"

-- FDOT "Act fc & Act E"
- 1.5



1.0





0.5




0.0
0 7 14 21 28
Time (Days)


Figure 29. Field camber measurements for AASHTO Type V girder 2.


2.5

Field Data

A Temperature Corrected
2.0
FDOT "Spec fc & Calc E"

--- FDOT "Act fc & Act E"
- 1.5


1.0 -





0.5




0.0
0 7 14 21 28
Time (Days)


Figure 30. Field camber measurements for AASHTO Type V girder 3.




































0 7 14 21 2Z
Time (Days)


Figure 31. Field camber measurements for AASHTO Type V girder 4.


2.0



1.5


0.5


Time (Days)


Figure 32. Summary of field camber measurements for all AASHTO Type V girders.



4.3 Supplemental Material Testing Summary


The supplemental material testing was performed periodically in conjunction with


the field camber measurements in order to observe the relationship between the actual


material properties and the time-dependent camber growth. Cylinders were made for


Field Data

A Temperature Corrected

FDOT "Spec fc & Calc E"

-x- FDOT "Act fc & Act E"


-------------- __ ------
------------
- -


A Corrected Camber

-FDOT "Spec fc & Calc E"

-x- FDOT "Act fc & Act E"




-------------------------------- --------------------------------


- ----- - -









each pour of the girders being observed for this investigation. The six 78-inch Bulb-Tee

girders were produced in two pours, the three AASHTO Type IV girders were produced

in one, and the four AASHTO Type V girders were produced in two. Each series of test

cylinders is identified by the type of girder and a letter representing which pour they were

made from. For example, the test cylinders made from the first pour of 78-inch Bulb-Tee

girders is identified with the letter "A." A table summarizing which pours represent

which girders is given in Table 5. The material tests were performed each week for the

first 28-days and were then tested more sparsely thereafter in order to obtain a long-term

model of the compressive strength and elastic modulus growth.

Table 5. Girder pour identification summary.

Pour A Pour B
78" Florida Bulb-Tee Girders 1-3 Girders 4-6
AASHTO Type IV Girders 1-3
AASHTO Type V Girders 1-2 Girders 3-4

In addition to the three 4-inch x 8-inch cylinders used for each test, a series of three 6-

inch x 12-inch cylinders were also tested on a few occasions for comparison. The

compressive strength and elastic modulus tests for the 6-inch x 12-inch cylinders were

performed by the Florida Department of Transportation Materials office in Gainesville,

Florida. Material data from the 6-inch x 12-inch cylinders was obtained for the 78-inch

Bulb-Tee girders and the AASHTO Type IV girders. Because there was little discernable

difference between the results of the 4-inch x 8-inch cylinder tests and the 6-inch x 12-

inch cylinder tests, it was decided that testing of only the 4-inch x 8-inch cylinder

specimens for the AASHTO Type V girders would be adequate. Graphic representations

of the compressive strength and the elastic modulus, obtained using the linear regression







47


analysis, are presented in the figures below. For the tabularized version of the materials

testing summary refer to Appendix G. For the mix design of each pour, refer to

Appendix F. Graphical representations of the results of the supplemental materials

testing are as follows:

The results of the material tests for pours "A" and "B" of the 78-inch Bulb-Tee
girders for both the 4-inch x 8-inch cylinder specimens and the 6-inch x 12-inch
cylinder specimens are summarized in Fig. 33 through Fig. 36.

The results of the material tests for pour "A" of the AASHTO Type IV girders for
both the 4-inch x 8-inch cylinder specimens and the 6-inch x 12-inch cylinder
specimens are summarized in Fig. 37 and Fig. 38.

The results of the material tests for pours "A" and "B" of the AASHTO Type V
girders for the 4-inch x 8-inch cylinder specimens are summarized in Fig. 39
through Fig. 42.

12000


10000 -


8000


6000

U)
4000
C.
E
a
S2000 --*-4-inch x 8-inch Cylinder
-*-6-inch x 12-inch Cylinder
0
o -4 K K) CJ P -Ph C i -4 -- -0 -C -C -. -. -. -. -. -. -. -. -. -
0 -. K (f M CD O CJ 0D -4 ^ 00 D 0 K -. M -Ph 0) 0) O -4 00 W WD 0
C" M CD OW CD -0 W a M "D Oc 0ca
Time After Casting (days)


Figure 33. 78" Bulb-Tee pour "A" compressive strength vs. time.












7000


6000


S5000


4000
0
S3000


L 2000


1000


0


Time After Casting (days)


Figure 34. 78" Bulb-Tee pour "A" elastic modulus vs. time.


10000

9000

8000

7000

6000

5000

4000

3000

2000

1000

0


0 7 14 21 28 35 42 49 56 63 70 77
Time (days)


-*-4-inch x 8-inch Cylinder
- 6-inch x 12-inch Cylinder


84 91 98 105 112 119 126


Figure 35. 78" Bulb-Tee pour "B" compressive strength vs. time.


--4-inch x 8-inch Cylinder

-*-6-inch x 12-inch Cylinder












6000


5000 I


4000
in

o 3000
S3000 ---- ---------- --- ---- -- ---T- -


S2000


1000 -- --- 4-inch x 8-inch Cylinder
--6-inch x 12-inch Cylinder

0
0 7 14 21 28 35 42 49 56 63 70 77 84 91 98 105 112 119 126
Time (days)


Figure 36. 78" Bulb-Tee pour "B" elastic modulus vs. time.

10000

9000

8000
7000 --- ---+ ---- ------- ------ ^-- ^ -,-- ---- -- '-- -- -- -- -- --- ---

6= 000 T- -T F T -/ -1- - ^ ^ - ^ - -
c 7000

6000 /



4000

C- 3000
E
U 2000
| -*-4-inch x 8-inch Cylinder
1000 - -6-inch x 12-inch Cylinder
1 0 0 0 - - - -







0
0 7 14 21 28 35 42 49 56 63 70 77 84 91 98 105 112 119 126 133 140
Time After Casting (days)


Figure 37. AASHTO Type IV pour "A" compressive strength vs. time.












7000


6000


' 5000


4000
0
3000


i 2000--- -- -


1000 I 4-inch x 8-inch Cylinder
-*-6-inch x 12-inch Cylinder
0
0 7 14 21 28 35 42 49 56 63 70 77 84 91 98 105 112 119 126 133 140
Time After Casting (days)


Figure 38. AASHTO Type IV pour "A" elastic modulus vs. time.

10000
90000 -------------------------------------------------------------
9000

8000 -----------

7000--

6000 --- -- i L

5000 -

In 4000 -

0. 3000 --
E
- 2000 ------ ------

1000 -
100 ^------------------ ------------------------------
0
0 7 14 21 28 35
Time After Casting (days)


Figure 39. AASHTO Type V pour "A" compressive strength vs. time.












6000


5000


4000


3000


2000


1000


0


7 14 21 28
Time After Casting (days)


Figure 40. AASHTO Type V pour "A" elastic modulus vs. time.


9000

8000

7000

6000

5000

4000

3000

2000

1000

0


0 7 14 21 28
Time After Casting (days)


Figure 41. AASHTO Type V pour "B" compressive strength vs. time.












6000


5000 --

i I
4000 ----


3000 -


2000 -


1000 -


0
0 7 14 21 28
Time After Casting (days)


Figure 42. AASHTO Type V pour "B" elastic modulus vs. time.









4.4 Florida Limerock Specimens

In addition to the specimens using granite as a coarse aggregate, several

specimens using Florida Limerock as a coarse aggregate were also investigated to

determine the effects of the type of coarse aggregate content on long-term camber

growth. The camber for these specimens was obtained from the prestressing yard

inspection records and not from actual measurements performed using the procedures

discussed in Chapter 3. These documented measurements were obtained for for:

Ten (10) AASHTO Type IV girders were 95-feet in length with thirty-seven (37)
0.6"-diameter, 270-ksi, "Lo-Lax" prestressing strands, and used FDOT Class VI
coarse limerock aggregate concrete with a specified 28-day compressive strength
of 8,500-psi.

Eight (8) 72-inch Florida Bulb-Tee girders were 129-feet in length with fourty
(40) 0.6"-diameter, 270-ksi, "Lo-Lax" prestressing strands, and used FDOT Class
VI coarse limerock aggregate concrete with a specified 28-day compressive
strength of 8,500-psi.

The measured field cambers for these specimens were compared to the predicted values

obtained using the Eng LFRD PSBeam v.1.85 design program. Detailed information on

the data obtained from the prestressing yard records is provided in Appendix I.

4.4.1 Camber Measurement at Release

The average initial camber measurement for the ten AASHTO Type IV girders

and the eight 72-inch Florida Bulb-Tee girders fabricated using Florida Limerock as the

coarse aggregate are shown in Fig. 43. It should be noted that the initial camber

measurements where performed while the girders were in the forms and that no camber

measurement was made after moving the girders to their storage location. As shown in

Fig. 13 and Fig. 43 the initial camber for the Florida Bulb-Tee sections was much closer

to that expected when using Florida Limerock as the coarse aggregate.














FDOT Predicted Camber
- -


FDOT Predicted Camber


0.0
Beam ID

*AASHTO Type IV 772" Bulb-Tee



Figure 43. Limerock 72" Bulb-Tee and AASHTO Type IV camber at release.











4.4.2 Camber Measurement Summary

The time-dependent camber growth for the 72-inch Bulb-Tee girders and the

AASHTO Type IV girders, both using Florida Limerock as a coarse aggregate, can be

seen in Fig. 44 and Fig 45, respectfully. The predicted values from the design program

were produced using the actual tested material properties given in Appendix I.


0 N) -4 M C) CW) C) C) C)
W N) 0 -4 W) NM W) 0 -W 0) M ) 0 -^ 0) N) O 0 -n
Time after Transfer (days)

Figure 44. 72" Bulb-Tee (Limerock) girder camber growth summary.











8.00

7.00

6.00

S5.00

S4.00 --------------- --- -- -- ------------------------------

0 3.00 -
2 .00 _^ ^ -- ------------------ ---------------- ------------ FedC m e
2.00 Field Camber

1.00 --FDOT
1.00 ------------ --------

0.00
0 14 28 42 56
Time after Transfer (days)

Figure 45. AASHTO Type IV (Limerock) girder camber growth summary.


This comparison is illustrated graphically for the AASHTO Type IV girders in

Fig 46 and presented in tabular form in Table 6. From this figure, it can be stated that the

type of coarse aggregate has an effect on the long-term behavior of these prestressed

girders. The design program overestimates the long-term camber by as much as 70% for

the girders using granite as a coarse aggregate, but only 20% for the girders using Florida

Limerock as a coarse aggregate.


Table 6. Tabular comparison of predicted and actual camber values for Limerock and
granite specimens of the AASHTO Type IV girder.
Limerock Specimens Granite Specimens
(A) (B) (A) (B)
Time FDOT Time FDOT
Field Field
After Predicted After Predicted
Camber Camber
Transfer Camber Difference Transfer Camber Difference
(days) n) (in) (B/A) (days) n) (in) (B/A)
0 2.35 2.70 1.15 0 0.64 1.13 1.77
30 3.976 4.67 1.17 0 1.02 1.13 1.10
60 4.257 5.39 1.27 30 1.147 1.96 1.71
60 1.34 2.27 1.69












2.0

1.8
S-----------------
1.6

1.4
w 1.2 7_ -. - -
-- -I
1.0

P 0.8

0.6

0.4 -- Limerock Specimens
Granite Specimens
0.2
--FDOT
0.0
0 14 28 42 56 70
Time After Casting (days)

Figure 46. Comparison of predicted camber to actual field camber for granite and
limerock specimens of AASHTO Type IV girder.


For the 72-inch Florida Bulb-Tee girders, comparisons were made to the predicted


values from the Eng LFRD PSBeam v.1.85 design program and the recommended


approach given by Equation 2 at 240-days after the transfer.


Table 7. Comparison of field measured camber to predicted camber at 240 days for
Bulb-Tee girders.

Mean
Interpolated Mean
Field FDOT % Recommended %
Camber Camber Difference Method Difference
(in) (in) (%) (in) (%)

Granite 3.10 9.29 199% 4.34 40.0%

Limerock 4.88 7.81 59.9% 3.48 -29.7%















CHAPTER 5
CONCLUSIONS AND RECCOMENDATIONS


The conclusions and recommendations presented in this thesis are based upon the

data collected during this project, analysis of this data, and previous research literature a

propos this project.

The camber increase with time was less than what was estimated for the 162 ft.
78-inch Florida Bulb-Tees and the 91 ft. AASHTO Type IV girders. It is
suggested that the FDOT LFRD PSBeam v.1.85 design program be modified to
account for this. One possible approach would be the use of the time-dependent
creep coefficient given by Section 5.4.2.3.2 of the AASHTO LRFD Bridge Design
Specification. This creep coefficient should not only be applied to the camber due
to the long-term loading of to the prestress force, but it should also be applied to
the deflection associated with the long-term loading due to the self-weight of the
member. This can be done using the relationship proposed by Nilson in Eq. 2.
Refer to Appendix H for example calculations showing this method.

For the influence of the thermal gradient on camber, there was little difference
between the empirically corrected camber measurements and the analytically
corrected camber measurements in the majority of cases. Either method is
suitable for the correction of camber due to thermal gradient effects.

Both the AASHTO and the ACI methods for calculating the elastic modulus were
fairly accurate for the 78-inch Bulb-Tee specimens for which an FDOT Class VI
concrete was used, and also for the AASHTO Type IV and AASHTO Type V
specimens for which an FDOT Class IV concrete was used.

Guidelines for storage of the girders with instruction of the amount of clearance
necessary between the ground and bottom flange should be implemented in order
to reduce the effect of differential shrinkage in the field.

Further investigation should be done with reference to the increase in camber
from immediately after transfer to when the girders have been relocated to
storage. This effect was consistently the most pronounced in heavy girders with a
large span to depth ratio.







59

* Further investigation should be done on the effect of aggregate type on the long-
term camber growth in prestressed girders to determine whether it is one of the
possible causes for the discrepancy between the predicted and actual camber
values.

















APPENDIX A
CAMBER AT RELEASE


1 Note: Cambers are analytically corrected for thermal effects.


78" Bulb-Tee Girders
FDOT Camber
Predicted Camber At After Camber Percent
Camber* Transfer Moving Increase Increase
Beam ID (in) (in) (in) (in) (%)
1 3.57 1.84 2.30 0.46 24.77%
2 3.57 1.47 2.03 0.56 38.07%
3 3.57 1.63 2.13 0.50 30.81%
4 3.31 2.05 2.57 0.51 24.98%
5 3.31 2.02 2.37 0.35 17.23%
6 3.31 1.81 2.25 0.44 24.49%
AASHTO Type IV Girders
FDOT Camber
Predicted Camber At After Camber Percent
Camber* Transfer Moving Increase Increase
Beam ID (in) (in) (in) (in) (%)
1 1.13 0.65 1.18 0.53 81.94%
2 1.13 0.61 0.90 0.29 46.64%
3 1.13 0.67 1.00 0.33 49.77%
AASHTO Type V Girders
FDOT Camber
Predicted Camber At After Camber Percent
Camber* Transfer Moving Increase Increase
Beam ID (in) (in) (in) (in) (%)
1 0.65 0.85 0.88 0.03 4.00%
2 0.65 0.90 0.87 -0.04 -3.89%
3 0.67 0.85 0.98 0.13 15.65%
4 0.67 0.70 0.67 -0.03 -4.00%
*FDOT predicted camber values based on actual tested material properties.






















APPENDIX B
FIELD CAMBER MEASUREMENTS


78" Florida Bulb-Tee 1
CFtherm = 0.0055 1/oF


Time


Time After
Release
(Days)


4/9/2004 8:00 AM 0.00
4/9/2004 11:00 AM 0.13
4/16/2004 12:00PM 7.17
4/23/2004 10:00 AM 14.08
4/23/2004 12:00 PM 14.17
4/23/2004 2:00 PM 14.25
4/29/2004 11:00 AM 20.13
5/7/2004 11:00 AM 28.13


5/21/2004 11:00AM 42.13 3.73
6/7/2004 7:30 AM 58.98 3.57
6/7/2004 9:30 AM 59.06 3.68


Top Bottom Top Bottom Empirical
Field Flange Flange Web Bulb Bulb Corrected
Camber Temp Temp Temp Temp Temp AT Camber
(in) (oF) (F) (F) (F) (oF) (oF) (in)
1.8411 1.84
2.43 2.30
3.66 3.36
3.33 3.18
3.61 3.31
3.87 3.44
3.51 91 78 74 74 74 10.5 3.30
3.64 93 78 74 74 74 11.5 3.41


- 4 4- 4


3.57


Analytical
Corrected
Camber
(in)
1.84
2.30
3.36
3.18
3.31
3.44
3.18
3.29


II A t


3.68


3.57


3.68


6/7/2004 12:30 PM 59.19 3.98 117 99 83 86 86 22 3.50 3.26
6/17/2004 11:00 AM 69.13 3.83 99 86 83 83 82 10 3.62 3.52
7/2/2004 11:00 AM 84.125 3.81 104 90 86 86 85 11.5 3.57 3.45
7/14/2004 11:00 AM 96.125 3.71 104 94 87 89 86 11.5 3.48 3.34
7/21/2004 12:00 PM 103.16667 3.89 100 90 82 84 81 12.5 3.62 3.62
7/28/2004 9:00 AM 110.04167 3.33 97 90 86 88 85 7 3.20 3.11
8/11/2004 7:00 AM 123.96 3.25 81 79 82 83 81 0 3.25 3.25
8/11/2004 10:00 AM 124.08 3.48 100 88 85 86 84 9 3.30 3.20
8/11/2004 12:00 PM 124.17 3.90 110 97 88 87 87 16.5 3.55 3.36
8/24/2004 10:00 AM 137.08333 3.50 97 86 84 84 83 8 3.35 3.26
9/9/2004 10:00 AM 153.08333 3.38 88 82 82 82 81 3.5 3.31 3.28
9/21/2004 10:00 AM 165.08333 3.28 72 73 74 74 75 0 3.28 3.28
10/5/2004 9:00 AM 179.04167 3.25 82 79 81 81 79 0.5 3.24 3.25
10/26/2004 9:00 AM 200.04167 3.18 70 69 74 73 69 0 3.18 3.18












78" Florida Bulb-Tee 2
CFthem = 0.0088 1/F

Top Bottom Top Bottom Empirical Analytical
Time After Field Flange Flange Web Bulb Bulb Corrected Corrected
Release Camber Temp Temp Temp Temp Temp AT Camber Camber
Date Time (Days) (in) (oF) (oF) (oF) (oF) (oF) (oF) (in) (in)
4/9/2004 8:00 AM 0.00 1.47 1.47 1.47
4/9/2004 11:00AM 0.13 2.22 2.03 2.03
4/16/2004 12:00 PM 7.17 3.62 3.14 3.14
4/23/2004 10:00AM 14.08 3.05 2.84 2.84
4/23/2004 12:00 PM 14.17 3.46 3.01 3.01
4/23/2004 2:00 PM 14.2 3.81 3.14 3.14
4/29/2004 11:00 AM 20.13 3.38 97 79 75 74 73 14.5 2.95 2.93
5/7/2004 11:00 AM 28.13 3.63 100 85 79 78 78 14.5 3.17 3.16
5/21/2004 11:00 AM 42.13 3.74 92 80 76 75 74 11.5 3.36 3.37
6/7/2004 7:30 AM 58.98 3.44 75 72 75 74 77 0 3.44 3.44
6/7/2004 9:30 AM 59.06 3.73 94 80 79 80 77 8.5 3.45 3.48
6/7/2004 12:30 PM 59.19 4.06 119 104 88 89 86 24 3.20 3.26
6/17/2004 11:00 AM 69.13 3.49 106 94 90 88 86 13 3.09 3.07
7/2/2004 11:00 AM 84.125 3.92 109 95 89 90 86 14 3.44 3.48
7/14/2004 11:00 AM 96.125 3.93 108 92 89 89 86 12.5 3.50 3.55
7/28/2004 9:00 AM 110.04167 3.63 98 90 86 88 85 7.5 3.39 3.39
8/11/2004 7:00 AM 123.96 3.35 81 79 82 83 81 0 3.35 3.35
8/11/2004 10:00 AM 124.08 3.63 101 89 85 85 84 10.5 3.29 3.30
8/11/2004 12:00 PM 124.17 3.98 110 95 88 87 86 16 3.42 3.46
8/24/2004 10:00 AM 137.08333 3.70 100 86 82 82 82 11 3.34 3.36
9/9/2004 10:00 AM 153.08333 3.63 89 82 82 81 82 4 3.50 3.51
9/21/2004 10:00 AM 165.08333 3.40 72 73 74 74 75 0 3.40 3.40
10/5/2004 9:00 AM 179.04167 3.35 80 78 81 80 79 0 3.35 3.35
10/26/2004 9:00 AM 200.04167 3.28 70 69 73 72 69 0 3.28 3.28
78" Florida Bulb-Tee 3
CFthen = 0.0090 1/F

Top Bottom Top Bottom Empirical Analytical
Time After Field Flange Flange Web Bulb Bulb Corrected Corrected
Release Camber Temp Temp Temp Temp Temp AT Camber Camber
Date Time (Days) (in) (oF) (oF) (oF) (oF) (oF) (oF) (in) (in)
4/9/2004 8:00 AM 0.00 1.63 1.63 1.63
4/9/2004 11:00AM 0.13 2.35 2.13 2.13
4/16/2004 12:00 PM 7.17 3.25 2.81 2.81
4/23/2004 10:00 AM 14.08 3.05 2.83 2.83
4/23/2004 12:00 PM 14.17 3.2 2.82 2.82
4/23/2004 2:00 PM 14.2 3.52 2.88 2.88
4/29/2004 11:00 AM 20.13 3.28 94 80 76 75 74 12.5 2.91 2.88
5/7/2004 11:00 AM 28.13 3.45 102 89 80 78 78 17.5 2.90 2.87
5/21/2004 11:00 AM 42.13 3.82 101 87 80 77 76 17.5 3.22 3.24
6/7/2004 7:30 AM 58.98 2.99 78 73 75 74 75 1 2.96 2.97
6/7/2004 9:30 AM 59.06 3.13 91 75 74 76 78 6 2.96 2.98
6/7/2004 12:30 PM 59.1 3.65 118 103 84 85 85 25.5 2.81 2.79
6/17/2004 11:00 AM 69.13 3.78 106 95 87 86 87 14 3.30 3.31
7/2/2004 11:00 AM 84.125 3.56 112 96 87 88 85 17.5 3.00 3.00
7/14/2004 11:00 AM 96.125 3.45 106 95 87 87 86 14 3.01 2.98
7/28/2004 9:00 AM 110.04167 3.25 97 90 86 87 89 5.5 3.09 3.08
8/11/2004 7:00 AM 123.96 2.98 82 79 82 82 81 0 2.98 2.98
8/11/2004 10:00 AM 124.08 3.18 101 88 85 85 84 10 2.89 2.87
8/11/2004 12:00 PM 124.17 3.53 111 97 88 87 87 17 2.99 2.97
8/24/2004 10:00 AM 137.08333 3.20 98 86 83 82 82 10 2.91 2.89
9/9/2004 10:00 AM 153.08333 3.10 88 82 83 83 82 2.5 3.03 3.04
9/21/2004 10:00 AM 165.08333 3.03 72 73 74 74 75 0 3.03 3.03
10/5/2004 9:00 AM 179.04167 2.98 82 80 82 82 79 0.5 2.96 2.97
10/26/2004 9:00 AM 200.04167 2.85 71 70 75 74 69 0 2.85 2.85












78" Florida Bulb-Tee 4
CFthen = 0.0129 1/F

Top Bottom Top Bottom Empirical Analytical
Time After Field Flange Flange Web Bulb Bulb Corrected Corrected
Release Camber Temp Temp Temp Temp Temp AT Camber Camber
Date Time (Days) (in) (oF) (oF) (oF) (oF) (oF) (oF) (in) (in)
6/28/2004 6:30 AM 0.00 2.05 75 79 81 80 80 0 2.05 2.05
6/28/2004 9:00 AM 0.10 2.57 79 79 82 81 81 0 2.57 2.57
7/2/2004 12:00PM 4.23 2.89 110 104 96 93 91 15 2.33 2.37
7/14/2004 12:00 PM 16.23 3.25 104 101 93 92 92 10.5 2.81 2.88
7/21/2004 12:00 PM 23.23 3.26 102 94 87 87 85 12 2.76 2.86
7/28/2004 9:00 AM 30.10 2.97 95 88 86 87 85 5.5 2.76 2.80
8/11/2004 7:00 AM 44.02 2.77 81 79 82 82 81 0 2.77 2.77
8/11/2004 10:00AM 44.15 2.99 99 92 89 90 86 7.5 2.70 2.75
8/11/2004 12:00 PM 44.23 3.34 109 99 92 90 87 15.5 2.67 2.82
8/24/2004 10:00AM 57.15 3.19 98 86 84 83 82 9.5 2.80 2.89
9/9/2004 10:00AM 73.15 2.97 88 81 82 82 81 3 2.85 2.89
9/21/2004 10:00AM 85.15 2.84 72 73 74 74 74 0 2.84 2.84
10/5/2004 9:00 AM 99.10 3.02 80 78 80 80 79 0 3.02 3.02
10/26/2004 9:00 AM 120.10 3.02 69 69 72 71 69 0 3.02 3.02
78" Florida Bulb-Tee 5
CFthen = 0.0106 1/oF
Top Bottom Top Bottom Empirical Analytical
Time After Field Flange Flange Web Bulb Bulb Corrected Corrected
Release Camber Temp Temp Temp Temp Temp AT Camber Camber
Date Time (Days) (in) (oF) (oF) (oF) (oF) (oF) (oF) (in) (in)
6/28/2004 6:30 AM 0.00 2.02 75 78 81 80 80 0 2.02 2.02
6/28/2004 9:00 AM 0.10 2.37 79 80 82 82 81 0 2.37 2.37
7/2/2004 12:00PM 4.23 3.26 114 103 94 92 89 18 2.64 2.66
7/14/2004 12:00PM 16.23 3.32 111 95 91 90 89 13.5 2.85 2.90
7/21/2004 12:00 PM 23.23 3.39 100 89 84 84 84 10.5 3.02 3.06
7/28/2004 9:00 AM 30.10 3.13 94 89 86 87 86 5 2.96 2.97
8/11/2004 7:00 AM 44.02 3.06 80 79 852 83 82 0 3.06 3.06
8/11/2004 10:00AM 44.15 3.23 98 87 84 84 84 8.5 2.94 2.97
8/11/2004 12:00 PM 44.23 3.56 107 94 88 87 87 13.5 3.05 3.12
8/24/2004 10:00AM 57.15 3.38 95 84 83 82 83 7 3.13 3.17
9/9/2004 10:00AM 73.15 2.98 85 83 84 86 83 0 2.98 2.98
9/21/2004 10:00AM 85.15 3.11 72 73 74 74 75 0 3.11 3.11
10/5/2004 9:00 AM 99.10 2.96 81 79 81 82 79 0 2.96 2.96
10/26/2004 9:00 AM 120.10 2.98 71 69 74 74 69 0 2.98 2.98
78" Florida Bulb-Tee 6
CFthen = 0.0131 1/oF
Top Bottom Top Bottom Empirical Analytical
Time After Field Flange Flange Web Bulb Bulb Corrected Corrected
Release Camber Temp Temp Temp Temp Temp AT Camber Camber
Date Time (Days) (in) (oF) (oF) (oF) (oF) (oF) (oF) (in) (in)
6/28/2004 6:30 AM 0.00 1.81 77 79 82 81 80 0 1.81 1.81
6/28/2004 9:00 AM 0.10 2.25 81 79 81 82 81 0 2.25 2.25
7/2/2004 12:00PM 4.23 3.44 112 105 96 94 91 16 2.72 2.89
7/14/2004 12:00PM 16.23 3.31 113 104 96 93 92 16 2.61 2.76
7/21/2004 12:00 PM 23.23 3.38 108 94 86 88 84 15 2.71 2.90
7/28/2004 9:00 AM 30.10 3.02 95 88 86 85 84 7 2.74 2.79
8/11/2004 7:00 AM 44.02 2.84 83 79 82 82 82 0 2.84 2.84
8/11/2004 10:00AM 44.15 3.09 94 87 85 85 83 6.5 2.83 2.89
8/11/2004 12:00 PM 44.23 3.42 109 98 90 89 87 15.5 2.72 2.90
8/24/2004 10:00AM 57.15 3.24 102 88 85 84 83 11.5 2.75 2.88
9/9/2004 10:00AM 73.15 2.99 92 87 88 88 85 3 2.87 2.90
9/21/2004 10:00AM 85.15 2.82 73 73 74 74 75 0 2.82 2.82
10/5/2004 9:00 AM 99.10 2.92 83 80 81 81 79 1.5 2.86 2.87
10/26/2004 9:00 AM 120.10 2.84 71 69 72 71 68 0.5 2.82 2.83












AASHTO Type IV 1
CFtherm = 0.0132 1/F
Top Bottom Top Bottom Empirical Analytical
Time After Field Flange Flange Web Bulb Bulb Corrected Corrected
Release Camber Temp Temp Temp Temp Temp AT Camber Camber
Date Time (Days) (in) (oF) (oF) (oF) (oF) (oF) (oF) (in) (in)
6/10/2004 9:30 AM 0.00 0.65 83 83 85 88 85 0 0.65 0.65
6/10/2004 11:30 AM 0.08 1.18 104 88 87 98 92 1 1.17 1.18
6/17/2004 9:00 AM 6.98 1.29 87 85 85 84 82 3 1.24 1.23
6/24/2004 3:00 PM 14.23 1.47 117 100 95 96 95 13 1.22 1.25
7/2/2004 9:00 AM 21.98 1.28 98 88 87 86 85 7.5 1.15 1.15
7/14/2004 10:00 AM 34.02 1.20 101 90 90 89 88 7 1.09 1.08
7/21/2004 9:00 AM 40.98 1.16 92 85 86 86 85 3 1.12 1.11
7/28/2004 9:00 AM 47.98 1.50 92 85 86 87 87 1.5 1.47 1.48
8/11/2004 7:00 AM 61.90 1.33 79 82 83 82 79 0 1.33 1.32
8/11/2004 10:00 AM 62.02 1.45 95 87 87 88 89 2.5 1.40 1.41
8/11/2004 12:00 PM 62.10 1.45 107 91 90 90 91 8.5 1.29 1.31
8/24/2004 10:00 AM 75.02 1.50 93 86 87 87 84 4 1.42 1.43
9/9/2004 10:00 AM 91.02 1.58 94 86 86 86 86 4 1.49 1.51
9/21/2004 10:00 AM 103.02 1.58 75 74 75 75 75 0 1.58 1.58
10/5/2004 9:00 AM 116.98 1.63 88 84 85 84 80 4 1.54 1.55
10/26/2004 9:00 AM 137.98 1.75 81 74 74 73 70 6 1.61 1.64
AASHTO Type IV 2
CFtherm = 0.0276 1/F
Top Bottom Top Bottom Empirical Analytical
Time After Field Flange Flange Web Bulb Bulb Corrected Corrected
Release Camber Temp Temp Temp Temp Temp AT Camber Camber
Date Time (Days) (in) (oF) (oF) (oF) (oF) (oF) (oF) (in) (in)
6/10/2004 9:30 AM 0.00 0.61 87 85 88 93 87 0 0.61 0.61
6/10/2004 11:30 AM 0.08 1.05 105 87 85 86 87 9.5 0.78 0.90
6/17/2004 9:00 AM 6.98 1.24 92 84 84 89 84 1.5 1.19 1.22
6/24/2004 3:00 PM 14.23 1.53 120 99 96 103 96 10 1.11 1.36
7/2/2004 9:00 AM 21.98 1.28 93 88 88 86 84 5.5 1.09 1.18
7/14/2004 10:00 AM 34.02 1.22 101 93 92 89 88 8.5 0.94 1.07
7/21/2004 9:00 AM 40.98 1.24 87 82 82 82 80 3.5 1.12 1.17
7/28/2004 9:00 AM 47.98 1.51 93 85 86 87 87 2 1.43 1.48
8/11/2004 7:00 AM 61.90 1.06 79 82 83 82 79 0 1.06 1.05
8/11/2004 10:00 AM 62.02 1.29 93 84 85 85 86 3 1.18 1.24
8/11/2004 12:00 PM 62.10 1.26 107 91 89 90 91 8.5 0.96 1.12
8/24/2004 10:00 AM 75.02 1.31 94 86 86 86 84 5 1.13 1.22
9/9/2004 10:00 AM 91.02 1.64 92 86 86 86 86 3 1.50 1.59
9/21/2004 10:00 AM 103.02 1.71 75 74 75 75 75 0 1.71 1.71
10/5/2004 3:36 AM 116.75 1.64 89 84 84 84 80 4.5 1.43 1.55
10/26/2004 9:00 AM 137.98 1.74 78 76 76 75 70 4.5 1.52 1.65
AASHTO Type IV 3
CFtherm = 0.0123 1/oF
Top Bottom Top Bottom Empirical Analytical
Time After Field Flange Flange Web Bulb Bulb Corrected Corrected
Release Camber Temp Temp Temp Temp Temp AT Camber Camber
Date Time (Days) (in) (oF) (oF) (oF) (oF) (oF) (oF) (in) (in)
6/10/2004 9:30 AM 0.00 0.67 86 84 87 95 89 0 0.67 0.67
6/10/2004 11:30 AM 0.08 1.17 104 88 85 84 87 10.5 1.02 1.00
6/17/2004 9:00 AM 6.98 1.25 95 87 86 84 84 7 1.14 1.12
6/24/2004 3:00 PM 14.23 1.47 116 103 99 105 100 7 1.35 1.36
7/2/2004 9:00 AM 21.98 1.28 95 89 89 87 84 6.5 1.18 1.16
7/14/2004 10:00 AM 34.02 1.39 101 88 88 88 88 6.5 1.28 1.28
7/21/2004 9:00 AM 40.98 1.37 90 81 80 80 80 5.5 1.27 1.27
7/28/2004 9:00 AM 47.98 1.49 92 86 86 87 87 2 1.45 1.46
8/11/2004 7:00 AM 61.90 1.59 78 82 83 82 79 0 1.59 1.59
8/11/2004 10:00 AM 62.02 1.91 96 86 85 84 85 6.5 1.76 1.80
8/11/2004 12:00 PM 62.10 1.64 109 91 89 90 91 9.5 1.45 1.48
8/24/2004 10:00 AM 75.02 1.71 96 87 86 86 84 6.5 1.58 1.60
9/9/2004 10:00 AM 91.02 1.69 93 86 85 85 86 4 1.60 1.62
9/21/2004 10:00 AM 103.02 1.71 75 74 74 75 75 0 1.71 1.71
10/5/2004 3:36 AM 116.75 1.76 88 82 84 82 80 4 1.68 1.69
10/26/2004 9:00 AM 137.98 1.76 77 72 72 71 70 4 1.68 1.69












AASHTO Type V 2
CFthen = 0.0037 1/F
Top Bottom Top Bottom Empirical Analytical
Time After Field Flange Flange Web Bulb Bulb Corrected Corrected
Release Camber Temp Temp Temp Temp Temp AT Camber Camber
Date Time (Days) (in) (oF) (oF) (oF) (oF) (oF) (oF) (in) (in)
9/28/2004 9:00 AM 0.00 0.90 81 78 79 79 79 0.5 0.90 0.90
9/28/2004 10:00AM 0.04 0.90 89 2 82 82 82 83 3 0.89 0.87
10/5/2004 9:00 AM 7.00 1.28 89 82 85 85 83 1.5 1.27 1.26
10/12/2004 9:00 AM 14.00 1.30 74 73 74 74 74 0 1.30 1.30
10/19/2004 9:00 AM 21.00 1.30 79 77 79 81 75 0 1.30 1.30
10/19/2004 11:00 AM 21.08 1.35 89 82 82 81 78 6 1.32 1.28
10/19/2004 1:00 PM 21.17 1.35 100 86 82 81 80 12.5 1.29 1.20
10/26/2004 9:00 AM 28.00 1.28 71 71 73 75 71 0 1.28 1.28
AASHTO Type V 3
CFthen = 0.0061 1/oF
Top Bottom Top Bottom Empirical Analytical
Time After Field Flange Flange Web Bulb Bulb Corrected Corrected
Release Camber Temp Temp Temp Temp Temp AT Camber Camber
Date Time (Days) (in) (oF) (oF) (oF) (oF) (oF) (oF) (in) (in)
9/28/2004 9:00 AM 0.00 0.85 78 80 80 80 80 0 0.85 0.85
9/28/2004 10:00 AM 0.04 1.00 87 82 83 83 83 1.5 0.99 0.98
10/5/2004 9:00 AM 7.00 1.25 87 82 84 84 83 1 1.24 1.24
10/12/2004 9:00 AM 14.00 1.28 74 73 73 74 74 0 1.28 1.28
10/19/2004 9:00 AM 21.00 1.33 81 76 78 77 75 2.5 1.30 1.30
10/19/2004 11:00 AM 21.08 1.40 91 82 80 80 78 7.5 1.34 1.31
10/19/2004 1:00 PM 21.17 1.43 102 86 83 82 80 13 1.31 1.27
10/26/2004 9:00 AM 28.00 1.33 76 71 74 73 71 1.5 1.31 1.31
AASHTO Type V 4
CFthem = 0.0075 1/oF
Top Bottom Top Bottom Empirical Analytical
Time After Field Flange Flange Web Bulb Bulb Corrected Corrected
Release Camber Temp Temp Temp Temp Temp AT Camber Camber
Date Time (Days) (in) (oF) (oF) (oF) (oF) (oF) (oF) (in) (in)
9/28/2004 9:00 AM 0.00 0.70 79 78 80 79 79 0 0.70 0.70
9/28/2004 10:00AM 0.04 0.73 90 82 83 82 81 4.5 0.70 0.67
10/5/2004 9:00 AM 7.00 1.20 88 82 85 84 82 2 1.18 1.18
10/12/2004 9:00 AM 14.00 1.25 74 72 73 74 74 0 1.25 1.25
10/19/2004 9:00 AM 21.00 1.10 80 76 77 76 75 2.5 1.08 1.07
10/19/2004 11:00 AM 21.08 1.15 87 80 79 79 78 5 1.11 1.09
10/19/2004 1:00 PM 21.17 1.20 99 86 82 81 80 12 1.09 1.06
10/26/2004 9:00 AM 28.00 1.15 71 71 74 74 71 0 1.15 1.15















APPENDIX C
EMPIRICAL THERMAL ANALYSIS


For the empirical thermal gradient camber correction method, a linear thermal

gradient approximation was made. This was calculated by subtracting the average

temperature of the bottom bulb from the average temperature of the top flange (Equation

C-1).

TA+TB TD +TE
AT (C-1)
2 2

where:

T, = temperature at location A, B, D, or E along the
cross section (oF)


In order to correct for the effect of the thermal gradient on the prestressed beam camber,

a thermal correction factor needed to be determined. This factor was obtained by first

determining the percent camber change relative to the early morning camber

measurement (AC%) where there was essentially no gradient (Equation C-2).

C C
AC% = (C-2)


where:

Co = morning field measured camber reading (in.)

C, = subsequent field measured camber reading (in.)









The thermal gradient versus normalized camber reading was plotted and a linear

regression of the data produced a thermal correction factor (Equation C-3) for the

adjustment of the field measured camber values (Equation C-4).

AC%/100
CFherm AC /10 (C-3)
AT

Ccorr = Cfield -(Cfield CFherm AT) (C-4)

where:

Field = field measured camber reading (in.)


Assumptions made to obtain this thermal correction factor were that a thermal gradient of

zero yielded no change in camber (i.e., the linear regression was forced through the

origin) and that negative thermal gradients did not produce negative camber effects (i.e.,

an increase in camber). Temperature field measurements were not made for the first

three camber readings of the 78-inch Bulb-Tee girders (girders 1, 2, and 3). The thermal

gradients were estimated for these readings based on the time of reading and ambient

temperature.












78" Bulb-Tee 1

Field Top Bottom Top Bottom
Measured Flange Flange Web Bulb Bulb
Camber AC% Temp Temp Temp Temp Temp AT CFtherm
Date Time (in) (%) (OF) (OF) (OF) (OF) (OF) (OF) (1/F)
6/7/2004 7:30 AM 3.57 0.00% 75 73 78 74 75 0
6/7/2004 9:30 AM 3.68 2.91% 94 79 78 85 90 0
6/7/2004 12:30 PM 3.98 11.31% 117 99 83 86 86 22
0.0055
8/11/2004 7:00 AM 3.25 0.00% 81 79 82 83 81 0
8/11/2004 10:00 AM 3.48 6.92% 100 88 85 86 84 9
8/11/2004 12:00 PM 3.90 19.99% 110 97 88 87 87 16.5
78" Bulb-Tee 2

Field Top Bottom Top Bottom
Measured Flange Flange Web Bulb Bulb
Camber AC% Temp Temp Temp Temp Temp AT CFtherm
Date Time (in) (%) (OF) (OF) (OF) (OF) (OF) (OF) (1/F)
6/7/2004 7:30 AM 3.44 0.00% 75 72 75 74 77 0
6/7/2004 9:30 AM 3.73 8.53% 94 80 79 80 77 8.5
6/7/2004 12:30 PM 4.06 18.17% 119 104 88 89 86 24
0.0088
8/11/2004 7:00 AM 3.35 0.00% 81 79 82 83 81 0
8/11/2004 10:00 AM 3.63 8.20% 101 89 85 85 84 10.5
8/11/2004 12:00 PM 3.98 18.65% 110 95 88 87 86 16
78" Bulb-Tee 3

Field Top Bottom Top Bottom
Measured Flange Flange Web Bulb Bulb
Camber AC% Temp Temp Temp Temp Temp AT CFtherm
Date Time (in) (%) (OF) (OF) (OF) (OF) (OF) (OF) (1/F)
6/7/2004 7:30 AM 2.99 0.00% 78 73 75 74 75 1
6/7/2004 9:30 AM 3.13 4.68% 91 75 74 76 78 6
6/7/2004 12:30 PM 3.65 21.95% 118 103 84 85 85 25.5
0.009
8/11/2004 7:00 AM 2.98 0.00% 82 79 82 82 81 0
8/11/2004 10:00 AM 3.18 6.72% 101 88 85 85 84 10
8/11/2004 12:00 PM 3.53 18.47% 111 97 88 87 87 17


2 UU'/o



20 00%


w-
S 1500%
U

.0
E 10 00%



5 00%



0 00%


0- Linear (FLBT (2))
^,^ ^^ FLBT(1)
m^ ^^^ ^ FLBT(2)
iy ^^ ^ FLBT(3)


S- Linear (FLBT (3))


5 10 15 20 25
Temperature Gradient (oF)














78" Bulb-Tee 4

Field Top Bottom Top Bottom
Measured Flange Flange Web Bulb Bulb
Camber AC% Temp Temp Temp Temp Temp AT CFtherm
Date Time (in) (%) (OF) (OF) (OF) (OF) (OF) (OF) (1/F)
8/11/2004 7:00 AM 2.77 0.00% 81 79 82 82 81 0
8/11/2004 10:00AM 2.99 8.14% 99 92 89 90 86 7.5 0.0129
8/11/2004 12:00 PM 3.34 20.79% 109 99 92 90 87 15.5
78" Bulb-Tee 5

Field Top Bottom Top Bottom
Measured Flange Flange Web Bulb Bulb
Camber AC% Temp Temp Temp Temp Temp AT CFtherm
Date Time (in) (%) (F) (OF) (F) (OF) (OF) (F) (1/F)
8/11/2004 7:00 AM 3.06 0.00% 80 79 852 83 82 0
8/11/2004 10:00AM 3.23 5.73% 98 87 84 84 84 8.5 0.0106
8/11/2004 12:00 PM 3.56 16.36% 107 94 88 87 87 13.5
78" Bulb-Tee 6

Field Top Bottom Top Bottom
Measured Flange Flange Web Bulb Bulb
Camber AC% Temp Temp Temp Temp Temp AT CFtherm
Date Time (in) (%) (OF) (OF) (OF) (OF) (OF) (F) (1/F)
8/11/2004 7:00 AM 2.84 0.00% 83 79 82 82 82 0
8/11/2004 10:00AM 3.09 8.80% 94 87 85 85 83 6.5 0.0131
8/11/2004 12:00 PM 3.42 20.24% 109 98 90 89 87 15.5


25 00%


( 1500%
u


E0
E 10 0ooo


5 10


15
Temperature Gradient (oF)












AASHTO Type IV 1

Field Top Bottom Top Bottom
Measured Flange Flange Web Bulb Bulb
Camber AC% Temp Temp Temp Temp Temp AT CFtherm
Date Time (in) (%) (OF) (OF) (OF) (OF) (OF) (OF) (1/F)
8/11/2004 7:00 AM 1.33 0.00% 79 82 83 82 79 0
8/11/2004 10:00AM 1.45 9.43% 95 87 87 88 89 2.5 0.0132
8/11/2004 12:00 PM 1.45 9.43% 107 91 90 90 91 8.5
AASHTO Type IV 2

Field Top Bottom Top Bottom
Measured Flange Flange Web Bulb Bulb
Camber AC% Temp Temp Temp Temp Temp AT CFtherm
Date Time (in) (%) (F) (OF) (F) (OF) (OF) (F) (1/F)
8/11/2004 7:00 AM 1.06 0.00% 79 82 83 82 79 0
8/11/2004 10:00AM 1.29 21.23% 93 84 85 85 86 3 0.0276
8/11/2004 12:00 PM 1.26 18.87% 107 91 89 90 91 8.5
AASHTO Type IV 3

Field Top Bottom Top Bottom
Measured Flange Flange Web Bulb Bulb
Camber AC% Temp Temp Temp Temp Temp AT CFtherm
Date Time (in) (%) (OF) (OF) (OF) (OF) (OF) (F) (1/F)
8/11/2004 7:00 AM 1.59 0.00% 78 82 83 82 79 0
8/11/2004 10:00AM 1.91 20.47% 96 86 85 84 85 6.5 0.0123
8/11/2004 12:00 PM 1.64 3.15% 109 91 89 90 91 9.5


/


/


* Type IV 1
* Type IV 2
Type IV 3
- Linear (Type IV 1)
- Linear (Type IV 2)
- Linear (Type IV 3)


15
Temperature Gradient (oF)


20 00%



S1500%
U


E 1000%


00
5 00%











AASHTO Type V 1

Field Top Bottom Top Bottom
Measured Flange Flange Web Bulb Bulb
Camber AC% Temp Temp Temp Temp Temp AT CFtherm
Date Time (in) (%) (OF) (OF) (OF) (OF) (OF) (OF) (1/F)
10/19/2004 9:00 AM 1.18 0.00% 81 77 78 78 75 2.5
10/19/2004 11:00AM 1.25 6.38% 91 82 80 80 78 7.5 0.005
10/19/2004 1:00 PM 1.25 6.38% 103 88 82 81 80 15
AASHTO Type V 2

Field Top Bottom Top Bottom
Measured Flange Flange Web Bulb Bulb
Camber AC% Temp Temp Temp Temp Temp AT CFtherm
Date Time (in) (%) (F) (OF) (F) (OF) (OF) (F) (1/F)
10/19/2004 9:00 AM 1.30 0.00% 79 77 79 81 75 0
10/19/2004 11:00AM 1.35 3.85% 89 82 82 81 78 6 0.0037
10/19/2004 1:00 PM 1.35 3.85% 100 86 82 81 80 12.5
AASHTO Type V 3

Field Top Bottom Top Bottom
Measured Flange Flange Web Bulb Bulb
Camber AC% Temp Temp Temp Temp Temp AT CFtherm
Date Time (in) (%) (F) (OF) (F) (OF) (OF) (F) (1/F)
10/19/2004 9:00 AM 1.33 0.00% 81 76 78 77 75 2.5
10/19/2004 11:00AM 1.40 5.66% 91 82 80 80 78 7.5 0.0061
10/19/2004 1:00 PM 1.43 7.55% 102 86 83 82 80 13
AASHTO Type V 4

Field Top Bottom Top Bottom
Measured Flange Flange Web Bulb Bulb
Camber AC% Temp Temp Temp Temp Temp AT CFtherm
Date Time (in) (%) (OF) (OF) (OF) (OF) (OF) (F) (1/F)
10/19/2004 9:00 AM 1.10 0.00% 80 76 77 76 75 2.5
10/19/2004 11:00AM 1.15 4.55% 87 80 79 79 78 5 0.0075
10/19/2004 1:00 PM 1.20 9.09% 99 86 82 81 80 12














25 00%




20 00%




( 1500%




l 0ooo%
5



5 00%o


o TypeVA(1)

a Type VA (2)

l- .A Type VB (3)

S* Type VB (4)

S-. Linear (Type VA (1))
S- Linear (Type VA (2))

S- Linear (Type VB (3))

Linear (Type VB (4))


5 10 15 20 25
Temperature Gradient (oF)

















APPENDIX D
ANALYTICAL THERMAL ANALYSIS



Analytical Thermal Analysis
--written by Jonathan Sanek, Universtiy of Florida Department of Civil and Coastal Engineering

78" Bulb-Tee Girder, Pour A
ORIGIN- 1 E ORIGIN
Input Field Temperature Measurments

0.00 0 0 0 0 0 0 0 0 0 0
0.13 0 0 0 0 0 0 0 0 0 0
7.17 0 0 0 0 0 0 0 0 0 0
14.08 0 0 0 0 0 0 0 0 0 0
14.17 0 0 0 0 0 0 0 0 0 0
14.25 0 0 0 0 0 0 0 0 0 0
20.13 91 78 74 74 74 97 79 75 74 73
28.13 93 78 74 74 74 100 85 79 78 78
42.13 93 80 77 77 77 92 80 76 75 74
58.98 75 73 78 74 75 75 72 75 74 77
59.06 94 79 78 85 90 94 80 79 80 77
59.19 117 99 83 86 86 119 104 88 89 86
tcamber:= FLBT1:= FLBT2:=
amer 69.13 99 86 83 83 82 106 94 90 88 86

84.125 104 90 86 86 85 109 95 89 90 86
96.125 104 94 87 89 86 108 92 89 89 86
110.0416667 97 90 86 88 85 98 90 86 88 85
123.96 81 79 82 83 81 81 79 82 83 81
124.08 100 88 85 86 84 101 89 85 85 84
124.17 110 97 88 87 87 110 95 88 87 86
137.0833333 97 86 84 84 83 100 86 82 82 82
153.0833333 88 82 82 82 81 89 82 82 81 82
165.0833333 72 73 74 74 75 72 73 74 74 75
179.0416667 82 79 81 81 79 80 78 81 80 79
200.0416667) 70 69 74 73 69) 70 69 73 72 69)











Input Field Temperature Measurments (cont...)


Height vector 0 0 0 0 0
corresponding to 0 0 0 0 0
temperature readings 0 0
0 0 000
/'0 0 0 0 0 0

5 0 0 0 0 0
Hve:= 35 (in) 0 0 0 0 0
65 94 80 76 75 74
.78) 102 89 80 78 78
101 87 80 77 76
78 73 75 74 75
91 75 74 76 78
118 103 84 85 85
FLBT3:=
106 95 87 86 87
112 96 87 88 85
106 95 87 87 86
97 90 86 87 89
82 79 82 82 81
101 88 85 85 84
111 97 88 87 87
98 86 83 82 82
88 82 83 83 82
72 73 74 74 75
82 80 82 82 79
71 70 75 74 69)












Input Material Testing Data


S:= 5.3x 10 6


taken from Table 5 of NCHRP Report 276


(days) Ec :


4309)
5228
5304
5336
5444
(ksi)
5588
6005
6070
6126
6017)


E(t):= for i E..last(t)
out linterp(temod,Ec, t)

out


Section Properties

H:= 78 (in


L:= 1942.625 (in)

Section Shape

b(z):= 60 if 0 [60-11.75(z-3)] if 3 [13-2.(z-7)] if 7 7 if 10 [7+2.1.(z-60)] if 60 28 if 70 < z< H


A= 1105.007



Q =41563.094


c = 37.613


HIg c)2.b(z)
I := (z c)2.b(z) dz
0


Ig = 935547.485


(inA2) Cross-Sectional Area



(inA3) First Moment Area



(in) Location of Neutral Axis
from top of member

(inA4) Gross Moment of Inertia


temod :'


0
7
14
21
28
42
84
109
136
200)


-H
A := b(z) dz
0
H
Qy := z.b(z) dz


Qy
C:=










Calculations

Extract Thermal Gradient and Normalized based on Minimum Measured Temperature
Along Profile...

Tvec(Beam):= for i ..rows(Beam)
min. min(submatrix(Beam, i, i, E, cols (Beam)))

for j E .. cols(Beam)
Tg,.. Beam. min.

Tgi,j -Tgi,j if gi,j >0

T gi 0 otherwise


outi ((submatrix(T ,i,i, E,cols(T ))))T

out

Linear Interpolation of Thermal Gradient for variable, z...

Tgrad(Beam,z) := for i e ..rows(Beam)
out. linterp(Hvec, Tvec(Beam)i,z)

out


Example Calculation of Internal Moment Due to Positive Thermal Gradient


time:= 15 Beam:= FLBT1


T(z) := Tgrad(Beam, z)time (deg F)


oT() :=-E(tcamber)time.u-.T(z) (ksi)

M H
Mint:= oT(z)-b(z)(z -c) dz Mint= 4.429x 10 (kip*in)
*O


-Mint-L2
corr 8E(tcambeti. Ig
8Et*tcamber)time.g


A = -0.37
corr











Analytical Thermal Analysis
--written by Jonathan Sanek, Universtiy of Florida Department of Civil and Coastal Engineering

78" Bulb-Tee Girder, Pour B
ORIGIN- 1 E ORIGIN

Input Field Temperature Measurments


tcamber :


0.00
0.10
4.23
16.23
23.23
30.10
44.02
44.15
44.23
57.15
73.15
85.15
99.10
120.10)


Height vector
corresponding to
temperature readings


5
Hvec := 35
65
,78)


FLBT4::


FLBT5::


FLBT6::











Input Material Testing Data


c := 5.3x 10 6


taken from Table 5 of NCHRP Report 276


(days) Ec::


4759)
4677
4813
5099
4932
5133
5222
5370
5365
5160)


(ksi)


E(t) := for i E .. last(t)
out linterp(temodEc, t)

out


Section Properties

H:= 78 (in)

L:= 1942.625 (in)

Section Shape

b(z):= 60 if 0 [60-11.75(z-3)] if 3 [13-2.(z-7)] if 7 7 if 10 [7+2.1.(z-60)] if 60 28 if 70 < z

A= 1105.007



Q =41563.094


c = 37.613


HIg c)2.b(z)

I := (z c)2.b(z) dz
0


Ig = 935547.485


(inA2) Cross-Sectional Area



(inA3) First Moment Area



(in) Location of Neutral Axis
from top of member

(inA4) Gross Moment of Inertia


temod :


0
4
16
22
34
43
56
72
84
120)


AH
A := b(z) dz


H zb(z) dz
Q := z.b(z) dz


c Q
C:=










Calculations

Extract Thermal Gradient and Normalized based on Minimum Measured Temperature
Along Profile...

Tvec(Beam):= for i ..rows(Beam)
min. min(submatrix(Beam, i, i, E, cols (Beam)))

for j E .. cols(Beam)
Tg,.. Beam.. min.

Tgi,j -Tgi,j if gi,j >0

T gi 0 otherwise

outi ((submatri(Tg ,i, i, ,cols(T ))))T

out

Linear Interpolation of Thermal Gradient for variable, z...

Tgrad(Beam,z) := for i e ..rows(Beam)
out linterp(Hvec, Tvec(Beam)i,z)

out


Example Calculation of Internal Moment Due to Positive Thermal Gradient


time:= 8 Beam:= FLBT4

T(z) := Tgrad(Beam, z)time (deg F)


CT(Z) := -E(tamber)time.a T(z)

-H
Mint := oT(Z).b(z).(z c) dz



-Mint.L2
corr 8E(tcambeti. Ig
8Et*etamber)time.g


(ksi)


Aorr = -0.238
corr


Mint= 2.431x 103 (kip-in)











Analytical Thermal Analysis
--written by Jonathan Sanek, Universtiy of Florida Department of Civil and Coastal Engineering

AASHTO Type IV Girder, Pour A

ORIGIN- 1 E ORIGIN
InDut Field Temperature Measurments


tcamber ::


" 0.00
0.08
6.98
14.23
21.98
34.02
40.98
47.98
61.90
62.02
62.10
75.02
91.02
103.02
116.98
137.98)


Height vector
corresponding to
temperature readings

0
11.02
Hvec := 25.51 (in)
41.5
54.02)


TYPEIV1:=


83
104
87
117
98
101
92
92
79
95
107
93
94
75
88
81


85 88 85)
87 98 92
85 84 82
95 96 95
87 86 85
90 89 88
86 86 85
86 87 87
83 82 79
87 88 89
90 90 91
87 87 84
86 86 86
75 75 75
85 84 80
74 73 70)


TYPEIV2:


87
105
92
120
93
101
87
93
79
93
107
94
92
75
89
78

86
104
95
116
95
101
90
92
78
96
109
96
93
75
88
77


87)
87
84
96
84
88
80
87
79
86
91
84
86
75
80
70)

89
87
84
100
84
88
80
87
79
85
91
84
86
75
80
70 )


TYPEIV3::


84 87
88 85
87 86
103 99
89 89
88 88
81 80
86 86
82 83
86 85
91 89
87 86
86 85
74 74
82 84
72 72











Input Material Testing Data


c := 5.3x 10 6


taken from Table 5 of NCHRP Report 276


(days) Ec::


4506)
4911
5390
5191
5456
5830
5886
5672
5853
5887)


(ksi)


E(t) := for i E .. last(t)
out linterp(temodEc, t)

out


Section Properties

H:= 54.02 (in)

L:= 1092.32 (in)

Section Shape

b(z):= 20.08 if 0 < z 8.03
[ 20.08- 2.015(z 8.03)] if 8.03 < z < 14.01
8.03 if 14.01< z< 37
[8.03+ 2(z-37)] if 37 28 if 45.98

-H
A := b(z) dz


-H
Q := z.b(z) dz

c -
C:=
A
HIg c)2.b(z)
I := (z ).2b(z) dz
0'


A = 807.739


Q = 23960.324



c = 29.663


I =268621.613
g


(inA2) Cross-Sectional Area



(inA3) First Moment Area



(in) Location of Neutral Axis
from top of member

(inA4) Gross Moment of Inertia


temod :


0
7
14
21
34
40
61
74
102
138)











Calculations

Extract Thermal Gradient and Normalized based on Minimum Measured Temperature
Along Profile...

Tvec(Beam):= for i ..rows(Beam)
min.- min(submatrix(Beam, i, i, E, cols(Beam)))

for j e E.. cols(Beam)
Tgi <- Beam. min.
i, j 1 3 1
Tgi,j Ti,j if Ti,j >0

Tg <- 0 otherwise


outi ((submatrixT g, i, i, E, colsT g))))T

out

Linear Interpolation of Thermal Gradient for variable, z...

Tgrad(Beam,z):= for i E..rows(Beam)
outi linterp(Hvec, Tvec(Beam)i,z)

out


Example Calculation of Internal Moment Due to Positive Thermal Gradient


time:= 12 Beam:= TYPEIV1

T(z) := Tgrad(Beam, z)time (deg F)


CT(Z) := -E(tamber)time-a T(z) (ksi)

M H
Mint:= {oT(z).b(z)-(z c) dz Mint = 732.438
*'O


-MintmL
Aorr := 8E(tcamber)timeig


A o= -0.072
corr


(kip*in)




(in)







83


Analytical Thermal Analysis
--written by Jonathan Sanek, Universtiy of Florida Department of Civil and Coastal Engineering

AASHTO Type V Girder, Pour A
ORIGIN- 1 E ORIGIN

Input Field Temperature Measurments

0.00" 82 79 80 79 79" 81 78 79 79 79)
0.04 89 82 82 82 82 89 82 82 82 83
7.00 88 83 85 86 83 89 82 85 85 83
14.00 74 73 74 74 74 74 73 74 74 74
tcamber:= TYPEV1:= TYPEV2:=
amber 21.00 81 77 78 78 75 79 77 79 81 75

21.08 91 82 80 80 78 89 82 82 81 78
21.17 103 88 82 81 80 100 86 82 81 80
28.00) 76 72 73 72 71) 71 71 73 75 71)
Height vector
corresponding to
temperature readings 78 80 80 80 80 79 78 80 79 79
87 82 83 83 83 90 82 83 82 81
87 82 84 84 83 88 82 85 84 82
8.5
74 73 73 74 74 74 72 73 74 74
Hv,,, := 28.5 (in) TYPEV3:= TYPEV4:=
ec 81 76 78 77 75 80 76 77 76 75
50
91 82 80 80 78 87 80 79 79 78
S63 )
102 86 83 82 80 99 86 82 81 80
76 71 74 73 71) 71 71 74 74 71)

Input Material Testing Data


a := 5.3 x 10 6 taken from Table 5 of NCHRP Report 276

( 0 (4909)

7 5130
temod:= 14 (days) Ec:= 5361 (ksi) E(t) := for i ..last(t)
22 5419 outi -linterp(temod Ec t)
28) 5323) out











Section Properties

H:= 63 (in)

L := 972.625 (in)


Section Shape

b(z):= 42 if 0 z < 5
[42-8.667(z-5)] if 5 [16-2.(z-8)] if 8 8 if 12

[8+2-(z-45)] if 45
28 if 55 < z< H


z 55


-H
A := b(z) dz
0
-H
Q := z.b(z) dz
0


Qy
C:=


A =1013.107



Qy = 31446.978


c = 31.04


HIg (z c)2.b(z) dz
I := (z c)2.b(z) dz
0


Ig = 521157.365


(in^2) Cross-Sectional Area



(in^3) First Moment Area



(in) Location of Neutral Axis
from top of member

(in^4) Gross Moment of Inertia











Calculations

Extract Thermal Gradient and Normalized based on Minimum Measured Temperature
Along Profile...

Tvec(Beam):= for i ..rows(Beam)
min. min(submatrix(Beam, i, i, E, cols(Beam)))
1
for j e E.. cols(Beam)
Tg. Beam. min.
i, j 1, J 1
Tgi, Ti,j if Tgij >0

Tgi, 0 otherwise


out i ((submatrix(T ,ii, i, cols(T g))))T

out

Linear Interpolation of Thermal Gradient for variable, z...

Tgrad(Beam,z):= for i E..rows(Beam)
out. linterp(Hec, Tvec(Beam)i, z)

out


Example Calculation of Internal Moment Due to Positive Thermal Gradient


time:= 6 Beam:= TYPEVI


T(z) := Tgrad(Beam,z)time (deg F)


CT(Z) :=-E(tcamber)time.-.aT(z) (ksi)

HM
Mint:= OCT(z).b(z).(z c) dz Mint = 2.103x 103 (kip*in)
0'


-Mint.L
Acorr : 8.E(tcamber)time.ig


Aorr = -UUT88











Analytical Thermal Analysis
--written by Jonathan Sanek, Universtiy of Florida Department of Civil and Coastal Engineering

AASHTO Type V Girder, Pour B
ORIGIN- 1 E ORIGIN

Input Field Temperature Measurments

0.00" 82 79 80 79 79\ 81 78 79 79 79\
0.04 89 82 82 82 82 89 82 82 82 83
7.00 88 83 85 86 83 89 82 85 85 83
14.00 74 73 74 74 74 74 73 74 74 74
tcamber:= TYPEV1:= TYPEV2:=
amber 21.00 81 77 78 78 75 79 77 79 81 75

21.08 91 82 80 80 78 89 82 82 81 78
21.17 103 88 82 81 80 100 86 82 81 80
28.00) 76 72 73 72 71) 71 71 73 75 71)
Height vector
corresponding to
temperature readings 78 80 80 80 80" 79 78 80 79 79
87 82 83 83 83 90 82 83 82 81
87 82 84 84 83 88 82 85 84 82
8.5
74 73 73 74 74 74 72 73 74 74
Hv,,, := 28.5 (in) TYPEV3:= TYPEV4:=
ec 81 76 78 77 75 80 76 77 76 75
50
91 82 80 80 78 87 80 79 79 78
S63 )
102 86 83 82 80 99 86 82 81 80
76 71 74 73 71) 71 71 74 74 71)


Input Material Testing Data


a := 5.3 x 10 6 taken from Table 5 of NCHRP Report 276


( 0 (4796")
7 5164
temod:= 14 (days) Ec:= 5331 (ksi) E(t) := for i ..last(t)
22 5466 out linterp(temod Ec, t)
28) 5313) out











Section Properties

H:= 63 (in)

L := 972.625 (in)


Section Shape

b(z):= 42 if 0 z < 5
[42-8.667(z-5)] if 5 [16-2.(z-8)] if 8 8 if 12

[8+2-(z-45)] if 45
28 if 55 < z< H


z 55


-H
A := b(z) dz
0
-H
Q := z.b(z) dz
0


Qy
C:=


A =1013.107



Qy = 31446.978


c = 31.04


HIg (z c)2.b(z) dz
I := (z c)2.b(z) dz
0


Ig = 521157.365


(in^2) Cross-Sectional Area



(in^3) First Moment Area



(in) Location of Neutral Axis
from top of member

(in^4) Gross Moment of Inertia











Calculations

Extract Thermal Gradient and Normalized based on Minimum Measured Temperature
Along Profile...

Tvec(Beam):= for i ..rows(Beam)
min. min(submatrix(Beam, i, i, E, cols(Beam)))
1
for j e E.. cols(Beam)
Tg. Beam. min.
i, j 1, J 1
Tgi, Ti,j if Tgij >0

Tgi, 0 otherwise


out i ((submatrix(T ,ii, i, cols(T g))))T

out

Linear Interpolation of Thermal Gradient for variable, z...

Tgrad(Beam,z):= for i E..rows(Beam)
out i- linterp(Hec, Tvec(Beam)i, z)

out


Example Calculation of Internal Moment Due to Positive Thermal Gradient


time:= 6 Beam:= TYPEV4


T(z) := Tgrad(Beam,z)time (deg F)


CT(Z) :=-E(tcamber)time. T(z) (ksi)

HM
Mint := OT(z)-b(z)-(z c) dz Mint = 1.41 x 103
0O


-Mint-L
Acorr : 8.E(tcamber)time.ig


Ac = -0.059
COTT


(kip*in)




(in)


















APPENDIX E
TABULATED AMBIENT DATA


2004 4 9 0


Yea I Mot I Da I Hou Tep(C ep(F ep 0)Tm 0)R O


Temp (C) Temp (F) Temp (C) Temp (OF) RH SOLRD
(60 cm) (60 cm) (200 cm) (200 cm) (%) (W/m2)


19.07 66.33


2004 4 9 1 18.96 66.13 19.32 66.78 96 0
2004 4 9 2 18.94 66.09 19.23 66.61 96 0
2004 4 9 3 19.15 66.47 19.36 66.85 96 0
2004 4 9 4 19.14 66.45 19.32 66.78 96 0
2004 4 9 5 19.09 66.36 19.32 66.78 95 0
2004 4 9 6 19.17 66.51 19.37 66.87 95 12
2004 4 9 7 19.57 67.23 19.70 67.46 93 77
2004 4 9 8 21.01 69.82 20.88 69.58 87 288
2004 4 9 9 22.11 71.80 21.78 71.20 81 329
2004 4 9 10 23.74 74.73 23.14 73.65 74 622
2004 4 9 11 25.70 78.26 24.81 76.66 65 760
2004 4 9 12 26.57 79.83 25.84 78.51 61 825
2004 4 9 13 26.82 80.28 26.60 79.88 55 577
2004 4 9 14 27.89 82.20 27.50 81.50 51 637
2004 4 9 15 28.99 84.18 28.68 83.62 43 685
2004 4 9 16 28.93 84.07 29.20 84.56 39 490
2004 4 9 17 28.75 83.75 29.12 84.42 35 286
2004 4 9 18 26.50 79.70 27.10 80.78 42 82
2004 4 9 19 23.25 73.85 24.07 75.33 59 0
2004 4 9 20 21.54 70.77 22.46 72.43 71 0
2004 4 9 21 19.80 67.64 20.71 69.28 76 0
2004 4 9 22 18.73 65.71 19.55 67.19 84 0


2004 4 9 23


17.82 64.08


18.45 65.21 90


d .1. 4-


19.47 67.05 95


2 Highlighted entries are when field measurements were made (I 78" Bulb-Tee A, I 78"

Bulb-Tee B, I AASHTO Type IV A, I AASHTO V A and B, and I All Girders)


Year I Month| Day I Hour