Experimental Validation of Bracing Recommendations for Long-Span Concrete Girders

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Experimental Validation of Bracing Recommendations for Long-Span Concrete Girders
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M.S. Thesis
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English
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Beery, Megan Salvetti
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University of Florida
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Gainesville, FL
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theses   ( marcgt )

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During the construction process, flexible support conditions provided by steel reinforced neoprene bearing pads supporting precast, prestressed girders may allow the girders to become unstable, rolling about an axis parallel to the span of the girders. Imposed skew and/or slope angles significantly reduce bearing pads roll stiffness, which reduces girder buckling capacity due to gravity loading. In this thesis, roll stiffnesses for bearing pads under skew and slope conditions are determined from experimental data gathered using a test device designed to measure such values. The test device reproduces the forces and deformations that act on a bearing pad in the field while simultaneously permitting axial load, skew angle, and slope angle to be controlled independently, so that the effect of each on bearing pad roll stiffness can be quantified. In total, 108 bearing pad tests were performed on three different standard bearing pads, with varying severities of imposed skew and slope angle. Documentation of full scale girder buckling tests designed and conducted to experimentally quantify the influence of bearing pad roll stiffness on girder buckling capacity is also included in this thesis. The pads used to support each end of the test girder during the buckling tests were the same pads previously tested to determine roll stiffness. In total, nine buckling tests were conducted, with various skew and slope conditions imposed on the bearing pads. Validation of analytical models (corresponding to the test setup) was carried out by comparing the buckling capacity predictions from analytical simulations to experimental test results.

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1 EXPERIMENTAL VALIDATION OF BRAC ING RECOMMENDATIONS FOR LONG-SPAN CONCRETE GIRDERS By MEGAN SALVETTI BEERY A THESIS PRESENTED TO THE GRADUATE SCHOOL OF THE UNIVERSITY OF FLOR IDA IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF SCIENCE UNIVERSITY OF FLORIDA 2012

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2 2012 Megan Salvetti Beery

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3 To my husband, Kevin Beery

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4 ACKNOWLEDGMENTS The work presented in this thesis could not have been completed without the unwavering support and guidance of a number of individuals. I would like to express my deep and sincere gratitude to my advisor, Dr. Gary Consolazio, whose motivation, encouragement, knowledge, and attention to detail have been invaluable to me. I thank you for seeing my potential from the first day I set foot in your office and for providing valuable feedback that cultivated my ow n professional confidence and expertise. I also thank the co-chair on my committee, Dr. H.R. (Trey) Hamilton for bringing his vast design knowledge to the table, as well as bringing hum or into the engineer ing equation. Both Dr. Consolazio and Dr. Hamilton were always available to answer my questions, and I thank you both for always teaching me (and questioning me) to the point of full unders tanding. I would also like to thank Dr. Ron Cook for serv ing on my supervisory committee. Appreciation is extended to ev eryone at the FDOT M. H. Ansley Structures Research Center for their insight during the planning phase and exception al work performed during the fabrication phase of the project. I thank you fo r your precision and patience, and for making me feel so welcome every time I vi sited the lab. I would like to es pecially thank David Wagner for being such a fantastic co-project manager and fr iend. I could not have asked for a better research partner, turning the tes ting plans into reality through his se lfless commitment to this project. My officemates ensured that I was constant ly engaged and entertained along the way, and for that I am very grateful. In particular, I cant thank Daniel Getter enough, for his friendship and for always offering his expertise and advice whenever asked of him. I would also like to thank my family members for the support and love they continuously provide me. I thank my mother, Lynda Salvetti, for instilling in me a drive to succeed at an early age, and for supporting my decisi ons since I was old enough to pick my own outfit. I thank my

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5 father, Joseph Salvetti, and step-mom, Cindy Sa lvetti, for being proud of me no matter what. I thank my grandpa, Joseph Strenk, for sparking and cu ltivating my interest in engineering. I thank my brother, Danny Salvetti, and step-sister, Ki mberly Goss Stuetzer, for reminding me to have fun during my studies. Perhaps most importantly, I am eternally grateful to my husband, Kevin Beery, for his unconditional love and understanding throughout this journey.

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6 TABLE OF CONTENTS page ACKNOWLEDGMENTS...............................................................................................................4 LIST OF TABLES................................................................................................................. ..........9 LIST OF FIGURES................................................................................................................ .......10 LIST OF ABBREVIATIONS........................................................................................................15 ABSTRACT....................................................................................................................... ............16 CHAPTER 1 INTRODUCTION..................................................................................................................18 Objective...................................................................................................................... ...........19 Scope.......................................................................................................................... .............19 Literature Review.............................................................................................................. .....20 Bearing Pad Properties....................................................................................................20 Girder Buckling...............................................................................................................21 2 ISOLATED BEARING PAD ROLL STIFFNESS TESTS....................................................25 Experimental Test Setup........................................................................................................ .25 Instrumentation................................................................................................................ .......26 Test Procedure................................................................................................................. .......27 Positioning Stage.............................................................................................................27 Clamping Stage...............................................................................................................28 Rolling Stage.................................................................................................................. .28 Test Program................................................................................................................... ........29 Repeated Axial Compression..........................................................................................32 Variation of Axial Compression Load............................................................................32 Results........................................................................................................................ .............33 Location of Pressure Re sultants on Bearing Pads..................................................................34 Data Trends.................................................................................................................... .........35 Effect of Skew and Slope Combined...............................................................................36 Effect of Skew.................................................................................................................36 Effect of Slope................................................................................................................ .36 3 INTRODUCTION TO GIRD ER BUCKLING TESTS.........................................................46 Scope of Test Program.......................................................................................................... ..46 Experimental Constraints....................................................................................................... .47 Length of Test Girder......................................................................................................47 Loading Conditions.........................................................................................................47

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7 Elastic Buckling...............................................................................................................49 4 BUCKLING ANALYSIS.......................................................................................................52 Overview....................................................................................................................... ..........52 Finite Element Model of Experimental Test Setup................................................................52 5 DEVELOPMENT OF TEST-GI RDER CROSS-SECTIONS................................................59 Precast Segment Cross-Section Design..................................................................................60 Design of Girder Cross-Section.......................................................................................60 Design of Closure St rip Cross-Section...................................................................................62 Design of End Block Cross-Section.......................................................................................63 6 CONSTRUCTION OF TEST GIRDER.................................................................................72 Precast Segments............................................................................................................... .....72 Closure Strips................................................................................................................. .........73 End Blocks..................................................................................................................... .........74 Material Tests and Properties.................................................................................................75 Girder Post-Tensioning and Grouting....................................................................................76 7 GRAVITY LOAD SIMULATOR..........................................................................................97 Gravity Load Simulator Design..............................................................................................98 UF/FDOT Gravity Load Simulators.......................................................................................99 Effect of Gravity Load Simulator Self Weight Equilibrium................................................100 8 EXPERIMENTAL BUCKLI NG TESTS PROGRAM........................................................114 Buckling Test Setup............................................................................................................ ..114 Test Matrix.................................................................................................................... ........114 Test Procedure................................................................................................................. .....115 Setting Skew and Slope Angles.....................................................................................115 Placing the Test Girder..................................................................................................116 Buckling Test Procedure...............................................................................................117 Instrumentation................................................................................................................ .....117 Displacement Transducers.............................................................................................118 Load Cells..................................................................................................................... .119 Strain Gages...................................................................................................................119 9 RESULTS........................................................................................................................ .....131 Experimental Buckling Test Results....................................................................................131 Measured Load-Displacement Curves..........................................................................131 Data Curve Fitting.........................................................................................................132 Calculation of Buckling Capacity.................................................................................133 Buckling Capacity Results............................................................................................134

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8 Buckling Finite Element Model............................................................................................135 Moment-Rotation Curves from Roll Stiffness Tests.....................................................135 Scaling of Moment-Rotation Cu rves from Isolated Tests.............................................137 Elastic Modulus Used in Finite Element Buckling Model...................................................139 Finite Element Buckling Model Results...............................................................................140 10 CONCLUSIONS..................................................................................................................155 APPENDIX A BEARING PAD TEST DEVI CE FABRICATION PLANS................................................157 B FULL SCALE TEST GIRDER FABRICATION PLANS...................................................163 C COMPRESSIVE STRENGTH AND ELASTIC MODULUS TEST RESULTS................174 D DYWIDAG JACK CALIBRATION FORM.......................................................................177 E GRAVITY LOAD SIMULATO R FABRICATION PLANS..............................................180 F CATCH FRAMES FABRICATION PLANS......................................................................199 G BUCKLING TESTS INSTRUMENTATION PLAN..........................................................207 LIST OF REFERENCES.............................................................................................................219 BIOGRAPHICAL SKETCH.......................................................................................................222

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9 LIST OF TABLES Table page 2-1 Bearing pad dimensions, shear modulus, durometer hardness, and configurations tested for each specimen....................................................................................................38 2-2 Mean roll stiffness and reduction in ro ll stiffness due to non-ideal (skewed, sloped) conditions..................................................................................................................... ......38 5-1 Section properties of precast segments..............................................................................65 5-2 Section properties of closure strips....................................................................................65 5-3 Section properties of end blocks........................................................................................65 6-1 Summary of cylinder materi al tests performed within one week of buckling testing for each girder component.................................................................................................79 6-2 Compressive strength and modulus of elasti city of cylinders tested within one week of buckling testing............................................................................................................ ..79 6-3 Sequence of incremental post-tensioning fo rces applied to girder during stressing..........80 6-4 Grout cube strength test results..........................................................................................80 8-1 Test matrix................................................................................................................ .......121 8-2 Placement method, per test basis.....................................................................................121 9-1 Buckling capacity results.................................................................................................142 9-2 Sigmoid curve functional paramete rs for each test configuration...................................142 9-3 Experimental and finite element buckli ng capacities for each test configuration...........142

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10 LIST OF FIGURES Figure page 1-1 Description of physical system..........................................................................................23 1-2 Plan view of girder, pad, and support with skew angle defined........................................23 1-3 Elevation view of girder, pad, a nd support with slope angle defined................................24 2-1 Bearing pad test device.................................................................................................... ..39 2-2 Elevation view of test device: imposi ng slope (positioning stage) and applying axial load (clamping stage).........................................................................................................39 2-3 Imposing skew during the positioning stage......................................................................40 2-4 Applying loads to outriggers during rolling stage.............................................................40 2-5 Identification of bearing pad dimensions...........................................................................41 2-6 Representative moment-rotation curves............................................................................41 2-7 Moment-rotation curves for a ll tests, grouped by pad specimen.......................................42 2-8 Pressure distributions and axial load resultant positions on bearing pad: beginning, intermediate, and end of rolling stage................................................................................43 2-9 Bulging of the internal elastome r layers during roll stiffness test.....................................44 2-10 Bearing pad roll stiffnesses for all configurations tested...................................................45 2-11 Mean bearing pad roll stiffnesses for all configurations tested.........................................45 3-1 Overview of test setup..................................................................................................... ..50 3-2 Physical length a nd span length defined............................................................................50 3-3 Moment diagrams for simply supported beam with various loading conditions...............51 4-1 Test setup overview........................................................................................................ ...55 4-2 Test girder buckling system model....................................................................................56 4-3 Eccentricities of load application point a nd bearing pad relative to center of gravity of test cross-section.......................................................................................................... ..57 4-4 Load application on test girder buckling analysis..............................................................57

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11 4-5 Load procedure for buckling analysis................................................................................58 5-1 Exploded view of test gird er with prestressing shown......................................................66 5-2 Test cross-secti on design flowchart...................................................................................67 5-3 Iterative process of precas t segment cross-section design.................................................68 5-4 Typical shipping of bridge girders.....................................................................................68 5-5 Final precast segment cross-section...................................................................................69 5-6 Final closure strip cross-section.........................................................................................70 5-7 End block width, controlled by bearing pad size and skew angle.....................................70 5-8 Final end block cross-section.............................................................................................71 6-1 Casting dates for girder components a nd final orientation of girder in FDOT laboratory..................................................................................................................... ......81 6-2 Precast segments formwork aligned on si ngle pretensioning bed at Dura-Stress.............81 6-3 Placing concrete in the precast segment formwork...........................................................82 6-4 Unstressed post-tensioning bars placed in ducts to keep ducts straight during placing of concrete.................................................................................................................... ......82 6-5 Tarp covers applied to each segment during curing..........................................................83 6-6 Precast segments after formwork removed at Dura-Stress................................................83 6-7 Precast segment arrival at the FDOT laboratory................................................................84 6-8 Duct couplers located within closure strips in bottom flange of girder.............................84 6-9 Duct couplers in closure strips, sealed with tape pr ior to concrete placement..................85 6-10 Closure strip formwork.................................................................................................... ..85 6-11 Placing concrete into the closure strip formwork..............................................................86 6-12 Embedded steel plate at t op surface of closure strip..........................................................86 6-13 Finished closure strip with formwork removed.................................................................87 6-14 Concrete used in closure strip and en d block concrete mix, showing presence of Propex Fibermesh 150 reinforcing fibers.......................................................................87

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12 6-15 Open end block formwork reveali ng mild reinforcement and lifting loops......................88 6-16 Anchorage zone mild steel reinforcement in end blocks...................................................89 6-17 Completed end block formwork........................................................................................90 6-18 Placement of concrete in north end block formwork.........................................................90 6-19 End block after removal of formwork...............................................................................91 6-20 Leveling plates and anchor pl ates at bottom of end block.................................................91 6-21 Moist cured cylinde rs submerged in a tank of lime water.................................................92 6-22 Typical cylinder failure types observe d during compressive strength testing...................92 6-23 Bar identification numbers used during post-tensioning...................................................93 6-24 Test girder during post-tensioning, braced against steel catch frames using timber blocking....................................................................................................................... .......93 6-25 Post-tensioning jack setup................................................................................................ ..94 6-26 Post-tensioning jack and pressure gage.............................................................................94 6-27 Camber measurement at midspan of test girder immediately after completion of post-tensioning................................................................................................................ ...95 6-28 Grout mixer and high capacity air compressor..................................................................95 6-29 Lifting the test girder into testi ng position, prior to end block fabrication........................96 7-1 Undesirable horizontal rest raining component that develo ps in an anchored loading system......................................................................................................................... .....104 7-2 Dimensions, defined........................................................................................................104 7-3 Instantaneous center....................................................................................................... ..105 7-4 UF/FDOT gravity load simulator.....................................................................................106 7-5 Spherical roller bearing................................................................................................... .107 7-6 Hydraulic jack connection to simulator center pin..........................................................107 7-7 Gravity load simula tor displaced shape...........................................................................108 7-8 Knife edge at load applicati on point at top of test girder.................................................109

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13 7-9 UF/FDOT gravity load simulator and load frame in testing position..............................109 7-10 Definition of percent of si mulator load applied laterally.................................................110 7-11 Gravity load simulator model..........................................................................................110 7-12 Results of simulator analysis: theoretical pe rcent of load applied laterally to the beam at the load application point (s elf weight excluded in model).........................................111 7-13 Results of simulator analysis: theoretical pe rcent of load applied laterally to the beam at the load application point (s elf weight included in model)..........................................111 7-14 Effect of simulator self weight and c ounterweights on verticalness of load line of action......................................................................................................................... .......112 7-15 Counterweight system......................................................................................................113 8-1 Overall test setup......................................................................................................... .....122 8-2 Roll stiffness results..................................................................................................... ....123 8-3 Bearing pad skew angle or ientation in buckling tests......................................................123 8-4 Beveled plate used to impos e slope angle on bearing pads.............................................123 8-5 Beveled plate and bearing pad positi oned between end block and end support..............124 8-6 Bearing pad orientation a nd initial pressure distribu tions during buckling tests.............124 8-7 Final bearing pad pressure di stributions during buckling tests........................................125 8-8 Sweep of test girder....................................................................................................... ..125 8-9 Jack used to straighten test girder....................................................................................126 8-10 Typical load time history.................................................................................................126 8-11 Naming convention for buck ling test instrumentation.....................................................127 8-12 Midspan displacement transducers..................................................................................128 8-13 South end block displacement transducers......................................................................129 8-14 Load cells, located at gravity load simulator locations....................................................129 8-15 Vibrating wire strain gage s, cast into closure strips........................................................130 9-1 Test girder in buckled configuration................................................................................143

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14 9-2 Definition of applied load (P)..........................................................................................143 9-3 Measured absolute load-displacem ent data.....................................................................144 9-4 Measured incremental load-displacement data................................................................144 9-5 Southwell hyperbola fit....................................................................................................145 9-6 Data curve fitting procedure............................................................................................145 9-7 Best fit hyperbolas for each configuration.......................................................................146 9-8 Hyperbolic curve fit and Southwe ll buckling load for test A-45-0-1..............................146 9-9 Definition of buckling capacity.......................................................................................147 9-10 Description of in-situ roll test.......................................................................................147 9-11 Moment-rotation data from in-situ tests..........................................................................148 9-12 Data curve fitting procedure, in-situ case shown.............................................................149 9-13 Moment-rotation curves, from isolat ed and in-situ roll stiffness tests.............................150 9-14 Moment-rotation curves, test configurati onA-0-0, from isolated bearing pad tests (BPTD) and in-situ tests...................................................................................................150 9-15 Bearing pad contact areas during testing.........................................................................151 9-16 Bearing pad contact areas during both isolated roll stiffn ess tests and buckling tests....151 9-17 Moment-rotation curves, from isolated ro ll stiffness tests (scaled and original) and in-situ roll stiffness tests..................................................................................................152 9-18 Moment-rotation curves, scaled fr om isolated bearing pad tests.....................................153 9-19 Comparison of experiment al and FE buckling curves.....................................................153 9-20 Buckling curves from experimental tests and finite element models..............................154

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15 LIST OF ABBREVIATIONS A cross-sectional area (in2) C.G. center of gravity Ix strong axis moment of inertia (in4) Iz weak axis moment of inertia (in4) J torsional constant (in4) O.C. on center OD outer diameter My end moment about y-axis y height of centroid (in) vertical asymptote horizontal asymptote diameter 0 functional parameter 1 functional parameter 2 functional parameter

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16 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 Science EXPERIMENTAL VALIDATION OF BRAC ING RECOMMENDATIONS FOR LONG-SPAN CONCRETE GIRDERS By Megan Salvetti Beery May 2012 Chair: Gary Consolazio Cochair: H. R. (Trey) Hamilton Major: Civil Engineering During the construction process, flexible s upport conditions provide d by steel reinforced neoprene bearing pads supporting pr ecast, prestressed girders may allow the girders to become unstable, rolling about an axis parallel to the sp an of the girders. Imposed skew and/or slope angles significantly reduce bearing pads roll st iffness, which reduces girder buckling capacity due to gravity loading. In this thesis, roll stiffnes ses for bearing pads under skew and slope conditions are determined from experimental data gathered usi ng a test device designed to measure such values. The test device reproduces the forces and deform ations that act on a be aring pad in the field while simultaneously permitting axial load, skew angle, and slope angle to be controlled independently, so that the effect of each on beari ng pad roll stiffness can be quantified. In total, 108 bearing pad tests were performed on three di fferent standard beari ng pads, with varying severities of imposed skew and slope angle. Documentation of full scale girder bu ckling tests designed and conducted to experimentally quantify the influe nce of bearing pad roll stiffne ss on girder buckling capacity is also included in this thesis. Th e pads used to support each en d of the test girder during the

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17 buckling tests were the same pads previously tested to determine roll stiffness. In total, nine buckling tests were conducted, with various sk ew and slope conditions imposed on the bearing pads. Validation of analytical models (corres ponding to the test setup) was carried out by comparing the buckling capacity predictions from analytical simulations to experimental test results.

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18 CHAPTER 1 INTRODUCTION Precast, pretensioned concrete bridge girders in simple span construction are typically supported on reinforced neopr ene bearing pads (Figure 1-1A). Neoprene bearing pads transfer vertical load from the girder to the support and allow lateral m ovement of the girder, due to thermal expansion and contraction. During girder erection, the self weight of the girder is gradually applied to the bearing pad as the cables from the crane supports are removed. Before diaphragm or deck installation, the girder may beco me unstable and rotate a bout an axis parallel to the span of the girder (Figure 1-1B). Bearing pad roll stiffness combined with the effects of bracing stiffness and torsional bu ckling dictates the point of gi rder instability under girder self-weight (gravity) loading. In the case of girders supported by reinforced neoprene bearing pads, the roll stiffness of the end restraints can be severely reduced by skew angle (Figure 1-2) and slope angle (Figure 1-3). According to the Precast Concre te Institute (PCI) Bridge Design Manual (2003), skew angle is defined as the an gle between the centerlin e of a support and a line normal to the roadway centerline (Figure 1-2). Slope angle is define d as the vertical angle between the bottom surface of the girder and the top surface of the bearing pad (Figure 1-3), and may be produced by camber (induced by eccentric prestressing of the girder), construction tolerances, bridge grade, or a combination of all three. Previous analytical research (Consolazio et al. 2007) has been conducted to quantify the roll stiffness of bearing pads under various angles of skew and slope. It was found that the roll stiffness of bearing pa dsand therefore the buckling capacity of bridge girdersis signif icantly reduced by the imposition of skew and slope angles.

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19 Objective The research presented in this thesis is to experimentally expand upon the previous analytical research (Consolazio et al. 2007) conducted to determine the effect of imposed skew and slope angles on the roll stiffness of bear ing pads and the buckling capacity of girders supported on these bearing pads. There were two di stinct phases of the wo rk presented in this thesis: isolated roll stiffness tests and girder buckli ng tests. In the isolated roll stiffness tests, roll stiffnesses for bearing pads under skew and slop e conditions are derived from the experimental data gathered from a test device designed to measure such values. In the second phase, a full scale girder buckling test progr am was designed and conducted to experimentally quantify the influence of bearing pad roll stiffness on girder buckling capacity. The pads used to support each end of the test girder were the same pads prev iously testedto determine roll stiffnessin the first (roll stiffness) phase of this study. Scope In the first phase of the current study, an expe rimental test device wa s developed to enable determination of bearing pad roll stiffness under the types of loading conditions that arise during bridge construction. The test de vice reproduces the forces acting on a bearing pad in the field while simultaneously permitting axial load, skew angle, and slope angle to be controlled independently, so that the effect of each on beari ng pad roll stiffness is quantified. A total of 108 tests were performed on three di fferent standard bearing pads, w ith varying severity of imposed skew and slope angle. In the second phase of the current study, th e scope of the experimental test program included the design and construction of a full scale test girder; a ve rtical loading system; and end supports that enabled various combinations of slope and skew to be imposed on the supporting bearing pads. In total, nine (9) buckling test s were conducted, with various skew and slope

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20 conditions imposed on the supporting bearing pads. Analytical models corresponding to the test setup were developed and used to simulate the experimental buckling te sts. Validation of the models was then carried out by co mparing the buckling capacity pr edictions from the analytical simulation to experimental test results. Literature Review Although roll stiffness of a bearing pad is impor tant regarding girder instability during the construction process, most research to date has focused on bearing pad stiffnesses that relate to the final constructed configuration of the bridge The roll stiffness of bearing pads regarding girder instability during the c onstruction stage has not been ad equately explored. Similarly, several research pr ograms have conducted experimental te sts to investigate girder instability, primarily focusing on lateral torsi onal buckling. The effect of reduced roll stiffnessdue to skew and slope angleson girder buckling cap acity has not yet been quantified. Bearing Pad Properties Isolated experimental beari ng pad tests have been conduc ted to quantify bearing pad stiffness parameters, such as the effect of shear strain rate on the shear modulus of bearing pads (Allen et al., 2010), stress capaciti es and stress-strain limits of co tton duck bridge bearing pads in shear, compression, and rotation (Lehman et al., 2005), and long term load effects on bearing performance (Doody and Noonan, 1999). Muscarella and Yura (1995) also experimentally analyzed isolated bearing pads to determine th e shear, compressive, and rotational stiffnesses, with emphasis on the difference in behavior of flat and tapered bearings. However, the rotational stiffness they calculated was about an axis perpe ndicular to the span of the girder, or a rotation induced by service loads, as opposed to gird er instability during construction. Similarly, Vidot-Vega et al. (2009) experimentally determin ed the rotational stiffn ess of multiple bearing pads resisting moment in series due to rotation about an axis perpendicular to the span of the

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21 girder, using a test device comprised of a contin uous span over the support, pertaining to the final constructed config uration of the bridge. Using analytical modeling, Yazdani et al. ( 2000) computed bearing pad shear, axial, and roll stiffnesses to determine the effect of ne oprene bearing pads on th e performance of fully constructed precast prestressed concrete bridges. Green et al. (2001) fo cused on the effect of skew angle on the performance of the final c onstructed bridge, examining the deflection and tensile stresses in girders with varying severity of skew, also through the use of analytical models. The current study, therefore, is unique in that it focused on experimentally evaluating the influence of imposed skew and slope angles on the roll stiffnessabout an axis parallel to the girder spanof bearing pads as related to gi rder instability during th e construction process. Girder Buckling As previously stated, several experimental tests have been conducted to investigate girder instability, including lateral tors ional buckling testing of steel I-shapes (Yura and Phillips, 1992), lateral-torsional buckling behavior of fiber reinforced polymer I-s haped cross-sections (Stoddard, 1997), and lateral stability of slender rectangul ar reinforced concrete beams (Kalkan, 2009). Deaver (2003) investigated to rsional bracing by simulating buckli ng of a two-beam system with midspan bracing. Mast examined the lateral bend ing stability of prestr essed concrete beams when they are suspended from lifting loops (198 9) and supported below by elastomeric bearing pads and on trucks and tractors (1993). Lateral-torsional buckli ng and rollover instability of prestressed girders supported on bearing pads was investigated by Hurff (2010). However, Hurff focused on the instability due to girder se lf-weight eccentricity caused by fabrication imperfections (prestress eccentricity, cracking, sola r radiation) and support conditions (unlevel bearing surface). The current study, therefore, is unique in that experimental tests were performed to quantify the buckli ng capacity of a test girder supported on bearing pads with

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22 known roll stiffnesses under skewed and slope d conditions. Additionally, the experimental buckling tests were used to validate finite el ement buckling models, which incorporated the roll stiffness results from the isolated roll stiffness tests.

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23 A Girder Bearin g p a d Support B Bearing pad Girder Rolling motion about centerline of bearing pad along axis parallel to the girder span Figure 1-1. Description of physi cal system. A) Girder suppor ted on bearing pads during bridge construction. B) Rolling motion of girder that occurs during instability (buckling). Girder Support Support centerline Bearing pad Skew angle Roadway centerline Skew angle Figure 1-2. Plan view of girder, pad, and support with skew angle defined

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24 Girde r Su pp or t Slope angle Bearing pad Figure 1-3. Elevation view of girder, pa d, and support with slope angle defined

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25 CHAPTER 2 ISOLATED BEARING PAD ROLL STIFFNESS TESTS Experimental Test Setup An experimental test device (Figure 2-1) was developed to enable determination of bearing pad roll stiffness under the types of loading c onditions that arise during bridge construction. A key aspect in the design of the te st device was the need to maintain a constant axial load on the bearing pad (to simulate consta nt gravity-induced girder reacti ons) as roll rotation of the pad occurred. Equally important, the test device was designed to be capable of simulating girder support conditions in which skew, slope, or combin ed skew and slope are present. A structural tube within the device represents the bridge girder axis and is us ed to impose, and hold constant, the slope angle (Figure 2-2) and the axial load on the pad. Tw o 5 in. thick steel bearing plates at the center of the test device, which were effectiv ely rigid in comparison to the stiffness of the bearing pad, represent the bottom surface of th e girder and the top surface of the bridge abutment, respectively. Simulating a skewed a lignment between girder and bearing pad was achieved by positioning the pad at the desired skew angle (relative to the axis of the tube, Figure 2-3) between the steel bearing plates. As c onstructed, the test device was capable of imposing desired combinations of axial load, skew angle, and slope angle on the bearing pad for the purpose of evaluating pad roll stiffness. Fabr ication plans for the bearing pad test device can be found in Appendix A. Each bearing pad test conducted in this study consisted of three stages: positioning, clamping, and rolling. In the positioning stage, th e bearing pad and test device were configured to impose the desired skew and slope angles on the pad. Subsequently, the pad was clamped within the test device such that a target axia l load on the pad was ach ieved. Holding the axial load constant, a moment was then applied to the test devicethrough ap plication of vertical

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26 loads acting at the ends of the outriggers (Figure 2-1)to produce a ro ll rotation on the pad, thereby simulating the unrestrained rolling motion of a girder during instability (buckling) in the field. For each test thus perf ormed, bearing pad roll stiffness was quantified by determining the slope of the linear relationship between moment imposed on the pad, and the resulting measured roll angle. Instrumentation Axial load cells (Interface, model 1232, 100 kip capacity), which were used to measure total axial load applied to the bearing pad, were located below the steel bearing plates and were arranged in a statically determin ate tripod configuration (Figure 2-1) to ensure that contact between load cells and bearing plates was mainta ined at all times. Using a tripod configuration also enabled the location of the bearing pad pressu re resultant to be determined, relative to the center of the bearing pad, at any point during a ro ll stiffness test. Washer load cells (Interface, model LW25100, 30 kip capacity) were used to measur e vertical roll loads applied to the ends of the outriggers and to compute ro ll moments imposed on the bearing pad. As the roll loads (and corresponding moments) were applied, an in clinometer (FRABA Po sital CanOPEN, +/0.087 rad. range, 17 rad. resolution) measured the roll angle imposed on the bearing pad. Redundancy in roll angle measurement was achie ved by using displacement transducers (TML model CDP-50 and CDP-100, 50 mm and 100 mm (2 i n. and 4 in.) stroke, respectively) to measure relative vertical displa cements between the steel beari ng plates. Knowing the horizontal distance between the displacement transducers, th e roll angle imposed on the bearing pad could be calculated from the relative displacement meas urements and used to confirm the inclinometer reading. Displacement transducers were also us ed to monitor horizontal movements of the bearing plates to confirm that shear deforma tions generated in the bearing pad remained negligibly small during testing.

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27 Test Procedure As noted earlier, each bearing pad roll stiffne ss test conducted in this study involved three distinct stages: positioning, clamping, and rol ling. Rotations and loads imposed on the pad during each of these stages are identified using coordinate axes defined in Figure 2-1. Examining the global x-y-z coordinate system, both the xand y-axes are level (horizontal), have their origins at the top surface of the undeformed bearing pad, and ar e aligned with the centerlines of the outriggers and tube, respectiv ely. The global z-axis is alig ned vertically; positive upward. Positioning Stage Each test began by positioning the test devi ce on the bearing pad so as to produce the desired slope and skew angles. Slope angle was defined as the vertical angle (Figure 2-2) between the axis (aligned with the sloped tube) and the y-axis (defined previously). Slope was imposed on the bearing pad by rotating the uppe r portion test device (t he portion above the bearing pad) about the global x-axis of the sy stem. In non-sloped tests, the tube was positioned level (horizontal) and the yand -axes were identical. Once the desired slope angle was imposed, the elevations of the y-positive and y-negative ends of the tube (Figure 2-2) were locked-off at the correct heights, such that they remained constant throughout the test. Note that the line passing through the y-positive and y-negative hinges was sloped, and aligned with the -axis, ensuring that the top portion of the test device rolled about the -axis, thereby mimicking girder moti on during a buckling/overturning event. Skew angle was imposed, during insertion of the bearing pad between the bearing plates, by rotating the bearing pad about the z-axis (Figure 2-3). Skew angle was defined as the angle between the long axis of the bearing pad and the x-axis of the test device. When positioning the bearing pad at the desired skew angle, the be aring pad was also centered at the z-axis as illustrated in Figure 2-3.

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28 Clamping Stage During the clamping stage, axial load was grad ually applied to the bearing pad by applying clamp loads to the top surfaces of both ends of the tube (Figure 2-2). At the beginning of the clamping stage, the piston of the hollow core hydraulic jack (Figure 2-1) on the y-positive end was fully retracted, and the y-negative end of the tube was locked-o ff. As the piston was subsequently extended, the y-pos itive end of the tube moved in the negative z-direction (downward), while the movement of the y-negative end of the tube rema ined restrained. This caused the load produced by the hydraulic jack on the y-positive end of th e tube to be mirrored on the y-negative end. In applying the clamp lo ads through restrained movement, a slight increase of the slope on the pad occurred but wa s accounted for in advance such that the tube was at the correct slope at the e nd of the clamping stage. Full app lication of the target axial load signified the end of the clamping stage, after whic h the load was held cons tant for the remainder of the test (to within an acceptabl e deviation from the target axia l load of +/-5% of the target axial load). Since the clamp loads were applied perpendicu lar to the top surface of the tube (Figure 22), the potential existed for inducing a shear load on the beari ng pad (in the y-direction) when the test device was configured with a non-zero slope angle. Therefor e, to properly simulate field conditions (where no shear load would be induced), a shear re straint rod (Figure 2-2) was used to prevent the top frame from moving in the y-di rection relative to the bottom bearing plate. Rolling Stage Girder roll in the field, as would occur duri ng buckling, was simulated in the laboratory by rolling the test device ab out an axis parallel to the longitudi nal axis of the bottom of the tube, aligned with the center of the b earing pad, referred to as the -axis (Figure 2-2). When performing a non-sloped test, th e tube was level and the -axis was aligned to the y-axis. Equal

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29 and opposite vertical roll loads we re applied to the ends of th e outriggers to impose moment about the centerline of the bearing pad (Figure 2-4). At the beginning of the rolling stage, no roll loads were applied to the ends of the outriggers. As the rol ling stage progressed, moment and corresponding roll rotation were increased in a step-wise manne r, allowing the change of roll rotation to be measured at each load increment. The individual roll loads were applied iteratively to create the moment on the bearing pad, first gradually increasing the upward load to the x-negative outrigger until a specific target was reached, and then by increasing the downward lo ad to the x-positive outrigger until the loads being read by both roll load cells were equal. Throughout the roll stage of each test, the method of roll load application was load-controlled. A hydraulic jack provided the upward load to the x-negative outrigger, which was increased gradually until a specific load difference was read between the two roll load cells. With the hydrauli c jack locked off, the displacement of the x-negative end of the outrigger was maintained wh ile load was applied to the x-positive end of the outrigger. A nut was threaded downward to b ear against the end of the x-positive outrigger; the downward displacement produced was depende nt upon the number of turns of the nut. By turning the nut until both roll load cells read equal loads (to within an acceptably small tolerance), a pure moment was induced on the beari ng pad about its centerlin e. Multiple sets of moment and roll angle were achieved using this iterative process, allowing moment to be measured as a function of roll rotation, to ultima tely determine the roll stiffness of a bearing pad. Test Program Composite bearing pad details for prestressed co ncrete girder cross-se ctions are specified in the Florida Department of Transportation (FDOT) Design Standards, Index No. 20500 (2010). The three different pad sizes (d enoted A, B, and C; Figure 2-5) tested for roll stiffnesses in this study were those typically used in conjunction wi th the American Association of State Highway

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30 and Transportation Officials (AAS HTO) Type V and VI sections as well as the Florida Bulb-T sections (FDOT 2010). Basing the standard bear ing pad sizes on girder cross section, the AASHTO Type V and VI and Florida Bulb-T sections are often used in long span configurations, making them more prone to girder instability than the smaller sections. Two specimens of each pad type were tested, for a to tal of six specimens (denoted A1, A2, B1, B2, C1, and C2), so that the repeatability of the test results could be evaluated. Although the FDOT Design Standards (2010) specify required shear moduli for the standard bearing pads, the AASHTO LRFD Bridge Design Specifications Table 14.7.5.2-1 (2004) provides a relationship between shear modulus and durometer hardness. To determine whether the bearing pads acquired for this st udy were manufactured in accordance with the FDOT requirements, the durometer hardness of each specimen was measured. The measured values were then compared to the equivalent durometer hardnesses that were determined to match the shear moduli specified by FDOT. It was found that each specimen had a measured durometer hardness equal to or exceeding the FDOT requirements (Table 2-1), except specimen C2. In addition to confirming durometer hardness, prior to the end of the test program, external elastomer cover material around the edges of bearing pads C1 and C2 was trimmed off to visually confirm the thicknesses of the internal elastomer layers. Both of the bearing pads modified through this trimming pro cessreferred to as pads C1mod and C2mod to distinguish from the original, unchanged pads C1 and C 2had internal elastomer layers of uniform thickness, to within the tole rance suggested by the National Cooperative Highway Research Program (NCHRP) Report 449 (Yura et al. 2001) revisions to the AASHTO M251 Specification of +/-3 mm (+/-0.12 in.).

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31 Each bearing pad specimen was first test ed under non-skewed, non-sloped conditions and then tested under different comb inations of skew and slope to determine the effect of each on bearing pad roll stiffness. Maximum slope an gle tested was 0.04 rad. (based on camber, construction tolerance, and bridge grade) and the maximum skew angle tested was 45 deg. At the extreme, a combination of both 0.04 rad. of slope and 45 deg. of skew was tested. Intermediate slope angles of 0.02 rad. and 0.03 rad. were also included in the study to quantify roll stiffness reduction as a function of slope severity. The naming system used to identify each configuration tested was T-x-y, where x=skew angle (deg.), and y=slope angle (ra d.). For example, test configuration T-45-04 refers to a test performed at a 45 deg. skew angle and a 0.04 rad. sl ope angle. Bearing pad specimen identifiers (A1, A2, B1, B2, C1, C2) were also combined wi th configuration indicat ors to identify specific tests. For example, A1-45-04 refe rs to a test performed on bearing pad specimen A1 at a 45 deg. skew angle and a 0.04 rad. slope angle. When discussing an averaged valuesuch as roll stiffnessbetween two specimens, A-45-04 refers to the average value of all of the tests performed on A1-45-04 and A2-45-04. Using this naming convention, the skewed and sloped test conditions that were conducted on each bearing pad are presented in Table 2-1, in which an X indicates that tests were performed in that given configuration. Multiple test repetitions were performed in each configuration and on each specimen to ensure re peatability of the test device and results. Individually determined axial load levels were assigned to each bearing pad type (A, B, C) to ensure similar bearing pad axial pressures, rega rdless of bearing pad si ze. Also, while all pad configurations were tested under high axial lo ad (pressure), for cases B1-0-0, B2-0-0, and C1-0-0, additional low load (press ure) tests were also performed.

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32 Repeated Axial Compression Prior to conducting this study, it was not known whether repeat ed loading, which is known to cause softening of neoprene when loaded in shear (Gent 2001), would a ffect the roll stiffness results obtained. Cyclic softening of neoprene unde r shear loading is called the Mullins effect and is recognized by the American Society for Testing and Materials (ASTM) as a phenomenon that must be accounted for when experimentally determining the shear modulus of a bearing pad (2003). Although there is no ASTM requirement for testing a bearing pad cyclically in compression, it was deemed necessary to do so in this study to determine if a similar effect occurred when testing for the roll stiffness. Multiple tests were performed on each bearing pad specimen, and in each configuration, however signi ficant softening of the bearing pad was never observed. Therefore, it was conc luded that no axial softening phe nomenon, similar to the Mullins effect for shear, was present at the lo ad levels used in the test program. Variation of Axial Compression Load As noted previously, selected roll stiffness te sts were performed at both low and high axial loads to determine whether variations in axial lo ad would affect bearing pad roll stiffness. The low and high loads assigned to each bearing pad t ype were chosen to approximate the self weight end reactions of the Florida Bulb-T 72 and 78 se ctions, at the longest length reasonable for current design practice (Consolazio et al. 2007). At the maximum practical span length of 43 m (140 ft.), the end reaction of the Florida Bulb-T 72 was used as the low axial load, whereas the end reaction of a Florida Bulb-T 78 with a span of 49-55 m (160-180 ft.) was used as the high axial load. Roll stiffness test results indicated that, over an axial load range that is typical of field conditions, bearing pad roll stiffnes s was not significantly affected by axial load level (average roll stiffness at low load was approximately 22% smaller than roll stiffness at high load).

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33 Ultimately, the high axial load level was chosen for the remainder of the test program, to represent the self we ight of a long span Florida Bulb-T 78. Results For a given girder cross-secti on, span length, and bearing pad, gi rder stability is greatest when bearing pad roll stiffness is maximized. Ideal conditions for maximizing bearing pad roll stiffness correspond to the T-0-0 (non-skewed, n on-sloped) configuration included in the test program. Confirming the ideal nature of the non-skewed, non-sloped configuration, the T-0-0 test results for each pad always had a higher initial roll stiffness than pads tested in the most severe non-ideal configuration, T-45-04 (45 deg. skew, 0.04 rad. slope). In Figure 2-6, a representative set of moment-rota tion results, obtained from test ing pad B2 in the T-0-0 and T45-04 configurations, illustrate s the extent to which roll s tiffness may be reduced by the introduction of non-ideal conditions. Performed on the same bearing pad specimen and at the same axial load level, the tests that generated the results shown in Figure 2-6 differed only in skew and slope. As will be demonstrated later, intermediate configurations (e.g. T-45-0, skewed but not sloped) had, on average, roll stiffnesses that fell between the tw o extreme cases (ideal: T-0-0 and severe: T-45-04). As shown in Figure 2-6, data from the ideal case exhibit an initial, linear roll stiffness that is followed by an apparent soften ing (reduction in stiffness) at la rger roll angles. This stiffness reduction corresponds to the upper b earing plate of the test device gradually losing contact with the pad and eventually rolling off the pad. With regard to the calculation of girder buckling capacity, it is the initial, linear roll stiffness of the bearing padand therefore the slope of the initial, linear portion of the moment-rotation (ro ll) curvethat is of primary importance. An algorithm was established to consistently determ ine the number of points contained within the initial, linear portion of each moment-rotation data set obtained, through which a linear

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34 regression line was generated. The roll stiffness (kr) of each bearing pad was defined as the slope of the linear regression line th rough the initial, linear porti on of the moment-rotation curve (Figure 2-6). Moment-rotation curves obtained for all roll sti ffness test performed in this study, grouped by bearing pad specimen, are presented in Figure 2-7. Generally, the moment-rotation curves for the intermediate cases fell between the two extreme cases (T-0-0 and T-45-04), with good repeatability of the data within each specimen and configuration. Whereas tests with zero slope generally exhibited both linear a nd nonlinear portions of the moment-rotation curve, most of the tests with non-zero slope exhibited moment-rota tion curves that remained essentially linear throughout the entire test. Location of Pressure Resultants on Bearing Pads Initial roll stiffness, as well as whether a bearing pad exhibite d linear or non-linear behavior, depended upon the location of pressure resultants on the bearing pad. Under conditions of combined skew and slope, significant reductions in roll stiffness were clearly evident from the test data. Such reduction of stiffn ess occurs due to the eccentricity of the pressure resultant of the axial load on the bearing pad. As a girder (or th e bearing pad test device) rolls on a bearing pad, the pressure distribution on the pad becomes more concentrated on the side of the pad that corresponds to the direction of roll. This causes the location of the pressure resultant to move as well, becoming increasingly eccentric from the center line of the girder with increasing roll angle. Figure 2-8 presents pressure distribut ions and pressure resultant locations at various stages of roll angle leading ultimately to girder instab ility. In the non-skewed configurations (Figure 28A and Figure 2-8B) a large eccentricity between the gird er centerline and the pressure resultant is available to resist overturning moment app lied during girder roll. In contrast, although the skewed, non-sloped case (Figure 2-8C) begins with a concentric loading similar to the non-

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35 skewed, non-sloped case (Figure 2-8A), a smaller eccentricity develops during girder roll, thereby decreasing the roll stiffness. The smallest available eccentricity occurs under the skewed, sloped configuration (Figure 2-8D), which also produces th e least roll stiffness. For configurations in which the moment-rotation curv es are non-linear, the eccentricity is most important at intermediate roll a ngles where the response transitions from linear to non-linear. At the point of girder instability, th e instantaneous eccentricity is an indicator of the secant stiffness at the corresponding roll angle, which is why th e non-skewed cases (wit h larger eccentricities) exhibit larger overall stiffnesses than do the skewed cases (recall Figure 2-7). The presence of an eccentric pressure distribution at the end of the rolling stage of tests conducted in the nonskewed, non-sloped configuration (Figure 2-8A) is evidenced by bulging at the edge of the pad, as shown in Figure 2-9. Linearity of the moment-rotation curve is contro lled by the portion of the bearing pad that remains in contact with the girder as it become s unstable. In sloped configurations, a larger portion of the bearing padopposite the direction of girder roll remains in contact with the girder than in the non-sloped conf igurations. Losing contact with th e girder on the side of the pad opposite the direction of girder roll causes nonlinearity in the moment-rotation curve. Data Trends Individual roll stiffnesses, determined from each test conducted in this study, are shown in Figure 2-10, together with mean values computed for each combination of bearing pad type, skew, and slope. For convenience, the mean ro ll stiffness for each combination of pad type, skew, and slope are also reproduced in Figure 2-11. Table 2-2 also presents corresponding roll stiffness reductions due to combinations of sk ew and slope as compared to the ideal T-0-0 configuration. Excluding the A-002 mean results, within each b earing pad type, the ideal case (T-0-0) had the largest roll stiffness, and the extreme skew and slope case (T-45-04) had the

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36 smallest roll stiffness, with intermediate configurations producing roll stiffnesses falling between the two. Examining Figure 2-11, the roll stiffness of the type C bearing pads was generally decreased after the modificati on of the bearing pads (C-0-0 to Cmod-0-0), which can be attributed to the trimming of the outer layer of rubber. Effect of Skew and Slope Combined The combination of skew and slope produced th e most severe reduction of roll stiffness. When slope is combined with skew, the average reductions of roll stiffnessrelative to the ideal T-0-0 case for configurations T-45-02 and T45-04 were 81% and 85%, respectively. This indicates that reducing the slope angle from 0.04 rad. to 0.02 rad. has little benefit if skew is also present. Furthermore, comparisons of results from test configurations T-45-02 and T-45-04 for each pad type (i.e., A-45-02 vs. A-45-04, B-45-02 vs. B-45-04, C-45-02 vs. C-45-04) reveal that the roll stiffness decreases onl y slightly in going from th e T-45-02 to the T-45-04 condition. Effect of Skew Comparing test results for configur ations T-0-0 to T-45-0 in Figure 2-11, it is evident that significant reductions in bearing pad roll stiffness resulted from the presence of skew only, regardless of specific bearing pa d type (A, B, C). Average roll stiffness reduction due to skew alone for all of the bearing pad types was 49%, with little varia tion in percent reduction when comparing different pad types. Effect of Slope There was an inconclusive trend in the roll stiffness reduction due to imposed slope angle alone. Decreasing roll stiffness due to increasing sl ope was observed in the type B bearing pads (i.e. roll stiffness decrease from B-0-0 to B-002, and from B-0-02 to B-0-03). However, for the modified type C bearing pads, when comparing the ideal (Cmod-0-0) co nfiguration to sloped configurations (Cmod-0-02 and Cmod-0-03), an insignificant reductions of stiffness resulted

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37 from imposed slope angle. [Note that roll stiffn ess reductions due to slop e alone as produced by configurations Cmod-0-02 and Cmod-0-03 are calculated in comparison to Cmod-0-0 (as opposed to C-0-0)]. Roll stiffne ss reduction due to slope was also inconclusive due to results obtained from the type A bearing pads, where the roll stiffness in creased from A-0-0 to A-0-02, but decreased from A-0-0 to A-0-04. However, this apparent anomaly may be related to the fact that the range of scatter in the data obtained for configuration A-0-02 was greater than that of any other configuration tested on the type A bearing pads (Figure 2-10).

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38 Table 2-1. Bearing pad dimensions, shear modul us, durometer hardness, and configurations tested for each specimen Bearing pad type A B C Bearing pad length, L (in.) 11 14 12 Bearing pad width, W (in.) 24 24 23 Bearing pad height, H (i n.) 1-29/32 2-9/16 2-9/16 Number of internal plates 3 4 4 Shear modulus (psi) 110 110 150 Equivalent durometer hardness (Grade) 50 50 60 Bearing pad specimen A1 A2 B1 B2 C1 C2 Measured durometer hardness (Grade) 53 50 53 52 61 53 Low axial load level (kip) 67 67 69 High axial load level (kip) 92 92 101 101 97 97 Test Configuration T-0-0 X X X, X* Test Configuration T-0-02 X X X* Test Configuration T-0-03 X X* Test Configuration T-0-04 X Test Configuration T-45-0 X X X Test Configuration T-45-02 X X X Test Configuration T-45-04 X X X Test configuration perform ed on modified bearing pad. Table 2-2. Mean roll stiffness and reduction in roll stiffness due to non-ideal (skewed, sloped) conditions Roll stiffness, kip-ft./rad. [Roll stiffness reduction] Configuration Pad A Pad B Pad C Pad Cmod 7004 11427 9737 6079 T-0-0 [0%] [0%] [0%] [38%]* 8597 7282 5810 T-0-02 [-23%] [36%] [4%] 5291 5490 T-0-03 [54%] [10%] 5360 T-0-04 [23%] 4067 5661 4490 T-45-0 [42%] [50%] [54%] 1740 1610 1764 T-45-02 [75%] [86%] [82%] 1339 1416 1372 T-45-04 [81%] [88%] [86%]

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39 y-axis Hollow core hydraulic jack Bearing plates Tripod of axial load cells x-axis z-axis Outrigger Outrigger Tube Hinge Shear restraint rod Shear restraint anchor Hydraulic jack Outrigger load cell Outrigger load cell (not visible) x-positive end x-negative end y-negative end y-positive end Hinge Figure 2-1. Bearing pad test device (photo courtesy of University of Florida, Department of Civil and Coastal Engineering) Tube Hollow core hydraulic jack z-axis Bearing pad Bearing plates Hinge Hinge Outrigger Shear restraint rod y-axis Shear restraint anchor A A Axial load cells Locking nut Load cell Load cell Nut -axis Slope angle Clamp load B B Slope angle C l a m p l o a d ( a p p l i e d p e r p e n d i c u l a r t o t u b e ) y c o m p o n e n t z c o m p o n e n t Figure 2-2. Elevation view of te st device: imposing slope (positioning stage) and applying axial load (clamping stage)

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40 A Bearing plate x-axi s y-axis Tube Bearing pad, 0 deg. skew angle Bearing plate x-axi s Bearing pad, 45 deg. skew angle y-axi s Tube B Figure 2-3. Imposing skew during the positioning stage, 0 deg. and 45 deg. skew shown (see Section A-A, Figure 2-2) Outrigger Axial load cells Roll angle Roll load Roll load Equidistance between roll loads creates moment about bearin g p ad centerline z-axis x-axi s Outrigger Tube Bearing pad Hydraulic jack Outrigger load cell Clevis Outrigger load cell Displacement control nut Figure 2-4. Applying loads to outriggers dur ing rolling stage (see Section B-B, Figure 2-2)

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41 10 gage steel plates (typ.) H 0.25 in. elastome r cover (typ.) 0.5 elastomer layer (typ.) in. internal H L or W W L L or W 0.25 in. elastomer cover layer (typ.) T yp ical section: Bearin g p ad t yp es B & C Plan view Bearing pad types A, B & C Typical section: Bearing pad type A Figure 2-5. Identification of bear ing pad dimensions (see Table 2-1 for actual dimensional values) Roll ( rad. ) Mo m e nt ( k i p f t ) 0 0.005 0.01 0.015 0.02 0.02 5 0 10 20 30 40 50 60 7 0 T-0-0 Linear portion T-0-0 Nonlinear portion T-0-0 Linear regression T-45-04 Linear portion T-45-04 Linear regression k-0-0r1 k-45-04r1 Figure 2-6. Representative moment-rotation curves configurations T-00 and T-45-04 (obtained from testing bearing pad B2)

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42 T-0-0 Tmod-0-0 T-0-02 Tmod-0-02 T-0-03 Tmod-0-03 T-0-04 T-45-0 T-45-02 T-45-04 ARoll (rad.)Moment (kip-ft.) 0 0.005 0.01 0.015 0.02 0 10 20 30 40 50 60 70 Roll (rad.)Moment (kip-ft.) 0 0.005 0.01 0.015 0.02 0 10 20 30 40 50 60 70 B CRoll (rad.)Moment (kip-ft.) 0 0.005 0.01 0.015 0.02 0 10 20 30 40 50 60 70 Roll (rad.)Moment (kip-ft.) 0 0.005 0.01 0.015 0.02 0 10 20 30 40 50 60 70 D ERoll (rad.)Moment (kip-ft.) 0 0.005 0.01 0.015 0.02 0 10 20 30 40 50 60 70 Roll (rad.)Moment (kip-ft.) 0 0.005 0.01 0.015 0.02 0 10 20 30 40 50 60 70 F Figure 2-7. Moment-rotation curves fo r all tests, grouped by pad specimen. A) Pad A1. B) Pad A2. C) Pad B1. D) Pad B2. E) Pad C1. F) Pad C2.

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43 A girde r instability non-skewed, non-sloped intermediate roll angle e bearing pad end of girder p ressure resultan t e initial conditions girder centerline girder roll B non-skewed, sloped e e C skewed, non-sloped e e D skewed, sloped e e e e Figure 2-8. Pressure distributions and axial load resultant pos itions on bearing pad: beginning, intermediate, and end of rolling stage. Configurations: A) Non-skewed, non-sloped. B) Non-skewed, sloped. C) Skew ed, non-sloped. D) Skewed, sloped.

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44 Figure 2-9. Bulging of the internal elastomer laye rs during roll stiffness te st (photo courtesy of University of Florida, Department of Civil and Coastal Engineering)

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45 Ro l l S t i f f n e s s ( k i p f t ) / r a d 0 4000 8000 12000 16000 2000 0 Specimen 1 Specimen 2 Mean A-0-0 A-0-02 A-0-04 A-45-0 A-45-02 A-45-04 B-0-0 B-0-02 B-0-03 B-45-0 B-45-02 B-45-04 C-0-0 Cmod-0-0 C mod-0-02 C mod-0-03 C-45-0 C-45-02 C-45-04 Figure 2-10. Bearing pad roll stiffnes ses for all configurations tested Ro l l S t i ffness ( k i p f t .)/ r ad.0 4000 8000 12000 16000 20000A-0-0 A-0-02 A-0-04 A-45-0 A-45-02 A-45-04 B-0-0 B-0-02 B-0-03 B-45-0 B-45-02 B-45-04 C-0-0 Cmod-0-0 C mod-0-02 C mod-0-03 C-45-0 C-45-02 C-45-04 7004 8597 5360 4067 1740 1339 11427 7282 5291 5661 1610 1416 9737 6079 5810 5490 4490 1764 1372 Figure 2-11. Mean bearing pad roll sti ffnesses for all configurations tested

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46 CHAPTER 3 INTRODUCTION TO GIRD ER BUCKLING TESTS The point at which a girder may reach instab ility in the field, during construction of a bridge, is dictated by several fa ctors, including cross-sectional properties of the girder, span length, geometric imperfections such as sweep, a nd bearing pad roll stiffness. As discussed previously in Chapter 2, bearing pad roll stiffness is signific antly reduced when skew, slope, or a combination of the two is imposed on a pad. In a previous analytical st udy (Consolazio et al. 2007), it was shown that imposition of skew and/or sloperesulting in reduced bearing pad roll stiffnessleads to decreased gird er buckling capacity. In the phase of the present study that is described in this and following chapters, a full scale girder buckling te st program was designed and conducted to experimentally quantify the infl uence of bearing pad roll stiffness on girder buckling capacity. Scope of Test Program The scope of the experimental test program included the design and construction of: a full scale test girder; a vertical loading system (c onsisting of gravity load simulators); and end supports that enabled various combinations of slope and skew to be imposed on the supporting bearing pads (Figure 3-1). The pads used to support each e nd of the test girder were the same pads previously testedto determine roll stiffn essin the first phase of this study. Rigid end supports elevated the test girder approximately 8 ft. above the lab floor to provide vertical clearance for gravity load simulators that were positioned beneath the beam (Figure 3-1). Each gravity load simulator (described in detail later) applied vertical load to the test girder in a manner that did not introduce any lateral stiffn ess. In total, nine (9) buckling tests were conducted, with various skew and slope conditi ons imposed on the suppo rting bearing pads. Analytical models corresponding to the test setup were developed and used to simulate the

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47 experimental buckling tests. Validation of the models was then carried out by comparing the buckling capacity predictions from the analytical simulation to experime ntal test results. Experimental Constraints Length of Test Girder Buckling tests were performed inside the FDOT M. H. Ansley Structures Research Center laboratory where the available length the strong floor permitted a maximum physical test girder length of 102 ft. With the overall (end to end) gi rder length limited to 102 ft., the effective girder span lengthas measured from center of bearin g pad to center of bear ing padhad to be a few feet shorter to accommodate pad skew at each end of the girder (Figure 3-2). For each pad skew angle tested, both bearing pads had to be complete ly contained within the footprint of the girder end blocks (i.e., no part of the pad was perm itted to protrude beyond the end of the physical length of girder). For reasons th at will be discussed in detail later, the type A bearing pads (described previously in Chapter 2) were used to support the e nds of the girder during the buckling tests. Rotating the t ype A bearing pad to the maximum skew angle of 45 deg. and allowing 5/8 in. clearance between the corner of the pad and edge of the girder end block (Figure 3-1), required that the ce nter of the bearing pad be locate d 13 in. from the edge of the test girder, making the span length 99 ft .-10 in., or approximately 100 ft. Loading Conditions Under field loading conditions, gi rder buckling is induced by the self weight of the girder, which consists of a uniformly distributed vertical load acting through the cen ter of gravity of the girder cross-section. To emulate such field loading conditions in the laboratory, id eally a uniform load would be applied, with no late ral restraint, through the center of gravity of the girder. In this study, devices called gravity load simulators (described in detail later) were designed, fabricated, and used to apply vertical loadswit hout lateral restraintto the test girder. Since

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48 such devices apply point loads ra ther than uniformly distributed loads, the uniform field loading condition was approximated in the laboratory using two point loads located approximately at the third points of the girder span (Figure 3-1). Originally, two possible loading conditions were investigated to determine the level of error that would be introduced by replacing the ideal uniform load ing condition with point loads: a single concentrated load applied at midspan, an d two equal concentrated loads applied at the third points. For each of the three loading conditi ons of interest (uniform load, midspan point load, and third point loads), moment diagrams for a simply supported beam, each with the same maximum moment, are presented in Figure 3-3. As shown, the shape of the uniformly loaded moment diagram is most closely matched by the pair of concentrated loads as opposed to the single concentrated load. In fact, the areas under the moment diagrams produced by uniform load and third point loads are exactly e qual. Therefore, two point loads we re applied to the test girder using gravity load simulators located approximate ly at the third points of the girder (applying loads at the precise third points was not practical due to laboratory strong floor embed locations). Gravity induced self-weight lo ads on the girder act, by de finition, through the center of gravity of the cross-section. A pplying laboratory loads through th e center of gravity, however, would have required the introduction of holes thr ough the web of the test girder, creating issues such as the potential for localized crushing of the concrete in the web, or cracking. To avoid these concerns, the point loads were instead applie d at the centerline of th e top surface of the test girder (Figure 3-1). Finite element analyses of both the center of gravity loading scenario and the top surface loading scenario were conducted to determine if the buckling loads corresponding to each loading scenario were sufficiently in agreement. Analysis results indicated minimal

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49 difference in buckling loads, therefore it was deemed acceptable to load the test girder at the top surface of the top flange. Elastic Buckling The buckling tests conducte d in this study were perf ormed for the purposes of experimentally demonstrating sensitivity of buc kling capacity to changes in bearing pad roll stiffness, and to collect data for validation of numerical models. Furthermore, to establish confidence in the experimental data, it was desira ble to demonstrate repeatability of the test results. Given these objectives, cracking of the concrete girder (parti cularly partial section cracking) was undesirable as it might have obscure d the influence of the pad roll stiffness and would have been very challenging to reproduce analytically. Additionally section cracking could have lead to differences in beam response from on e test repetition to the ne xt (for a fixed bearing pad configuration). ACI 318-11 Table R18.3.3 states th at if a girder enters the transition zone (i.e., the zone between the unc racked and fully cracked condi tions), then cracked section properties must be used to determine girder deflection. Since deflection was a key parameter measured during each laboratory bu ckling tests, it was desirable to design the te st girder to buckle elastically so that partia lly cracked section properties w ould not need to be used in interpreting the test results. Elastic behavior also ensured repeatability of the tests (which will be clearly demonstrated later in this thesis) and ensured that the only fact or influencing buckling capacity was bearing pad roll stiffness.

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50 Bearing pad Gravity load simulator Gravity load simulator End block Test girder End support Applied load (P) Applied load (P) Figure 3-1. Overview of test setup 45 deg. (maximum bearing pad skew angle tested) End bloc k Type A bearing pa d 5/8 Span length (99-10) Ph y sical len g th ( 102 ) Figure 3-2. Physical length and span length defined

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51 uniform load midspan point load third point loads L/2 L/3 L w P PP L/3 MomentDistance alon g len g th Mmax L/3 L/2 L 02L/3 Figure 3-3. Moment diagrams for simply suppor ted beam with various loading conditions

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52 CHAPTER 4 BUCKLING ANALYSIS Overview To facilitate the design of a test girder cross section that would buckle elastically at a span length of approximately 100 ft., fi nite element models of the gi rder and support system were developed using the finite element code ADINA (ADINA 2010). Girder models employing a variety of different trial crosssectional shapes were analyzed under the planned experimental test loading conditions to arrive at a cross-sectional sh ape that was expected to buckle elastically at a span length of 100 ft. This chapter descri bes the finite element models and the analysis procedures that were used to quantify girder bu ckling load and arrive at a suitable girder crosssectional shape. Finite Element Model of Experimental Test Setup As noted previously, buckling tests were pe rformed on a full scale test girder using a vertical loading system consisting of gravity load simulators and load frames. For reasons that will be discussed later in this thesis, it was nece ssary to construct the test girder in a segmental manner. Consequently, three component types, each with a distinct cross-sectional shape, were used to form the overall girder : precast segments, closure st rips, and end blocks (Figure 4-1). Gravity load simulators were used to apply vertical load to the top of the te st girder at the closure strip locations. To determine a girder cross-se ctional shape that would buckle elastically at a 100 ft span, buckling capacity analyses are carried out by co nducting large displacement analyses on systemlevel models (Figure 4-2) that combined beam elements (re presenting the test girder) and spring elements (representing the bearing pad). In this approach, loads are incrementally applied to the structure, and at each level of loading, static equi librium of the structure (stability) is solved for

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53 in the deformed configuration of the structure (i.e., taking into account the changes of geometry that have occurred as a result of the loads). In order to use such an approach to solve buckling problems, member imperfections (e.g., sweep) must be introduced into the initial configuration of the structure. Sweep imperfec tion of the girder is introduced by superimposing a second order lateral parabolic shape on the girder with maxi mum sweep occurring at mid-span. Inclusion of sweep in the girder model accounts for constructi on imperfections and also aids in initiating girder instability under the applied loads. Concrete components of the test girder are modeled using a li near elastic material model. During the test girder cross sect ional shape development stage of this project, a representative elastic modulus of 4,770 ksi was used for the concre te. This modulus was la ter updated to reflect results of modulus tests on concrete cylinders from the test girder. To achieve both computational efficiency and accuracy, a combination of standard Hermitian beam elements and warping beam elements are used to model the girder. Warping effects (resulting from torsion) ar e accounted for by means of an additional warping degree of freedom when using warping beam elements. In contrast, plane sections remain planar when using Hermitian beam elements. The slender precast segments and closure strips are modeled with warping beam elements to capture warpi ng effects if necessary. The relatively rigid end blocks are modeled using Hermitian elements. Regardless of type of element (Hermitian or warping), resultant cross-sectional properties are varied along the length of the test girder, depending on the section (precast segment, closur e strip, or end block) pr esent at each location (Figure 4-2). The girder elements are geometrically lo cated at the center of gravity (C.G.) of the test cross-section. The eccentricity between the bearing pad (described below) and the C.G. of the section is represented in th e model using rigid links (Figure 4-3). Similarly, rigid elements

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54 extend upward to loading points at the top surface of the physical beam. Ve rtical point loads are applied to these locations to simulate vertical loads applied by each gravity load simulator. Each bearing pad in the system model is represented using a set of six (6) spring elements consisting of three translational spring s and three rotationa l springs (Figure 4-2). Translational springsrepresenting the shear stiffness of the b earing pad (along the x-axis or y-axis) and axial stiffness (along the z-axis)are linear and base d on stiffness results fr om previous research (Consolazio et al. 2007). Simila rly, rotational springs representi ng pad torsional stiffness (about the z-axis) and roll about an axis perpendicular to the span of the beam (about the x-axis) were modeled as linear springs, with stiffnesses de termined from results of previous research (Consolazio et al. 2007). In cont rast, rotational springs about the y-axis (i.e., the roll axis) are nonlinear derived from roll stiffness results (moment-roll curves) quantified in Chapter 2, from the isolated bearing pad experiments. Loads acting on the girder model include uni form self-weight (graving loading), which acts through the center of grav ity of the section (Figure 4-4A), and concentrated vertical loads applied to the top of the section at the two closur e strip locations (Figure 4-4B). To analyze the girder for the purpose of quantifying buckling cap acity, loads are applied to the model in two stages (Figure 4-5). The uniform loading is increased in small steps (increments) from zero to the full self weight of the girder, th en held constant while the magnitude of the applied point loads is incrementally increased. At each incremental load step, girder displacements are computed by numerically satisfying static equi librium of the girder in the de formed geometric configuration. A buckling simulation is complete once equilibrium can no longer be estab lished, indicating that structural instability (b uckling) has occurred.

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55 Bearing pad Load frame Gravity load simulator Load frame Gravity load simulator End bloc k Closure strip Precast segment End block Closure strip Precast segment Precast segment Figure 4-1. Test setup overview

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56 Y (NORTH) X (EAST) Z End blocks: standard Hermitian beam elements Precast segments: warping beam elements Closure strips: warping beam elements P P Test girder shown straight for clarity Axial and rotational springs represent bearing pad Rigid beam elements to center of gravity (c.g.) of precast segment Test girder discretized into 82 beam elements Interface between end block and precast segment Interface between closure strip and precast segments Rigid beam element to load application (top of section) P P Sweep Figure 4-2. Test girder buckling system model

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57 Eccentricity load Eccentricity pad Center of gravity (C.G.) Rigid link to loading location Rigid link to bearing pad Bearing pad P P Axial and rotational springs re p resent bearin g p ad Precast segment End block Center of gravity (C.G.) Figure 4-3. Eccentricities of load application point and bearing pad relative to center of gravity of test cross-section A Uniform load (w) Beam elements along girder centroidal axis Concentrate d vertical load Rigid link to top of section P PB Figure 4-4. Load application on test girder buckling analysis. A) Uniform load. b) Concentrated vertical loads.

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58 Applied load Time P critical w selfweight Self weight a pp licatio n Concentrated load at which girder instability (buckling) occurs Uniform load (w) Concentrated vertical load (P) Figure 4-5. Load procedure for buckling analysis

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59 CHAPTER 5 DEVELOPMENT OF TEST-GIRDER CROSS-SECTIONS Under ideal circumstances, buckl ing tests would be performed on a typical section used in long-span girder construction. During the course of this project, the standard section for long-span construction was updated from the Fl orida bulb-tee (FBT) to the current Florida I-beam (FIB). Using the same pad types tested in the roll stiffness experiments, finite element buckling analyses were performed with the cross-sectional propert ies of several of the FBT and FIB sections. In the case of the non-skewed, non-sloped bearing pad orientations, the load required to buckle either type of section at th e available test span le ngth of 100 ft would cause significant cracking in the girder. To avoid violating one of the ini tial test setup constraints (the girder must remain in the uncrack ed zone), alternative cross-sec tions were explored that would buckle elastically in the laborator y at a 100 ft. span length. Prelim inary analysis indicated that the resulting test cross-section w ould need to be significantly more slender than a typical FBT or FIB section. To limit stresses induced during tran sportation, the test gird er was composed of three individual prestressed precast segments that were transporte d on a flatbed truck. Using segmental construction, post-tensioning was used to form a continuous test girder of the prestressed precast segments, clos ure strips, and end blocks (Figure 5-1). At the junction between each precast segment was a closure strip, which served as a means of connecting the precast segments together and also served as the location at which concentrated point loads would be applied. End blocks were used to provide sufficient bearing surface areas for the bearing pads located at the ends of the test gi rder, and to provide an anchorage points for the post-tensioning. The remainder of this chapter de tails each component of the segmental test girder and summarizes the basi s for design of each component. Complete construction drawings for the test girder can be found in Appendix B.

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60 Precast Segment Cross-Section Design Design of Girder Cross-Section Several analytical tools were used in th e test girder design process to determine cross-sectional properties of trial cross-sections (Mathcad), predict buckling loads (the finite element analysis software package ADINA), and calculate stresses throug hout the test girder using the predicted buckling loads (Mathcad). The procedure for designing the test girder cross-section is summarized in Figure 5-2. Beginning with the st andard Florida bulb-tee cross-section, a buckling analysis was performed. The strong and weak axis internal moments obtained from the buckling analysis (due to the pr edicted buckling loads) we re used to calculate concrete stresses along the length of the test gi rder, which also accounted for stresses due to prestressing. These stress calculati ons were performed at various st ages in the life of the test girder: during prestressing, during transport, a nd during testing. The calcu lated stresses at each stage were compared to the transition zone tens ile and compressive stress limits required by the FDOT Structures Design Guidelin e (2012) .3.1.C.3 and ACI318-11 .3.3, .4.1, and .4.2. If the calculated stress at any point ex ceeded these stress limits, then the trial cross-section design was rejected and a new cross-section was developed. A separate crosssectional analysis program was used to dete rmine cross-section properties (e.g., moments of inertia, torsional constant, warp ing constant) of trial sections by specifying the cross-section geometry. The cross-section properties of the new trial section were subsequently incorporated into the buckling model, and the process of determining the internal moments and checking stresses was repeated. Following this iterative process, several diffe rent test cross-sections were designed and evaluated to check for exceedance of permi ssible stress limits. For each iteration, the cross-section was altered to decr ease the buckling capacity of the test girder, thereby decreasing

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61 the stresses in the test girder. For long span slen der flexural elements, buckling capacity is highly sensitive to the weak axis moment of inertia (Iz) and torsional constant (J), in that decreasing either property decreases the buc kling load. Main taining a large strong ax is moment of inertia (Ix)and therefore maintaining a large strong-axi s moment capacity of the test girderis necessary to avoid cracking unde r the applied buckling load. The process of increasing sle nderness and reducing buckling capacity was initiated with the standard FBT78 cross-section, where portions of the protruding top and bottom flanges were removed (Figure 5-3). An iterative trimming process, ea ch subsequent section was designed to be less wide than the previous iteration, wh ile the height remained unchanged, effectively reducing the buckling load while maintaini ng moment capacity. Once the flanges were completely removed and the cross-section was st ill predicted to crack under the applied buckling load, the web thickness was trimmed as well. After several iterations, the sl enderness of the cross-section became an issue in regard to limiting stresses during shipping. Ty pically, if a girder is 100 ft long, it is transported by spanning between a truck and a trailer thus acting as a simply supported beam (Figure 5-4). Braces are provided at the ends to tie the girder to the truck or trailer and to brace it against overturning. In this manner, long-span prestresse d girders can be brought to a job site as one piece. However, the test girder cross-section in this project was designed to be very slender (relative to a typical bridge gird er), and would have been damaged in transport if the test girder were cast and transported as a single 100 ft unit. Consequentl y, the girder was designed to consist of three segments of approximately equa l length to facilitate shipping without damage. To further optimize the section, the trimming approach was continued until only minimum concrete cover (as per ACI 318-11 .7.3) was pr ovided to the post-tens ioning in the bottom

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62 flange. The final precast segmen t test cross-section (Figure 5-5) is thin (compared to a typical bridge girder) and as tall as a FBT78, with a small weak axis moment of inertia and torsional constant, coupled with a large strong axis mome nt of inertia to preven t cracking during buckling. Section properties for the final girder cross-section are summarized in Table 5-1. DYWIDAG galvanized steel duct (2.05 in. outer diameter) cast in each gi rder segment formed a conduit to accommodate DYWIDAG post-tensioned bar (1 i n. diameter), extending through the full length of the test girder (Figure 5-1). Pretensioned strand (0.6 in. diameter) was cast in each precast segment, which provided additional compression at the bottom of the segments to prevent cracking during transport and te sting. The pretensioned strand at the top of the section was lightly stressed, and served pr imarily to hang shear reinforc ement hooks prior to casting the segments. Mild reinforcement running along the length of each segment was placed throughout the depth of the section. Design of Closure Strip Cross-Section The primary function of the closure strips was to provide adequate c over for post-tensioned bar couplers and bar coupler housings that were placed between each precast segment. Typically in segmental construction using post-tensioned ba rs (as opposed to strands), the maximum length of bar available is less than the span length, and it therefore becomes necessary to couple post-tensioned bars together to form longer cont inuous bars. This approach was required in the case of the project test girder, because the total girder length wa s 100 ft and the DYWIDAG post-tensioned bar was only available in mill le ngths up to 60 ft. Acrylic bar coupler housings (3.2 in. outer diameter) were cast in the closure strips to form a conduit sufficiently large to accommodate DYWIDAG post-tensioned bar couplers (2 in. diameter). The width of the closure strip (9.5 in.) was controlled by minimum concrete cover requirements for the bar coupler housings, per ACI 318-11 .7.3 (Figure 5-6). Closure strip cro ss-section properties are

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63 presented in Table 5-2. As noted earlier, concentrated vert ical loads were app lied to the top of the test girder using gravity load simulators, at locations correspondi ng approximately to the span length third points. In an effort to mini mize localized cracking cause d by the application of concentrated point loads, closure strips were located at these loading locations, which permitted the loads to be applied to a wider cross-section. Embedded steel plates also served to minimize localized cracking at the top of the closur e strips. Grout tubes were provided for each post-tensioning duct at the closure strips. Design of End Block Cross-Section As noted previously, the end bl ocks were designed to allow sufficient bearing surface areas for the bearing pads located at th e ends of the test girder, and to provide anchorage points for the post-tensioning. For each bearing pad skew angle te sted, the bearing pads had to be completely contained within the footprint of the girder end blocks (i.e., no part of the pad was permitted to protrude beyond the width of the girder end bloc k). Consequently, the width of the end blocks (Figure 5-7) was selected so that the bearing pads had a large enough area to bear completely against the end block even at the maximum skew angle testeda 45 deg. skewed configuration. The end block cross-sectional shape is presented in Figure 5-8, with cross-section properties presented in Table 5-3. Anchorage zone reinforcement required for the post-tensioning bars wa s cast into the end blocks. In post-tensioned members, the anchorag e zone is defined as the portion of the member through which the concentrated prestressing force is transferred to the concrete and distributed across the section (ACI 318-11 .2), and is the general expression for combined general and local zones (FHWA 2004). In this project, DSI engineers supplied specifications for local zone reinforcement (mild steel), including the bar sizes and configuration, and concrete strength required before stressing the bars. Separately, ge neral zone reinforcement, was designed by the

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64 UF research team for the end blocks, and consis ted of a cage of hoops a nd ties in both vertical and horizontal orientations. Leveling plates were cast into the concrete en d blocks to provide a bearing surface for the anchor plates provided by DSI. Grout tubes for the post-tensioning duct protruded from the exterior of the end blocks. Lifting loops consisting of prestressing strand were cast in the end blocks and were designed to support and lift the test girder into place for testing after post-tensioning was complete.

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65 Table 5-1. Section properties of precast segments Section property name Section property value Area A 405.0 (in.2) Height of centroid y 38.39 (in.) Moment of inertia Ix 246,400 (in.4) Moment of inertia Iz 1,136 (in.4) Torsional constant J 3,765 (in.4) Table 5-2. Section properties of closure strips Section property name Section property value Area A 741.0 (in.2) Height of centroid y 39.0 (in.) Moment of inertia Ix 375,700 (in.4) Moment of inertia Iz 5,573 (in.4) Torsional constant J 20,640 (in.4) Table 5-3. Section properties of end blocks Section property name Section property value Area A 2,184 (in.2) Height of centroid y 39.00 (in.) Moment of inertia Ix 1,107,000 (in.4) Moment of inertia Iz 142,700 (in.4) Torsional constant J 442,200 (in.4)

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66 End blocks: provide sufficient bearing surfaces for pads, and provide an anchorage point for post-tensioning Closure strips: provide section for post-tensioning bar couplers, and location of concentrated loads application Prestressed strand (cast into precast segments) Post-tensioning bars continuous throughout test girder (composed of precast segments, closure pours, and end blocks) Bar coupler Post-tensioning bars Prestressed strand Figure 5-1. Exploded view of test girder with prestressing shown

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67 Previous cross-section New trial cross-section Develop new trial cross-section, decreasing buckling capacity by decreasing weak axis moment of inertia and torsional constant Determine cross-section properties of standard sections Perform buckling analysis using cross-section properties Perform stress calculations using internal moments obtained from buckling analysis, also accounting for stresses due to prestressing Determine cross-section properties of new trial section Stress check: do calculated stresses exceed the limits? Cross-section design complete no yes Figure 5-2. Test cross-s ection design flowchart

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68 Portions of bottom flange removed Portions of top flange removed Trial section (intermediate stage of design process) Final test cross-section Florida bulb-tee 78 cross-section Florida bulb-tee 78 cross-section Florida bulb-tee 78 cross-section x-axis z 6-6 60 28 7 8 10 4 3 3 3 Figure 5-3. Iterative process of pr ecast segment cross-section design Figure 5-4. Typical shipping of bridge girders (photo courtesy of Dr. Robert I. Carr)

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69 0.6 pretensioned strand stressed to 10 kips (2) 1 post-tensioned bar stressed to 30 kips each; Galvanized steel duct (OD 2.06) #4 @ 16 OC alternate hook directions #4 bars continuous (4) 1 post-tensioned bar stressed to 95 kips each; Galvanized steel duct (OD 2.06) (2) 0.6 pretensioned strands stressed to 43 kips each 4 10.75 6 1-11 6-6 8 Figure 5-5. Final precast segment cross-section

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70 Embedded plat e #4 double leg stirrup Acrylic tube bar coupler housing (OD 3.2) Bar coupler #4 bars continuous Grout tube (4) 1 post-tensioned bar stressed to 95 kips each (2) 1 post-tensioned bar stressed to 30 kips each Grout tube 9.5 6-6 Embedded plat e 1 post-tensioned bar #4 bars continuous #4 double leg stirrup Acrylic tube bar coupler housing (OD 3.2) Bar coupler 1 post-tensioned bar Precast segment Galvanized steel duct (OD 2.06) Precast segment Closure stri p Figure 5-6. Final closur e strip cross-section width = 2-4 1.5 45 deg. (maximum bearing pad skew angle tested) Type A bearing pad End block Figure 5-7. End block width, controlled by bearing pad size and skew angle

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71 (2) 1 post-tensioned bar stressed to 30 kips each Vertical hoop (4) 1 post-tensioned bar stressed to 95 kips each; Galvanized steel duct (OD 2.06) #4 bars continuous Horizontal tie Horizontal hoop Vertical tie Lifting loop Top bar local zone reinforcement Bottom bar local zone reinforcement 2-4 6-6 #4 bars continuous Horizontal tie Horizontal hoop Top bar local zone reinforcement Bottom bar local zone reinforcement Vertical hoop Lifting loop Vertical tie 1 posttensioned bar Precast segment End block Figure 5-8. Final end block cross-section

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72 CHAPTER 6 CONSTRUCTION OF TEST GIRDER The test girder was constructed in a segmenta l manner, and consisted of three (3) precast prestressed segments, two (2) closure strips and two (2) end blocks. The precast segments were cast at Dura-Stress Inc. in Leesburg, FL and sh ipped to the FDOT M.H. Ansley Structures Research Center (referred to in this chapter as the FDOT laboratory) in Tallahassee, FL. Oriented as shown in Figure 6-1, the closure strips and end blocks were cast in place at the FDOT laboratory after which the test girder was post-tensioned a nd grouted. Cylinders cast from batches of concrete placed in the end blocks and closure strips were tested for compressive strength and modulus of elasticity. This chapter documents th e construction of the test girder including the casting of each section and posttensioningand summarizes the material tests performed on the cylinders cast from each batch of concrete. Precast Segments The precast segments were cast at Dura-Stre ss Inc. in Leesburg, FL. All three segments were cast on a single bed, with pretensioned strands spanning continuous ly throughout all three precast segments (Figure 6-2). Each segment was cast (Figure 6-3) on a separate day, within five days of each other (casting da tes are indicated in Figure 6-1). Although different concrete batches were used for each segment, the mix design was the same for all segments, with specified 28-day concrete compressive strength of 6,500 psi. For each precast segment concrete batch, eleven 4 in. x 8 in. (diameter x height) cyli nders were cast for later use in strength and modulus testing, to determine the material proper ties of the test girder at the time of buckling tests. Unstressed post-tensioning bars were tem porarily placed in the pos t-tensioning ducts to increase the stiffness of the ducts while placing the concrete and to help maintain straight duct alignment (Figure 6-4). After concrete placement, tarp s were draped over each segment during

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73 the curing stage (Figure 6-5). Once the concrete reached th e specified strength (verified by testing cylinders from correspond ing batches) required for pres tress transfer, the prestressed strands were cut and the segments were left to cure without a tarp (Figure 6-6). Approximately two weeks after casting the last of the three segm ents, Dura-Stress transported the segments on a flatbed trailer (Figure 6-7) to the FDOT laboratory. Closure Strips Closure strips located at approximately the thir d points of the span of the test girder were cast in place at the FDOT laboratory ( casting dates are indicated in Figure 6-1). DYWIDAG bar couplers and bar coupler housings (larger diameter duct, to provi de space for the bar coupler) were positioned within th e closure strips (Figure 6-8). Bar coupler housings were fabricated from acrylic tubecut in half lengthwise and clam ped around transition piecesto provide visual confirmation of the location of the couplers wi thin the closure strips Prior to placing the concrete, the bar coupler housings were taped to ensure that no concrete seeped into the void around the couplers (Figure 6-9). Mild reinforcing steel extending from the ends of the precast segments overlapped inside the cl osure strips, providing additional continuity to the test girder (Figure 6-9). Formwork for the closure strips was fabr icated at the FDOT laboratory (Figure 6-10), and the closure strips were cast in place (Figure 6-11) between the precast segments. The bottom of the formwork was built up to the same elevation as the bottom surface of the precast segments, to ensure a flat, continuous bottom surface of the test girder. To protect the c oncrete at the top of the closure strips against localized cracking (dur ing subsequent girder testing during which time concentrated loads would be applied at the closur e strip locations), a steel plate was cast at the top of each closure strip, em bedded flush with the top surface of the concrete (Figure 6-12).

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74 Grout tubes were connected to the coupler housings (Figure 6-9) and passed through holes in the formwork, allowing the tubes to be acc essible after the concre te had cured and the formwork had been removed, as shown in Figure 6-13. Both closure strips were poured on the same day (2011-08-30), from the same batch of c oncrete. The concrete p oured in the closure strips (and end blocks) had a specified 28-day concrete compressive strength of 8,000 psi and utilized Propex Fibermesh 150 reinforcing fibers (Figure 6-14) to aid in preventing localized section cracking, particularly at the bottom of th e girder. Ten 4 in. x 8 in. cylinders were cast from the closure strip batch of concrete fo r later use in strength and modulus testing. End Blocks One function of the girder end blocks wa s to provide a cross-section capable of accommodating post-tensioning anchorage zone rein forcement, anchor and leveling plates, and lifting loops. Like the closure st rips, the end blocks were cast at the FDOT laboratory. Figure 615 shows the south end block formwork with one side wall removed to expose the interior details. Lifting loops (composed of prestressing strand) were cast into th e end blocks and were designed to support and lift the completed test gi rder after it had been post-tensioned. Anchorage zone reinforcement (Figure 6-16), consisting of mild reinforcing steel, served to distribute the concentrated post-tensioning forces more uni formly over the concrete section. Embedded vertical leveling plates (Figure 6-16) were also cast into the end blocks to provide bearing surfaces for the post-tensioning anchor plates. Figure 6-17 shows the final configuration of the formwork for the end blocks, and Figure 6-18 shows concrete being placed in the north end block. After formwork removal (Figure 6-19), grout tubes protruded from the faces of the end blocks so that they were accessible during the post-tensioning operation. Leveling plates cast flush with the surface of the end bl ocks are clearly visible in Figure 6-20A (prior to installation

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75 of the post-tensioning anchor plat es and anchor nuts). Each of the two end blocks was poured from a different batch of concrete, on different days (casting dates are indicated in Figure 6-1), however the mix design for both batches was the same: specified 28-day concrete compressive strength of 8,000 psi and Propex Fibermesh 150 reinforcing fibers to aid in preventing localized cracking. For each end block concrete batch, a minimum of ten 4 in. x 8 in. cylinders were cast for later use in st rength and modulus testing. Material Tests and Properties Each time a concrete component of the test gird er was cast, 4 in. x 8 in. cylinders were also cast for the purpose of later quan tifying material properties. Test s were performed to determine compressive strength (fc) and modulus of elas ticity (E) of the cylinders at the time of the buckling tests. Approximately half of the cylinde rs were field cured and the other half moist cured. Field cured cylinders were cured in the cas ting yard with the test girder sections for precast segments and in the FDOT structures labora tory in the case of the closure strips and end blocks. Prior to removal of formwork from each cast girder component, the corresponding cylinders remained in plastic molds. After fo rmwork removal, cylinders were demolded and cured in the open air (field cure d) or fully submerged in a tank of lime water (moist cured, Figure 6-21). Several moist cured cylinders were test ed for compressive strength at intermediate stages of the project (e.g., prior to post-tensioning, to ensure ade quate strength before stressing), the results of which are documen ted in Appendix C. Compressive strength and elastic modulus tests were performed within one week of the gi rder buckling tests (cylinders tested between 2011-12-08 and 2011-12-12, buckling tests perf ormed between 2011-12-12 and 2011-12-15) to provide data needed for subsequent finite element model validation. Table 6-1 provides a summary of the quantity of cylinde rs (field and moist cured) that were tested for compressive

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76 strength and elastic modulus within one week of buckling testing. Specific dates on which each cylinder material test was perfor med are documented in Appendix C. Compressive strength tests were conducted in accordance with the Standard Test Method for Compressive Strength of Cylindrical Concrete Specimens (ASTM C 39). Modulus of elasticity tests were conduc ted in accordance with the Standard Test Method for Static Modulus of Elasticity and Poissons Ratio of Concrete in Compression (ASTM C 469). Compressive strength tests were conducted at the University of Florida (on 2011-12-08) and elastic modulus tests were conducted in the F DOT State Materials Office (SMO ) laboratory in Gainesville, Florida (on 2011-12-09 and 2011-1212). Average compressive st rengths and elastic moduli measured for each component of the test girder are shown in Table 6-2. Specific results obtained for individual cylinder tests are documented in Appendix C. Qualitatively, the majority of cylinders tested for compressive strength (both moist cured and field cured) broke in either a Type 1 (cone) or Type 4 (shear) fracture mode (Figure 6-22). Girder Post-Tensioning and Grouting The final stage of the segmental constructi on process involved post-tensioning the various components of the girder (end blocks, precast segm ents, and closure strips) together to form a continuous girder and subsequently grouting th e post-tensioning ducts. On 2011-09-20, the test girder was post-tensioned using a sequence of in cremental post-tensioning force applications (21 in total) that were designed to ensure that th e test girder would not cr ack during stressing. Each bar was assigned an iden tification code (Figure 6-23) and stressed incrementally in the sequence documented in Table 6-3. It should be noted that, because the precast segment cross-section was so slender, there was concern that even with the use of the stressing sequence indicated in Table 6-3, incremental eccentric stressing forces might cause the girder to deflect laterally and crack prior to achieving a final symmetric pos t-tensioned condition. Consequently, throughout

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77 the post-tensioning and grouting operation, the test girder was braced against lateral movement at several locations along its length by inserting timber blocking betw een the girder and surrounding steel catch frames (Figure 6-24). Each bar was stressed from the north end of the test girder using a DYWIDAG compact lightweight hydraulic jack (operate d by a DSI technician). The jack fit over a pull rod that was threaded to the post-tensioning bar protruding fr om the anchor nut. The jack nose contained a ratchet device which allowed the anchor nut to be tightened (inside the jack) by turning a nut located on the exterior of the jack with a wrench (Figure 6-25). A pressure gage connected to the jack (Figure 6-26) was used to determine the force level in each bar, per the jack calibration form provided by DYWIDAG (Appendix D). Additionally, a Geokon load cell was aligned with the jack on the post-tensioned bar (Figure 6-25) with the intent of providing independent confirmation of the load level. However, the lo ad cell readings were deemed inaccurate because the load was slightly eccentric on the load cell. Therefore, the hydraulic pressure gage (and associated calibration form) was the sole method of determining load level in each bar during the stressing sequence. Once the pressure gage indi cated that the target pr estress level had been attained, the anchor nut was tightened and the ja ck was moved onto the next bar in the sequence. Once all bars were fully stressed, the jack was m oved to the south end of the beam and a series of bar liftoff tests were performed to confirm that the south end prestress levels were consistent with the north end prestress levels. These checks se rved two purposes: 1) to ensure that the bars and bar couplers had not snagged at any point al ong the length of the gi rder during stressing, and 2) to ensure that no bars lost any prestress force during the final increments in the stressing sequence. After all of bars were post-tensioned, the camber measured at midspan (Figure 6-27) was 11/16 in. which was in excellent agreement with the predicted camber of 3/4 in.

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78 Upon completion of post-tensioning, the ducts surrounding the post-tensioning bars were pumped full of grout to mechanically bond the post -tensioning bars to the test girder. Grout was mixed with a CG550 single tub grout pl ant mixer provided by DYWIDAG (Figure 6-28) and pumped through the ducts. Grout cube samples were cast and subsequently tested in accordance with the Standard Test Method for Co mpressive Strength of Hy draulic Cement Mortars (ASTM C 109) at the FDOT State Materials Office (S MO) laboratory in Gain esville, Florida (on 2011-10-26). Grout strength measurements obtaine d from these tests are presented in Table 6-4. After post-tensioning and grouting, the test gird er was lifted into testing position (Figure 6-29) using the lifting loops cast into each end block.

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79 Table 6-1. Summary of cylinder material tests perfo rmed within one week of buckling testing for each girder component Moist cured cylinders Field cured cylinders Date poured Girder component concrete batch from which cylinders were cast Compressive Strength Modulus of Elasticity Compressive Strength Modulus of Elasticity Total cylinders 2011-05-18 Precast segment: exterior A 2 3 3 3 11 2011-05-19 Precast segment: exterior B 2 3 3 3 11 2011-05-23 Precast segment: interior 2 3 3 3 11 2011-08-26 South end block 3 3 2 3 11 2011-08-30 Closure strips 3 3 1 3 10 2011-08-30 North end block 3 3 1 3 10 Table 6-2. Compressive strength an d modulus of elasticity of cylinders tested within one week of buckling testing Moist cured cylinders Field cured cylinders Compressive Strength Modulus of Elasticity Compressive Strength Modulus of Elasticity Date poured Girder component concrete batch from which cylinders were cast (psi) (ksi) (psi) (ksi) 2011-05-18 Precast segment: exterior A 8200 5150 6340 4620 2011-05-19 Precast segment: exterior B 8520 5200 5830 4770 2011-05-23 Precast segment: interior 7910 5070 7140 4930 2011-08-26 South end block 9120 5380 7510 4850 2011-08-30 North end block 9440 5020 7080 4230 2011-08-30 Closure strips 7580 4750 5260 3630

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80 Table 6-3. Sequence of incremental post-tensioni ng forces applied to girder during stressing Bar forces (kip) Increment ID 1 ID 2 ID 3 ID 4 ID 5 ID 6 1 19 2 19 19 3 19 19 19 4 19 19 19 19 5 31 19 19 19 6 31 19 19 31 7 31 19 31 31 8 31 31 31 31 9 31 31 31 31 6 10 31 31 31 31 6 6 11 31 31 31 31 6 30 12 31 31 31 31 30 30 13 64 31 31 31 30 30 14 64 31 31 64 30 30 15 64 31 64 64 30 30 16 64 64 64 64 30 30 17 95 64 64 64 30 30 18 95 64 64 95 30 30 19 95 64 86 95 30 30 20 95 95 86 95 30 30 21 95 95 95 95 30 30 Table 6-4. Grout cube strength test results Specimen Strength (psi) Cube 1 12,770 Cube 2 13,510 Cube 3 13,150 Average 13,140

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81 North end block (Poured 2011-08-30) Closure strip (Poured 2011-08-30) Closure strip (Poured 2011-08-30) Precast segment: Interior (Poured 2011-05-23) South end block (Poured 2011-08-26) NORTH EAST Precast segment: Exterior B (Poured 2011-05-19) Precast segment: Exterior A (Poured 2011-05-18) Figure 6-1. Casting dates for gi rder components and final orie ntation of girder in FDOT laboratory Figure 6-2. Precast segments formwork aligned on single pretensioning bed at Dura-Stress (photo courtesy of University of Flor ida, Department of Civil and Coastal Engineering)

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82 Figure 6-3. Placing concrete in the precast segment formwork (photo courtesy of University of Florida, Department of Civ il and Coastal Engineering) Figure 6-4. Unstressed post-tensioni ng bars placed in ducts to k eep ducts straight during placing of concrete (photo courtesy of University of Florida, Department of Civil and Coastal Engineering)

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83 Figure 6-5. Tarp covers applied to each segment during curing (photo courtesy of University of Florida, Department of Civ il and Coastal Engineering) Figure 6-6. Precast segments after formwork re moved at Dura-Stress (photo courtesy of University of Florida, Department of Civil and Coastal Engineering)

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84 A B Figure 6-7. Precast segment arrival at the FDOT la boratory (photos courtesy of University of Florida, Department of Civil and Coasta l Engineering). A) Segments on flatbed trailer. B) End view of segments. Acrylic tube coupler housing Bar coupler Post-tensioned bar Transition piece Clamp Figure 6-8. Duct couplers located with in closure strips in bottom fl ange of girder (photo courtesy of University of Florida, Department of Civil and Coastal Engineering)

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85 Figure 6-9. Duct couplers in closur e strips, sealed with tape prio r to concrete placement (photo courtesy of University of Florida, Depa rtment of Civil and Coastal Engineering) Figure 6-10. Closure strip formwork (photo courtesy of University of Florida, Department of Civil and Coastal Engineering)

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86 Figure 6-11. Placing concrete into the closure strip formwork (phot o courtesy of University of Florida, Department of Civ il and Coastal Engineering) Figure 6-12. Embedded steel plate at top surface of cl osure strip (photo courtesy of University of Florida, Department of Civ il and Coastal Engineering)

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87 Figure 6-13. Finished closure st rip with formwork removed (phot o courtesy of University of Florida, Department of Civ il and Coastal Engineering) Figure 6-14. Concrete used in closure strip and end block conc rete mix, showing presence of Propex Fibermesh 150 reinforcing fibers ( photo courtesy of University of Florida, Department of Civil and Coastal Engineering)

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88 A B Figure 6-15. Open end block formwork revealin g mild reinforcement and lifting loops (photos courtesy of University of Florida, Depart ment of Civil and Coastal Engineering). A) Side view. B) Isometric view.

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89 A B Figure 6-16. Anchorage zone mild steel reinfo rcement in end blocks (photos courtesy of University of Florida, Department of Ci vil and Coastal Engineering). A) Elevation view at top of cross section. B) Elev ation view at botto m of cross section.

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90 A B Figure 6-17. Completed end block formwork (phot os courtesy of University of Florida, Department of Civil and Coastal Engineer ing). A) South end block. B) North end block. Figure 6-18. Placement of concrete in north end block formwork (photo courtesy of University of Florida, Department of Ci vil and Coastal Engineering)

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91 Figure 6-19. End block after removal of formwork (photo courtesy of University of Florida, Department of Civil and Coastal Engineering) A B Figure 6-20. Leveling plates and anchor plates at bottom of end block (photos courtesy of University of Florida, Department of Ci vil and Coastal Engineering). A) Embedded leveling plates flush with surface of end bl ock. B) Post tensioning anchor plates and anchor nuts installed.

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92 Figure 6-21. Moist cured cylinde rs submerged in a tank of lim e water (photo courtesy of University of Florida, Department of Civil and Coastal Engineering) A B Figure 6-22. Typical cylinder failu re types observed during compre ssive strength testing (photos courtesy of University of Florida, Depart ment of Civil and Coastal Engineering). A) Type 1 (cone failure). B) Type 4 (shear failure).

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93 ID 1 ID 2 ID 3 ID 4 ID 6 ID 5 NORTH EAST Figure 6-23. Bar identification numbers used duri ng post-tensioning (south end of girder shown) Timber blocking Catch frame Post-tensioning jack Timber blocking Figure 6-24. Test girder during post-tensioning, braced against steel catch frames using timber blocking (photo courtesy of University of Florida, Department of Civil and Coastal Engineering)

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94 Load cell Post-tensioning jack Figure 6-25. Post-tensioning jack setup (photo courtesy of Univers ity of Florida, Department of Civil and Coastal Engineering) Figure 6-26. Post-tensioning jack and pressure gage (photo courtesy of University of Florida, Department of Civil and Coastal Engineering)

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95 Figure 6-27. Camber meas urement at midspan of test gird er immediately after completion of post-tensioning (photo courtesy of University of Florida, Department of Civil and Coastal Engineering) Figure 6-28. Grout mixer and high capacity air compressor (photo courtesy of University of Florida, Department of Civ il and Coastal Engineering)

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96 Figure 6-29. Lifting the test gi rder into testing position, prior to end block fabrication (photo courtesy of University of Florida, Depa rtment of Civil and Coastal Engineering)

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97 CHAPTER 7 GRAVITY LOAD SIMULATOR As previously discussed, concentrated vertical point loads were applied to the top of the test girderthrough the use of gravity load simula torsto induce buckling (lateral deflection) of the girder in the experimental tests in a manner that did not introduce lateral stiffness into the system. Typically in experimental testing, a test specimen will deflect princi pally in the direction that the load is being applied i n. For example, when a simply-supported beam is tested in flexure, a vertical point load can be applied at midspan an d the beam will deflect vert ically at the point of loading. In such a case, load application can be achieved through the use of a jack that is anchored to a stationary (effectiv ely rigid) test frame which react s against the test specimen. In contrast, in a buckling test of th e type conducted in this study, th e girder not only deflects in the direction of the applied load (ver tically), but it also deflects late rally (perpendicular to the load direction). If a typical load a pplication methodwhere the jack is anchored to a stationary positionwere used in a buckling experiment, the load frame would resist lateral motion of the test specimen and a horizontal component of restraining force would develop (Figure 7-1). This condition is unacceptable, because the lateral load component would artificially increase the measured buckling capacity of the girder. To main tain vertical load and zero lateral restraining force as buckling occurs, a speci al type of load application frame (called a gravity load simulator) can be used that translates freely with the test girder as it buckles laterally. This chapter discusses the mechanics and design of the gravity load simulators designed and employed in this project, includ ing a novel modification to previ ous designs by other researchers that improves the accuracy a nd performance of the system.

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98 Gravity Load Simulator Design The first gravity load simulator was developed by Yarmici and Yura (1967) to test structures permitted to sway. As designed, the simulator acts as a horizontally unstable truss structure (i.e., zero lateral stiffn ess) which provides vertical load application without horizontal restraint to the test specimen. As shown schematically in Figure 7-2, the simulator consists of two inclined arms that are conn ected to the ground and to a rigi d triangle at the center of the simulator via pins. The source of loada hydraulic jac kis attached at the base of the rigid triangle, also through a pinned connection. As is noted by Yarmici and Yura (1967), For the type of mechanism shown, equilibrium requires that the line of action of the load passes through the instantaneous center, that is, the point of intersection of the two ar ms. The position of the instantaneous center changes as the mechanism is deflected. With carefully chosen geometry (top width, arm length, load hei ght, and base width; Figure 7-2), the load line of action will remain vertical and through the instantaneous center, regardless of the deflected position (Figure 7-3). Additional guidance for determining op timal geometry for the simulator can be found in Yarmici and Yura (1967). The original simulators, at Le high University, had 80 kip load capacity and could translate laterally 16 in., for performing buckling tests on full scale building frames (Yarmici and Yura, 1967). Since then, several other rese archers have constructed gravit y load simulators for various test programs. Lateral torsional buckling tests of steel I-shapes were conduct ed at University of Texas at Austin (Yura and Phillip s, 1992). At the University of Te xas at Houston, two simulators (6 in. displacement capacity, 150 kip load capacity) were constructed to investigate torsional bracing by simulating buckling of a two-beam sy stem with midspan bracing (Deaver, 2003). A gravity load simulator at the Georgia Instit ute of Technology (7.5 in. displacement capacity, 60 kip load capacity) was used to experimentally investigate late ral-torsional buckling behavior

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99 of fiber reinforced polymer I-shaped cross-s ections (Stoddard, 1997) a nd also to examine the lateral stability of slender rectangular reinforced concre te beams (Kalkan, 2009). Also at the Georgia Institute of Technology, a relativel y large gravity load simulator (12.875 in. displacement capacity, 300 kip load capacity) was used to study the stability of prestressed concrete beams (Hurff, 2010). It s hould be noted that Hurff observed that the load line of action was not perfectly vertical when the simulato r swayed from its orig inal centered position. Postulating that self weight of the simulator caused this issue, a control mechanism was installed that forced the simulator to act as a stable m echanism, in which the position of the simulator was manually adjusted until the applied load was vert ical. Further investigations into the simulator self weight issue were not conducted by Hurff. UF/FDOT Gravity Load Simulators A pair of gravity load simulators (one of which is shown in Figure 7-4) has been designed and fabricated for this project, with a maximum lateral deflection capacity of 16 in. and vertical load capacity of 50 kip each. The UF/FDOT simulato rs have the same geometry as the original simulator developed by Yarmici and Yura (1967 ). High-quality spherical roller bearings (Figure 7-5) are used to prevent bindi ng (due to shaft bending or simulator geometry fabrication imperfections) and minimize friction at the pinned connections, thereby mi nimizing restraint of the simulator to lateral motion. The bearings used in the simulators are self-aligning accommodating misalignment between the shaft a nd housing without increasing frictionwhich allows out of plane bearing rotation of .5 deg. Th e bearings are housed in thick plates that are bolted and welded to the simulators (Figure 7-4A). PVC end caps serve as bearing seals that prevent dust from entering the bear ings and creating friction (Figure 7-4B). A hydraulic jack is connected to the center pin of each simulator (Figure 7-6), allowing the hydraulic jack to rotate freely about the pin and maintain vertical load application as the simulator displaces (Figure 7-

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100 7). Two safety mechanisms are included in the design of the simulators: one temporary restraint and one permanent restraint (Figure 7-4). The temporary restrain ts are engaged when the simulators are not in useremoved during buckling teststo keep each simulator from displacing laterally under its own weight. For safe ty during a buckling test, permanent restraint chainswhich are slack dur ing normal operation (Figure 7-4A)connect the bottom of the rigid triangles to the base beams. The restraint chai ns allow full range of motion expected during a buckling test (expected deflection of 10 in. out of the maximum allowable displacement of 16 in.), but prevent the simulators from displacing further than desired (Figure 7-7). The completed simulators were positioned below the test girder closure strips. Load frames were designed to transfer the vertical load from the gravity load simulator (below the test girder) to the load application point (at the top of the test girder). A threaded rod in line with the hydraulic jack connected the load frame to the simulator (Figure 7-7). A knife edge (Figure 7-8) was used to apply point loads to the top of the test girder, which allowe d the girder to rotate freely about the y-axis within the load frame as it buckled (Figure 7-7). When loaded, the simulators could be pushed laterally by hand from the equilibrium position, and upon release, would float back to equilibrium. Figure 7-9 shows a photograph of one of the gravity load simulators and load frame in te sting position. Full fabrication pl ans for the simulators can be found in Appendix E. Effect of Gravity Load Simula tor Self Weight Equilibrium Prior to performing buckling experiments, the performance of each simulator was tested to ensure that the load line of ac tion remained vertical. Restraini ng the test girder centered above the simulators, the loaded simulators maintained equilibrium as expected and the direction of load was confirmed to be vertical using a carpent ers level. Subsequently, a trial buckling test was performed in which load was applied to the te st girder, which was allowed to freely deflect

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101 laterally. Both simulators reached equilibrium in a position such that the applied load was not perfectly vertical. Specifically, the middle pin of each simulator was displaced further than the load application point (at the top of the test girder). This cond ition caused a lateral load applied to the test girder in the direction of buckling (Figure 7-10). With the simulators floating in this manner of equilibrium, the simulators were pushed (by hand) until vertical alignment was reached. Upon release, each simulator floated back to the equilibrium position with a non-vertical load line of action. In the displaced configuration observed during this trial buckling test, the load line of action was not vertical as ex pected, indicating that additional forces (such as the weight of the simulator) affected the system during the test. As mentioned in the previous section, Hurff (2010) observed that the Georgia Tech simulator di d not reach equilibrium with a vertical load orientation unle ss the simulator was in the undeformed (centered) position. Hurff fixed this problem by using a lateral control mechanism that caused the simulator to become a stable structure. While this so lution proved effective for maintain ing proper load orientation, the lateral restraint provid ed by the control mechanism is unde sirable for buckling experiments. Ideally, the girder should be perm itted to deflect laterally (buckl e) without restraint, which is consistent with an un-braced field condition. Th us, an alternative solution was developed which allows unrestrained lateral motion and maintain s vertical load orient ation throughout the full range of motion. To further investigate how the self weight of the gravity load simulator influences its equilibrium position, numerical models of the simulator were developed (Figure 7-11). In the initial simulator model, rigid beam elements repr esent the components of th e simulator, the self weight of which (due to gravity) are neglected. The inclined arm beam elements are attached to hinges at the base of the system, with end moment (My) releases at the connection to the rigid

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102 triangle. Moment transfer between the elements of the rigid triangle ensures that the rigid triangle acts as a single unit. The connection of the gravity load simulator at the middle pin and the load application point to the test girder (the knife edge) is represented in the model using a beam element. Releasing the end moment (My) of this element at the connection to the rigid triangle allows the element to rota te freely about the middle pin of th e simulator. Initial strain is applied to this element, simulating the tensi on applied through the us e of the jack during a buckling test. A prescribed displ acement is applied at the load application point, representing the lateral deflection of the test girder. The load appl ication point is modeled as a roller support (free to rotate about the y-axis and translate along the xaxis), representing the knife edge at the top of the test girder. Yarmici and Yura (1967) describe that the theoretical load applied by a gravity load simulator is generally not truly vertical, and that a slight lateral load is applied to the test specimen as a result of this non-vertical orientatio n. Neglecting gravity, the results of the simulator analysis (Figure 7-12) are consistent with Yarmici and Yura (1967). The analysis indicates thatwithin the range of lateral deflec tions expected in the buckling experimentsthe lateral load component is, at most, approximately -0.02% of the applied vert ical load. Note that Yarmici and Yuras sign convention (Figure 7-10) states that a negati ve percentage corresponds to a lateral load that is rest raining the beam, and a positive pe rcentage corresponds to a lateral load that is driving the beam in the direction of buckling. For example, the simulator analysis results (Figure 7-12) show that, when the test girder has displaced 5 in., under zero-gravity conditions, the lateral force component is approxima tely -0.02%. Thus, if a 10 kip load is applied vertically, 0.002 kip would develop laterally at the top of the beam restraining the beam slightly.

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103 To determine the effect of self weight on si mulator equilibrium, gravity is introduced into the simulator model via mass proportional body forces (and therefore taking the self weight of the simulator into account), and the analysis descri bed above is repeated. The self weight causes much larger lateral loads to de velop in the direction of buckli ng, and those loads increase with increasing displacement (Figure 7-13). This occurs because the se lf weight of the simulator is eccentric relative to the idealized instantaneous centerthe point of intersection of the two inclined arms when neglecting gravit yas shown conceptually in Figure 7-14A. Recall that Hurff (2010) corrected this problem by providing late ral restraint to the gravity load simulator. In this study, an alternative solu tion was employed that avoi ds restraining lateral motion. The system consists of weights placed eccentrically from the instantaneous center which counterbalance the eccentric self weight of the simulator (Figure 7-14B). With acceptable counterweight magnitude and eccentricity, the eff ect of the simulator self weight can be corrected, and the load line of action remains vertical. The counterweights are an excellent option because there is no addition stiffness adde d to the system (permitting unrestrained lateral motions), and the counterweights can be adjusted to maintain vertical load regardless of the displaced shape of the test gi rder. The physical counterweight system was fabricated using barbell weights of various sizes, slid onto a steel pipe that was mounted to the rigid triangle of the simulator (Figure 7-15). For each simulator, two (2) 25 lb weights and one (1) 45 lb weight were available for the counterweight system. Sma ll clamps ensured that the weights did not slide unless physically pushed along the pi pe. Details of the counterweight system are included in the gravity load simulator fabrica tion plans, found in Appendix E.

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104 Original position of test girder Deflected position of test girder Tension jack Anchor point Restraining component Vertical component Figure 7-1. Undesirable horizontal restraining component that deve lops in an anchored loading system (After source: Yarmici and Yura, 1967) Rigid triangle Hydraulic jack attachment point Inclined arms Load line of action Pin Hinge Top width Jack Base width A r m l e n g t h Load height Figure 7-2. Dimensions, defined (Aft er source: Yarmici and Yura, 1967)

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105 Original position of test girder Deflected position of test girder Original position of gravity load simulator Deflected position of gravity load simulator Instantaneous center Hydraulic jack attachment point Load line of action Tension jack Figure 7-3. Instantaneous center (Aft er source: Yarmici and Yura, 1967)

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106 A Counterweight Load frame Threaded rod connecting simulator to load frame Hydraulic jack Permanent restraint chains Temporary restraint (disconnected during buckling test) Inclined arm Rigid triangle Spherical roller bearing (PVC end cap not shown for clarity) Test girder Bearing housing B Figure 7-4. UF/FDOT gravity load simulator. A) Schematic view. B) Photograph (photo courtesy of University of Florida, Department of Civil and Coastal Engineering).

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107 Figure 7-5. Spherical roller bearing (photo courtesy of SKF) Figure 7-6. Hydraulic jack connect ion to simulator center pin (photo courtesy of University of Florida, Department of Civ il and Coastal Engineering)

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108 Knife edge Buckled position of test girder (translated laterally and rotating about y-axis) Load frame Threaded rod connecting simulator to load frame Counterweight Permanent restraint chains Temporary restraint (disconnected during buckling test) Hydraulic jack Load application point X Z Figure 7-7. Gravity load simulator displaced shape

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109 Figure 7-8. Knife edge at load app lication point at top of test gird er (photo courtesy of University of Florida, Department of Ci vil and Coastal Engineering) Figure 7-9. UF/FDOT gravity load simulator and load frame in testing position (photo courtesy of University of Florida, Department of Civil and Coastal Engineering)

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110 Slope of load = percent of load applied laterally ( orientation) positive Applied load Load application point Tension jack Figure 7-10. Definition of percent of simulator lo ad applied laterally (After source: Yarmici and Yura, 1967) Prescribed displacement Roller support End moment (M) releasedyRigid triangle Gravity load simulator comprised of rigid beam elements Initial strain applied to beam element, representing tension load applied to test girder HingeHinge Load application point to test girder X Z D i s p l ac e m e n t ( i n )Time step 10 10 0 0 Figure 7-11. Gravity load simulator model

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111 Prescribed lateral displacement at load application point (in.)Percent of load applied laterally 0 1 2 3 4 5 6 7 8 910 -0.03 -0.02 -0.01 0 0.01 0.02 0.03 0.04 self weight omitted Figure 7-12. Results of simulator analysis: theoretical percent of load applied laterally to the beam at the load application point (self weight excluded in model) Prescribed lateral displacement at load application point (in.)Percent of load applied laterally 0 1 2 3 4 5 6 7 8 910 -0.25 0 0.25 0.5 0.75 1 1.25 1.5 1.75 self weight omitted self weight included Figure 7-13. Results of simulator analysis: theoretical percent of load applied laterally to the beam at the load application point (self weight included in model)

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112 A Load application point displacement warmwarmwtriangleearmetriangleearmNon-vertical load B Load application point displacement warmwarmwtrianglewcounterWeightecounterWeightVertical load Figure 7-14. Effect of simulator self weight and counterweights on verticalness of load line of action. A) Counterweights omitted, load is skewed. B) Counterweights included, load is vertical.

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113 Counterweights Figure 7-15. Counterweight system (photo courtesy of University of Florida, Department of Civil and Coastal Engineering)

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114 CHAPTER 8 EXPERIMENTAL BUCKLING TESTS PROGRAM Buckling Test Setup An overview of the test setup is shown in Figure 8-1. To accommodate the gravity load simulators, the test girder was elevated approxima tely 8 ft. above the lab floor and rested on rigid end supports. Because the test girder was elevat ed overhead, catch frames were designed to support the test girder should it become fully unstable during testing. Five catch frames were fabricated: two positioned at the ends, one positioned at midspan, and two positioned near the third points (Figure 8-1). The catch frames allowed the test gi rder up to 9 in. of lateral movement at midspan before the test girder came into cont act with the catch frames. Full fabrication plans for the catch frames can be found in Appendix F. Each end support was fabricated with the test girder suspended in testing position, built up below the end blocks. Made of eight solid concrete blocks, the end supports were built up one level at a time and weld ed together to create a rigid support (Figure 8-1). A pad of Hydro-Stone was poured at the base and at the top of the end supports, to ensure that the bearing surface for the end blocks on the ground was level and to provide a level surface for the bear ing pad contact area, respectively. Test Matrix The bearing pads used to support the ends of the test girder we re the same pads previously tested for roll stiffness in the first pha se of this project. As shown in Chapter 2, among all bearing pad types tested, Type A bearing pads had the least amount of variation in individual roll stiffness results under all combinations of skew and slope angles (resul ts reproduced in Figure 82). Therefore, pad Type A was chosen to support th e ends of the girder during the buckling tests. To best illustrate the influence of roll stiffne ss on buckling capacity, the gi rder was to be tested with bearing pads oriented at the extreme valu es of skew and slope that were previously

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115 investigated (A-0-0, A-45-0, A-0-04, and A-4504). Recall that, in the abbreviated naming convention, the first letter denot es pad type, the following number denotes skew angle (in degrees), and the last number denotes slope angle (in 10-2 radians). However, during buckling testing in test configuration A-4504, the test girder buckl ed under its own self weight (i.e., with no additional applied vertical lo ad). Consequently, a configur ation with an intermediate combination of skew and slope was required. Re ducing skew from 45 deg. to 15 deg. increased buckling capacity enough to allow a test to be perf ormed with applied load and with the pad in a skewed and sloped configuration. The test matrix for the buckling testswith number of tests performed per configurationis presented in Table 8-1. Test Procedure There were two main phases to the setup porti on of the buckling test s: 1) imposing skew and slope angles on the bearing pa d, and 2) placing the test girder on the bearing pads. After the setup portion each buckling test (setting the beari ng pads and placing the gi rder on the pads) was completed, the buckling test was performed. This section documents the procedure for setting up and performing the buckling tests. Setting Skew and Slope Angles Prior to performing each buckling test, beari ng padslocated between the end blocks and rigid end supportswere oriented at the desired skew and slope angle. Skew angle was set by rotating the bearing pad about th e z-axis of the pad relative to the test girder (Figure 8-3). Slope angle was set by placing a beveled plate (Figure 8-4) between the bear ing pad and rigid end support (Figure 8-5). Bearing pads were orientated in th e buckling tests such that the pressure distributions during buckling test ing matched that of the pres sure distributions during roll stiffness testing (Chapter 2). Conceptually, Figure 8-6 shows the initial pressure distribution of each test configuration, and Figure 8-7 shows the final pressure distribution for each test

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116 configuration. In the sloped test s, the thick ends of both bevele d plates faced north, creating a pressure concentration on the north portion of the bearing pads. This scenario represents the pressure distribution on the pair of bearing pa ds that would be produ ced by girder grade (as opposed to girder camber). Placing the Test Girder As the skew and slope angles were set, the te st girder was liftedvia lifting loops cast into the end blocksto allow adjustments. Once the bear ing pad skew and slope angles were set, the test girder was lowered onto the pads for a buckling test. As shown in Figure 8-8A, the beam swept naturally to the east. Measured at the centroid height, the sweep was found to be 2.87 in. under end configuration A-0-0. For mo st tests, a hydraulic jack was used to push the test girder toward the west at the centroid, effectively removing sweep from the system (i.e., pushing the girder straight) (Figure 8-8B). The jack used to straighten the test girder was mounted to the midspan catch frame, as shown in Figure 8-9. For comparison, two different methods for placing the test girder on the be aring pads were used: Method A: The test girder was straightened using the jack, lowered onto the bearing pads, and then allowed to sweep freely by slowly retracting the jack, and; Method B: The girder was set down on the pads in the swept position. Method A is advantageous because the sweeping mo tion of the test girder could be directly recorded during a buckling test (a s the jack is slowly retracted). However, when Method A was used, it was observed that as th e test girder deflected into the swept position, torsion was introduced to the bearing pad about its z-axis. Th is outcome is undesirable because pad torsion is not present in the field, nor was not present in the roll stiffness tests. To determine the effect of torsion in the pad on the buckling capacity of the te st girder, test configur ation A-0-0 was tested under both conditions (using Method A and Method B). Examining the load-displacement curves

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117 presented in Chapter 9 for test configuration A-0-0, the effect of torsion on the bearing pads is insignificant. Table 8-2 summarizes the placement method of each individual test performed per configuration (e.g., A-0-0-1 was the first test pe rformed in configuration A-0-0, A-0-0-2 was the second test performed in c onfiguration A-0-0, etc.). Buckling Test Procedure Similarly to the roll stiffness tests, load was applied iteratively to the test girder, first gradually increasing the applied load at the nort h simulator until a specific target was reached, and then increasing the load at the south simulato r until the loads were equal in both locations (Figure 8-10). Once the loads were approximately equal at both simulators, the simulator counterweight system was adjusted at each locati on to ensure vertical load application. Load orientation was confirmed to be vertical using a carpenters leve l. After the counterweights were adjusted, a data point was established (Figure 8-10), at which time the applied load and girder deflection was measured. Instrumentation Several types of instrumentation devices displacement transducers (displacement sensors, lasers, and string pot entiometers), load cells, and st rain gages (both external and vibrating wire strain gages cast into the concre te)were used in the buckling tests. A naming convention for the instrumentation was developed to reflect the instrument type and its specific location on the test girder. As summarized in Figure 8-11, each instrument name has the same format of T-LD-F-H, where T i ndicates the type of instrument while -LD-F-H indicates the location of the measurement. For example, the instrument shown in Figure 8-11 is an external strain gage mounted to the east f ace of the test girder top flange. Therefore, the instrument shown in Figure 8-11 is named SG-N24-E-76, which means that th e device is a strain gage, located 24 ft north of midspan, mounted to the east face, at a height of 76 in. from the bottom of the girder.

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118 The full instrumentation plan (Appendix G) furt her describes the naming convention, as well as provides an overview of all of the instrumentation by name. Displacement Transducers Displacement sensors, string potentiometers a nd laser gages were used to measure girder deflection at various points along its length. All three types of displacement transducer were used at midspan, but only displacement sensors were used at the end blocks. Laser gages (Balluff model BOD 66M) measured lateral displacement at the centroid height near the gravity load simulator locations. Because midspan lateral deflection was a key parameter measured in a buckling test, the midspan of the test girder was heavily instru mented with displacement transducers (Figure 8-12). Displacement transducers were mounted to the ce ntral catch frame and us ed to record midspan deflections along both the x-axis and z-axis. A laser gage (Balluff model BOD 66M) and a displacement sensor (TML model SDP-200D) were m ounted next to one another at the centroid height to measure lateral disp lacement (along the x-ax is). The laser gage (Dx-N0-W-38) was used as the primary lateral displacement m easuring device during a buckling test, while the displacement sensor (Dx-S0-W-38) provided redundancy to the lase r gage. String potentiometers (SpaceAge Control model 62-60-82E1) measured bot h lateral and vertical displacement of the test girder, providing additional redundancy to the lateral displacement measurement provided by the laser gage.The end blocks were also heavily instrument ed with displacement sensors, as shown in Figure 8-13. All displacement transducers monitori ng the end blocks were TML model SDP-50, mounted to the rigid end supports Vertical displacement transdu cers (along the z-axis, Dz) and horizontal displacement transducers (along the x-ax is, Dx) were used to calculate the roll angle imposed on the bearing pad. Knowing the horizont al distance between the vertical (Dz)

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119 displacement transducers and the vertical dist ance between the horizontal (Dx) displacement transducers, the roll angle imposed on the bearing pad at the end block coul d be calculated from the relative displacement measurements, and used to confirm each other. Horizontal displacement transducers along the y-axis (Dy) were used to calculate to rsional rotation in the bearing pad. Load Cells Load cells measured the applied vertical load to the test girder at the gravity load simulator locations. An Interface load cel l (model 1220, 50 kip capacity) was installed in line with the threaded rod connecting the gravity load simulator to the load frame. This cell directly measured the load applied to the test girder (Figure 8-14). Additionally, a pair of Geokon load cells (model 3000, 50 kip capacity) were mount ed in line with the load frame rods that flank each side of the test girder (Figure 8-14). These cells provided load m easurements that were redundant with the Interface load ce ll. The average of the Interface load cell readings on each gravity load simulator (named F-N15-C and F-S15-C, located at the north and south s imulators, respectively) were used to monitor the load applied to the te st girder and determine the buckling capacity of the test girder. These load cells (F-N15-C and F-S 15-C) were also used to generate the load-time history presented in Figure 8-10. Strain Gages Strain gages (both external and cast into the concrete) were used to detect cracking, if it occurred. Several external strain gages (Kyowa 60mm and 1 20 ohm) were mounted to the test girder at locations most likely to crack, namely on the bottom of the precast segments close to the interface with each closur e strip (see Appendix G for speci fic locations). The remaining external strain gages were placed at increments along the length of the beam on the east and west faces of both the top and bottom flanges, to captu re the strain profile if necessary. A pair of

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120 vibrating wire strain gages (Geokon model 4200) were cast into each cl osure strip, located vertically between th e post-tensioning coupl er housings (Figure 8-15). These gages were used detect cracking should it occur in the closure strips. The vibrati ng wire strain gages were also used to measure true strain in the test gird er over time, including during the post-tensioning stage, whereas the external strain gages measured incremental strain (caused by applied vertical load during a buckling test).

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121 Table 8-1. Test matrix Test configuration Skew angle (deg.) Slope angle (rad.) Number of tests performed A-0-0 0 0 3 A-45-0 45 0 2 A-0-04 0 0.04 3 A-15-04 15 0.04 1 Table 8-2. Placement method, per test basis Test ID Placement method A-0-0-1 A A-0-0-2 A A-0-0-3 B A-45-0-1 B A-45-0-2 B A-0-04-1 A A-0-04-2 A A-0-04-3 A A-15-04-1 A

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122 A End support Gravity load simulator Load frame Test girder NORTH EAST Catch frame B Figure 8-1. Overall test setup. A) Schematic. B) Photograph (photo courtesy of University of Florida, Department of Civ il and Coastal Engineering).

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123 Ro l l S t i f f n e s s ( k i p f t ) / r a d 0 4000 8000 12000 16000 2000 0 Specimen 1 Specimen 2 Mean A-0-0 A-0-02 A-0-04 A-45-0 A-45-02 A-45-04 B-0-0 B-0-02 B-0-03 B-45-0 B-45-02 B-45-04 C-0-0 Cmod-0-0 C mod-0-02 C mod-0-03 C-45-0 C-45-02 C-45-04 Figure 8-2. Roll stiffness result s, reproduced from Chapter 2 x-axis (East) y-axis (North) Skew angle Type A bearing pad South end block Figure 8-3. Bearing pad skew angl e orientation in buckling tests Figure 8-4. Beveled plate used to impose slope angle on beari ng pads (photo courtesy of University of Florida, Department of Civil and Coastal Engineering)

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124 Figure 8-5. Beveled plate and bear ing pad positioned between end block and end support (photo courtesy of University of Florida, Depa rtment of Civil and Coastal Engineering) 45 deg. skew angle Test configuration A-0-0 Beveled plate orientation: thick end to the North x-axis ( East ) y-axis (North) x-axis ( East ) y-axis (North) x-axis ( East ) y-axis (North) x-axis ( East ) y-axis (North) Test configuration A-45-0 15 deg. skew angle Test configuration A-0-04 Test configuration A-15-04 Figure 8-6. Bearing pad orientat ion and initial pressure dist ributions during buckling tests

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125 x-axis (East) y-axis (North) x-axis (East) y-axis (North) x-axis (East) y-axis (North) x-axis (East) y-axis (North) Test configuratio n A-0-0 Test configuratio n A-45-0 Test configuratio n A-0-04 Test configuratio n A-15-04 Lateral deflection at midspan to the East End block roll about y-axis of test girder Figure 8-7. Final bearing pad pressure distributions dur ing buckling tests A Test girder sweeps naturally to the east x-axis (East) y-axis (North) sweep B Force exerted on test girder from hydraulic jack to remove sweep Test girder straight due to hydraulic jack x-axis (East) y-axis (North) Figure 8-8. Sweep of test girder A) Unrestrained position. B) After hydraulic jack applied.

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126 Figure 8-9. Jack used to straight en test girder (photo courtesy of University of Florida, Department of Civil and Coastal Engineering) Time (minutes)Applied load (kip) 0 5 10 15 20 25 30 35 40 0 6 12 18 North simulator South simulator Data points Figure 8-10. Typical load time history (test A-0-0-2 shown)

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127 NORTH (y-axis) EAST (x-axis) SOUTH WEST LD (ft) H (in.) Midspan z-axis T LD F H Type of instrumentation: Dx, Dy, Dz : displacement transducer along x, y, and z-axis (respectively) Sx, Sz : string potentiometer along x, and z-axis (respectively) F : force VW : vibrating wire strain gage SG : strain gage LD = longitudinal distance from midspan: defined in figure below specify north (N) or south (S) of midspan F = face of beam: specify east (E), west (W), or centerline (C) H = height: defined in figure below Example instrument (strain gage) Figure 8-11. Naming convention for buckling test instrumentation

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128 A X (East) Z Y ( North ) String potentiometer Sx-N0-C-78 Displacement sensor Dx-S0-W-38 Laser gage Dx-N0-W-38 String potentiometer Sz-N0-C-0 String potentiometer Sx-N0-C-0 B Figure 8-12. Midspan displacement transducers. A) Schematic. B) Photograph (photo courtesy of University of Florida, Department of Civil and Coastal Engineering).

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129 A Dx-S51-W-76 Dx-S51-W-2 Dz-S51-W-2 Dz-S51-E-2 Dy-S51-E-2 Dy-S51-W-2 X (East) Z Y (North) B Figure 8-13. South end block displacement tran sducers. A) Schematic. B) Photograph (photo courtesy of University of Florida, Depa rtment of Civil and Coastal Engineering). Interface load cell Threaded rod Geokon load cells Figure 8-14. Load cells, located at gravity load s imulator locations (photo courtesy of University of Florida, Department of Ci vil and Coastal Engineering)

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130 Figure 8-15. Vibrating wire strain gages, cast into closure strips ( photo courtesy of University of Florida, Department of Civ il and Coastal Engineering)

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131 CHAPTER 9 RESULTS As discussed in Chapter 3, there were two primary goals of the second phase of the project. The first objective was to experimentally determ ine the buckling capacity of the test girder supported on bearing pads with various configur ations of skew and sl ope angles. The second objective was to use these experimental results to validate and calibrate a finite element buckling model. The results of the experi mental buckling tests are presente d in this chapter, including the measured data, a data curve fitting scheme, a method for calculating buckling capacities, and the computed buckling capacities themselves. Additiona lly, the results of the experimental tests are compared to the finite element analysis results. Aspects of the validated finite element model bearing pad roll stiffness, conc rete elastic modulus specified, and load-displacement resultsare also presented. Experimental Buckling Test Results It is important to note that, of the nine (9 ) individual buckling e xperiments performed and presented in this chapter, only one test (A-45-0-1) was carried out until buckling of the test girder occurred (Figure 9-1). The remaining tests were termin ated before the test girder became fully unstable, to ensure cracking did not occur (a nd therefore maintain rep eatability). Therefore, the last measured data point presented for an individual test does not in dicate that buckling has occurred, but rather it indicates the load and displacement level at which the test was concluded. Measured Load-Displacement Curves For each test, vertical load was applied at the top of the test girder at the gravity load simulator locations (Figure 9-2), and midspan lateral (x-axis) displacement was measured roughly at the centroid of the test girder. Data points were established when the Interface load cell readings (F-N15-C and F-S15C, located at the north and s outh simulators, respectively)

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132 measured approximately the same applied load. In this chapter, the average of these load cell readings is defined as the applied load (P) (Figure 9-2). Midspan lateral displacements presented in this chapter were measured using displacement sensor Dx-N0-W-38. Measured load-displacement curves for each test are shown in Figure 9-3. For each curve, the displacement of the first data point indicates the sweep of the test girder under only its own self weight. Note that sweep was recorded using displacement sensor Dx-N0-W-38 for the tests conducted following method A (recall Chapter 8), whereas the sweep was measured using a tape rule for the tests conducted following method B. By shifti ng the displacement data along the x-axis to the origin (Figure 9-4)corresponding to incremental mi dspan displacement caused by applied loadexcellent repeatability is observed between tests with th e same configuration. Data Curve Fitting A method developed by Southwell (1932) is commonly used to characterize the load-displacement behavior of buckling experime nts and also to predic t the buckling capacity without performing the experiment al test until buckling occurs Using the Southwell method, a rectangular hyperbola with asymptot es passing through the origin of c oordinates is fitted to loaddisplacement data obtained from a buc kling experiment using the equation: 0 xyxy (9-1) where and are the asymptotes of the hyperbola (Figure 9-5). Rearranging the equation provides a more familiar form: 2 22x y x x (9-2) To fit a curve through multiple sets of data, individual data sets are commonly averaged together to form a single data set and a curve is fit to th e averaged data. This approach works best when each data set includes approximately the same num ber of points, and data are recorded at the

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133 same interval. However, the data from the buckli ng tests were not recorded in this manner. As shown in Figure 9-4, data for individual tests within each configuration were measured at unequal intervals, and the range of each test was not equal. Thus simply averaging the data for each configuration would bias the average toward tests in which data were captured at smaller intervals. To avoid this issue, the following procedure was used to process the data for each individual test and develop a characteristic fitted curv e for each configuration: A hyperbola (Equation 9-2) was fitby using least-squares errorto each individual test data set (Figure 9-6A) The hyperbolas within each test configurat ion were resampled at equal displacement intervals, specifically 1/20th of the maximum displacemen t within a configuration (Figure 9-6B) A single hyperbola was fit to the cloud of resa mpled data for each configuration (Figure 96C) This procedure was applied to each test configur ation, with the final hyp erbola results shown in Figure 9-7. Calculation of Buckling Capacity Using the Southwell method (1932), buckling capacity is approximately equal to the horizontal asymptote ( ) of the best fit hyperbola. Recall that among the buckling experiments conducted, one test (A-45-0-1) was run until buckling occurred. Thus, this case can be used to test the accuracy of approximating the buckling load using the fitted value For this test, the buckling load was measured as 13.1 kip. However, as shown in Figure 9-8, the Southwell method estimates the buckling load ( ) as 18.7 kip, overestima ting by 43%. As stated by Southwell (1932), the analysis may be expected to apply best to cases in which the initial deflection [sweep] was small. In other words, the Southwell method works best when the primary instability is lateral to rsional buckling. However, for th e experiments conducted in this

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134 study, the test girder in itial sweep was large eno ugh that the failure mode was a mixture of lateral torsional buckling and roll-over instability as opposed to pure lateral torsional buckling instability. Due to the slenderness and post-tensi oning levels necessary to elastically buckle the test girder at 100 ft, the test girder had a sweep that was more than twice the acceptable level in practice. As per the 2010 FDOT Standard Specifications for Road and Bridge Construction (FDOT 2010), maximum allowable girder sweep was limite d to 1/8 in. of sweep per 10 ft of girder length, but not to exceed 1.5 in. for Florida Bulb T-beams and Florida-I Beams. The minimum sweep of the test girderin test configuration A-0-0was 2.8 in. Because of these large initial displacements, the asympt ote of the hyperbola ( ) is not the ideal defini tion of the buckling load for the experiments performed in this study. In stead, an alternative definition for buckling capacity is employed, still inco rporating the Southwell hyperbola. Using the fitted hyperbola (Eqn. 9-2), the buckling load is defined as the poin t at which the slope drops to below 1/10th of its initial value (Figure 9-9). This rule agreed with the data set from the one test case that was carried out to buckling during testing (A-45-0-1, as noted in the following section). Buckling Capacity Results Using the 10% buckling rule, the ideal case, A-0-0 (non-sk ewed, non-sloped), had the largest buckling capacity, and the skewed, sl oped case (A-15-04) had the lowest buckling capacity. The intermediate cases (A-45-0 and A-0-04) both had buckling capacities between the two extremes. Table 9-1 provides a summary of the buckling capacity for each test configuration, as well as the percent reduction in buckling capacity from the ideal (A-0-0) case. There was good agreement between the calculated buckling ca pacity of A-45-0 and the measured buckling capacity of test A-45-0-1, which buckling in the lab at a measured load of 13.1 kip. Using the

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135 10% buckling rule, the buckling capacity for A-45-0 is calculated as 12.8 kip (2.3% error relative to test A-45-0-1). In the case of test configuration A-15-04, determining the buckli ng capacity through the use of the 10% rule is not applicable, because th e test girder had such a large sweep (5.7 in.) compared to what is acceptable in practice. This magnitude of initial lateral displacement (sweep) caused the test girder to purely overturn, as opposed to buckle. While a hyperbola can be fit through the data, the buckling load cannot be defined and will not be presented for the remainder of this thesis. Buckling Finite Element Model The results of the experimental buckling test s were used to validate the finite element buckling model. This section discusses the mode l and several of its components, including the development of the moment-rotatio n curves that were used to represent the bearing pad, the modulus of elasticity test girder concrete, and the results obtaine d from each test configuration. Moment-Rotation Curves from Roll Stiffness Tests Originally, the nonlinear roll stiffness of the bearing pads were to be modeled using the moment-rotation curves obtai ned from the isolated roll stiffness tests using the bearing pad test device (Chapter 2). However, axial (vertical) load levels on the pads were different between the isolated tests and the buckling te sts. This difference altered th e moment-rotation behavior during buckling tests as compared to the isolated tests. Therefore, additional roll stiffness tests were performed on the bearing pads under buckling tes ting conditions, with the bearing pads located beneath the test girder in test configuration A-0-0. Under these conditions, the bearing pads were tested in-situ. In this section, the in-situ test procedure and results are presented, and the results are compared to the isolated roll stiffness re sults obtained using the bearing pad test device (denoted isolated in this chapter).

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136 For the in-situ tests, a lateral load was applied to the top flange of the test girder near each end block, and the girder was allowed to roll about the y-axis of the bearing pad (Figure 9-10A). The load was applied by a hydraulic jack mounted to the catch frames at each end of the test girder, and measured with an inline load cell (Figure 9-10B). Displacement sensors at the end blocks along the x-axis (Dx) measured the rela tive horizontal displacem ent between the top and bottom of the end blocks. Given the vertical di stance between each pair of sensors (Dx-N51-W-2 and Dx-N51-W-76; Dx-S51-W-2 and Dx-S51-W-76), the end block roll angle was calculated. Three in-situ roll tests were performed (on 2011-12-19 and 2011-12-20). The measured data are shown in Figure 9-11. In the finite element model, bearing pad ro tational resistance is modeled using nonlinear rotational springs which are simp ly defined by a moment-rotation cu rve. Therefore, the measured moment-rotation data from the roll stiffness tests were averaged and subsequently fitted to a representative function for input into the finite element model. To maintain equal weight when averaging the curves, the measured load-displacement curves (Figure 9-12A) from individual tests were resampled at an equa l interval of 0.0003 rad (Figure 9-12B), and the resampled curves were averaged (Figure 9-12C). The averaged data exhibit an in itial, linear roll stiffness (slope of moment-rotation curve) that is followed by an apparent softeni ng (reduction in stiffness), until the slope of the moment-rotation curve effectiv ely equals zero and the moment-rotation curve plateaus. A sigmoid function, which has a shape that matches the average data closely, was chosen to represent the moment-rotation curves for the bearing pads. A basic sigmoid function takes the following functional form: 1 () 1 x fx e (9-3)

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137 However, to fit the moment-roll curves, the basic functional fo rm must undergo a variety of transformations. Thus, the data were fit (by using least-squares error) with the following modified functional form: 21 0() 1 x fx e (9-4) where 0, 1, and 2 are functional parameters. This same process of resampling, averaging, and fitting the data was then applied to the moment-rotation curves obtai ned from the isolated roll stiffness tests using the bearing pad test device. Similarly to the in-situ roll stiffness tests, the measured data has an initial linear stiffness that gradually decreases, closely matching the modified sigmoid curve shape. The best fit sigmoid curves for the moment-rotation curves of the isolated and in-situ roll stiffness tests are shown in Figure 9-13. The functional parameters of the best fit sigmoid curve for each test configurationboth isolated and in-situ roll stiffness testsare presented in Table 9-2 (data units: kip, in., and rad). Scaling of Moment-Rotation Cu rves from Isolated Tests The axial load applied to the type A bearing pa ds during the isolated roll stiffness tests was approximately 92 kip, which was chosen to be repres entative of the self we ight end reactions of a realistic long span girder (Florida Bulb-T sec tions). However, during bu ckling testing, the test girder was constrained to a 100 ft span length, which required a more slender and therefore lighter girder cross-section to be used, resulti ng in a reduced axial load applied to the pad. During buckling testing, the axial loaddue to th e self weight of the slender test girder and applied vertical loadswas approximately 40 kip. Thus, the ratio of axial load during buckling testing to axial load during isolated roll stiffn ess testing was approximately 0.43. Under this reduced axial load, the in-situ moment-rotation beha vior of the bearing pads was different than

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138 measured during the isolated tests, as shown in Figure 9-14. Although both the in-situ and isolated moment-rotation data have similar initial roll stiffness, the plateau value differs significantly. As shown in Figure 9-14, the plateau of the moment-rotation curve occurs at a much lower moment than the in-situ tests. The difference in moment-rotation behavior can be attributed to the difference in pre-compression, which affects the contact area between the pad with the end block (or test device) as it rolls. In non-slope d test configurations (A-0-0 an d A-45-0), rotational stiffness is reduces as the end block (or test device) gradually loses contact as the test device rolls off the pad, hence the gradually nonlinear nature of the moment-rotation curv e. Initially, under non-sloped conditions, the bearing pad is fully in contact with the bot tom of the end block or test device, and thus the initial roll stiffness of the bearing pad is not affect ed by the magnitude of axial load. However, during the in-situ roll stiffness tests (and buckling tests)in which pre-compression is reduced relative to the isolated testsa smaller rotation is required for the end blocks to lose contac t with the pads (Figure 9-15). Consequently, the in-situ plateau moment is reduced relative to the isolat ed tests. The plateau moment s hould then be proportional to the axial pre-compression. Thus, the roll capacity should differ by the ratio of axial load during testing (0.43 in this case). A similar phenomenon also occurs for sloped cases. However, the initial contact area of the end block (or test device) with the bearing pad is appr oximately proportional to axial pre-compression (Figure 9-16). Thus, the initial roll stiffness is also proportional to the precompression. Like the non-sloped cases, the roll capacity is proportional to axial precompression. Therefore, for sloped cases, both the initial stiffness and plateau moment of the moment-rotation curve are decreased by the ratio of applied axial load (0.43 in this case).

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139 For use in the buckling finite element mode l, moment-rotation curves obtained from the isolated roll stiffness tests were scaled by a factor of 0.43 (equal to the ratio of axial loads). In non-sloped test configurations (A-0 -0 and A-45-0), the scale factor was applied to the plateau of the moment-rotation curve only, while maintaining the initial slope (Figure 9-17A and Figure 917B). However, for the sloped configuration (A-004), the scale factor was applied to both the initial slope and the moment plateau (Figure 9-17C). Examining the moment-rotation curves from test configuration A-0-0 (Figure 9-17A), the scaled curve closely matches the in-situ curve for both the initial stiffness and moment plat eau. The final scaled curves for each test configurationused in all subsequent finite element buckling analysesare compared in Figure 9-18. Elastic Modulus Used in Finite Element Buckling Model Concrete components of the test girder were modeled using a linear elastic material model. As discussed in Chapter 6, the elastic modulus was determined for the precast segments using field cured and moist cured cylinders. The averag e elastic modulus for the field cured cylinders was 4,770 ksi, and the average of the moist cure d cylinders was 5,140 ksi. Two separate finite element buckling analyses were performed in te st configuration A-0-0 (using the scaled roll stiffness curves), each with an elastic modulus corresponding to the field cured or moist cured results. The buckling curves predicted by both models are presented in Figure 9-19, along with the best fit hyperbola generated from the experime ntal data. As shown, the model with the field cured elastic modulus more accurately represents th e experimental results. This can be attributed to the web thickness of the precast segments, which matched the diameter of the concrete cylinders (4 in.). Therefore, th e conditions imposed on the field cured cylinders (cured alongside the test girder) were more representative of th e precast segments than the moist cured cylinders

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140 (inside a tank of lime water). Thus, the field cure d elastic modulus (4,770 ksi) is used in all subsequent finite element models. Finite Element Buckling Model Results A finite element buckling analysis was performe d for each of the three test configurations, using the scaled roll stiffness curv es and field cured elastic modulus as described in the previous sections. Using the same buckling rule used on th e experimental results, the buckling capacity of a finite element analysis was defined as the point at which the slope of the load-displacement curve drops to below 1/10th of its initial value. The buckling curves and capacities of the finite element analyses are shown in Figure 9-20, along with the buckli ng curves and capacities generated using hyperbolas fitted to the experi mental data. The buckling capacities calculated from the experimental tests and finite elem ent analyses are also summarized in Table 9-3. Generally, good agreement is observed between the shape of the curvesparticularly in the non-sloped casesand also between the pred icted buckling capacities. In the non-sloped cases (A-0-0 and A-45-0), the finite element buc kling capacity was lower than the experimental buckling capacity. However, in the sloped case (A -0-04), the initial slope and buckling capacity of the model are slightly larger than the experime ntal results. This disagreement can most likely be attributed to a difference in the theoretical initial contact area of th e bearing pad, caused by the initial sweep during a buckling test. If, as a simplification, linear elas tic bearing pad response is assumed, then the ratio of initial contact ar eas between buckling tests and isolated roll tests would be equal to the ratio of applied axial load Thus, scaling the isolated roll stiffness curves by the ratio of the applied axial loads should accurately reflect this difference. However, because relatively large sweep was present in the test gi rder, the end blocks initially rolled about the bearing pad as the test girder was being placed. Therefore, the contact area in the buckling tests may actually have been less than the theoretical contact area accounted for by using the scale

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141 factor. Thus, the initial slope a nd buckling load obtained from the experimental results would be smaller than the finite element prediction (as seen in the A-0-04 case). Therefore, based on the acceptable levels of di fference observed between the shape of the experimental buckling curves and the finite el ement analysis buckling curves, and based on a maximum difference of 15% between experiment ally and analytically determined buckling capacities, the finite element modeling methods employed in this study are considered to be experimentally validated.

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142 Table 9-1. Buckling capacity results Test configuration Skew angle (deg.) Slope angle (rad.) Buckling capacity (kip) Buckling capacity percent reduction from A-0-0 (%) A-0-0 0 0 15.4 0.0% A-45-0 45 0 12.8 16.9% A-0-04 0 0.04 11.8 23.4% Table 9-2. Sigmoid curve functional pa rameters for each test configuration Test configuration 012 A-0-0 (isolated) -458.1 916.1 373.2 A-0-0 (in-situ) -156.7 313.5 1370.2 A-45-0 (isolated) -363.3 726.6 324.2 A-0-04 (isolated) -986.3 1972.5 143.8 Table 9-3. Experimental and finite element buckling capacities for each test configuration Test configuration Experimental buckling load (kip) Finite element model buckling load (kip) Percent difference A-0-0 15.4 13.9 -9.7% A-45-0 12.8 10.9 -14.9% A-0-04 11.8 12.2 3.4%

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143 A B Figure 9-1. Test girder in buckled configuration, test A-45-0-1 ( photos courtesy of University of Florida, Department of Civil and Coasta l Engineering). A) Ph otograph taken above girder. B) Photograph taken below girder. Gravity load simulator Gravity load simulator Applied load (P) Applied load (P) NORTH (y-axis) EAST (x-axis) Figure 9-2. Definition of applied load (P)

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144 Midspan lateral displacement (in.)Applied load, P (kip) 0 1 2 3 4 5 6 78 0 3 6 9 12 15 18 A-0-0-1 A-0-0-2 A-0-0-3 A-45-0-1 A-45-0-2 A-0-04-1 A-0-04-2 A-0-04-3 A-15-04-1 Figure 9-3. Measured absolute load-displacement data Midspan lateral displacement (in.)Applied load, P (kip) 0 0.5 1 1.5 2 2.5 3 3.5 44.5 0 3 6 9 12 15 18 A-0-0-1 A-0-0-2 A-0-0-3 A-45-0-1 A-45-0-2 A-0-04-1 A-0-04-2 A-0-04-3 A-15-04-1 Figure 9-4. Measured incremental load-displacement data

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145 AsymptoteAsymptote x y 0 Figure 9-5. Southwell hyperbola fit AMidspan lateral displacement (in.)Applied load, P (kip) 0 1 2 3 45 0 2 4 6 8 10 12 14 A-45-0-1 measured A-45-0-2 measured A-45-0-1 hyperbola A-45-0-2 hyperbola Midspan lateral displacement (in.)Applied load, P (kip) 0 1 2 3 45 0 2 4 6 8 10 12 14 A-45-0-1 resampled A-45-0-2 resampledB CMidspan lateral displacement (in.)Applied load, P (kip) 0 1 2 3 45 0 2 4 6 8 10 12 14 A-45-0 resampled A-45-0 hyperbola Figure 9-6. Data curve fitting procedure. A) Be st fit hyperbolas for each individual test through measured data. B) Resampled data on hype rbola at regular in terval. C) Test configuration hyperbola fit th rough resampled cloud of data.

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146 Midspan lateral displacement (in.)Applied load, P (kip) 0 1 2 3 4 56 0 3 6 9 12 15 18 A-0-0 A-45-0 A-0-04 A-15-04 Figure 9-7. Best fit hyperbol as for each configuration Midspan lateral displacement (in.)App l i ed l oad P ( k i p)0 1 2 3 4 56 0 5 10 15 2 0 Best fit hyperbola Measured data = 18.7 kip Figure 9-8. Hyperbolic curve fit and Sout hwell buckling load for test A-45-0-1

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147 Midspan lateral displacement (in.)App l i ed l oad P ( k i p)0 1 2 3 4 56 0 3 6 9 12 15 1 8 1 Initial slope 1/10 th initial slope Buckling capacity Figure 9-9. Definition of buckling capacity (A-45-0 configuration shown) A Applied load (F) Moment arm B Figure 9-10. Description of in-si tu roll test. A) Schematic of te st. B) Loading setup, mounted to catch frame (photo courtesy of Univers ity of Florida, Department of Civil and Coastal Engineering).

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148 Roll (rad.)Moment (kip-in.) 0 0.002 0.004 0.006 0.0080.01 0 25 50 75 100 125 150 175 Measured data Figure 9-11. Moment-rotation data from in-situ tests (A-0-0)

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149 ARoll (rad.)Moment (kip-in.) 0 0.002 0.004 0.006 0.0080.01 0 25 50 75 100 125 150 175 Measured data Roll (rad.)Moment (kip-in.) 0 0.002 0.004 0.006 0.0080.01 0 25 50 75 100 125 150 175 Resampled data (every second data point shown for clarity) B CRoll (rad.)Moment (kip-in.) 0 0.002 0.004 0.006 0.0080.01 0 25 50 75 100 125 150 175 Average curve Sigmoid Figure 9-12. Data curve fitting procedure, in-sit u case shown. A) Measured data. B) Resampled data. C) Average curve and best fit sigmoid curve.

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150 Roll (rad.)Moment (kip-in.) 0 0.002 0.004 0.006 0.0080.01 0 100 200 300 400 500 600 A-0-0 (isolated) A-0-0 (in-situ) A-45-0 (isolated) A-0-04 (isolated) Figure 9-13. Moment-rotation curves, from is olated and in-situ roll stiffness tests Roll (rad.)Moment (kip-in.) 0 0.005 0.01 0.015 0 100 200 300 400 500 A-0-0 (isolated) A-0-0 (in-situ) Figure 9-14. Moment-rotation curves test configurationA-0-0, from isolated bearing pad tests (BPTD) and in-situ tests

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151 A Larger roll angle End block roll: isolated roll stiffness tests E q ual lift-of f End block Non-compressed bearing pad outline Initial configuration: pre-compressed bearing pad during isolated roll stiffness tests (smaller axial load) B Smaller roll angle Non-compressed bearing pad outline Initial configuration: pre-compressed bearing pad during buckling tests and in-situroll stiffness tests (smaller axial load) End block Equal lift-off End block roll: buckling tests and in-situ roll stiffness tests Figure 9-15. Bearing pad contact areas during testing. A) During isolated roll stiffness tests. B) During buckling tests. Initial configuration: pre-compressed bearing pad during isolated roll stiffness tests ( lar g er axial load ) Smaller contact width Larger contact width Beveled plate: equal slope angle in both cases End block Initial configuration: pre-compressed bearing pad during buckling tests and in-situroll stiffness tests ( smaller axial load ) Figure 9-16. Bearing pad contact areas during both isolated roll st iffness tests and buckling tests

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152 ARoll (rad.)Moment (kip-in.) 0 0.002 0.004 0.006 0.0080.01 0 100 200 300 400 500 600 A-0-0 (isolated) A-0-0 (scaled) A-0-0 (in-situ)Roll (rad.)Moment (kip-in.) 0 0.002 0.004 0.006 0.0080.01 0 100 200 300 400 500 600 A-45-0 (isolated) A-45-0 (scaled)B CRoll (rad.)Moment (kip-in.) 0 0.01 0.02 0.03 0 200 400 600 800 1000 1200 A-0-04 (isolated) A-0-04 (scaled) Figure 9-17. Moment-rotation curves, from isolated roll stiffness tests (scaled and original) and in-situ roll stiffness tests. A) A-0-0. B) A-45-0. C) A-0-04.

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153 Roll (rad.)Moment (kip-in.) 0 0.005 0.01 0.015 0.02 0 100 200 300 400 A-0-0 (scaled) A-45-0 (scaled) A-0-04 (scaled) Figure 9-18. Moment-rotation curves, scal ed from isolated bearing pad tests Midspan lateral displacement (in.)Applied load, P (kip) 0 1 2 3 4 56 0 3 6 9 12 15 18 Experimental FE analysis: field modulus FE analysis: moist modulus Figure 9-19. Comparison of expe rimental and FE buckling cu rves (configuration A-0-0)

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154 AMidspan lateral displacement (in.)Applied load, P (kip) 0 1 2 3 4 56 0 3 6 9 12 15 18 Experimental buckling load Model buckling load Experimental Finite element analysis Midspan lateral displacement (in.)Applied load, P (kip) 0 1 2 3 4 56 0 3 6 9 12 15 18 Model buckling load Experimental buckling load Experimental Finite element analysisB CMidspan lateral displacement (in.)Applied load, P (kip) 0 1 2 3 4 5 6 7 89 0 3 6 9 12 15 18 Model buckling load Experimental buckling load Experimental Finite element analysis Figure 9-20. Buckling curves from experimental tests and finite element models. A) A-0-0. B) A-45-0. C) A-0-04.

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155 CHAPTER 10 CONCLUSIONS Roll stiffnesses of various types of standard bearing pads were quantified under the effects of skew angle, slope angle or a combination of skew and slope. A bearing pad test device was designed and fabricated to impose axial load, sk ew, and slope on bearing pads, and to enable measurement of roll rotation as a function of moment applied. Additionally, gi rder buckling capacities of a full scale test gird er were quantified unde r the effects of skew angle, slope angle or a combination of skew and slope. The pads used to support each end of the test girder were the same pads previously tested to determine roll stiffness. Gravity load simulators were designed and fabricated to apply vertical load to the test girder without imposing artificial lateral restraint. In both types of testing (bearing pad and gird er buckling), multiple test repetitions were performed under identical conditions, to ensure that reasonable repeatab ility of the data was achieved. Based on the isolated roll stiffness test results for all three pad type s tested, substantial reductions in roll stiffness arose from the combin ed effects of skew and slope. Although not as severe as the combination of skew and slope, it was found that skew angle alone significantly reduced the roll stiffness of a bearing pad as we ll. Regarding the buckli ng tests, reductions in buckling capacities resulted from the imposition of skew or slope angle alone. A severe reduction was observed in the combination of skew and slope combined, with the most extreme case (A-45-04) causing the test girder to buckle under its own self-weigh t without any superimposed loads. It is therefore recommended th at consideration be given to requiring bearing pads to be oriented to match girder alignment (to elimin ate skew angle), and al so to provide beveled bearing plates such that the bottom of the plate of the unloaded girder is parallel to the beam seat.

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156 These requirements would eliminate the adverse effects of skew and slope, both of which have been experimentally demonstrated to reduce b earing pad roll stiffness and girder buckling capacity. Further analytical studies s hould be conducted to examine th e effects of roll stiffness on Florida I-Beam (FIB) girders, with typical lengths. Such studies can be executed using the finite element buckling modeling techniques documente d in this thesis. The buckling capacity determination rulein which the buckling load is defined as the point at which the slope of the load-deflection curve drops to be low 1/10th of its initial values hould continue to be used in future studies to determin e girder buckling capacity.

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157 APPENDIX A BEARING PAD TEST DEVI CE FABRICATION PLANS This appendix includes drawings for the fabrica tion of the bearing pad test device, used in the isolated roll stiffness tests.

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163 APPENDIX B FULL SCALE TEST GIRDER FABRICATION PLANS This appendix includes drawings for the fabrica tion of the test girder, used in the full scale buckling tests.

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174 APPENDIX C COMPRESSIVE STRENGTH AND ELASTIC MODULUS TEST RESULTS This appendix includes the compressive strengt h and elastic modulus test results, from cylinders cast from the test girder, used in the full scale buckling tests.

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175 Table C-1. Compressive strength test re sults performed for each girder component Date poured Batch Curing Date tested Age (days) Fracture type Compressive strength (psi) moist 28 day 28 7540 moist 9/19/2011 124 1 8828 moist 12/8/2011 204 4 7564 moist 12/8/2011 204 1 field 12/8/2011 204 4 6368 field 12/8/2011 204 4 6131 5/18/2011 Precast segment: Exterior A field 12/8/2011 204 4 6514 moist 28 day 28 7720 moist 9/19/2011 123 1,2 9154 moist 12/8/2011 203 4 8160 moist 12/8/2011 203 1 8238 field 12/8/2011 203 4 5956 field 12/8/2011 203 4 5680 5/19/2011 Precast segment: Exterior B field 12/8/2011 203 1 5858 moist 28 day 28 8070 moist 9/19/2011 119 1,2 9004 moist 12/8/2011 199 irregular 6646 moist 12/8/2011 199 4 8088 field 12/8/2011 199 4 6348 field 12/8/2011 199 4 7855 5/23/2011 Precast segment: Interior field 12/8/2011 199 4 7223 moist 9/13/2011 18 4 8812 moist 9/13/2011 18 4 8806 moist 12/8/2011 104 1 9060 moist 12/8/2011 104 1 9514 moist 12/8/2011 104 4 8783 field 12/8/2011 104 4 7693 8/26/2011 South end block field 12/8/2011 104 1 7335 moist 9/13/2011 14 4 8346 moist 9/13/2011 14 4 8154 moist 12/8/2011 100 1 9490 moist 12/8/2011 100 1 8808 moist 12/8/2011 100 1 10016 8/30/2011 North end block field 12/8/2011 100 1 7082 moist 9/13/2011 14 4 6124 moist 9/13/2011 14 4 6322 moist 12/8/2011 100 1 8292 moist 12/8/2011 100 4 7366 moist 12/8/2011 100 irregular 7090 8/30/2011 Closure pours field 12/8/2011 100 4 5264

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176 Table C-2. Elastic modulus test results performed for each girder component Date poured Batch Curing Date tested Age (days) Poisson's ratio Modulus of Elasticity (ksi) moist 12/9/2011 205 0.34 5450 moist 12/9/2011 205 0.31 5000 moist 12/9/2011 205 0.23 5000 field 12/9/2011 205 0.27 4550 field 12/9/2011 205 0.28 4750 5/18/2011 Precast segment: Exterior A field 12/9/2011 205 0.27 4550 moist 12/9/2011 205 0.32 5600 moist 12/9/2011 205 0.2 5000 moist 12/9/2011 205 0.3 5000 field 12/9/2011 205 0.31 4650 field 12/9/2011 205 0.31 4950 5/19/2011 Precast segment: Exterior B field 12/9/2011 205 0.29 4700 moist 12/12/2011 208 0.27 5000 moist 12/12/2011 208 0.27 5050 moist 12/12/2011 208 0.27 5150 field 12/9/2011 205 0.32 5050 field 12/9/2011 205 0.28 5000 5/23/2011 Precast segment: Interior field 12/9/2011 205 0.27 4750 moist 12/12/2011 208 0.27 5500 moist 12/12/2011 208 0.27 5250 moist 12/12/2011 208 0.28 5400 field 12/9/2011 205 0.25 4600 field 12/9/2011 205 0.25 4950 8/26/2011 South end block field 12/9/2011 205 0.27 5000 moist 12/12/2011 208 0.27 5000 moist 12/12/2011 208 0.31 5050 moist 12/12/2011 208 0.26 5000 field 12/9/2011 205 0.27 4300 field 12/9/2011 205 0.26 4250 8/30/2011 North end block field 12/9/2011 205 0.26 4150 moist 12/12/2011 208 0.25 4600 moist 12/12/2011 208 0.28 5050 moist 12/12/2011 208 0.31 4600 field 12/9/2011 205 0.27 3700 field 12/9/2011 205 0.26 3700 8/30/2011 Closure pours field 12/9/2011 205 0.25 3500

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177 APPENDIX D DYWIDAG JACK CALIBRATION FORM This appendix includes the DYWIDAG jack calibration form, used to determine the prestress levels in the post-tensioned bars, in the full scale buckling tests.

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180 APPENDIX E GRAVITY LOAD SIMULATOR FABRICATION PLANS This appendix includes drawings for the fabrication of the gravity load simulators, used in the full scale buckling tests.

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199 APPENDIX F CATCH FRAMES FABRICATION PLANS This appendix includes drawings for the fabrication of the gravity load simulators, used in the full scale buckling tests.

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207 APPENDIX G BUCKLING TESTS INSTRUMENTATION PLAN This appendix includes drawings of the inst rumentation used in the full scale buckling tests.

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219 LIST OF REFERENCES AASHTO. (2004). LRFD Bridge Design Specifications, 2nd Ed., AASHTO, Washington D.C. ADINA System 8.7 [Computer software]. (2010). Theor y and Modeling Guide, Volume I: ADINA. ADINA R&D, Inc. Allen, D. T., Cook, R. A., and Ansley, M. H. (2 010). Shear Stiffness of Neoprene Bearing Pads Under Long-Term Loads. Transportation Research Record: Journal of the Transportation Research Board No. 2172 Washington, D.C., 38-46. ASTM C39. (2001) Standard Test Method for Compressive Strength of Concrete Cylinders Cast in Place in Cylindrical Molds. Ameri can Society of Testing and Materials, ASTM International, West Conshohocken, PA. ASTM C109. (2011). Test Method for Compressi ve Strength of Hydrau lic Cement Mortars (Using 2-in. or [50-mm] Cube Specimens). Am erican Society for Testing and Materials, ASTM International, West Conshohocken, PA. ASTM C469. (1994) Standard Test Method for Stat ic Modulus of Elasticity and Poissons Ratio of Concrete in Compression. American So ciety of Testing and Materials, ASTM International, West Conshohocken, PA. ASTM D4014-03. (2003). Standard Specificati on for Plain and Steel-Laminated Elastomeric Bearings for Bridges. American Society for Testing and Materials, ASTM International, West Conshohocken, PA. Consolazio, G. R., Hamilton III, H. R., Bui L., and Chung J. ( 2007). Lateral Bracing of LongSpan Florida Bulb-Tee Girders. Structures Research Report No. 2007/52290 Engineering and Industrial Experiment Station, Univers ity of Florida, Gainesville, Florida. Deaver, J. E. (2003). Laboratory Tests on Tors ional Braces for Steel Bridge Girders with Normal Supports. M.S. Thesis, Department of Civil and Environmental Engineering, University of Houston, Houston, TX. Doody, M. E., and Noonan, J. E. (1999). LongTerm Performance of Elastomeric Bridge TBearings. Transportation Research Record: Journal of the Transportation Research Board No. 1688 Washington, D.C., 139-146. FDOT. (2010). FDOT Design Standards Specification Structures Design Office, Florida Department of Transportati on, Tallahassee, Florida. FDOT. (2010). FDOT Standard Specifications for Road and Bridge Construction Florida Department of Transportation, Tallahassee, FL. FDOT. (2012). FDOT Structures Design Guidelines Structures Design Office, Florida Department of Transportation, Tallahassee, FL.

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220 Gent, A. N. (2001). Engineering with Rubber: How to Design Rubber Components 2nd Edition, Hanser Gardner Publications Inc., Cincinnati, Ohio, 312-313. Green, T., Yazdani, N., Spainhour, L., and Cai, S. C. (2001). Effect of Bearing Stiffness and Skew Angle on Performance of Precast Concrete Bridges. Transportation Research Record: Journal of the Transportation Research Board. No. 1770 Washington, D.C., 27-33. Hurff, J. B. (2010). Stability of Precast Pres tressed Concrete Bridge Girders Considering Imperfections and Thermal Effects. Ph.D Dissertation, Sch ool of Civil and Environmental Engineering, Georgia In stitute of Technology, Atlanta, GA. Kalkan, I. (2009). Lateral Torsional Buckling of Rectangular Reinforced Concrete Beams. Ph.D. Dissertation, School of Civil and Envi ronmental Engineering, Georgia Institute of Technology, Atlanta, GA. Lehman, D. E., Roeder, C. W., and Larsen, R. A. (2005). Design of Cotton Duck Bridge Bearing Pads. J. Bridge Eng. 10(5), 555-563. Mast, R. F. (1989). Lateral Stability of Long Prestressed Concrete Beams, Part 1. PCI Journal V. 34, No. 1, Jan-Feb, pp. 34-53. Mast, R. F. (1993). Lateral Stability of Long Prestressed Concrete Beams, Part 2. PCI Journal V. 38, No. 1, Jan-Feb, pp. 70-88. Muscarella J. V., and Yura, J. A. (1995). A n Experimental Study of Elastomeric Bridge Bearings with Design Recommendations. FHWA/TX-98/1304-3 PCI. (2003). PCI Bridge Design Manual Precast/Prestressed Concrete Institute, Chicago, Illinois. Stoddard, W. P. (1997). Lateral-Torsional Buck ling Behavior of Poly mer Composite I-Shaped Members. Ph.D. Dissertation, School of Ci vil and Environmental Engineering, Georgia Institute of Technology, Atlanta, GA. Vidot-Vega, A. L., Possiel B., Robinson B ., Kowalsky M. J., and Gabr M. A. (2009). Evaluation of Rotational Stiffness of Elas tomeric Bearing Pad-Anchor Bolt Connections on Deep Foundation Bents. J. Bridge Eng. 14(6), 487-495. Yarimci, E., Yura, J. A., and Lu, L. W. (1967) Techniques for Testing Structures Permitted to Sway. Experimental Mechanics V. 7, No. 8, Aug., pp. 321-331. Yazdani, N., Eddy, S., and Cai, C. (2000). E ffect of Bearing Pads on Precast Prestressed Concrete Bridges. J. Bridge Eng. 5(3), 224-232.

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221 Yura, J.A., Kumar, A., Yakut, A., Topkaya, C., Becker, E., and Collingwood, J. (2001). Elastomeric Bridge Bearings : Recommended Test Methods. NCHRP Report No. 449 Washington D.C. Yura, J.A., and Phillips, B.A. (1992). Br acing Requirements for Elastic Steel Beams. Research Report 1239-1 Center for Transportation Research, The University of Texas, Austin, TX.

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222 BIOGRAPHICAL SKETCH The author was born in Boynton Beach, FL. She began attending the University of Florida in the September 2004, where she received the degree of Bachelor of Scien ce in civil engineering in December 2008. She then continued with graduate studies at the University of Florida, where she anticipates receiving a Master of Science de gree in civil engineering in May 2012, with an emphasis in civil structures. Upon graduation, the author will pursue a career in bridge design.