DEFORMATION AND CRACKING OF PARTIALLY PRESTRESSED CONCRETE BEAMS UNDER STATIC AND CYCLIC FATIGUE LOADING BY Muhamed H. Harajli and Antoine E. Naaman August 1984 Rep-ort No. UMEE 84R1 Department of Civil Engineering The University of Michigan College of Engineering Ann Arbor, Michigan 48109

Department of Civil Engineering The University of Michigan DEFORMATION AND CRACKING OF PARTIALLY PRESTRESSED CONCRETE BEAMS UNDER STATIC AND CYCLIC FATIGUE LOADING BY Muhamed H. Harajli and Antoine E. Naaman August 1984 Report No. UMEE 84R1 A Report on a Research Project Sponsored by The NATIONAL SCIENCE FOUNDATION Grant CEE-82 11563 and CEE-84 02194 Ann Arbor, Michigan

ABSTRACT This study was conducted to evaluate the fatigue resistance of partially prestressed concrete beams. All beams were 9in x 4.5in (229x114 mm2) cross section, 10 ft (3.05 m) long, simply supported, 9 ft (2.74 m) span and loaded in four point bending. Twelve different sets of beams were tested. Each set consisted of 2 identical specimens designed with the same input parameters. One control beam was tested under static load to determine the ultimate load resistance. The second beam was tested under cyclic fatigue loading at a constant load range fluctuating between 40% and 60% of the observed ultimate load capacity of the static specimen. The main input variables were the partial prestressing ratio (PPR) and the reinforcing index (X). Four different levels of PPR and three different levels of c covering both fully prestressed and fully reinforced were explored. The six partially prestressed and the three fully reinforced beams survived 5 million cycles without suffering fatigue failure. The three fully prestressed beams which were loaded beyond cracking failed respectively at 1.21, 2.17 and 1.94 million cycles by fracturing of the prestressing strands in the constant moment region. The stress ranges from strain measurements in the strands observed in the early cycles were 10 ksi (68.95 Mpa), 16 ksi (110 Mpa) and 19 ksi (131 Mpa) respectively. Throughout the

test, measurements of deflections, crack widths, curvatures and reinforcement strains were systematically recorded. A comprehensive set of data was obtained in these tests and could be used as a data base for any future studies. A qualitative analysis of these data is also provided. ii

ACKNOWLEDGEMENT This research was supported by the National Science Foundation under grants No. CEE 82-11563 and CEE 8-4-02194 respectively to the University of Illinois at Chicago and to the University of Michigan, with Dr. Michael P. Gaus as program director. The writers are very grateful for that support. Sincere thanks are due to professor A. Andonian for his advise and constructive comments on all aspects of the data gathering phase. Also the help of D. Fanella and S. Watcharaumnuay in casting the beam specimens, J. Gramsas in fabricating the various fixtures for the experiment, and L. Jhonson in calibrating the electronic instrumentation is greatly appreciated. iii

LIST OF FIGURES Figure Page 1.1 S-N Curves For Reinforcing Steel............... 11 1.2 S-N curve For Prestressing Strands............ 12 2.1 Planned Experimental Program For The Two Working Phases............ 23 2.2 Beam Dimensions And Steel Lay-Out............. 24 2.3 Beam Cross Sections......................... 26 2.4 Beam Preparation: (a) Strain Gages Instrumentation, b) Reinforcing Cages, (c) Wood Mold And Prestressing bed............................. 34 2.5 Beam Preparation: (a) Prestressing Operation, (b) Torch Cutting For Strand Release, (c) Cast Beams.............................. 38 2.6 Strain Gages 1 Used On The Prestressing Strand 2 Used On The Reinforcing Bars............. 39 2.7 Typical Strain Gage Mounting On The Prestressing Strands And Reinforcing Bars................... 39 2.8 Instrumentation: Deflection And Crack Width Measurement.................................. 44 2.9 Crack Width Measuring Device................... 44 2.10 Dial Gage Mounting For Strand Slip Measurement. 45 2.11 Close Up View Of Instrumentation: Deflection, Crack Width and Curvature...................... 46 2.12 Beam Setting In Testing Machine................ 48 2.13 General Test Setup: Loading Machine And Data Acquisition System............................ 50 2.14 Close Up View Of Test Setup.................... 51 3.1 Typical Beam Failures: PS3, PD1................. 61 3.2 Typical Beam Failures: PP1D3, PPlS1........... 62 3.3 Typical Beam Failures: PP2D3............. 63 3.4 Crack Width Variation With Load At Different PPR: iv

(a) = 2/3omax, (b) w = max................... 65 3.5 Crack Width Variation Versus Reinforcing Steel Stress At Different PPR: (a) w = 1/3 wmax (b) =w 2/3 wmax' (c) w = wmax.................... 66 3.6 Effect Of c On Load-Curvature Relationships: (a) PPR Close to 0.33, (b) PPR Close To 0.67........ 67 3.7 Comparison Of Observed Fatigue Life With Existing Data........................................ 74 3.8 Load-Deflection Curves For Beams: (a) PS2 (Static) (b) PD2 (Cyclic)............................... 75 3.9 Load-Deflection Curves For Beams PS3 (Static) And. PD3 (Cyclic)................................... 76 3.10 Load-Deflection Curves For Beams: (a) PP2S2 (Static), (b) PP2D2 (Cyclic).................... 77 3.11 Load-Deflection Curves For Beams: (a) PP1S2 (Static), (b) PP1D2 (Cyclic)................... 78 3.12 Load-Deflection Curves For Beams: (a) RS2 (Static) (b) RD2 (Cyclic)............................. 79 3.13 Observed Deflection Versus Number Of Cycles ( = 1/3max).................. 81 3.14 Observed Deflection Versus Number Of Cycles (o = 2/3w ) * —-.............................. 82 max 3.15 Observed Deflection Versus Number Of Cycles (c = o ax )...................................... 83 max)83 3.16 Observed Crack Width Versus Number Of Cycles ( = 1/3max).................................. 86 3.17 Observed Crack Width Versus Number Of Cycles (= 2/3max).-................................. 87 3.18 Observed Crack Width Versus Number Of Cycles (a = )...................................... 88 max 3.19 Variation of Curvature Versus Number Of Cycles For Various Beam Specimens.......................... 90 APPENDIX A Al Load-Deflection Curves For Beams: (a) PS1 (Static) (b) PD1 (Cyclic)................................ 109 A2 Load-Deflection Curves For Beams: (a) PP2S1 (Static) v

(b) PP2D1 (Cyclic)......................... 110 A3 Load-Deflection Curves For Beams: (a) PP2S3 (Static) (b) PP2D3 (Cyclic)....................... 111 A4 Load-Deflection Curves For Beams: (a) PP1S1 (Static) (b) PP1D1 (Cyclic).............................. 112 A5 Load-Deflection Curves For Beams: (a) PP1S3 (Static) (b) PP1D3 (Cyclic)............................. 113 A6 Load-Deflection Curves For Beams: (a) RS1 (static) (b) RD1 (Cyclic)......................... 114 A7 Load-Deflection Curves For Beams: (a) RS3 (Static) (b) RD3 (Cyclic)................................. 115 A8 Load-Deflection Curve Of Beam PP2D1 After 5 Million Cycles In Comparison With Its Control Static Beam (PP2S1)...................................... e116 A9 Load-Deflection Curve Of Beam PP2D2 After 5 Million Cycles In Comparison With Its Control Static Beam (PP2S2) 117 A10 Load-Deflection Curve Of Beam PP2D3 After 5 Million Cycles In Comparison With Its Control Static Beam (PP2S3).......................................... 118 All Load-Deflection Curve Of Beam PP1Dl After 5 Million Cycles In Comparison With Its Control Static Beam (PP1S1)..... 119 A12 Load-Deflection Curve Of Beam PP1D2 After 5 Million Cycles In Comparison With Its Control Static Beam (PP1S2).......................................... 120 A13 Load-Deflection Curve Of Beam PP1D3 After 5 Million Cycles In Comparison With Its Control Static Beam (PP1S3)........................................ 121 A14 Load-Deflection Curve Of Beam RD2 After 5 Million Cycles In Comparison With Its Control Static Beam (RS2)............................................ 122 A15 Load-Deflection Curve Of Beam RD3 After 5 Million Cycles In Comparison With Its Control Static Beam (RS3)....................................... 123 vi

LIST OF TABLES Table Page 1.1 Proposed S-N Equations For Prestressing Strands.. 12 2.1 Summary Of Reinforcing Parameters.............. 27 2.2 Concrete Mix Proportions.......................... 30 2.3 Stress-Strain Characteristics Of Prestressing Strands.......................................... 31 3.1 Stresses In the Reinforcement At Time Of Loading. 56 3.2 Comparison Of Observed And Computed Ultimate Moments For All Test Beams....................... 58 3.3 Calculated Concrete Nominal Tensile Stresses and Observed Stress Ranges In The Reinforcement...... 73 3.4 Measured Crack Spacing And Number Of Cracks...... 85 3.5 Stresses In The Prestressing And Reinforcing Steel At Pmin and Pmax' Cycle No. 1.................. 93 3.6 Stresses In The Prestressing And Reinforcing Steel At Pmin And Pmax' Cycle No. 3................. 94 3.7 Stresses In The Prestressing And Reinforcing Steel At Two Load Levels Pmin And Pmax (Static Beams).. 95 min max 3.8 Deflection And Load Characteristics Of Beams Loaded To Failure After 5 million Cycles............... 97 APPENDIX B B1 Ultimate Load Cycle For Beam PP2D1.............. 125 B2 Ultimate Load Cycle For Beam PP2D2......... 126 B3 Ultimate Load Cycle For Beam PP2D3........... 127 B4 Ultimate Load Cycle For Beam PP1D1........... 128 B5 Ultimate Load Cycle For Beam PP1D2.......... 129 B6 Ultimate Load Cycle For Beam PP1D3...........0 130 B7 Ultimate Load Cycle For Beam RD2.............. 131 B8 Ultimate Load Cycle For Beam RD3................ 132 vi i

IS Data For Beam PS1..................... 133 2S Data For Beam PS2......................... 135 3S Data For Beam PS3..........................137 4S Data For Beam PP2S1.................................. 139 5S Data For Beam PP2S2.............................141 6S Data For Beam PP2S3........................... 143 6S Data For Beam PP2S3......143 7S Data For Beam PP1S1............................145 8S Data For Beam PP1S2........................... 147 9S Data For Beam PP1S3............................. 149 10S Data For Beam RS1............................. 151 11S Data For Beam RS2........................ 153 12S Data For Beam RS3............................. 155 1D Data For Beam PD1............................ 157 2D Data For Beam PD2.......................... 158 3D Data For Beam PD3.................... 160 4D Data For Beam PP2D1.............................. 162 5D Data For Beam PP2D2............................ 164 6D Data For Beam PP2D3...................... 166 7D Data For Beam PP1D1............................ 168 8D Data For Beam PP1D2........................ 170 9D Data For Beam PP1D3............................. 172 10D Data For Beam RD1.............................174 11D Data For Beam RD2.............................. 176 12D Data For Beam RD3............................ 178 viii

LIST OF NOTATIONS A = area of prestressing steel ps A = area of tension reinforcing steel S A' = area of compression reinforcing steel S b = width of beam cross section d = depth of reinforcement d = depth of prestressing steel ps ds = depth of reinforcing steel f = prestressing steel stress ps f = ultimate strength of prestressing steel pu f = reinforcing steel stress f = yield stress of reinforcing steel y f = concrete strength f = stress range in the concrete cr f = maximum stress level max fm = minimum stress level M = ultimate moment u M = nominal moment ML = live load service moment M, = dead load service moment N = number of cycles PPR = partial prestress ratio Pma = maximum load level in the fatigue load range max min = minimum load level in the fatigue load range min P = ultimate load S = safe stress range w = reinforcing index ix

max = maximum reinforcing index max Af = stress range in the prestressing steel = stress range in the reinforcing steel Of = increase in stress in the prestressing steel above pS zero load level bA = ultimate deflection x

TABLE OF CONTENTS INTRODUCT I ON.................. 1 1.1 General.................... 1 1.2 Fatigue in Partially Prestressed Beams...3 1.3 Literature Background.............6 1.3.1 Concrete.................6 1.3.2 Reinforcing bars............... 1.3.3 Prestressing strands............ 1.3.4 Prestressed and partially prestressed beams. 13 1.4 Objectives and Summary........... 18 EXPERIMENTAL PROGRAM........21 2.1 Beam Parameters......... 21 2.1.1 Input variables............. 21 2.2 Materials.................29 22..1 Concrete.............29 2.2.2 Prestressing steel............ 30 2.2.3 Reinforcing steel.............. 31 2.3 Beam Fabrication............. 32 2.3.1 Preparation of reinforcing cages..... 32 2.3.2 Tensioning procedure........... 33 2.3.3 Concrete casting............. 35 2.4 Instrumentation...........37 2.4.2 Deflection................. 40 2.4.3 Crack width................. 41 2.4.4 Curvature..... 42 2.4.5 Slip................... 42 2.4.6 Data acquisition system.......... 43 xi

2.5 Test Setup.................. 47 2.6 Test Procedure................ 49 2.6.1 Static test................49 2.6.2 Fatigue test............... 52 TEST RESULTS.............54 3.1 Calculation of Effective Prestress..... 54 3.2 Static Load Test...............54 3.2.1 Cracking load................ 54 3.2.2 Ultimate load.....55 3.3 Behavior of Static Test Specimens....... 57 3.3.1 Load-deflection........... 57 3.3.2 Crack width................ 60 3.3.3 Load-curvature............. 64 3.4 Fatigue Test..............69 3.4.1 Fatigue life............. 69 3.5 Behavior of Fatigue Test Specimens...... 72 3.5.1 Deflection............. 72 3.5.2 Cracks and crack width..........84 3.5.3 Average curvature............89 3.6 Reinforcement Stresses....... 91 3.7 Ultimate Load After Cycling........ 92 OBSERVATIONS AND CONCLUSIONS.. 98 4.1 Observations.............98 4.2 Conclusions................. 100 LIST OF REFERENCES............. 102 APPENDIX A................. 108 APPENDIX B................ 124 xii

CHAPTER I INTRODUCT ION 1.1 General Due to the widespread use of concrete structures in different types of applications, fatigue is becoming increasingly an important aspect in design. Fatigue is a -process of progressive and irreversible deterioration in the material subjected to repetitive loads. There are several reasons given by the ACI committee 215 ( 1 ) to indicate that the fatigue strength of concrete might be an important design consideration; these include: 1. Use of concrete members in different types of applications which undergo continuous repetition of load, such as prestressed concrete in railway and highway bridges, reinforced concrete pavements, marine structures and the like. 2. Widespread use of ultimate strength design procedures and higher strength materials. 3. New recognition of the effects of repeated load on a member, which lead to increase in the crack widths and deflections in comparison to identical static load. In addition to the reasons mentioned above, the continuously increasing traffic volume and heavy loads, specially on highway and railway bridges, requires a special attention for and better understanding of the fatigue characteristics of these structures. 1

2 Fatigue strength is rarely properly considered in the current design codes and this is also the case for prestressed concrete. Little guidance is given to engineers concerning the design of prestressed concrete members for fatigue. Numerous tests conducted on prestressed strands and reinforcing bars tested freely in air have shown that 1) the stress range, 2) the minimum stress level and 3) the length of the specimen are all factors that influence fatigue life. The stress range was observed to be one of the most important factors in the fatigue life of prestressing strands and reinforcing bars. Every thing else being equal, the higher the stress range the lower is the fatigue life. Most of the experimental tests conducted on structural concrete beams (22-25,29,31,32,34) showed that their fatigue life is mainly governed by the fatigue fracture of the tension reinforcement. Fatigue fracture of the concrete in compression,when the concrete is part of a flexural concrete beam is very rare and not likely to occur. Many of these tests have also indicated that the stress range in the reinforcement resulting from repetitive application of live loads is one of the main factors that dictate the fatigue life of the beam element. Most of the earlier fatigue tests available in literature on prestressed concrete flexural beams refered to the fictitous nominal tensile stress in the concrete calculated by assuming uncracked section as being an important index for fatigue studies. However it is becoming

3 increasingly evident that the stress range in the steel is the basic influencing factor to be considered and also the most important factor in controlling the fatigue resistance of structural concrete beams. This is particularly true in the case of partial prestressing. 1.2 Fatigue in Partially Prestressed Beams Partially prestressed concrete beams are defined here as concrete beams reinforced with a combination of prestressed and non prestressed reinforcement intended to resist flexure. Such beams are generally designed to crack under full service load (dead plus live load). Partially prestressed concrete can offer some advantages over fully reinforced or fully prestressed concrete. Compared to fully reinforced concrete, partial prestressing offer better cracking and deflection control (short and long term) and lesser use of materials; compared to fully prestressed concrete, partial prestressing offers better camber and a higher ductility and energy absorption to failure ( 54 ). Improved ductility is an important factor in earthquake resistance design. Today it is possible to design partially prestressed beams following the same ACI code design philosophy prescribed for reinforced or prestressed concrete, namely: design to satisfy ultimate strength as well as serviceability criteria. Serviceability criteria includes

4 allowable stresses, cracking, deflection, corrosion and fatigue. Although a reasonable number of investigations hasdealt with the fatigue behavior of reinforcing bars and prestressing strands tested freely in air, little information exists on the fatigue behavior of partially prestressed beams and experimental data are greatly needed. It is generally agreed that a different fatigue life may be observed for a prestressing strand tested freely or as a part of a concrete member. Some of the reasons were summarized in ( 28 ): a) In a free test the effect of gripping and the effect of strand untwisting may substantially influence the observed fatigue life. b) Fretting action between the concrete and the strand might reduce the net sectional area of the strand. This effect increases the stress range of the prestressed strand and therefore reduces its fatigue life. c) Extensive slippage of tendons in pretensioned members due to a possible bond failure will result not only in a higher stress range in the strands but also in excessive crack widths and deflections. This condition will lead to unserviceable conditions hence failure for all practical purposes. Partially prestressed beams are generally more susceptible to fatigue failure than equivalent reinforced

5 concrete beams. Naaman ( 28 ) explains this characteristics as follows. In fully reinforced and fully prestressed concrete members the stress changes in the concrete and in the steel under the effect of repetitive loads are not critical. This is particularly the case in fully prestressed concrete where the stress change in the prestressing'strand is of the order of few ksi. However, in partially prestressed concrete beams, the section is generally uncracked under the sole effect of the dead load and will crack due to first application of live load. Subsequent applications of live loads will lead to cracks opening at the decompression stress which is lesser than the cracking stress. First cracking or subsequent crack opening will shift upward the location of the neutral axis of bending of the section leading to a higher rate of increase in the steel stress and correspondingly in the concrete extreme fiber compression stress (to maintain equilibrium of forces and moments in the section). These repetitive changes in stresses create fatigue damage in the corresponding materials, reduce bond properties at the interface between steel an concrete and lead to substantial increase in crack widths and deflections under service loads. Because the stress range generated by live loads are believed to be higher for partially prestressed than for fully prestressed or fully reinforced beams, it is expected that the effect of fatigue loading on the corresponding

6 increase in crack widths and deflections will be more pronounced, hence deserve careful investigation. 1.3 Literature Backqround 1.3.1 Concrete Fatigue of concrete is generally influenced by many factors such as range and rate of loading, load history, material properties and environmental conditions ( 1 ). The failure of concrete under cyclic fatigue loading results from progressive microcracking which leads to progressive damage in the concrete indicated by the increase in the level of strain at fmin and fmax' The fatigue failure of concrete, when part of a concrete flexural member, is very unlikely to occur. Computerized analysis on more than 200 partially prestressed beams ( 27 ) indicated only 3 possible cases of slabs and hollow core slabs where fatigue of concrete may have been critical. Tests conducted on plain concrete specimens (4-7) have shown that concrete could sustain about 10 million cycles for a stress range between 0 and 50% of its static strength. The fatigue strength of concrete (stress range) decreases almost linearly with increasing number of cycles when plotted on a semi-log scale. The relation between fmin' fmax and N is often expressed in terms of an S-N diagram. However, for the purpose of design, the relation suggested by ACI committee 215 on fatigue of concrete to

7 achieve at least 10 million cycles (modified Goodman diagram) could be used: fr = 0.4f'c fmi/2 ( 1.1 where fcr and f'c are the stress range and the static strength of concrete respectively while'fmin is the minimum stress level of the concrete in compression. 1.3.2 Reinforcing bars Reinforcing steel exhibit a good resistance to fatigue. Although fatigue failure of reinforcing bars has not been a controlling factor in the fatigue life of reinforced concrete flexural members, the trend in the concrete structure toward using ultimate strength design approach and higher yield strength reinforcement makes fatigue characteristics of reinforcing bars of more concern to designers. The most important parameters that influence the fatigue life of reinforcing bars are summarized in a study conducted by the Portland Cement Association (PCA) in 1975 10 ). The study was sponsored in part by NCHRP to investigate the fatigue strength of deformed reinforcing steel bars. A total of 353 deformed bars from 5 United states manufacturer were tested. The following important observations were obtained ( 10 ):

8 1) Stress range, minimum stress, bar diameter, bar grade and bar geometry are all factors that influence the fatigue life of reinforcing bars. 2) The stress range in the reinforcing bar is the primary factor in determining its fatigue life. 3) The lowest stress range at which fatigue fracture occurred in No. 11 bar grade 60 was 21.3 ksi at a minimum stress level equal to 17.5 ksi. 4) Increasing the minimum stress level by 3 ksi was found to be equivalent to changing the stress range by 1 ksi. 5). Every thing else being equal, the fatigue strength of reinforcing bars increases with decreasing bar grade and with increasing yield strength. 6) Transverse lugs and manufacture bar identification marks cause stress concentration at the intersection of the base of transverse lugs and longitudenal ribs induced during the deformation process. The magnitude of this stress concentration depends primarily on the ratio of the lug radius at the base of deformation to its height (r/h). All fatigue fractures in the test were initiated at the base of transverse lug or bar mark. Based on these test results, the following equation was recommended for design for straight hot-rolled reinforcing bar with no welds and no stress raisers (more severe than deformation meeting ASTM standards (A615) ): fr 21 - min/3 + 8r/h ( 1.2 ) where

9 fr = stress range in ksi fin = minimum stress level in ksi (tension positive) min r/h = ratio of transverse lug base radius to lug height (a value equal to 0.3 is suggested in the absence of any information) This last formula was adopted by ACI committee 343, 1977 report (11) and currently adopted in AASHTO specifications ( 3 ). Typical S-N curves from the PCA test ( 10 ) are shown in figure 1.1. 1.3.3 Prestressing strands ACI committee 215 ( 1 ) pointed out that fatigue of prestressing steel and anchorages is generally unlikely to be a critical design factor in uncracked prestressed concret beams. However, fatigue should be considered in prestressed concrete structures to 1) allow provisions for design of cracked sections under service loads and 2) permit the use of prestressing in structures that undergo significant load repetitions and overloads ( such as bridges, vibrating equipments and the like ). Based on fatigue studies (13,14,20,21,45), many mathematical equations have been proposed in the technical literature to describe the fatigue characteristics of prestressing strands. A summary of the proposed equations is shown in table 1.1. It could be observed from this table that these equations are expressed in terms of stress range, number of cycles N and minimum stress level f min as being

10 the most important parameters that influence the fatigue life of the strands. Some other factors might also be important such as type of prestressing steel, steel treatment, anchorage type and degree of bond A fatigue life of 2 million cycles for stress relieved strands is considered normal for most applications. A typical stress range versus number of cycles of prestressing strands tested in air collected from various investigations (13,14,15,47) are shown in figure 1.2. Best fit line of data given as a function of stress range versus number of cycles to failure was expressed as follows (60): (S/f ) = -0.1231ogN + 0.87 ( 1.3 ) pu where S = maximum safe stress range for a fatigue life of N cycles f = ultimate strength of the prestressing strand pu N = number of cycles to failure It is important to indicate that most fatigue failures in these test data occurred at the grips or occurred because of fretting between a failed wire and adjacent wires in the strands. Based on a fatigue study of prestressed beams Irwin ( 19 ) pointed out that prestressing strands might exhibit an endurance limit at a stress range of about 0.13 f at a pu mean stress level equal to 0.66fp. Such values seem quite optimistic in view of more recent results.

11 ist i fr ksi- -- - 40 -^<1~~~~~~~ ^Si*;g.. I..'t~,, 20 0',, I, I 1' 001 0.10 LO 10.0 N, millions 80. 0o. 0.o L0 10.0 so wito, 0.3 Oilhal~~ilff 40._0. 20 - _ 0. 40-LI I I 0. 01 I 1.0 10.0 M, miUgio Fig.1.1 S-N Curves For Reinforcing Steel Bars (Ref. 10 )

Table 1.1 Proposed S-N Equations For Prestressing Strands Fisher and Viest (21) LogION - 9.354 -00.0423fr 0.0102fs,min -fr " fs.max "' fs,min Warner and Hulabos (14445) LogioN - 1.4332/R + 5.5212 - 0.0.486R R - Smax - (0.83Smin + 23) valid for 401 < Sin < 60%, 0 < R < 15% Hilmes and Ekberg (20 ) Sr - (1640 - 11.5Smin)N-0.320 for 40,000 < N < 400,000 Sr - (115.5 - -. 78Smin)N-0'1154 for 400,000 <N < 4,000,000 Van Horn (13 ) LoglON 6.356 - 0.1373R + 0.00303Rs2 Rs - Sax - (1.05min 4+ 8.0) valid for 40% < Smin < 60%, 0 < R, < 20% Number of specimens OWarner and Hulsbos[(fp) m. = 60 %] 33 *Warner and Hulsbos(fp),mm = 40 %] 24 O Tide and Vanhorn [(fps) m = 60 %] 65 Tide and Vanhorn (fp)m = 40 %] 74 0.50 - AGylltoft [(fps),n = 0 A Gylltoft [(fps) mn - 0 1; grip failures > Edward and Picard [(fp) mm = 60 % ] 0.40 \ | \ - (s \) = -0.123 log N + 0.87 _ 0.30 - 0.20 0.10 - \A A. 103 104 10s 106 107 Number of cycles N., log scale Fig. 1.2 S-N Curve For Prestresslng Strands (Ref. 60 )

13 For design purposes, the fatigue requirement in prestressed concrete structures is accounted for by limiting the stress range in the prestressing strands and/or limiting the nominal tensile stress in the concrete under service load. The 1971 FIP ( 39 ) suggested a maximum stress range in the prestressing strands equal to 0.15f at a minimum pu stress level equal to 0.75fp for a 2 million cycles fatigue life (based on Smith diagram). Recent tests however have shown that the above stress range is on the unsafe side ( 23 ). In 1974, ACI committee 215 ( 1 ) limited the stress range in prestressing strands to O.lfpu. However, recently, the ACI committee suggested that this stress range be lowered. 1.3.4 Prestressed and partially prestressed beams Ozel and Anderman ( 24 ), tested eight 6in x 8in x 20' long beams prestressed with 7/16" strands. Six of the beams were subjected to a constant fatigue load range producing a different nominal tensile stresses in the bottom tension fiber. Five of the beams failed in fatigue by fatigue failure of the prestressing strands. The rate of deflection increase with cyclic load was slightly reduced for the first 30,000 cycles but showed a significant increase prior to failure. Bond failure of the prestressing strand was observed to be insignificant in these tests. Hanson, Hulsbos and Vanhorn ( 22 ), conducted fatigue tests on 6 concrete I beams with 18" overall height and 3" web width prestressed with 270 ksi grade strands. The beams

14 were simply supported and subjected to a symmetrical two point load. All the six beams were initially overloaded to about 80% of their calculated ultimate load resistance for studying the effect of precracking on the fatigue performance of fully prestressed beams. After overloading, the beams were cycled under fatigue load fluctuating between 19% and 45% up to 2 million cycles producing a nominal tensile stress in the concrete of 5-6vf'. At the end of 2 c million cycles, little structural damage was observed. The maximum fatigue loads were increased to between 48% and 54% to produce a nominal tensile stress varying between 8/f'c c and 0l/f'c until failure. Failure in the beams was partly due to strand fracturing and partly due to failure of shear stirrups. Based on the result of their test they suggested that the nominal tensile stress in the concrete be limited to 6/f'. Also they indicated that the fatigue life of the beams were less than expected from available data on the fatigue life of the strands. Abeles, Brown and Hu ( 25 ), tested 33 fully prestressed small scale flexural beams under different load ranges varying between a minimum load level equal to 30% and a maximum load level equal to 50-90% of the ultimate load capacity of the beams. Slippage of the strands contributed significantly to failure of the beams in these tests. They concluded that strand fatigue life for beams with good bond between the concrete and the strand exceed the fatigue life of strands tested freely in air. However, specimens that

15 suffered strand slippage showed a tremendous reduction in the fatigue life of the strands. This was attributed to the increase in stress range that result from a decrease in the effective prestress due to slippage. Rabbat, Kar, Russel and Bruce (.23 ), tested 6 composite full-size type II AASHTO beam specimens, 50' long, with blanketed and draped tendons. The main purpose was to study and compare the behavior of blanketed and draped tendons in prestressed beams under fatigue loading. All specimens were precracked statically prior to fatigue loading. Three beams were cycled under load producing zero tensile stress while the remaining beams were cycled under a load producing 6Vf'c. Crack former were used for all test specimens. They observed that fatigue life of the beams designed under 6/f'c nominal tensile stress were significantly less than those designed at zero tensile stress. Specimens cycled at zero tensile load survived 5 million cycles while those at 6/f' failed between 3.2 and 3.7 million cycles by fracturing of the prestressing strands. They concluded that beams designed for 6/f'c nominal tensile stress under full service load could be vulnerable to fatigue failure. The maximum stress range in the strands observed in the 3rd cycle was 12.8 ksi and increased to 20.1 ksi in subsequent cycles before failure. In this test the strands in the beams suffered slippage of different magnitudes for the various test beams.

16 Dave and Garwood ( 30 ), tested 9 I section beams three of which were tested under cyclic fatigue loading. The beams were partially prestressed bonded post tensioned class "3". The fluctuating test load varied between 29% and 58% of the design ultimate load. All beams survived 3 million cycles. Bennet and dave ( 29 ), tested 9 partially prestressed beams under repeated two point loading. The load range varied between around 25% and 50% of the ultimate design moment. All beams survived 3 million cycles except one beam which failed at 2.6 million cycles by fatigue fracturing of the prestressing strand. Fauchart, Kavyrchine and Trinh (31,32), tested a number of partially prestressed rectangular and T beams from fully prestressed to fully reinforced. All beams were tested under a constant cycle load range with minimum load equal 15% and maximum load equal to 45%-75% of the beam ultimate load capacity. Stresses in the reinforcement were measured by extensometers. Measured and calculated stresses were comparable to within 10% difference. The most important conclusion from their test is that the failure of the test beams by fatigue can be fairly well predicted from the fatigue life of the prestressing strand alone. Foo and Warner ( 34 ), tested 6 pretensioned partially prestressed concrete beams under constant load cycle. All test units were identical and prestressed with 7-wire

17 strands. Beams were simply supported and loaded at two point load. Deflection and curvature were mostly marked in the early load phase, and became progressively less with increasing number-of cycles. Five beams failed in fatigue by successive fracturing of the reinforcing bars and wires in the prestressing strands. They observed that cyclic loading helps in 1) destroying local bond specially around the prestressing strand, 2) extending and widening existing cracks, and 3) initiating new cracks locally. They also concluded that fatigue failure in the prestressed strands or reinforcing bars are equally likely in partially prestressed beams. Also the fatigue performance of reinforcing and prestressing steel is not significantly different from that observed in specimens tested freely in the air. Mansur (41), tested 12 partially prestressed beams having 12x6 in cross section. All beams were loaded at two point load and were designed to have identical load capacity. The purpose of this test was to examine the effect of post fatigue loading on the ultimate load capacity and deformation of partially prestressed beams. Three different levels of partial prestressing ratio equal to 0, 0.41 and 0.67 respectively were explored. For each level of partial prestressing ratio, 4 beams were tested. One beam was tested under static load to determine its ultimate load capacity, while the remaining three beams were subjected respectively to 11,000, 33,000, and 100,000 cycles prior to the static cycle to failure. Every beam in the fatigue test

18 was cycled between 10% and 60% of the ultimate load capacity of the static specimen. In these tests, all beams that were preloaded in fatigue were observed to gain strength. The increase in strength was higher for higher values of partial prestressing ratio. Also it was observed that most of the beam deformation (crack width, deflection and curvature) occured in the early stage of cyclic loading. One of the main drawback of many of the investigations available in the technical literature is the lack of some technical information related to the experiment. Although the observed fatigue life is generally given in all studies, very few investigations give simultaneously information on measured and/or calculated stresses in the reinforcement, basic material properties, crack widths, deflections, and their variation under fatigue. None gives a complete set of data related to the above variables or obtained under the same conditions. 1.4 Obiectives and Summary The objective of this study is to investigate the behavior of partially prestressed concrete rectangular members under cyclic fatigue loading. The particular feature of this study is that a special emphasis was devoted to instrument the beams under load hence providing a complete set of data related to a number of input and output variables. This include materials properties, loads, stresses and strains, curvatures, crack widths, and

19 deflections under static and cyclic loads. This report describes the first set of tests on rectangular beams. It is expected that the study will be extended to include T beams and hollow core slabs. This report concentrates on providing a complete data base. Analytic models to predict crack width, deflection and fatigue life based on the tests and data described herein are in progress. A total of 12 sets of beams were tested. The main parameters utilized in this investigation are the reinforcing index w and the partial prestressing ratio PPR. The reinforcing index is representative of the total tensile force (and/or moment) taken by the steel at ultimate. The partial prestressing ratio is representative of the amount of tensile force or moment taken by the total steel. Four levels of partial prestressing ratios were selected, namely, 0, about 0.33, about 0.67 and 1. The value of PPR, 0 and 1, represent respectively fully reinforced and fully prestressed concrete, while the values of 0.33 and 0.67 represent two different levels of partial prestressing. For every level of partial prestressing ratio, 3 levels of reinforcing index were utilized, namely, about 0.1, 0.2 and 0.3. Two beams were designed for each set of variables. One beam was tested under monotonically increasing load up to failure as a control specimen, while the second beam was tested under high cycle fatigue with a constant load range between 40 and 60% of the ultimate load capacity of the beam tested under static loading. Each beam

20 in the dynamic series was cycled up to 5 million cycles, or failure, whichever occurred first. Chapter 2 of this report includes extensive details of the experimental program and the input variables. Chapter 3 present the results of all the static and cyclic tests. This include data on the fatigue life of the members, the variation of deflection, crack width, curvature and stresses in the tension reinforcement under static and fatigue loading. Chapter 4 provides a brief summary of the observations and conclusions.

21 CHAPTER II EXPERIMENTAL PROGRAM 2.1 Beam Parameters 2.1.1 Input variables A flow chart of the planned experimental program is shown in figure 2.1. A rectangular beam cross section was used throughout. Its dimension and span length are shown in figure 2.2. The major variables included the reinforcing index w and the partial prestressing ratio PPR. For each combination of reinforcing index and partial prestressing ratio, two beams were tested; one beam was tested under static load as a control specimen and the other was tested under fatigue load. The reinforcing index and partial prestressing ratio were defined as follows: = (Apsfps + Asfy - A' f )/bdf' ( 2.1 ) Ps ps s y s y c PPR = (M)p/(M)p+s ( 2.2 ) where A s, A, A = area of prestressing steel, tension P sand compression non prestressed steel respectively. fps f= stress in the prestressing steel and yield stress of non prestressed stell respectively. (Mu) p (Mu) s= ultimate moment contribution of the uP u p+s prestressing steel and total steel respectively.

22 The values of fs was estimated from prior non-linear analysis. The three target reinforcement indices were respectively 1/3wmax, 2/3wmax and max, where max correspond to the limit between under-reinforced and over reinforced sections. max is equal to 0.3 -for purely max prestressed rectangular section and corresponds approximately to the maximum reinforcement ratio 0.75pbal for purely reinforced sections ( 16 ). The target values of the partial prestressing ratio were 1, 0.33, 0.67 and 0. However, it is not possible to achieve simultaneously, an exact level of reinforcing index, an exact level of partial prestressing ratio and an exactly specified nominal moment resistance. Moreover once theoretical values are arrived at, they can not be achieved exactly in practice because of non continuous sizes in reinforcing bars and strands. Hence trial and error was used for selecting reinforcement areas as close as possible to the theoretical values. The beams were designed using a specially written computer program for non-linear analysis to calculate the "exact" input variables of the test specimens, namely, w and PPR, as well as the nominal moment resistance of the beam. The computer program also allowed evaluating the deflection and curvature of the beams under monotonically increasing load thus facilitated planning for the test in advance. The design was also checked using ACI 318-83 ( 2 ) approach for designing concrete sections. Beam cross section and steel reinforcement for all beam specimens are shown in

23 EXPERIMENrAL PROGRAM REMARKS i i+'~ " %+ 1 THREE TYPES OF SECTIONS T RECT. H.C. (Selected tests only on hollow-cored slabs) I ^ I THREE LEVELS OF WImax/3 2wmax7 /3 max -REINFORCEMENT FOR ~,_.~ l EACH TYPE OF SECTION I I FUR LEELS OF PARTIAL PRESTRESSING 0 0.33 0.67 1 - PPR FOR EACH SECTION I ~~I *~~ I;AND EACH LEVEL OF T r. | REINFORCEMENT V TMO TEST STATIC FATIGUE BEAMS FOR EACH (1) (1) SET OF VARIABLES WORKING PHASE I TWO WORKING (Includes all tests on rectangular PHASES sections and selected tests on H.C. sections) Fig. 2.1 Planned Experimental Program For The Two Working Phases

P/2 P/2 4.5 (, --------— _-~ ~10' ---. tETTr - — rrrTrm-F - 1f-i^Yf i'iii i 1 gg gi ^j ^EjK^i i iii hli iiiillii1^ aigJ^A-L- _L A - L J- L -1L-i-L- -l 9 o 0 o AL \ —— L —-LL-L —- - LliL0L0 0 -15 Wire mesh confinement A 0 41 5 1 (1/2" opening gage 19). 0 I ~ ~~~ ~ ~~~~~~~~;. l__.5 / a ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~* l 3 ------ 3 3 9' i I 1/2 section A-A Shear reinforcement a Dl (high yield). Av = 0.01 in2/leg fy = 140 ksi O'Prestressing strand location Stirrup spacing = 4" for beams with ( = 0.1, 0.2 0 Reinforcing bar location = 2" for beams with C = 0.3 Piq. 2.2 Beam Dimensions And Steel Lay-out

25 figure 2.3. Beams designation with their reinforcement and their corresponding reinforcing indices and partial prestressing ratios are shown in table 2.1. 2.1.2 Cyclic load range For each beam, two design criteria~ were used to determine the level of cyclic loading. In all cases the maximum load was selected to generate a maximum moment Mmax max 1) less than 60% of the predicted nominal moment resistance and 2) less than the moment which would induce a predicted stress in the prestressing strand equal to 95% of its proportional limit stress and a predicted stress in the reinforcing steel less than 90% of its yield strength. Nonlinear analysis of the designed specimens in addition to experimental measurement of the tension reinforcement stresses of the static test beams had shown that the first criteria governs for all the beams considered in the experimental program. Keeping the maximum moment less than 60% of the nominal moment resistance leads to a safety factor against flexural failure of about 1.67, which compares well with the current safety provisions implied in the ACI code, as shown next. Let us Define: Mu = Mn = 1.4MD + 1.7ML ( 2.3 ) where the subscripts u,n,D and L refer, respectively, to required strength, nominal strength, dead load and live

26 4.5 Cd u4 9.V C -o o o AP Aa 0 a Ap I 1= strand-270 ki p * - 2p ~tmnd-270 kl Ap = 3% strand -270 ksl PS1-PD1 PS2-PD2 PS3-PD3 AP *AP A5*C OAp, -Ap = a 0., ~ ~ ~ As0 Ap = Ils/' strand-250 k5i Ap 1l%' strand-270 kl Ap = 23W/' strand-270 ksl As = 2# 2-60 ksl A, 3#2-60 kd As = 2#3-60 ksl PP2S1-PP2D1 PP2S2-PP2D2 PP2S3-PP2D3 1' A jlaAl 30 Le * AIM AS * *__!* Ap = lS,1e strand -250 kid AP * 1 s strand 250 k3l#Ap * * l t strnd-250 kal Ap = 1%' strand-270 ksl As - 2#3-602ka As 1- 2#4-60 ks As I 3#4-60 ksi A's' 2#3-60 ksl PP1S1-PPlDl PP1S2-PP1D2 PP1S3-PP1D3 II II As As AS A A 3-A k - As-~3#360 ks=As I 3#4-60 kAl As = 3#5-60 kai RS1-RD1 RS2-RD2 RS3-RD3 Fig. 2.3 Bean Cross Sections

Table 2.1 Summary Of Reinforcing Parameters Prentressing einforcing Compressive f Beam Steel Steel o e PPR ______ | ( A ), itn2. (A@), in (pl) ______ PS 1(1 strand) 2 D1 0 5570 0.14 1.0 PD1 (0.085) (0.017) PS2 2(" *trand) 2 1 D1 5300 0.28 0 1.0 PD2 (0.170) (0.017) 5660 0.26 PS3 |3({" strand) 2 1 D1 5730 0.37 1.0 PD3 (0.255) _(0.017) PP2S1 1(.strand) 2 2 2 D 6576 0.10 6576 0010 0,.62 PP2D1 (0.058) (0.10) (0.017) PP2S2. 1( strand) 3 2 2 2 D1 520 0 85290 0*20 0.68 PP2D2 (0.085) (0.15) (0.017) __ _ _ |PP233 2(" strand) 2 3 2 1 D1 ~~~8 ~6200 0.30 0.74 PP2D3 (0.170) (0.22) (0.017) PPISl 1( strand) 3 3 3 2 3 6 013 33 -----—'b6040 0.13 0933 PP1D1 (0.058) (0.33) (0.22) PP1S2 1(516 strand) 2 1 4 2 1 D1 PPlD2 | 1(0.05) ((007580)6 0.20 033 ( PPI1D2 (0.058) (0,40) (0.017)

Table 2.1 (Continue) Prestresaing Reinforcing Compresoive r | Beam Steel Steel Steel a __ (), in2 (A ), in2 (AI), in2 (psi)__ PP1S3 1(" strand) 3 1 4 2 I D1 5998 0.30 0.34 PP1D3 (0.085) (0.60) (0.017) RS1 3 I 3 2 1 D1 0 5940 0.12 0 RD1 (0.33) (0.017) RS2 0 314 2 D1 7000 0.17 RD2 _(0.60) (0.017) 5870 0.20_ RS3 3 5 2 D1 7000 0.23 RD3 (0.93) (0.017) 5553 0.29 Note: P- Fully Prestreseed R - Fully Reinforced PP1 - Partially Prestressed(PPR=0.33) PP2 - Partially Preetressed(PPR=0.67) S - Static Load D - Dynamic (Cyclic) Load 1,2,3 after S and D represent the level of Reinforcing Index at 0.1,0.2,0.3 fu = 270 Ika.(*" strand) Ep 28600 ksl. fpu = 250 ksi.( strand) Eps - 28000kai

29 load. The value of > is taken equal to 0.9 for flexure. In equation ( 2.3 ), the safety factor on the average is equal to (1.4+1.7)/2x0.9 = 1.72, which is close to the above 1.67. The minimum load was selected so as the difference between the maximum load and the minimum load is about equal to the full design live load. This leads to a minimum moment of the order of 0.4 Mn as shown next: Assume: max = + ML = Mmin + ML = 0.60 Mn ( 2.4 ) max MD ML m n and Mn - 1.4MD + 1.7ML = l4Mmin + 1.7ML ( 2.5 ) in which the minimum moment Mmin simulates the dead load moment in a full size member. Using 4 = 0.9 and replacing ML by its value from (2.5) into (2.4) leads to Mmin = 0.4 Mn Note that for the same magnitude of the fluctuating load, the stress change in the steel depends on the value of the partial prestressing ratio and other design parameters. 2.2 Materials 2.2.1 Concrete Normal weight concrete was used throughout. The cement used was ASTM type III high-early strength. The aggregate was P stone of maximum size 3/8 inch (10 mm). The sand was masonry type sand. A superplasticizer (Melment) was added in about 0.6% by weight of cement to increase the workability

30 of the concrete. The mix proportions per cubic yard are shown in table 2.2. Table 2.2 Concrete Mix Proportions Cement "795 Ibs Aggregate 1840 lbs Sand 1358 lbs Water 36 gallons Super plasticizer 0.6% of the weight of cement The mix were designed to achieve a 6000 psi (41.4 Mpa) concrete strength (Actual concrete strengths for the various t'est specimens obtained at the time of loading are shown in table 2.1). 2.2.2 Prestressing steel Two types of prestressing steel 7 wire strands was used: 3/8 and 5/16 inch (9.53 and 7.94 mm) in diameter with 270 and 250 ksi (1862 and 1724 Mpa) specified ultimate strength respectively. The reason for using two different types of strands was due to the difficulty in obtaining the desired input variables with one strand size. The strands were supplied by (Florida wire and Cable Company) and their properties as supplied by the manufacturer are described in table 2.3.

31 The apparent modulus of elasticity measured in this study from strain gages attached to a single wire of the strand was 33500 and 32850 ksi for the 3/8 and 5/16 inch strands respectively. These high values are attributed to the fact that the strain gages were attached to one wire which is spirally oriented relative to the longitudinal axis of the strand. Actual moduli are of the order of 28600 ksi (197.2 KN/mm2) and 28000 ksi (193 KN/mm2) for the 3/8 and 5/16 inch strand respectively. Table 2.3 Stress-Strain Proporties of Strands 3/8" 5/16" strands strands Ultimate breaking strength (lbs) 23500 14900 Ultimate extension (in/in) 0.0495 0.0495 Force at 1% extension (lb) 21600 13100 Elongation at 0.7fpu (in/in) 0.00662 0.00625 Modulus of elasticity (ksi) 28600 28000 Cross sectional area (in2) 0.085 0.058 2.2.3 Reinforcing steel The longitudinal bars in the test beams were grade 60 deformed bars with size No.2, No.3, No.4, and No.5. The actual yield stress of the reinforcement varied between 63 ksi (434.4 Mpa) and 77 ksi (531 Mpa) depending on the size In converting the prestressing steel apparent strains (obtained from strain gages reading) into real stresses, the apparent strains were first multiplied by a factor equal to 1.171 and 1.173 for the 3'8" and 5/16" respectively, then used in the actual stress-strain curves of the crestressing steel oDrovioed.ty -he P^anrLfa;turer) to get the st.resses. Tnese -actors ( 1.171 and 1.-'73) were obtained bav c'v;-d ng the observed ap,a'renrt mooulus cf eLast'ic ty. o tte orestressino strands by the moculus of eiasticitv s;Dociec Cy tne Niansf-c cture'

32 of the bar. The modulus of elasticity was of the order of 29000 ksi (200 KN/mm2). Special high strength deformed steel wires (D1 type) supplied by Portland Cement Association, (PCA) was used for shear reinforcement. This wire was 0.12 inch (3 mm) in diameter, 0.01 in2 (6.45 imn2) in cross section and had an approximate yield strength of 140 ksi (965 Mpa). A low yield strength wire, (also type D1) of 40 ksi (276 Mpa) yield strength was used in the top and bottom of the beam (where and whenever no longitudinal reinforcement was provided) in order to support the shear reinforcement. This steel was not considered in designing the beam specimens, nor in the analysis of the test data. 2.3 Beam Fabrication 2.3.1 Preparation of reinforcing cages The reinforcing bars were cut in the laboratory to the required size. Their middle section was prepared for strain gage installation. Shear reinforcement was bent using a special bender and then spot welded, forming a closed type stirrup. The shear and longitudinal steel reinforcement were assembled and tied together. A one foot long wire mesh cage ( mesh gauge 19 with 1/2 inch opening) was added at each end to strengthen and stiffen the reinforcing cage. Then strain gages were attached. Additional stirrups were also provided at both ends of the beam to account for any possible bursting or spalling due to overstresses at release of the

33 pretensioned strands. A photograph of the cages is shown in figure 2.4 b. Before casting, the cages were placed in an'oii coated wood mold inside a prestressing bed. The wood mold was made of 3/4 inch (19 mm) thick ply wood and designed to accommodate 2 beams side by side at one time. The prestressing bed was 12 foot long (3.66 m) clear length, with a capacity to prestress up to 32 strands and 4 beams of the size used in this test. The prestressing bed was specially designed for the purpose of this test and was fabricated by Smedberg Machine and Tool, Inc. Chicago, Illinois. A photograph of the wood mold and prestressing bed is shown in figure 2.4 c. Strand pieces in 16 foot (4.9 m) length, were then inserted into the reinforcement cage, anchored at one end of the prestressing bed and positioned for prestressing. Note that the strands were already instrumented ( strain gages attached ). (Fig. 2.4 a). 2.3.2 Tensioning procedure The tension was applied by a 20 ton capacity, 2 inch stroke center hole hydraulic ram, driven by a hand pump. The hydraulic ram was calibrated with a proofing ring before use in order to make correlation between the pressure in the pump, the force transmitted at the head of the ram and into the strand, and also to check the calibration provided by the manufacturer for the pressure gauge. Each strand was pretensioned individually in increments of 2 kips (8.9 KN)

p~E BuIssa2~S~ d PUV pTOW pooM (0m)'ss6D BuTmaou t (q)'uoTlqusawnjsuI saeBD ulepaS (P):uoTqwasdald ureas Z -d~~~~~~. r ~' G 1X1;'_U ill-;' q1 so l t ='=S- s * ll *_~~~~~~~~~~~~~~~~~~~~~46 a- — c c - ~l.Ia r 5 ~~~~~~~ ~~~~~~...,..,~{ - — _.............. - t - _.....'''' i.' ~-_:! _-'" -. -f....iT _11 ~:::.-...:-: -- I. E- - _... _- "-. - T __ZEEE.; =t p=- -. —-~~r 1 f-'-, ( q )~~~~~~~~~~~~C; =~~ -i~,- ff S w- _ - ~~~~~1 f~~i_ | F L -= -i (e) w~~~~~ - ^

35 and strain gages readings monitored by a strain gage indicator was recorded. The tension force was increased until the desired force (70% of strand ultimate strength) on the strand was reached (16100 lbs (71.6 KN) and 10100 lbs (44.9 KN) for the 3/8 and 5/16 inch.strand respectively), and the readings from the strain gages were recorded'. Then the force was increased by about 750 lbs (3.34 KN) to account for estimated strand seating loss upon anchorage. After anchoring, the strains given by the strain gages were also measured. The initial force in the strand after anchorage was then obtained from the final strain gage reading using the average apparent modulus of elasticity of the two or three strain gages attached to this particular strand. Due to the short length of the prestressed strands (12.7'), the loss of prestress due to strand seating during the anchorage process was substantially high, thus resulting in a low initial prestress for some beam specimens. This problem was minimized for some beams by repeating the prestressing operation twice. A picture of the prestressing operation is shown in figure 2.5 a. 2.3.3 Concrete casting Concrete was poured depending on the case after a period of 1 or 24 hours from the time of pretensioning. Each two beams in the static and dynamic series were generally cast together. Concrete was mixed in the laboratory using a small rotary mixer. A laboratory size needle vibrator was

36 used for internal vibration of the concrete; care was taken not to damage the strain gage installations or disturb the position of the reinforcement cage. The concrete surface. was then levelled, trowel finished and covered with burlap and plastic sheets. An average of nine 3x6 inch concrete cylinders were taken for each two beams cast in order to determine the concrete strength. Three of the concrete cylinders were tested to determine the concrete strength just before releasing the prestressing strands; while the remaining 6 cylinders were used to determine the concrete strength just before starting the flexural load test. Forms were removed after 1 day of casting and the beams were moist cured (hosed) occasionally every 6 hours together with the concrete cylinders. The resistance of the strain gages were checked after removing the molds for any possible damage during casting; no such damage was encountered in this phase of testing. The prestressing strands were released 2 to 3 days after casting and also after the concrete strength had reached at least 3000 - 4000 psi (21- 28 Mpa) as obtained from cyclinder tests. The release was accomplished by cutting the strand with an oxygen torch, (Fig. 2.5 b). The beams were then lifted from the prestressing bed by two hooks inserted at the two ends before casting using a

37 specially designed laboratory crane. A photograph of some of the cast beams is shown in figure 2.5 c. 2.4 Instrumentation 2.4.1 Strain gages Strain gages were attached to the reinforcing bars and the prestressed strands at their mid span location. Two types of electrical strain gages supplied by Micromeasurement Group were used. One type EA-06-125BT (gage factor equal 2.05, transverse sentivity equal 0.2%, gage length equal 0.125 inch and matrix size 0.35Lx0.15W in2) were used on the reinforcing bars; the other type EAo6-230DS (gage factor equal 2.055, transverse sensitivity equal -0.1%, gage length equal 0.23 inch, matrix size 0.5Lx0.12W in2), being thinner, was used on the prestressing strands. Both types of gages had 120 ohms electrical resistance. A photograph of the type of strain gages used is shown in figure 2.6. Typical strain gage attachement to the prestressing strands and reinforcing bars is shown in figure 2.7. Before attaching the strain gages, the surface of the reinforcing bars and the prestressing strand was cleaned and L (Cnd -)CF(-^) +^.-J;-^ ^r- ^^- so v-' treated with "Fre n TF"/degreaser/, conditioned with "M-Prep" conditioner and neutralized with "M-Prep" neutralizer (all supplied by Measurement Group). Adhesive type "M-Bond 0-to E-la S'" was applied, then the strain gages were clamped to

qo - 0 J (q) luoTqpjadg 5 Papdiald uIP99G*Z~ ~e a f:)-rJ i/ - i f j h — HI _-M,..... - - U= -~ —i t z --- --- ~~~~~~~~~~~~~~~~~~~~~~~~~~__ i-~i ~ E _~~~~~~ f -- e e = S3| S 3 = ~ ~ - J - - - _ ~~~~''~ ~ ~ - -- i'~lG (q) _..S.~~. -~~ LD~~~~~~L r~~~~ = ~ rr He == A= B_ -,, (a) A_~~~~~~~~~~~~~~~~~

39 2. 2.6 Strain Gages Used 29 2ne Prestress, ing Stra~"s'Used On The Reinfo Ing Bars ig.2.7 Typic Strain GagM On The Prestress Strands And Rifrn Bars esn

40 the bar reinforcement surface using a rubber band (wrapped several times), and to the prestressing strand using a specially designed clamp. Clamping pressure was maintained for at least 6 hours required for the adhesive to cure. Occasionally, some of the strain gages were damaged during the installation procedure. These gages were removed and replaced using "M-bond 200" adhesive (curing time 2 minutes') replaced using "M-bond 200" adhesive (curing time 2 minutes) which performed similarly to the "AE-10/15" adhesive. The lead wires were then soldered and the resistance of the strain gages were checked before applying any coating c -; D material. "M cdat A" was then applied to insulate the strain gages, followed by "M-coat " to waterproof and protect the / 1 ( \strain gages from the fluid concrete. R^r; atL>- GT~c^ ^ar^ -4- 5C^<r ^ 2. ^__ rota at V" fk. w^ k3 Two strain gages were attached to the reinforcing steel, one on each exterior bar. Two or three strain gages were attached to each prestressing strand at the same section depending on the number of strands used in any one beam. Each strain gage was located on every 2n or 3r wire in the strand depending respectively on whether 3 or 2 strain gages were attached. 2.4.2 Deflection Deflection of the beam specimens during the test was measured at 5 inches away from mid span by two linear voltage differential transformers (LVDT) placed on either side of the beam at symetrical distances relative to midspan ( Fig. 2.8 ). The two LVDT's were Shaevitz 1000 DC-D having

41 + 1" stroke limit. During the test, both LVDT's were supported by two magnetic bases attached to the testing bed of the loading machine. Two dial gages were-used to mfeasure the deflection of the testing bed at the location of the end supports during one of the'static test in,.order to'accdunt for any possible differential deflection between the supporting bed and the beam specimen. The measured deflection at maximum load was found negligible in' all cases. An HP X - Y recorder was also used to trace the loaddeflection curve at the 1/3 loading points transmitted through the load ram. 2.4.3 Crack width During the test, crack width was measured at the location of a crack former at midspan. Two Schaevitz AC-500 MHR LVDT's (stroke limit equal + 0.5") were used for this purpose. Both LVDT's were attached on either side of the beam by a special device and located at 1" distance from the bottom tension fiber along the centroid of the reinforcing steel. Photographs of the crack width measurement in the beam and crack width measuring device are shown in figures 2.8 and 2.9 respectively. The crack width was also measured occasionally during the testing using a telescope mounted with a scale reticle to check and examine the readings of the LVDT; both readings were generally in good agreement.

42 2.4.4 Curvature For some beams ( PS2,PP2S3,PP1S3,RS2 ), curvature obtained during test was measured by two dial,gages placed along the constant moment region at midspan.. For the remaining beams these dial gages were replaced by two Schaevitz AC-125 HPA (stroke limit equal + 0.125"). The gage length was 10" (254 mm) and the height between the centerline of the two LVDT was 11.5" (292 mm). Curvature increase with load was measured for all beam specimens in the static test series (except beam RS1). Also Curvature variation with increasing number of cycles was measured for 7 beams in the dynamic series. 2.4.5 Slip Slip of the prestressed strand due to any- possible bond failure was measured during the static and cyclic test. One dial gage was attached to a stretch of one of the prestressed strands extending outside the beam ends. The dial gage was secured to the strand by a C-clamp and oriented in horizontal direction along the axis of the strand with its sensing bar supported directly on the vertical end faces of the beam. A photograph of the dial gage is shown in figure 2.10. As explained later, in no case was any significant reading observed indicating that no slippage has occured during testing.

43 A photograph of some of the various measuring instruments and their location in the beam is shown in figure 2.11. 2.4.6 Data acquisition system To simplify the systematic acquisition of the data, a computarized data acquisition system (trade name system 4000) supplied by Micromeasurement Groups was used..The system is composed of the data acquisition control unit itself, an HP 86 microcomputer, a video screen, a printer, and disk drive. The data acquisition system included a strain gage scanner capable of scanning up to 20 strain gage channels and a universal scanner capable of scanning up to 10 LVDT channels. A software program was supplied with the system. A data disk allows entering all the information related to the measuring instruments such as gage factor, transverse sensitivity, LVDT stroke, excitation voltage and the like. The program disk reads the information given by the data acquisition system and translates it into useful engineering units ( michrostrain, mm, inch etc... ). The use of this data acquisition system allowed full automization of the data. The program disk also allowed for direct plots of observed results as one channel versus another channel.

44:4|~~~~~~~~~~~~~~~~~~~~~~~~~4 = — I.~ -_, Flg. 2.8 Instrumentation: Deflection And Crack Width Measurement,-~-~C *' -F v b-S E;:jt-:A_:,.' ~~~~~-_- _ i-=- __ _-_- - o,. -- - -_i.=, r'X 0- s <D = -:.' Fig. 2. d' ~ — uv ~~~~~~~'- r * i. ~ _ I~5 -- Fig. ~ ig 2.9 Crackenaton Weldctho Masu ring Devlc

3uaainsea dTTS ueilS io uTuno a6e TeT _"''fJTd F — r 1;,'i "4, a rLL;d "f; LiL -r iiiliii F.-;. h.2-i Ic sJ: i9"~ — —' r3hq,, iC c. --- 1 llct, 1 ~ c- ": -h_ ( -I-' i TL-~ j I 7r. E Irb

46 L~~~ P ~L li- I'-, _l|!1 111 iambi J i~AFig. 2.11 Close Up View Of Instrumentation: Deflection, Crack Width And Curvature

47 2.5 Test Setup The beams were supported on two sliding rollers designed to allow rotational twisting between the two ends of the test beams. Both rollers were mounted on a 12'foot long and 2 foot wide steel testing bed. The rollers were adjusted to 9' (2.74 m) span and centered relative to the loading ram by a graduated tape fixed on the testing bed. They were then properly tightened by 4 bolts to prevent any lateral sway during the test. A photograph of beam setting is shown in figure 2.12. The load was transmitted to the concrete specimen through a steel beam with two adjustable loading pads. The steel beam was connected to a steel swivelhead bolted to the loading cell. The load pads were adjusted to a 1/3 load points, thus creating a constant moment region over 3' length (0.915 m), then tightened properly to the steel beam to prevent any possible movement during the test. The testing machine was an Instron's specially modified closed - loop servo controlled hydraulic machine with load and stroke control capability. It comprised a 110 kip dynamic capacity frame, a 55 kip dynamic actuator with 6 inch stroke, a 60 gpm hydraulic service manifold and a 40 gpm pump. The machine had a load and stroke digital voltmeter readout and was capable of high loading frequency

4,8: 0 B ea S tt Fig _ - - = ~ ~ ~ ~ ~ ~ " F i cx. 2. S ett ing I n T e st ing~~~~~ —~

49 for different cyclic wave functions. The sine wave is believed to best represent the live load cycle application on actual structures and therefore was adopted in this experiment. The testing machine was equipped with a load cell calibrated for 50 kips full capacity. A photograph of the test setup is,shown in figures 2.13 and 2.14. 2.6 Test Procedure 2.6.1 Static test Prior to the actual test, the beams were loaded initially to a small fraction (about 5%) of the ultimate load then unloaded so as to stabilize the beam and also to prevent any possible twisting. The strain gages and LVDT's connected to the data acquisition system were then zeroed and calibrated. The static load was applied at an approximate rate of 1 kip/min. At every load increment which ranged from 2.5 to 5% of ultimate load, the data from the various measuring devices were scanned by the data acquisition system and printed automatically by the printer without interrupting the loading sequence (the data aquisition system was capable of reading up to 30 channels per second). In addition, the load deflection history of the beam at the loading points was also monitored by an HP X - Y recorder. The overall testing time of one beam under static load took, on the average, 15 to 25 minutes depending

5O ii. X..... ilz.il - _ = ~~~~~~~. S..._.:.-:... | I —: X * } -- _0s —- - H -~-~:z~~~~~~~~~~~~~~~~.._ _ s w - =;FI~~'a i Fig. 2. 1 G e n ra T e s S e up L oain Mah n A n d Da ta Acquisition St __- A- L: Acui ito Sse

51 _!1 S i~~~~~~~~~~~~~~~~~~~~~~~~~~~; - - l l l a - - =~~~~~~~~~~~~~~-w _f~ il1!_ 0 —. I~~~~~~~~~~~~~~~~ __ ~~~~~~~~~~~~~~~~~ _'-w i~~~~~~2.=- 4~~~~~~~~~~. i1 0; —1 T~~~~iI 1.g E~ —— ~ —~ 0 p-=- L -;7 IH l -;> p w~~~~~~~~~; m-f n - o - ~~~~~~~~~~~~~~~~~~~~~= Fl..1 ClseU Vew0 Test bitu

52 on the maximum load capacity of the beam tested. At the end of every test, the ultimate load capacity of the beam was recorded on the print out and some remarks about the test were taken. The beam was then dismanteled for further inspection. 2.6.2 Fatigue test The static test was in general followed immediately by a fatigue test of the sister beam (having the same design variables). The maximum and minimum cyclic loads P and max Pmin were taken as 60 and 40% of the ultimate load capacity as observed from the statically tested beams. The instruments were initialized following the same procedure as in the static test. Then the load was applied statically to P then unloaded to P In order to stabilize the beam max min' for fatigue measurements, three subsequent static cycles at a rate of 1 kip/minute were applied between P in and Pmax and for each, strains, deflections, crack widths and curvatures were recorded. The cyclic test between Pmin and Pma was then started at a cyclic frequency ranging from 6 max to 7 cycles/sec depending on the compliance of the beam specimen considered. Throughout the test, readings were taken at a number of cycle intervals. Those readings were taken at a small cycle interval during the early stages of the test, then the intervals were increased at a later stage depending on the fatigue damage observed. For every reading, the cyclic load

53 was interrupted and a static cycle was applied between Pmin and Pmax During the static cycle, measurements were taken by the data acquisition system for 10 to 12 equally spaced load increments on-the loading and unloading portions of the cycle including Pmin and Pmax' Each fatigue test took on the average 8 to 10 days of continuous cycling. At the end of the test (5 million cycles) and if fatigue failure did not occur, the beam was unloaded to zero load and a static test was conducted up to destruction to examine the effect of prior cyclic fatigue on the ultimate load capacity and deformation of the beam.

54 CHAPTER III TEST RESULTS 3.1 Calculation of Effective Prestress A special computer program was written to determine the loss of prestressing force in the strands for the fully and partially prestressed units due to elastic shortening at transfer, shrinkage and creep in the concrete. The time step method was used. The detail of this method and its formulation are given elsewhere ( 60 ). The precompression force in the reinforcing steel at the time of testing due to shrinkage and prestressing force was also accounted for. Table 3.1, includes a description of the approximate time between tensioning and casting, age at loading, total prestress losses (computed as mentioned above), reinforcing steel precompression stress, and effective prestress in the prestressing strands at the time of testing. 3.2 Static Load Test 3.2.1 Cracking load A crack was initiated at the location of a crack former at midspan. In the fully reinforced and partially prestressed units, the crack former extended up to the nonprestressed reinforcement. The.cover to the centroid of the nonprestressed reinforcement was kept constant and equal 1" (25.4 mm) in all cases. For fully prestressed specimens, the crack former was 0.25" (6.35 mm) high.

55 Under increasing load or moment, the precompression stress in the concrete bottom fiber due to the prestressing force decreases. Cracking.develops when the tension stress exceeds the tensile strength of the concrete. For all beam specimens, cracking was initiated at the location of the crack former at midspan. However, visible tensile crac'ks spread along the length of the beam mostly in the constant moment region. These cracks developed shortly after initiation of the midspan crack. Cracking caused a noticeable change in stress increase in the tension steel and in the measured crack widths. The cracking load as well as other relevant data for each beam specimen in the static test series are given in Appendix B ( tables IS - 12S). 3.2.2 Ultimate load The ultimate load was taken in this test as the load corresponding to the maximum load on the load-deflection curves beyond which the beam suffered a reduction in strength and collapsed. The magnitude of the ultimate load varied depending on the level of the reinforcing index. The ACI 318-83 approach for calculating the ultimate moment capacity of flexural concrete section was used in calculating the theoretical moment capacity of the beams. However, the yield strength of the non prestressed reinforcement was taken equal to 70 ksi (483 Mpa) which

Table 3.1 Stresses In The Reinforcement At Time Of Loading At time of testing Beam Initial stran Time between Age at Prestres Reinforcing| Effective stress (ksi) tensioning an loadin losses steel stress prestress, |. | ____casting(hours) (days) (ksi) (ksi) fpe (ksi) PS1 185 24 28 15.8 -- 169.0 PD1 189 16.1 --- 173.0 PS2 154 2 20 16.8 --- 137.0 PD2 162 18.8 -- 143.0 PS3 159 24 26 22.7 -- 136.0 PD3 170 24.1 --- 146.0 PP2S1 175 24 15 10.0 6.0 165.0 PP2D1 175 10.0 6.0 165.0 PP2S2 1 189 2 1 30 21.6 1 10.7 1 167.0 PP2D2 179 _____19.0 10.4 160:0 PP2S3 149 2 25 16.1 13.3 133.0 PP2D3 146 _ 15.4 13.0 131.0 PPS 1 175 24 20 11.1 6.4 164.0 PP1D1 175 11.1 6.4 164.0 PP1S2 175 2 20 15.3 6.2 160.0 PP1D2 148 9.8 5.7 138,0 PP1S3 160 2 22 12.9 7.3 147.0 PPlD3 163 13.5 7.4 150.0 RS1 -- 19 -- 2.2 -- RD1 -- 31 -- 3.2 __ RS2.- -- 12 1 — 1.3 -- RD2 -- 26 -- 2.4 -- RS3 -- __ 13 -- 1.3 -- RD3 -- 81 - 3.3 t Note: Prestressed strands were released 2 to 3 days after casting * Precoinpression stress in the nonprestressed reinforcement (-ve)

57 represent the average observed from test. Comparison between the ACI predicted and observed ultimate moments are shown in table 3.2. The high ratio of test to calculated moment observed in the fully prestressed -beams is due in ptrt to the conservative equation specified by the ACI code for calculating the stress in the prestressing steel'fp r,, at ultimate. 3.3 Behavior of Static Test Specimens 3.3.1 Load-deflection The load-deflection curves for some of the test beams are shown in figures 3.8a,3.9,3.10a-3.12a along with some relevant plots from the fatigue test. Load-deflection curves for remaining beams are shown in figures A1-A7 of Appendix A. Numerical results are summarized in tables 1S-12S of Appendix B. It could be observed from these figures that for most reinforced and partially prestressed beams, the loaddeflection curve comprises 4 portions: 1) from zero load up to cracking, 2) from cracking up to yield, 3) from yield up to strain hardening if any and finally 4) from strain hardening up to ultimate. However, for under-reinforced fully prestressed beams only three stages generally exists. Note that for beam PS3 which was over-reinforced, a brittle failure was observed (Phot. is shown in figure 3.1).

58 Beam Ultimate moment Test/Calc. designation (k-inch) Calculated Test ACI (318-83) results ( 2 ) PS1 122.0 147.2 1.21 PS2 205.0 250.6 1.22 PS3 275.7 342.0 1.24 PP2S1 132.4 151.2 1.14 PP2S2 187.5 208.8 1.11 PP2S3 297.2 360.0 1.21 PP1S1 242.4 293.0 1.21 PP1S2 265.3 283.5 1.07 PP1S3 370.9 384.1 1.04 RS1 173.1 204.1 1.18 RS2 303.1 324.0 1.07 RS3 441.7 444.1 1.01 Mean = 1.14 S.D = 0.08 Table 3.2 Comparison Of Observed And Computed Ultimate Moments For All Test Beams

59 Prior to cracking all beams behaved essentially in an elastic manner. After cracking, fully reinforced concrete beams and beams with low PPR developed a relatively linear load-deflection response in comparison to beams fully prestressed or with high partial prestressing ratio. Reduction in stiffness resulted in all the test{ beams after cracking as expected, depending on the level of the reinforcing index and the partial prestressing ratio. For equal partial prestressing ratio, increasing the level of reinforcing index implies increasing the area of tension reinforcement, this in effect result in a stiffer beam and therefore in a low rate of deflection versus applied load. Also, for equal c, increasing the level of partial prestressing ratio results in a high pecentage of prestressing steel relative to the total steel and hence a small overall area of tension reinforcement. This leads to a larger deflection rate with increasing load. Although the fully prestressed beams had the highest stiffness before cracking, these beams suffered the highest stiffness reduction after cracking, (specially beam PS1). Yielding of the reinforcing steel occurred prior to that of the prestressing steel for all partially prestressed units because of the physical location of the reinforcing steel relative to the prestressing steel. Beam PS1 in the fully prestressed series yielded at a load of about 7 kips (31 KN) and showed substantial reduction in stiffness up to failure. Beam PS2 and PS3, because of their high reinforcing

60 index, did not show a clear yielding pattern. After yielding, fully reinforced beams RS1 and RS2 developed a well defined yield plateau followed by a strain hardening stage up to failure. However- Beam RS3 failed before reaching the strain hardening. stage. Strain hardening of the reinforcing steel is also evident in some partially prestressed units. Its effect however decreases with an increase in the reinforcing index and PPR. All beams in the static series failed in flexural compression (concrete crushing) at the top concrete fiber in the constant moment zone except beam PS3 where failure was due to spalling of the concrete cover surrounding the prestressed strands. Typical photographs of beam failure in both the static and fatigue beam specimens are shown in figures 3.1-3.3. The prestressing strand of beam PS1 broke shortly after reaching the peak of the load deflection curve. 3.3.2 Crack width Throughout the test, crack width was measured at the location of the crack former at mid span. Data results are summarized in table 1S-12S. Typical plots of crack width versus applied load is shown in figure 3.4. It could be seen that the rate of crack width increase, as described by the slope of the curves, depends on the partial prestressing ratio. It was generally observed that the higher the partial prestressing ratio, the higher is the slope of the crack

TGad Vsd:saanlTva uievE TPOTdAL 1 C-~ ME 7__ r L- -. i- I.........- _ f -,J - ~_-:i ~.._`1 s I A=- 1 P'I 9 1||1 l o~~~ti ~~~-f,- ~~~1

62, s,~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~...n,~.,.. 1-'..._ Fi.32[yialBaFiures: PPD3 PP1 _X~~~~~~~~~~~i.. |; = >~~~~I Ha_~~~~~~~~~~~~~~~~i I ~:I I |' I~~~~~~~~~~~~~~- I d... l~~~~-~~- Ir -.~~~~~~~r,.-' -i t~~~~~~~~~~p,; F Fig. 3.2 Typical Beam Fail~~~~~~~~~~~~- urs: PD, I

63 = _I~~~~~~~~~~~~~ Iir,~~~~~~~7 E- 1.1__ m c -' t 5 ~~~~~~~~~~~~~~~~~'I m a _ t~~~~~~~~ Fig.33TpclBanFiue PD

64 width versus load curve. Although the crack initiation in the fully prestressed beams was delayed due to prestressing, these beams suffered the highest rate of crack width - }. t - increase with load after cracking. Beams with reinforcing steel placed close to the bottom concrete tension fiber or beams with a high area of reinforcing steel (low level of PPR) showed more evenly distributed cracks, and less crack spacings. This may be due to the better overall bond characteristics of the tension reinforcement with the surrounding concrete. It has been shown (50,51,53) that crack widths can be expressed as a direct function of the average strain in the reinforcement and crack spacing. For a given reinforcement parameters, the crack spacing generally remains constant within the elastic range of loading. Hence for a linear increase in load, a linear increase in stress in the reinforcement thus in crack width is observed. Figure 3.5 show the variation of crack width versus reinforcing steel stress. The sudden decrease in the crack width rate in some curves is due to the formation of extra cracks with increasing load. 3.3.3 Load-curvature Curvature was measured at midspan over a gage length equal 10". Figure 3.6 shows the variation of curvature with the applied load for some of the test specimens. The curvature obtained was in general in a region where at least

65 0-4 PS2 -. - ^ PP2S2 0.3 -,~5 o.~ / <- c a)PP1S2:X.,, ~=-! 0.2 (a)..S2 0.1 0 3 6 9 12 15 Load P, kiPs 0.4 PS3 ~0.3'/ PP2S3 0.2 - PP1S3 (b)...R 0.1 - O. 0 4 8 12 16 20 Load P, kiPs Fig. 3.4 Crack Width Variation With Load At Different PPR: max~~~~.~n~

66 0.4 0.3 E C^ - Z'.. = PP2Sl 0.2 (a) o0.- ~'' 0 10 20 30 40 so50 60 fs' ksi 0-4 0.24 PP2S2 E 3- / E / 0~1 02E 0-3 - PP2S3 - 0o2 0 (C) I, 0.1 0 I I..... I -,,I' 0 10 20 30 40 50 60 fS. ksi Fig. 3.5 Crack Width Variation Versus Reinforcing Steel Stress At Different PPR: (a) X) = 1/3 max,' (b) X = 2/3 (jmax (c,; X = m-ax

67 21 - PP1S3 18 - - ^ 12' / (a) is 80 g PPI2S 0 10 20 30 40 Curvuture x104 (rad/in) 21 - PP2S3 18 15 - 12 PP2S23, () PP Close To 0 6 3 0 10 20 30 40 Curvature x 104 (rad/in) Fig. 3.6 Effect Of mi On Load-Curvature Relationships: (a) PPR Close To 0.33, (b) PPR Close To 0.67

68 two or three cracks were formed. Therefore it represents the average curvature over 10" length in the constant moment region of the beam. It is clear from these figures that the load-curvature curves show the same trends as the loaddeflection curves. The load-curvature curves and the load-deflection curves mentioned before reveal an important aspect of the behavior of concrete beams under monotonically increasing load, namely, ultimate deformation or ductility. It can be observed that the level of maximum curvature and/or deflection is most importantly related to the level of reinforcing index. Increasing the level of reinforcing index results in a larger neutral axis depth at ultimate and therefore less deformation capacity. The ductility of concrete beams depends globaly on the ductility of the reinforcement; prestressing steel is less ductile than reinforcing steel. Therefore, beams reinforced with prestressing steel are expected to be less ductile than beams reinforced with reinforcing steel. Fully prestressed beams showed the least ductility in comparison with the remaining beams in this test. However, partially prestressed beams (for both levels of partial prestresing) were observed to have the same order of maximum deformation as fully reinforced beams of approximately similar levels of reinforcing index. This increase in ductility is in favor of partial prestressing which also combines the advantages of both full prstressing and full reinforcing.

69 The effect of compression reinforcement in increasing the ductility of concrete beams is evident in figure 3.6a. It can be seen from this figure that the maximum curvature in beam PP1S1 is substantially larger than that of beam PP1S2 although both beams were Qf approximately equal observed strength (both beams have approximately equal tension reinforcing index). Compression reinforcement in beam PPlSl resulted in decreasing its total reinforcing index (see equation 2.1) and therefore in a dramatic increase in its maximum deformation compared to beam PP1S2. 3.4 Fatigue Test All specimens were tested under constant load range varying between 40 and 60% of the ultimate load capacity of the control specimen having the same input variables in the static test series. The average cycle frequency was equal 6.0-7.0 cycles/sec depending on the compliance of the test specimens and the frequency response of the actuator. Fatigue test datas for all beam specimens are summarized in tables 1D-12D of Appendix B. 3.4.1 Fatigue life All the 6 partially prestressed and the 3 fully reinforced beams survived 5 million cycles (beam RD1 was cycled only up to 3 million cycles) without suffering a major fatigue damage. Fully reinforced beams encountered the least fatigue damage in comparison with partially and fully

70 prestressed beams (fatigue damage is evaluated with respect to relative increase in deflection, curvature and crack width with increasing number of cycles). The three fully prestressed beams, PD1, PD2 and PD3 failed during cycling. The failure resultEed from fatigue, fracturing of the strands at the location of a crack in the constant moment region of the beam. One wire of the strand was broken at approximately 1 million cycle for beam PD1 and at around 2.0 and 1.8 million cycles for beams PD2 and PD3 respectively. One indication of a wire being broken is a clearly heard bang from inside the beam. The failure of one wire was generally accompanied by a sudden jump in the residual deflection of the load-delection hysteresis loop, substantial reduction in stiffness, increase in crack width and high increase in the area enclosed within the hysteresis loop. The failure of additional wires in the strands reduced the net tensile area of the prestressed steel and therefore increased its stress range. This in effect accelerated the fatigue damage of the beam and reduced its fatigue life. The observed stress ranges in the prestressing strands in the three fully prestressed beams during the early cycles were 10.0 ksi (69 Mpa), 16.0 ksi (110 Mpa) and 19.0 ksi (131 Mpa) for PD1, PD2 and PD3 (bottom strand) respectively. The stress ranges observed at last reading before failure of the strain gages (See tables 1D-3D) were 16 ksi (110 Mpa), 19.3 ksi (133 Mpa) and 27.1 ksi (187 Mpa) respectively. Beam PD1

71 failed at 1.212 million cycles after failure of its only prestressed strand. The maximum deflection, crack width and curvature at Pma measured in the last reading before max failure (1.1 million cycles) were 0.43", 0.35mm and 3x10-4 in-1 respectively. Beam PD2 failed at 2,2 million cycles after several wires in the strands were broken. The maximum deflection and crack width in the last reading ( 2.17 million cycles) were 0.9" and 1.27 mm respectively. Beam PD3 failed at 1.94 million cycles after the bottom strand totally failed; this was accompanied by a very large increase in crack width. The beam was considered failed for all practical purposes. The maximum measured deflection and curvature at 1.94 million cycles were 0.98" and 10.1x10-4 in-1 respectively. The fictitious nominal tensile stresses in the bottom concrete tension fiber was calculated assuming uncracked section for all beam specimens in the fatigue series. Results are summarized and compared with the observed stress ranges in the tension reinforcement in table 3.3. The large values of the calculated nominal tensile stresses indicate that little correlation exists in general between the fictitious nominal tensile stress and the fatigue life of the beam specimens in this test. A nominal tensile stress of up to 32.8/f' (PP1D3), did not result in c fatigue failure. Also, on the other hand a nominal tensile stress as high as 24.1/f'c in the fully prestressed beams (PD3), compared to the 61/f'c limit recommended by the ACI

72 committee, led to a fatigue failure of the beam at a reasonable number of cycles (1.94 million). Moreover, the stress ranges in the prestressing strands observed in the 3r cycle were compared with the SON curve shown earlier (Fig. 1.2). Results are shown in figure 3.7. This figure and also table 3.3, suggest that the stress range in the tension reinforcement is a far more indicative parameter for evaluating the fatigue life of the beam specimens than the fictitious nominal tensile stress. 3.5 Behavior of Fatique Test Specimens 3.5.1 Deflection The load-deflection curves for some beams are shown in figures 3.8b,3.9,3.10b-3.12b along with some relevant data pertaining to the beams tested. Load-deflection curves for the remaining beam specimens are shown in figures A1-A7 (Appendix A). These curves show the progressive variation of the load-deflection hysteresis loop measured between Pmin and Pmax with increasing number of cycles. It can be seen that the load-deflection for partially prestressed and fully reinforced beams remained stable throughout most of the test cycles. The continuous narrowing of the hysteresis loop of these beams with subsequent cycles is one indication of their stable behavior under cyclic fatigue loading. The residual deflection of beams PD1, PD2 and PD3 increased progressively with approximately constant load

Table 3.3 Calculated Concrete Nominal Tensile Stresses And Observed Stress Ranges In The Reinforcement Stresses under short term loading Observed for Observed at 3rd cycle last reading* Nominal tensile Nominal tensile Specimen stress at P=Pmin stress at P=Pmax Afps Afs Atfps tAfs N Psi x/f'c Psi x/f'c (ksi) (ksi) (ksi) (ksi) PD1 195.0 2.6 664.5 8.9 10.0 -- 16.0+ -- 1.21x106 PD2 340.9 4.5 1176.0 15.6 16.0 1 9.3 -~ 2.20x106 PD3 675.3 8.9 1828.0 24.1 19.0+ - 27.1+ - 1.94x106 PP2D1 424.6 5.2 882.1 10.9 5.8 18.1 7.0 15.1 5x106 PP2D2 612.4 8.4 1334.2 18.3 9.2 18.6 10.2 18.5 5x106 PP2D3 1116.0 14.2 2205.4 28.0 12.8 22.5 14.5 23.5 5x106 PP1D1 1233.4 15.9 2074.8 26.7 8.8 17.2 9.8 17.3 5xl06' PP1D2 1258.2 16.5 2103.6 27.6 7.9 14.3 8.4 14.8 ^5x106 PP1D3 1514.0 19.5 2543.1 32.8 6.9 12.4 7.6 12.9 5x106 RD1 1175.8 15.3 1817.1 23.6 - 15.6 -- 14.8 3x106 RD2 1798.2 23.5 2671.3 34.6 - 11.3 - 12.0 5x106 RD3 2255.5 30.3 3383.3 45.4 - 10.4 - 11.1 05x106 + Failed by fracturing of the prestressing strands, all other beams did not fai-I. * See Tables 1D-12D for more detailes.

74' This Study Numberofspecimens OWarner and Hulsbos[(fs) min = 60 %] 33 *Warnerand HulsbosE(fps) min =40 % - 24.' Tide and Vanhorn [fps) min = 60 %] 65 0 Tide and Vanhorn [(ps) min 40 %] 74 0.50 - Gylltoft [(fs) min0 ]. A Gylltoft [(fp) min 0 ]; grip failures 0 Edward and Picard [(fps) min = 60 %] 0.40- \.| \ ( fS-^) =-0.123 log N + 0.87 C3, - 0.30. 0.20 0.10 AA 6 samples ~ 103 104 105 106 107 Number of cycles N, log scale Fig. 3.7 Comparison Of Observed Fatigue Life With Existing Data (Ref. 60 )

75 Deflection, mm 0 10- 20 30 40 50 15:I| 60 12 _ c.. - -- - ---'- T (a) 9 4. _ _ 40 o r 0 Mr / 20 De I ton, Inch0 0.50 1.00 1.50 200 Deflection, inches 0 C 0 8 r n. Defn, d d in ch 0 (5 8 1 4 17 20 mm lo- / // / _ _ _ _ 6.5. - m Pmor ~A ortesai es.2-3a D eflecion, // / /_______ ^P iled. in c ~L(6 cycleD o _ o~ o 2 -o Numberof 5J 4 -o.~ m o a 0 cycles; 5 0.26 afpe. 16.0 ksi P. - x PP. - 1 t -- Au for the tatilc tot 1. 52" - 39 ~m 0 0.15 0.3 Deflection, inch Fig. 3.8 Load-Deflection Curves For Beams: (a) PS2 (Static) (b) PD2 (Cyclic)

Deflection, mm 0 5 10 15 20 25 30 35 20.0 C = 0.37 17.5 PPR = 1 80 Averoge stress ronge 12.3 ksl Flurbyp Stress ronge In the lowest strond * t9.0 ksi of concrete cover 415.0 e1 /In tenslon 15.0 60 12.5 Pmax 10.0 o 0 Pmln 00 0 _ 7.5 b b& bbbb b b..o P I)3 S^W_ WI g- V Number of Cycles - 20 ~/~' ( ~P/2 P/2 5 2.5 -_ I_ __ Ap = 3%W etrands-270 ksl 0.0 ~ 0 0.25 0.50 0.75 1.00 1.25 1.50 Deflection, Inches Fig. 3.9 Load-Deflection Curves For Beams PS3 (Static) And PD3 (Cyclic)

77 Deflection, mm 0 5 10 15 -20 25 30 35 40 45 50 12. P s. >^ - ~~40 1 6 Pm__ a: - -yb- - - 30 0: (a) m PP202 4.r -20 S O I l I | I I I 0 0.25 0.50 0.75 1.00 1.25 1.50 1.75 2.00 Deflection, Inches Deflection. d 0 d in ________-I, I, -—, —. - I.... S.08 7 8 9 10 11 12 13 mm 7.0., P,~L 0P,, z 06 Prno ax Number of l7.^~,^ m-~ o- cycics/6/ -6.0. PP2 (b) II, C~~~~- -i~5.0D 0 PiPmin. =n * 0.4 Pu' 0 KUU U U cycles PPZD2 a 0 20fp At. - 9.2 kni PPR - o.~e Afe - 18.6 kui &J for the static test. X.76 a 45 - 0 0.2 0.4 Deflection, inch Fig.3.10 Load-Deflection Curves For Beams: (a) PP2S2(Static) (b) PP2D2 (Cyclic)

78 Deflection, mm 0 5 10 15 20 25 30 35 40 ----, -I-, ---- -- - ----, -, -- a a 77 16 14 j 1_ - 60 12 *cr~~~~ r~z 10 PM-. = (a) a. ~PL eel D~ )mh rE k 46CL 8 _I_' - PP 2 4 1.o 8r / a s 5 I20 4 - 20 2S,, 2 t Ao A r. 2p= W 0A ---- I --- I ___ I ___ I _ 2-M4 kW__ 0 0.25 0.50 0.75 1.00 1.25 1.C Deflection, inches Deflection (b) 0 0 in. 0 10 o~- p~~ B~ 1 -10 10 nnx o ofc; J pB'6moz ^x z 06 T5 / ^"^^y^ ^X^ Pmi~n 20.4 ~Pu ~, o ~ S 90 Numbe of 6. 0cn~I 0 =,, (b) /6.-= 1 1c < ** - / n PPi02 - 0.20 aftp 7.9 kgj PPR a 0.33 A"t, - 14.3 )si au Eor the statie tot 1.42- 36 - — ___0_ _ Deflection, inch Fig. 3.11 Load-Deflection Curves For Beams:'= PP1S2(Static) (b) PP1D2 (Cyclic)

79 Deflection, mm 0 10 26 30 40 50.18 ", 80 15 0.~~~ -60 0 12 z "- — ~/ n ~ ~^ o: ( a ) 9 9R- // / m2 -40 to 6J - - 0 O O As - 3.4-0 k 0 0.50 1.00 1.50 2.00 Deflection, Inches Deflection o c 0 0 i0n. 0 7.62 III 7 9 10 11 12 13 mm /2- ~ - P 0.6 / " - -- 10 (o ~,, R (b) = 6 / Pmin 0.4 Pu 0 - 2 2 -__ - Number of -4/,F ~7 cycles * - 0.20 Afp -- 2 ^ J3R02 PPR - 0 Aft - 11.3 kni &au or the static teet 2.16' 55 mm 0 0.25 0.5 Deflection, inch Fig. 3,12 Load-Deflection Curves For Beams: (a) RS2 (Static) (b) RD2 (Cyclic)

60 deflection slope for most of their fatigue life. However, prior to failure, the residual deflection is observed to increase dramatically, accompanied by a tremendous increase in the area enclosed within the load-deflection loop -and a substantial reduction in stiffness. This behavior is a clear indication of the degree of distress and softening suffered by these beams due to fatigue. The variation of maximum deflection for the various beams versus number of cycles N, measured at P is shown max in figures 3.13-3.15. It can be seen that the curves show three different portions when plotted on a semi-log scale: In the first few hundred cycles there is relatively sharp increase in deflection followed by a second portion with a steady state increase up to 80-90% of the total number of cycles (log scale) and/or total life of the beam. In the third portion, generally all beams showed a sharp increase in deflection with increasing number of cycles. However, the increase in deflection is more pronounced in the fully prestressed beams in comparison with the partially prestressed or the fully reinforced ones indicating that these beams were about to fail. A similar behavior was observed by Bennet and Dave ( 29 ). Generally it can be observed from these figures (3.13-3.15) that the rate of deflection variation with number of cycles (drawn on semi-log scale) tends to increase with an increase in the level of partial prestressing ratio

0.7 PPR 0.6Pu f, f (mm) ~~~_______(kipe) (ksi) (ki) Failed at 0 g 0.6 1 0.14 1 4.90 10.0 -- 1.212 x 10ocycls 0.6 1'%' 2 0.10 0.62 4.80 5.8 18.1 Q3a ~ 3 0.13 0.33 9.75 8.8 17.2 (t 0.5 4 0.12 0 6.80 -- 14.9 PPIDI I ~~~~~~~~~~~~~PDI ~ 0.4 3 o --------— D~10 ~r ro/ E ^ P201 I 0.2 — 5 0.1 5 x U0 0 I I I l I 0 1 10 102 103 104 10 106 107 Number of Cycles N, log scale Fig. 3.13 Observed Deflection Versus Number Of Cycles ( < = 1/3 &max)

PPR 0.6Pu Af O (mm) C 0.7 - (kips) (ke (ksi) (mm Falled at 3:: 01 0.26 1 8.37 16.0 --- 2.19x10cycles. 12 0.20 0.68 7.00 9.2 18.6 cd 0.6 3 0.20 0.33 9.50 7.94.3PD2 1.d- 4 0.20 0 10.80 -- 11.3 (a C 0.5 - 0 RD2.) 0.4 10 I0 ~ PP2D2 / E E 0.3 -5 X 5 X 1I 0.2 5 5x10' 0.1,I.... I, l.. I l. I I 1 10 102 103 103' 104 1 107 Number of Cycles N, log scale Fig. 3.14 Observed Deflection Versus Number Of Cycles ( X = 2/3 miax )

in Failure of ~ (mm) 0.7 1.94 K 106 cycles 20 0.6. 0.5 oC ~~~~ ~ ~~~~~~.) --. ~' -{,~~ 2.5 o 0.4 RD3 0 Io)o-^^"^ ~50.0 _.~ ~ PD$ ( 0.3 a 7.5 a ] PPR 0.6Pu Afp A f. E ____k i k s {(kips) ksI (ki) 4.5 10.2 1 0.37 10 11. o 19.0. 5 — - 2 0.-30o 0..34 1o2.55 6.9 12.4 n o 3 0.30 0.74 12.00 12.R 22.5 9go 0 OD,, I 0, o —4;5 -- 10.4 o 2.5 ~ In the lowest strand I0 102 103 104 105 106 107 Number of cycles N, log scale Fig. 3.15 Observed Deflectidn Versus Number Of Cycles ( = )

84 for approximately equal reinforcing index (this obsevation is clearer in figs. 3.14 and 3.15). Moreover, within the load range adopted in this study, the reinforcing index seems to have little influence on the beam deflection response with increasing number of cycles.for most specimens (compare 3.13-3.15). However, for fully prestressed beams, the rate of deflection increase with increasing number of cycles was larger, the larger the reinforcing index. This observation for the fully prestressed beams is not general because the fatigue life of the fully prestressed beam with w close to 0.3 (PD3) was governed by the fatigue life of the strand closest to the bottom tension fiber. 3.5.2 Cracks and crack width At the beginning of fatigue tests, crack spacing was measured for most of the beam specimens. Cracks that may have developed due to cyclic fatigue were checked occasionally; no such cracks developed for all the test beams. A summary of the average crack spacing and number of observed cracks are shown in table 3.4. All beams were cracked during the first static cycle to Pmax. In particular, beams PD1, PD2 and PD3 cracked at loads corresponding respectively to 53%, 51% and 49% of the ultimate load capacity of their sister (control) beam tested under static loading. The crack width at Pmax in the first cycle was 0.15, 0.25 and 0.16 mm for PD1, PD2 and PD3 respectively measured at 1" from the bottom tension fiber.

85 The variation of crack width with increasing number of cycles (drawn on a semi-log scale) is shown in figures 3.16-3.18. Similar to the trend observed in deflection, crack width showed in general 3 different portions of Table 3.4 Measured Crack Spacing And Number Of Cracks Beam Average crack Number of Designation spacing cracks (in) PD1 8.2 6 PD3 4.8 11 PP2D1 4.3 11 PP2D2 3.1 20 PP2D3 3.6 19 PP1D1 3.3 22 PP1D2 4.2 18 RD3 3.4 22 behavior (as described for deflection), specially for fully prestressed beams. However, this behavior was less pronounced for an increase in the level of reinforcing index specially for partially prestressed and fully reinforced specimens. Also, similar to the deflection trend, the rate of crack width tended to increase with increase in the partial prestressing ratio. This trend is more substantial for PPR equal 1 and PPR equal about 0.72. Fully reinforced beams showed little increase in the crack width with loading. cycles.

0.5 E ) PPR 0.6Pu A f A f E (kips) (ks (ksi) 0.4 1 0.14 1 4.90 10.0 -- Faiedat ^3 w - ____ ____ ____ ______ - -- 1.212 x 10" cycl s 0. 2 0.10 0.62 4.80 25.8 1y8.1J (D. 3 0.13 0.33 9.75 8.8 17.2 0.3 (03 ^^^o-' " 0PDI ~ ^cy^^0^^ PP1P1.. r^>frfl 2-DO 0.2 ^ -----,_^^ ^u ol^ -— O^8^,^ — ^ --— (>-^ —~ ~^~~~PP201 v 0 C) C.) 0 II I Ii ___ I 1 10 102 13 104 105 106' Number of Cycles, log scale Fig. 3.16 Observed Crack Width Versus Number Of Cycles (&L.. = 1/3 6max)

h*w o^W~~ ~Crack width at 0.6 Pu, mm "n 0 0 0 0 0 0 o:. k i i> Ln,,I. 0 ~ ~~~ ~~~~~~ - 1% 31 * fr 0 C2 r^ \3 N hj hW jN - 1 ^ \ ~~~~0000^ (1) \ -- -- - 0 0 0 a P, ~ ~ ~ ~ ~ ~ 0 o a rr2 \ o ro *~j ohi[ (t 0'O i 9*< * *.. -g a' O; 0 0 w 0 ~~~~~ 0 0~~~~0 -4 -,0~ -- -,, < (Em) - 00,\ ~ -~ I - ( " \' Cfl r o a' 1I *'\^i - -~ t~'I 0 -- w a' I I I I iI C,) 0 C ) a a a -~ 0 El u CD. (D% \0 0? 5 SI~~~ II 0^ ~1-~ 9f i' O O^ ^, ~~~~ W LB

| | PPR 0.6Pu f A f) (kips) (ksIT (ksi Q0.7 H1 0.37 1 11.50 19.0 Foiure! 7- Failure (it 2 0.30 0.74 12.00 12.8 22.5 1.94 X 106 cycles 3 0.30 0.34 12.55 6.9 12.4 E 0.6-'-............ E * In the lowest strand k5 3PD3. 0.5 m 0.4 o.0.3'-,DPP2D3 0.20.1 PP1D3 t(D1 I0 10 2 103 104 105 106 107 Number of cycles N, log scale Fig. 3.18 Observed Crack Width Versus Number Of Cycles ( ~ = Omax)

89 For most of the beam specimens, the crack depth remained practically constant during the entire-test. In the case of fully prestress~ed beams,, cracks in the constant moment region, propagated upward with increasing number of cycles at relatively small rate. HaSwevVr, after one.,or several wire failures, these cracks were observed to propagate well into the compression zone of the beam branching out in two or three different directions. Among all test specimens, only beam RD3 developed inclined shear cracks at its end supports during the first cycle to Pmax* The crack propagated to about 2" (51 mm) from the top compression fiber and showed no sign of width increase througout the entire test (See figure 2.14-Test setup). 3.5.3 Average curvature The average curvature was measured for 7 beams in the dynamic test over 10" gage length. Variation of curvature versus number of cycles drawn on a semi-log scale is shown in figure 3.19. It can be seen that a very similar trend exist between curvature and deflection variation with increasing number of cycles. Also similar observation can be made i.e 1) three stages of behavior comprising every curve, 2) increase in the slope of the aveage curvature versus logN with increasing PPR and 3) the relatively insignificant effect of the reinforcing index.

90 5.0 5. PPR 0.6Pu a 4p, f fs _ __| _-_, PPR |(kips) (ks)) (ksi) (- 1 0.14 1 4.90 10.0 qP 40.]2 0.10 0.62 4.80 5.8 18.1 4.0 3 0.13 00.33'9.75 8.8 L?.'2:;'. PP1Ol 0: | ~PP2D E0 < 2(.0 1.0 I.!!! I 1 10 101 10 3 10= 10 10' 107 Number of Cycles N, log scale C I PPR 0.6Pu A fps a fs (kips) (ksi) (ksi) failed s 1 0.37 1 11.50 19.0j - at 1.94 106 6O 2 0.20 0.68 7.00 9.2 18.6 cycles TM 5.0 P 3 0.20 0.33 9.50 7.9 14.3 "-~m 4 0.29 0 15.00 -- 10.4 CL * In the lowest strand 2 P2P=02 a' 0 |o 4.0 I. I I I 3.0 2.0 1 10 -102 1 0 4 10' 10 10' 107 Number of Cycles N, log scale Fig. 3.19 Variation Of Curvature Versus Number Of Cycles For Various Beam Specimens

91 3.6 Reinforcement Stresses The measured strains (or stresses) in the te nsion reinforcement for the different test; beams showed a' continuous increase in strain measured at Pma and Pmin and max mmtin generally a continuous increase in the mean stress level and the stress range with increasing number of cycles. The increase in the stress range of prestressed strands during cyclic loading could be either due to reduction in the effective prestress resulting from slippage, (a similar phenomena was observed by Rabbat et al (23) ), or could be due to stress redistribution resulting from the cyclic creep of concrete with increasing number of cycles. However, slip measurement during the test (Fig. 2.10) showed no sign of strand slippage. Moreover, strand slippage leads theoretically to a reduction in the stresses measured at Pmin and Pma. Therefore the increase observed in this study m max' was attributed to cyclic creep only. Although most of the beams cracked well before Pmin, specially those with low PPR, the strains in the prestressing strands and reinforcing bars measured during the first cycle at Pmin were smaller than those measured during the 2nd and 3rd cycles. This phenomena resulted in stress ranges in the reinforcement higher in the first cycle than in subsequent cycles. These subsequent stress ranges were smaller than computed.

92 Measured and calculated stresses in the tension reinforcement at ma and Pmin for both static and cyclic beams are shown in tables 3.5,, 3.6 and 3.7. -In calculat-ing these stresses, a general equation based on equilibrium and compatability (elastic analysis) predicted by; Siriaksorn and Naaman ( 26 ) was used. These tables show that for most beam specimens, the measured and calculated stresses are quite comparable for the static beams and the first static cycle in the dynamic beams as well as at the maximum load level Pma in the 3rd cycle. In the fully and partially prestressed beams where the crack had to close under Pmin, the observed stress in the reinforcement was consistantly higher than predicted during 3rd cycle at Pmin This was attributed to the roughness of the crack which did not close to zero or near zero level. Also, it can be observed from table 3.6 that the difference between the observed and calculated stresses at P is smaller for beams that min cracked at smaller load level (PPR close to 0.3 and PPR equal to 0). The difference reaches an insignificant level in the fully reinforced beams. 3.7 Ultimate Load After Cyclinq At the end of the fatigue test provided the beam did not fail before 5 million cycles, the test specimens were unloaded to zero load and then a static load test was conducted up to destruction. This test gives an indication of the performance of the test beams as to their ultimate

Table 3.5 Stresses in the prestressing and reinforcing steel at Pmin and Pmax Cycle 1 1 r I Load - 0.4 PU Load - 0.6 Pu Beam Afps (ksi) fs (ksi) (ksi) fa (kai Calc. Test.~ Calc. Test i. Calc. Test * Calc. Test ^ 6 6 6 6 PDL 2.4 2.3 0.1 - - - 22.9 18.8 4.1 PD2 3.8 3.8 0.0 - - - 28.2 25.9 2.3 PD3 5.1 4.7 0.4 - - - 21.7 20.3 1.4 PP2D1 7.8 4.4 3.4 10.0 7.2 2.8 25.9 17.8 8.1 36.2 38.6 2.4 PP2D2 9.6 9.4 0.2 11.8 9.6 2.2 29.4 27.4 2.0 38.9 35.0 3.9 PP2D3 14.0 15.3 1.3 17.1 15.0 2.1 34.0 35.3 1.3 47.0 45.1 1.9 PP1DI 18.7 15.8 2.9 26.5 24.7 1.8 33.5 31.4 2.1 48.6 49.8 1.2 PP1D2 16.2 15.7 0.5 23.7 25.2 1.5 28.7 28.1 0.6 42.8 43.6,..8 PP1D3 14.3 13.5 0.8 20.2 17.9 2.3 24.9 24.6 0.3 36.0 36:8 0.8 RD1 -- -- -- 33.2 28.6 4.6 - - 51.2 46.7 4.5 RD2 - - - 31.0 25.8 5.2 - - - 46.1 41.9 4.2 RD3 - - - 28.3 24.9 3.4 -- - -J 42.4 38.6 3.8 Mean =T1.1 ksi Mean - 2.9 ksi Mean = 2.5 k1i Mean 2.6 ksi S.D - 0.4 ksi S.D - 0.5 ksi S.D - 0.8 ksi S.D - 0.5 ksi * Load values are given in tables 1D-12D + 6 I Test-Calc.l

Table 3. 6 Stresses in the prestressing and reinforcing steel at Pmin and Pmax* Cycle # 3 Load - 0.4 PU Load - 0.6 P* Beam ypf (ksi) fe (ksi) AfP(k) f (kl) Calc. Test * Caic. Test * CaIc. Test +. Calc. Test 6 8 6 6. 6 PDI 2.8 11.1 8.3 -- - - 22.9 21.1 1.5 PD2 4.5 12.0 7.5 -- - 28.2 28.0 0.2 PD3 5.2 9.4 4.2 - - - 21.7 21.7 0.0 -- -- PP2D1 7.8 13.2 5.4 10.0 22.6 12.6 25.9 19.0 6.9 36.2 40.7 4.5 PP2D2 9.6 19.5 9.9 11.8 17.9 6.1 29.4 28.7 0.7 38.9 36.5 2.4 PP2D3 14.0 23.6 9.6 17.1 23.9 6.8 34.0 36.4 2.4 47.0 46.4 0.6 PP1D1I 18.7 23.5 4.8 26.5 33.5 7.0 33.5 32.3 1.2 48.6 50.7 2.1 PP1D2 16.2 21.1 4.9 23.7 29.4 $.7 28.7 29.1 0.4 42.8 43.8 1.0 PP1D3 14.3 17.8 3.5 20.2 24.9 4.7 24.9 24.7 0.2 36.0 37.3 l RD1 -- -- -- 33.2 32.5 0.7 -- - - 51.2 47.5 3.7 RD2 -- -- -- 31.0 31.7 0.7 -- -- - 46.1 43.0 3.1 RD3 - - - 28.3 29.0 0.7 -- -- -- 42.4 39.4 3.0 Mean 6.5 kei ean 5,0ksi Mean M 1.5 ksi Mean T 2.4 ksi S.D - 0.9 ksi S.D - 1.4 ksi S.D * 0.8 ksi S.D - 0.5 ksi * Load values are given in tables 1D-12D + 6 | Test-Calc.I

Table 3.7 Stresses in the prestressing and reinforcing steel at two load levels, Pmin and Pmax* (static beams) Load - 0.4 Pu. Load - 0.6 Pu Beam | 4fp (ksi) f (ki)ps (ksi) fe (ksi) Calc. Test 6' Calc. Test 6. T Calc. Tst c. Test | PS1 2.4 2.2 0.2 - -- -- 25.0 23.8 1.2 PS2 4.0' 4.2 0.2 -- -- - 32.2 31.8 0.4 - PS3 5.1 4.6 0.5 -- - -- 26.8 26.8 0.0 - PP2S1 7.7 5.3 2.4 10.1 11.0 0.9 25.7 19.1 6.6 36.4 45.3 8.9 PP2S2 8.2 7.8 0.4 9.4 8.2 1.2 28.7 25.9 2.8 37.0 35.0 2.0 PP2S3 13.4 13.0 0.4 16.2 16.8 0.6 33.3 32.5 0.8 45.8 44.6 1.2 w 01 PP1SI 18.7 12.9 5.8 26.5 23.7 2.8 33.5 24.1 9.4 48.6 47.4 1.2 PP1S2 15.2 13.4 1.8 21.8 20.0 1.8 27.4 25.9 1.5 40.5 36.5 4.0 PP1S3 14.4 14.6 0.2 20.4 16.7 3.8 25.0 25.8 0.8 36.8 33.5 3.3i RS1 - -- -- 33.2 21.7 11.5 -- -- - 51.2 36.2 15.0 RS2 - —, -- 30.9 25.5 5.4 - -- -- 45.9 40.5 5.4 RS3 - -- - 28.1 21.1 7.0 - -- - 42.2 34.6 7.6 Mean = 1.3 ksi Mean = 2.9 ksi Mean = 2.6 ki. Mean 4.2 ksi S.D - 0.7 ksi S.D = 0.9 ksi S.D = 1.1 ksi, S.D = 1.1 ksi * Load values are given in tables ID-12D + 6 = Test-Calc.I x - Disregarded

96 load capacity and ductility after being subjected to 5 million cycles. A summary of the ultimate load and maximum deflection for the various beams in this test is shown in table 3.8. Additional results (deflection, crack width and curvature) are summarized (except for beam RD1) in tables B1-B8 of Appendix B. Load-deflection curves of these beams compared with their sister static beams are shown in figures A8-A15 of Appendix A. It can be observed from the data that the static strength of the fatigue beams (after 5 million cycles) is not much different from that of their control static specimens. However, their ultimate deformation was generally smaller (except for PP1D2 and PP2D3).

97 Beam Deflection Deflection Pu Designation at Pu=0'at P=Pu,.. (in) (.in) (k'ips) PP2D1 0.13 3.10 8.06 PP2D2 0.17 1.63 11.25 PP2D3 0.21 1.59 19.57 PP1D1 0.15 3.26 15.60 PP1D2 0.20 1.80 15.50 PP1D3 1.00 21.80 RD1 3.19 11.29 RD2 0.18 1.76 17.20 RD3 0.16 0.85 24.70 Table 3.8 Deflection And Load Characteristics Of Beams Loaded To Failure After 5 Million Cycles

98 CHAPTER IV OBSERVATIONS AND CONCLUSIONS 4.1 Observations The following important pbservations were made in this study: 1. The rate of increase of deflection, crack width and curvature was significant in the early stages of load cycles. A second phase followed in which they remain essentially the same or increase at a small rate. Significant reduction in stiffness and rapid increase in deflection and crack width were observed in the last phase before failure. This sudden change of behavior is a result of fracturing of some individual wires in the strand which increases the stress range in the remaining tensile reinforcement. This increase in the stress range leads to a rapid fracturing of other wires and hence a rapid increase in deflections an crack widths. Failure of the beams occur shortly thereafter. 2. Failure of the strands in the three fully prestressed beams occurred in the constant moment region of the beam at the location of a crack as expected. Generally failure starts by fracturing of an external wire. The stresses and hence the stress ranges in the tension reinforcement are higher at the crack location than at any uncracked region in the beam. Therefore stress conditions at the crack control the fatigue life of the

99 tension reinforcement. The local debonding on either side of the crack during the cyclic process results in fretting and abrasion of the strand due to successive closing and opening of the crack under fluctuating load. This phenomenon adds to the probability of fatigue fracture in at least one of the strand's external'wires in contact with the surrounding concrete. 3. All prestressed and partially prestressed beams in this investigation showed no sign of bond failure. Therefore strand slippage did not contribute to the fatigue life of the specimens. 4. Fatigue failure in the beams resulted from fatigue fracturing of the strands. The stress ranges versus total number of cycles were compared with recently published data. The result suggest that the fatigue life of the beams could be predicted reasonably well from the fatigue life of strand samples tested freely in air, 5. The stress ranges observed in the early stages of cycles in the strands which failed by fatigue were 0.04fpu 0.07f and 0.06f. Calculated fictitious nominal pu pu' tensile stress in the corresponding fully prestressed beams were respectively 8.9/f' c 15.6v/f' and 24.1vf'. Moreover fictitious nominal tensile stresses of up to 32.8y/f' were obtained in PPC beams without failure. These results suggest that limiting the

100 fictitious tensile stress for the design of PC and PPC beams is not a rational design criterion. 6. Stresses in the tension reinforcement measured at P. and Pma increased with the number of loading cycles. max The stress increase was more pronounced for fully prestressed beams than for either partially prestressed or fully reinforced specimens. This phenomenon increased substantially the stress range under load and led to a reduction in fatigue life. 4.2 Conclusions The following conclusions could be drawn from this study: 1. For approximatly equal reinforcing index w, the rate of growth of crack width, deflection, and/or curvature under fatigue loading tends to be higher for beams with higher partial prestressing ratios. Large areas of non prestressed tension reinforcement (beams with low PPR) enhance the overall bond characteristics of the tension reinforcement and results in lesser stiffness deterioration with repeated loadings. 2. For approximately equal partial prestressing ratios and for equal load ranges expressed in percent of ultimate load, the reinforcing index appears to have little influence on the rate of increase of crack width, deflection and/or curvature with the number of loading cycles.

101 3. Stresses observed in the early cycling stages were comparable to stresses computed from linear.elastic cracked section analysis. 4. Beams that survived 5 million'cycles showed practically no reduction in ultimate load capacity when tested to failure after cycling. However a reduction in duttility was generally observed. In summary, it appears from this investigation that a reliable evaluation of the fatigue characteristics of prestressed and partially prestressed beams requires the development of a general model based on cracked section analysis to calculate under cyclic loading, stresses and stress ranges induced in the component materials. This model should take into account-the progressive time and cyclic dependent changes that accompany the structure throughout its design life time such as creep and shrinkage in the concrete, relaxation and prestress loss in the prestressing steel.

102 LIST OF REFERENCES 1. ACI Committee 215, "Consideration For Design of Concrete Structures Subjected to Fatigue Loading,'- ACI Journal, Vol. 71, No.3, March 1974, pp. 97-121. 2. ACI Standard 318-83, "Building Code Requirements For Reinforced Concrete," American Concrete Institute, Detroit, Michigan. 3. The American Association of State Highway and Transportation Officials, (AASHTO), "Standard Specifications For Highway Bridges," 12th Edition, 1977. 4. Murdock, J.W., and Kesler, C.E., "Effect of Stress on Fatigue Strength of Concrete Beams," ACI Journal, Proceedings, Vol.55, No.2, August 1958, pp. 221-231. 5. Hilsdorf, H.K., and Kesler, C.E., "Fatigue Strength of Concrete Under Varying Flexural Stresses," ACI Journal, Proceedings, Vol. 63, No. 10, October 1966, pp. 1059-1075. 6. Mccall, J.T., "Probability of Fatigue Failure of Plain Concrete," ACI Journal, Proceedings, Vol. 55, No. 2, August 1958, pp. 233-244. 7. Norby, G.M., "Fatigue of Concrete - A Review of Research," ACI Journal, Proceedings, Vol. 55, No. 2, August 1958, pp. 191-219. 8. Bennet, E.W., and Raju, N.K., "Cumulative Damage of Plain Concrete in Compression," Proceedings, International Conference of Structures, Solid Mechanics and Engineering Design in Civil Engineering Materials, University of Southampton, April 1969. 9. Shah, S.P, and Chandra, S., "Fracture of Concrete Subjected to Cyclic and Sustained Loading," ACI Journal, Proceedings Vol. 67, No. 10, October 1970, pp. 816-824. 10. Helgason, T., Hanson, J.M., Somes, N.F., Corley, W.G., and Hognestad, E., " Fatigue Strength of High-Yield Reinforcing Bars," Report for NCHRP Projects 4-7 and 4-7/1, Portland Cement Association (PCA), Research and Development Bulletin RD045.01E, Skokie, Illionois, March 1975, 372 pp. 11. ACI Committee 343, Report on "Analysis and Design of Reinforced Concrete Bridge Structures," ACI 343R-77, Detroit, Michigan, 1977, 118 pp.

103 12. Lane, R.E., and Ekberg, C.E., Jr., "Repeated Load Tests on 7-Wire Prestressing Strands," Progress Report No. 223.21, Fritz Engineering Laboratory, Lehigh University, Bethlehem, Pe., 1959. 13. Tide, H.R.,-and Van Horn,D.A., "A Statistical Study of the Static and-Fatigue Properties of High Strength Prestressing Strands," Report No. 309.2, Fritz Engineering Laboratory, Lehigh University, June 1966, 86 pp. 14. Warner, R.F., and Hulsbos, C.L., "Fatigue Properties of Prestressing Strands," PCI Journal, Vol. 11, No. 1, February 1966, pp. 32-52. 15. Edwards, A.D., and Picard, A., "Fatigue Characteristics of Prestressing Strands," Proceedings, ICE (London), Vol. 53, September 1972, pp. 323-336. 16. Naaman, A.E., "A Proposal to Extend Some Code Provisions on Reinforcement to Partial Prestressing," PCI Journal, Vol. 26, No. 2, March-April 1981, pp. 74-91. 17. Naaman, E.A., "Research Needs in Partial Prestressing," PCI Journal, Vol. 27, No. 4, July-August 1982, pp. 106-107. 18. Naaman, A.E., "Partially Prestressed Concrete Design, American View Point," International SymposiumNonlinearity and Continuity in Prestressed Concrete, University of Waterloo, Waterloo, Ontario, Canada, July 4-6, 1983. 19. Irwin, C.A.K., "Static and Repetitive Loading Tests on Full Scale Prestressed Concrete Bridge Beams," Transport and Road Research Laboratory, TRRL, Department of Transport, Report 802, England 1977. 20. Hilmes, J.B., and Ekberg, C.E., "Statistical Analysis of the Fatigue Characteristics of Under-Reinforced Prestressed Concrete Flexural Members," Iowa Engineering Experimental Station, Ames, 1965 (Iowa State University of Science and Technology). 21. Fisher, J.W., and Viest, I.M., "Fatigue Tests of Bridge Materials of the AASHTO Road Test," Special Report No. 66, Highway Research Board, 1961, pp. 132-147. 22. Hanson, J.M., Hulsbos, C.L., and Van Horn, D.A., "Fatigue Tests of Prestressed Concrete I-Beams," Proceedings, ASCF, Vol. 96, No. ST1, November 1970, pp. 2443-2463.

102 LIST OF REFERENCES 1. ACI Committee 215, "Consideration For Design of Concrete Structures Subjected to Fatigue Loading," ACI Journal, Vol. 71, No.3, March 1974, pp. 97-121; 2. ACI Standard 318-83, "Building Code Requirements'For Reinforced Concrete," American Concrete Institute, Detroit, Michigan. 3. The American Association of State kighway and Transportation Officials, (AASHTO), "Standard Specifications For Highway Bridges," 12th Edition, 1977. 4. Murdock, J.W., and Kesler, C.E., "Effect of Stress on Fatigue Strength of Concrete Beams," ACI Journal, Proceedings, Vol.55, No.2, August 1958, pp. 221-231. 5. Hilsdorf, H.K., and Kesler, C.E., "Fatigue Strength of Concrete Under Varying Flexural Stresses," ACI Journal, Proceedings, Vol. 63, No. 10, October 1966, pp. 1059-1075. 6. Mccall, J.T., "Probability of Fatigue Failure of Plain Concrete," ACI Journal, Proceedings, Vol. 55, No. 2, August 1958, pp. 233-244. 7. Norby, G.M., "Fatigue of Concrete - A Review of Research," ACI Journal, Proceedings, Vol. 55, No. 2, August 1958, pp. 191-219. 8. Bennet, E.W., and Raju, N.K., "Cumulative Damage of Plain Concrete in Compression," Proceedings, International Conference of Structures, Solid Mechanics and Engineering Design in Civil Engineering Materials, University of Southampton, April 1969. 9. Shah, S.P, and Chandra, S., "Fracture of Concrete Subjected to Cyclic and Sustained Loading," ACI Journal, Proceedings Vol. 67, No. 10, October 1970, pp. 816-824. 10. Helgason, T., Hanson, J.M., Somes, N.F., Corley, W.G., and Hognestad, E., " Fatigue Strength of High-Yield Reinforcing Bars," Report for NCHRP Projects 4-7 and 4-7/1, Portland Cement Association (PCA), Research and Development Bulletin RD045.01E, Skokie, Illionois, March 1975, 372 pp. 11. ACI Committee 343, Report on "Analysis and Design of Reinforced Concrete Bridge Structures," ACI 343R-77, Detroit, Michigan, 1977, 118 pp.

103 12. Lane, R.E., and Ekberg, C.E., Jr., "Repeated Load Tests on 7-Wire Prestressing Strands," Progress Report No. 223.21, Fritz Engineering Laboratory, Lehigh University, Bethlehem, Pe., 1959. 13. Tide, H.R., and Van Horn,D.A.,.."A Statistical-study of the Static and Fatigue Properties of High Strength Prestressing Strands," Report No. 309.2, Fritz Engineering Laboratory, Lehigh University, June 1966, 86 pp. 14. Warner, R.F., and Hulsbos, C.L., "Fatigue Properties of Prestressing Strands," PCI Journal, Vol. 11, No. 1, February 1966, pp. 32-52. 15. Edwards, A.D., and Picard, A., "Fatigue Characteristics of Prestressing Strands," Proceedings, ICE (London), Vol. 53, September 1972, pp. 323-336. 16. Naaman, A.E., "A Proposal to Extend Some Code Provisions on Reinforcement to Partial Prestressing," PCI Journal, Vol. 26, No. 2, March-April 1981, pp. 74-91. 17. Naaman, E.A., "Research Needs in Partial Prestressing," PCI Journal, Vol. 27, No. 4, July-August 1982, pp. 106-107. 18. Naaman, A.E., "Partially Prestressed Concrete Design, American View Point," International SymposiumNonlinearity and Continuity in Prestressed Concrete, University of Waterloo, Waterloo, Ontario, Canada, July 4-6, 1983. 19. Irwin, C.A.K., "Static and Repetitive Loading Tests on Full Scale Prestressed Concrete Bridge Beams," Transport and Road Research Laboratory, TRRL, Department of Transport, Report 802, England 1977. 20. Hilmes, J.B., and Ekberg, C.E., "Statistical Analysis of the Fatigue Characteristics of Under-Reinforced Prestressed Concrete Flexural Members," Iowa Engineering Experimental Station, Ames, 1965 (Iowa State University of Science and Technology). 21. Fisher, J.W., and Viest, I.M., "Fatigue Tests of Bridge Materials of the AASHTO Road Test," Special Report No. 66, Highway Research Board, 1961, pp. 132-147. 22. Hanson, J.M., Hulsbos, C.L., and Van Horn, D.A., "Fatigue Tests of Prestressed Concrete I-Beams," Proceedings, ASCE, Vol. 96, No. ST1, November 1970, pp. 2443-2463.

104 23. Rabbat, B.G., Kaar, P.H., Russell, H.G., and Bruce, R.N., Jr., "Fatigue Tests of Full-Size Prestressed Girders," Technical Report No. 113, Portland Cement Association, Research and Development Laboratories, June 1978. 24. Ozel, A.M., and Ardaman, E., "Fatigue Tests of Pretensioned Prestressed Beams," ACI Journal, Proceedings, Vol. 53, No. 4, October 1956, pp. 413-424. 25. Abeles, P.W., Brown, E.I., and Hu, C.H., "Fatigue Resistance of Under-Reinforced Prestressed Beams; Subjected to Different Stress Ranges; Miner's Hypothesis," ACI Journal, SP-41, Paper 11, 1974, pp. 237-277. 26. Naaman, A.E., and Siriaksorn, A., "Serviceability Based Design of Partially Prestressed Beams. Part 1: Analytic Formulation," PCI Journal, Vol. 24, No. 2, March-April 1979, pp. 64-89. 27. Siriaksorn, A., and Naaman, A.E., "Serviceability Based Design of Partially Prestressed Beams. Part 2: Computarized Design and Evaluation of Major Parameters," PCI Journal, Vol. 24, No. 3, May-June 1979, pp. 40-60. 28. Naaman, A.E., "Fatigue in Partially Prestressed Beams," ACI Publication SP 75-2, 1982, pp.25-46. 29. Bennet, E.W., and Dave, N.J., "Test Performance and Design of Concrete Beams With Limited Prestress," The Structural Engineer (London), Vol. 47, No. 12, December 1969, pp. 487-496. 30. Dave, N.H., and Garwood, J.J., "The Limit State Behavior of "Class-3" Post-Tensioned Beams Under ShortTerm, Sustained and Fatigue Loadings," In Behavior in Service of Concrete Structures, Colloquium Interassociation I.A.B.S.E., F.I.P, C.E.B., R.I.L.E.M., I.A.S.S., Liege, June 1975, pp. 319-330. 31. Fauchart, J., and Trinh, J., "Comportement Sous Charges Repetees de Poutrelles en Beton Arme Preconstraint," Annales de L'Institut Technique du Batiment et des Travaux Publics, Paris, Septembre-Octobre 1973, pp. 87-132. 32. Fauchart, J., Kavyrchine, M., and Trinh, J., "Complement to Ref. 29," Annales I.T.B.T.P., March 1975, pp. 23-32. 33. Corley, W.G., Hanson, J.M., and Halgason, T., "Design

105 of Reinforced Concrete For Fatigue," ASCE Journal, Vol. 104, No. ST6, June 1978, pp. 921-932. 34. Foo, M.H., and Warner, R.F.,"Fatigue Test"on Partially Prestressed Concrete Beams," In Partial Prestressing From Theory To.Practice, NATO Advanced Research Workshop, Paris, France, June 18-22, 1984. 35. Hawkins, N.M., "Fatigue Design Considerations For Reinforcement in Concrete BridgTe Decks," ACI Journal, Vol. 73, No. 2, February 1976, pp. 104-115. 36. Chang, T.S., and Kesler, C.E., "Fatigue Behavior of Reinforced Concrete Beams," ACI Journal, Vol. 55, No. 2, August 1958, pp. 245-259. 37. Ekberg, C.E., Walther, R.E., and Slutter, R.G., "Fatigue Resistance of Prestressed Beams in Bending," ASCE Journal, Structural Division, Vol.83, No. ST4, Proc. 1304. 38. Gylltoft, K., "Fatigue Tests of Concrete Sleepers," Division of Structural Engineering, University of Lulea, Research Report No. TULEA 1978:13. 39. FIP Commission on Prestressing Steel and Systems "Report on Prestressing Steels: Types and Properties," FIP, Wexham Spring, England, August 1976, 18 pp. 40. Venuti, W.J., "A Statistical Approach to the Analysis of Fatigue Failure of Prestressed Concrete Beams," ACI Journal, Proceedings Vol. 62, No. 11, November 1965, pp. 1375-1394. 41.. Mansur, M.A., "Partially Prestressed Concrete Beams Under Repeated Loading," International Symposium - Nonlinearity and Continuity in Prestressed Concrete, University of Waterloo, Waterloo, Ontario, Canada, July 4-6, 1983. 42. Balaguru, P.N., Naaman, A.E., and Shah, S.P., "Analysis of Prestressed Concrete Beams For Fatigue Loading," PCI Journal, May-June 1981, pp. 70-94. 43. Balaguru, P.N., Naaman, A.E., and Shah, S.P., "Serviceability of Ferrocement Subjected to Flexural Fatigue," The International Journal of Cement Composites, Vol. 1, No. 1, May 1979, pp. 3-9. 44. Balaguru, P.N., Namman, A.E., and Shah, S.P., "Ferrocement in Bending, Part II: Fatigue Analysis," Report No. 77-1, Department of Materials Engineering, University of Illinois at Chicago, Chicago, October 1977.

106 45. Warner, R.F., and Hulsbos, C.L., "Probable Fatigue Life of Prestressed Concrete Beams," PCI Journal, Vol. 11, No. 2, April 1966, pp. 16-39. 46. Magura, D.D., Sozen, M.A., and Siess, C.P., "A Study of Stress Relaxation in Prestressingg-/Rinforcement," PCI Journal, Vol. 9, No. 2,-April 1964, pp. 13-57. 47. Gylltoft, K., "Bond Properties of Strands in Fatigue Loading," Division of Structural Engineering, University of Lulea, Research Report No. TULEA 1979:22. 48. Watcharaumnuay, S., and Naaman, A.E., "Deflection of Partially Prestressed Concrete Beams Under Sustained and Cyclic Fatigue Loading," Report In Progress. 49. ACI Committee 224, "Control of Cracking in Concrete Structures," ACI Journal, No. 69, December 1972, ppo 717-753. 50. Nawy, E.G., and Huang, P.T., "Crack and Deflection Control of Pretensioned Prestressed Beams;" PCI Journal, Vol. 22, No. 3, May-June 1977, pp. 30-47. 51. Bennet, E.W., and Chandrasekhar, C.S., "Calculation of the Width of Cracks in'Class 3' Prestressed Beams," Proceedings, Institution of Civil Engineers (London), Vol. 49, July 1971, pp. 333-346. 52. Nilson, A.H., "Flexural Stresses after Cracking in Partially Prestressed Beams," PCI Journal, Vol. 21, No. 4, July-August 1976, pp. 72-81. 53. Gergely, P., and Lutz, L.A., "Maximum Crack Width in Reinforced Flexural Members," In Causes, Mechanisms and Control of Cracking in Concrete, SP-20, ACI, Detroit, 1968, pp. 87-117. 54. Park, R., and Thompson, K.J., "Cyclic Load Tests on Prestressed and Partially Prestressed Beam-Column Joints," PCI Journal, Vol. 22, No. 5, September-October 1977, pp. 84-111. 55. Park, R., and Thompson, K.J., "Ductility of Prestressed and Partially Prestressed Concrete Sections," PCI Journal, Vol. 25, No. 2, March-April 1980, pp. 45-69. 56. Cohn, M.Z., and Bartlett, M., "Nonlinear Flexural Response of Partially Prestressed Concrete Sections," Solid Mechanics Division, University of Waterloo, Waterloo, Ontario, Canada, Paper No. 168, October 1981. 57. Pfrang, E.O., Siess, C.P., and Sozen, M.A., "Load

107 Moment-Curvature Characteristics of Reinforced Concrete Cross Sections," ACI Journal, Proceedings, Vol. 61, No. 7, July 1964, pp. 763-778. 58. Mattock, A.H, "Rotational Capacity of Hinging Region in Reinforced Concrete Beams, ".Proceedings. Int'l. Symposium oh Flexural -echanics of Reinforced Concrete, ASCE, 1965, pp. 143-181. 59. Warwaruk, J., Sozeny M.A., and.Siess, C.P.,*"Strength and Behavior in Flexure of Prestretsed Concrete.Beams" University of Illinois Engineering Experiment Station, Bulletin No. 464, Urbana, Illinois, August 1962. 60. Naaman, A.E., "Prestressed Concrete Analysis and Design" Macgraw Hill Company, 1982. 61. Park, R., and Paulay, T., "Reinforced Concrete Structures," John Wiley and Sons, Inc., 1975.

108 APPENDIX A Load-Deflection Curves

109 Deflection, mm 0 10 - 20. 30 40 9 - I -—. i I.. 40 8 PS1'6^^.,,'.,''d 30 6 a,, 4o ) ~~ -20 a: (a) I B b at 1.M21 10. "y'. ^ |ro - ~' AV 10 2 0 0 II__ \! I U II_3 0 0 0.25 0.50 0.75 1.00 1.25 1.50 1.75 Deflection, Inches Deflection _ c- r'. r o 0 0 0 0 ~ o P13 i x' I 1 0 2 | 4 6 8 t0 mm 12 c5 Pmo.<, P. yymin /0 Pu m Pminff / ^ pmn^ e, I ~ ~~ ~ //9 failed at ~4 (b) J^ 3 -/ P n L 2 o... 0. Number of CY - wMw^ ^ ^'*;cycles 3 2 - < o.' PD1 5 - 0.14 A Pi p - 10.0 ksi 0 - Number of Q2 Def lection, inch Fig. Al Load-Deflection Curves For Beams: (a) PS1 ((Static) (b) PD1 (Cyclic)

110 Deflection, mm 0.0 25 50 75 100 9 40?8 1; PP2SI 7;- / ^ - 3..07w0~~~~~ /'2 ~30 c. 6 ~/ " Y — a' 5 mm-_ —iI, (a) -g 5 S 2D1 - 20'O O4 o 20 O O O O O j I~~0~ for ip, Is A straond-5Oksi I'g^ As 2#2 -60 kh 0 0.1 0 0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 Deflection, inches Deflection 0 d 0 0 d in. a254 — |,,- I I I —- 5.0 5.p mxOS / // / / 4 ~ 6 7 o mm e -PPR0.62Ap,, ~0.6 Pmin S0~~~~~~~~~~~ 3~ ~-4.5 0 Pm, z0.4 P, 2 Au for stotic test ^".0100 mm o 8 8 q o 0 0 Number o 3.0 Defle.tio.,0 0 o cycles in Cv or B PP?2- i.1 Af 5.8 ksi PPR-0.62 Afs, 18.1 ksi Au for static test 4"N 100mm 0 0 0.1 0.2 Deflection, inch Fig. A2 Load-Deflection Curves For Beams: (a) PP2S. (Static) (b) PP2Dl (Cyclic)

ll Deflection, mm 0 5 10 15 20 25 30 35 40 II — | --.-J --- - I --- 1 ---- T -—' 1 -- I ---- I- 100 20 — I 82- -J ~'- 1. 20 16 -. W I 0 - A60 z7 2 1 - (a) 0A,- 4 Ikd P203 oo[i___\ o.I I 762 a 0 25 0.50, 1 0 2 25 150mm Defletion,, inches Deflection p 5 >12 P2M|- _ _ _, Pmo, 0.6 P 10 (?- ^"o^^^ ^ox'O-610 (b%) 10 42 J 28~ 09 2 2 "~ ~ _,Number of c I 8 # # # # # cyles 2 PP2D3 0.30 A - 12.8 ksi j PPR * 0.74 Af* * 22.5 ksi jf G Au for the *tatic tet a 1. 53' * 40 mm 0. 0.25 0.5 Deflection, inch Fig. A3 Load-Deflection Curves For Beams: (a) PP2S3(Static) (b) PP2D3 (Cyclic)

112 Deflection, mm 0 10 20 30 40 50 60.70 80 -90'100 16' 14 -' 12 0 60. 10P z 0: 8 Vta- o 0 (a)'0 ppIOfl 40. o 0 0 0. C8 " 0 _t - -... I s 0 * 0 Deflection e 0_ c _i ci o c~ 20 PD e 03 10 11 12 13'mm I P.33 0 f 17.2 0 0 0-2PmSx 006 Pu5 Deeflection, inch () PA (b)(Cyc f / P Pmina'0.4 Pu I34 - - ~0 ^ ^' "9 -- Number of o CY a i in, cycles 2 PPDi 0.13 dfps - I.8 kni PPR - 0.33 t$ a 17.2 k.i ~,~ ~ Au for the *ftic test - 3.78 - 96 a* 0 0.25 0.5 Deflection, inch Fig. A4 Load-Deflection Curves For Bens, (a, pplsi(Static)

113 Deflection, mm 0 5 10 15 20 25 " 30 35 4b 24 I I' I I 100 20-, ""' ~' \ - o80 16 Se / ~|pn6 g o 0 (a) O. 12 PP`O03 " —. 8 -8Z - — 03 T- - go Fr Pm. 40. 4 ~ ~ - 20 Aa -W w*-M7 kW Oi~~~~~~~~~/,,~~Ag a 3,,, Ik 0 0.25 0.50 0.75 1.00 1.25 1.50 Deflection, Inches Deflection IcuL I I cj i O 0c O O in. O.q I. I I i,,. 8 9 10 11 12 13mm B ^:^______________,, J13 - - - 2 mber of 0 0.Pm250.6 P 12[ - 1t (b) 9 P-Jn'OO Pmin0.4 Pu ~6 ~ ~ o %' o_ ---- Number of m ", Cycles PPiD 03 0.3 Up - 6.9 ksi PPR * 0.34 Af - 12.4 ksi Aua for the static test 1.22" 31 mm 0 0.25 0.5 Deflection, inch Fig. A5 Load-Deflection Curves For Beams: (a) PPlS3(Static) (b) PP1D3 (Cyclic)

114 Deflection, mm 0 10 20 30 40 50 60 70 -I I- I. -I'- l _60 12 -. -': -..,,, *.,,6. 0. 0 o ROt 0 5' II 0"o o O O in. 35 |8 10 12 mm / In 1 - 1 7 3 4 F —X-P —- I A~~ 3 3- 60 k(i (b) 0 0 0.5 1.5 2 2.5 Deflectioneflection, inchinches FgDef A6 Load-Deflection Curves For Beams: (a).ctionRS1 (Static) ( b) RD ( Cyc ). O ~ l I I!,.! 8350. 8.0 2 2mm J ^ go^ PPR - 0. - (, 14.9 kT Oeflection, inch Fig. A6 Load-Deflection Curves For Beas: (a).RS1 (Static) (b) RD1 (Cycl.c)

115 Deflection, mm. 0 5 10 15 20 25 30 24s I I'/' I,. 24 _.^^ -_100 18- / -80 / z;0,~~~~~~ - 40 = 603 c: 12- R03. (a) I W7I 20 IT a/ 4.s' a./ l I - | l n 00 ~ ~ ~ t ~ —----— it. 0 0.25 0.50 0.75 1.00 1.25 Deflection, inches Defrection dt ""~ I.tI cS - U? <: in. [7: *,6 20 762 02 9 10.1 12mm 13 U'5 P in ~3 _/ R03 ~ PP " ~ A, - 10.4 ki.0 02 0(b) Deflection inch 0(0b) RD3 (sCyclic 0 6 7.5 3 R03 PPR0 at 1 10.4 ksAu for the static test 1.24 a 31Deflection "inch (b) RD3 (Cyclic)

Deflection, mm 0.0 25 50 75 100 9 - 40 PP2S14 7 (n ~~~~~~~~z 0~ ~ ~ ~~~~~~~~~~3 as- o ~ /I 6 NC 0L 5 ( -o / PP2D1 - 0 0 / -) 0, 20 o4 -0 -J / / ^~~~~~~~ ~~~~~~~4.5"-^ __3 J' ~~~~~~~~2 o — l^t~1 10 IAp=156 strand-25OksW A, =2#2-601Oks 0 0 0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 Deflection, inches Fig. A8 Load-Deflection Curve of Beam PP2D1 After 5 Million Cycles in Comparison With its Control Static Beam (PP2S1).

Deflection, mm 0 5 10 15 20 25 30 35 40 45 50 12 -PP2S2 50 10 - 40 (0 0 o8- z ineT~ Comparison/ -Wt is ot30 Ca -0 6'o U 6 PP2D2 4.' ( 0.. 0 20 4 g."r Li 2 10 Ap I= 1% *trand —270 kal As = 3#2 —60 ksl 0 0.25 0.50 0.75 1.00 1.25 1.50 1.75 2.00 Deflection, inches Fig. A9 Load-Deflection Curve of Beam PP2D2 After 5 Million Cycles in Comparison With its Control Static Beam (PP2S2).

Deflection, mm 0 5 10 15 20 25 30 35 40 ---- ^ ---- ^ ---- ^ ---- ^ ----, ---- ^ - -- ^ — I - I - 100 20 PP2S3 20 ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~~~~8 PU=19.6 K 80 16- Au=1.59" (0 I / -60 z 12 ab Lu ~tO /J- / -PP203 I S Ap -2 -0 40 0 0 0.i 8 0./ 0.5 05.7.0 12 0 1.20 4 -/ A9 * ** - AP - 2%W *lrnd-270 hel Ag = 243-60 kel 0 0.25 0.50 0.75 1.00 1.25 1.50 Deflection, inches Fig. A10 Load-Deflection Curve of Beam PP2D3 After 5 Million CycLes in Comparison With its Control Static Beam (PP2S3).

Deflection, mm 0 10 20 30 40.50 60 70 80 90 100 77 16 X PSl 14 60 12 10 // 8.- m/ /, 0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 Deflection, nches |^ 7 / o Po 20 Fig. All Loadn C e of Bm Aftp = r1l illinrnd-260 k in Comparison With its Control Static Be 3#3-M6P kl A's = 2#3-60 ktl' 0 I'' ____ I __ I ____'0 0 0.5 1.0 1.5 2.0 2.5 3.0.3.5 4.0 Deflection, inches Fig. All Load-Deflection Curve of Beam PP1D1 After 5 Million Cycles in Comparison With its Control Static Beam (PP1S1).

Deflection, mm 0 5 10 15 20 25 30 35 40 ---— I I 1 — l -- I I- I I 77 16 - PP1S2 14 - Pu=15. 5 K 14^ /^ ~ AU=1.8" 60 6 /= 12'; 10 6L t // /PP1D2 40 O o^ 0 8 o 0 0 y / A, 2#4-6 ks.I O~ 1 1 1 1 1 15. 00 " "' 20 0 0.25 0.50 0.75 1tri.0'lnd0 k1 As - 2t4-40 kel 0 0.25 0.50 0.75 1.00 1.25 1.50 Deflection, inches Fig. A12 Load-Deflection Curve of Beam PP1D2 After 5 Million Cycles in Comparison With its Control Static Beam (PP1S2).

Deflection, mm 0 5 10 15 20 25 30 35 40 24 ---— | 100 20- PPS 80 *16 9. Z,~~~~~~~~~~~~~~~~~Z ~ "-rr / f/ v'.^60 i: 12 2. go / /-ppt03 U* Lu w ^..j~~ / / 40 a 8 5 0. " 4 1 _ --- 20 Ap - I%' trand-270 kil Al - 314-60 kel 0 0 0.25 0.50 0.75 1.00 1.25 1.50 Deflection, inches Fig. A13 Load-Deflection Curve of Beam PP1D3 After 5 Million Cycles in Comparison With its Control Static Beam (PP1S3).

Deflection, mm 0 _ 10 20 30 40 50 18 RS2 _ 80 15 60 12 z- / / /RD2 P1 to 9 45* 40/ 0 6 / / ^.~ 140 -2 olrr A 3 4-40 ksl 0 0 0 0.50 1.00 1.50 2.00 Deflection, inches Fig. A14 Load-Deflection Curve of Beam RD2 After 5 Million Cycles in Comparison With its Control Static Beam (RS2).

Deflection, mm 0 5 10 15 20 25 30 24 ~~~~~~~~24 - ^ ^ —-a~RS3 100 18 - 80 CL -~~~~~~~~~~~'60 e: 12 - / / ^ RD3 ~ 12 6 - 1.01 [ I iJ (O /~~~~~~~~~~~~~~~~~A 3 A5-O *sl 0 0 0.25 0.50 0.75 1.00 1.25. Deflection, inches Fig. A15 Load-Deflection Curve of Beam RD3 After 5 Million Cycles in Comparison With its Control Static Beam (RS3).

124 APPENDIX B Data -Tables

Table B1 Ultimate Load Cycle For Beam PP2D1 Load P Moment at Deflection Crack width Curvature midspan (Kip) (Kip-in) (inch) (mm) (in-lx04 0.00 0.00 0.13 0.08 1.29 1.00 18.00 0.14 0.08 1.42 2.00 36.00 1.80 0.10 1.74 3.00 54.00 0.23 0.14 2.26 1 - 01 4.00 72.00 0.29 0.18 2.81 5.00 90.00 0.33 0.22 3.27 6.00 108.00 0.40 0.31 4.10 7.10 127.80 0.63 0.704 6.53 7.80 140.40 1.26 2.08 12.50 8.06 145.08 3.10 -- 24.10............~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~,'..., H

Table B2 Ultimate Load Cycle For Beam PP2D2 Load P Moment at Deflection Crack width Curvature midspan (Kip) (Kip-in) (inch) (mm) (in1x104) 0.00 0.00 0.17 0.08 1.58 1.25 22.50 0.19 0.08 1.76 2.50 45.00 0.24 0.10 2.20 3.75 67.50 0.30 0.14 2.89 g-J %,) 5.00 90.00 0.38 0.19 3.61 0 7.50 135.00 0.52 0.26 4.94 9.17 165.06 0.72 0.58 7.67 9.80 176.40 0.88 0.73 9.35 10.50 189.00 1.11 0.92 11.51 11.25 202.50 1.63 1.32 16.20

Table B3 Ultimate Load Cycle For Beam PP2D3 Load P Moment at Deflection Crack width Curvature midspan (Kip) (Kip-in) (inch) (mm) (in-xlO4) 0.00 0.00 0.21 0.13 2.50 45.00 0.26 0.14 3.75 67.50 0.30 0.15 5.00 90.00 0.34 0.17 -- 7.50 135.00 0.45 0.23 11.25 202.50 0.62 0.32 -- 15.00 270.00 0.80 0.43 -- 17.50 315.00 1.08 0.69 18.50 333.00 1.26 0.80 19.57 352.26 1.59 *,,...........................,

Table B4 Ultimate Load Cycle For Beam PP1D1 Load P Moment at Deflection Crack width Curvature midspan (Kip) (Kip-in) (inch) (mm) (in-x104) 0.00 0.00 0.15 0.06 1.19 2.50 45.00 0.21 0.08 1.62 3.75 67.50 0.26 0.10 2.02 5.00 90.00 0.32 0.13 2.50 7.50 135.00 0.43 0.18 3.42 10.00 180.00 0.53 0.23 4.28 11.25 202.50 0.59 0.25 4.73 14.25 256.50 1.00 0.73 9.32 15.13 272.34 1.85 1.04 19.30 15.60 280.80 3.26 - 25.70

Table B5 Ultimate Load Cycle For Beam PP1D2 Load P Moment at Deflection Crack width Curvature midspan (Kip) (Kip-in) (inch) (mm) (inIx104) 0.00 0.00 0.18 0.04 1.52 1.25 22.50 0.22 0.04 1.62 3.75 67.50 0.30 0.07 2.30 6.25 112.00 0.41 ).12 3.17 8.75 157.50 0.51 0.15 4.00.1 11.25 202.50 0.60 0.19 4.80 13.13 236.34 0.69 0.22 5.49 14.43 259.74 0.87 0.59 8.00 15.00 270.00 1.22 0.73 11.94 15.50 279.00 1.80 -- 18.26

Table B6 Ultimate Load Cycle For Beam PP1D3 Load P* Moment at Deflection Crack width Curvature midspan (Kip) (Kip-in) (inch) (mm) (in-lx04) 8.37 150.66 0.45 0.13 11.01 198.18 0.52 0.14 12.55 225.90 0.55 0.17'-I 14.32 257.76 0.61 0.18 - 15.42 277.56 0.64 0.20 17.62 317.16 0.71 0.22 18.72 336.96 0.76 0.23 19.82 356.76 0.91 0.44 21.80 392.40 1.01 0.53 * This beam was loaded to failure starting at Pmin

Table B7 Ultimate Load Cycle For Beam RD2 Load P Moment at Deflection Crack width Curvature midspan (Kip) (Kip-in) (inch) (mm) (inlx104) 0.00 0.00 0.18 0.04 2.20 39.60 0.23 0.05 4.41 79.38 0.31 0.08 7.71 138.78 0.43 0.12 - 9.91 178.38 0.51 0.14 -- _. 12.11 217.98 0.58 0.17 - 13.77 247.86 0.64 0.19 16.08 289.44 0.77 0.35 16.47 296.46 0.95 0.56 - 17.20 309.60 1.76 -

Table B8 Ultimate Load Cycle For Beam RD3 Load P Moment at Deflection Crack width Curvature midspan (Kip) (Kip-in) (inch) (mm) (in-x1o4) 0.00 0.00 0.16 0.02 2.50 45.00 0.21 0.02 5.00 90.00 0.27 0.04 - 7.50 135.00 0.33 0.07 - M 10.00 180.00 0.39 0.09 12.50 225.00 0.45 0.11 -' 17.50 315.00 0.56 0.14 21.25 382.50 0.67 0.17 22.50 405.00 0.71 0.18 24.70 444.60 0.85 0.35 -

TABLE IS 04 r^ Tp oBeam Designation: PS1 f'V at time of loading = 5570 Psi ~Type of Loading: Static Effective prestress, fpe 169.0 Ksi ~~~0 ~Reinforcing steel = -- Prestressing steel = 1 3/8"-270 Ksi Stress in the Tension Reinforcement(c): fe =E E. E...(Es.29xl03 Ksi) (a) Note: 1,2,3, etc. are the locations of strain gages. fps Ep.p. (Ep=28.6xIO Ksi) (b) Load Moment Stress in Reinforcing Bar Increase in stress in the prestressed Deflection Crack Curvature P at fo(ksi) Strand fps (ksi) (in) width (mm) (kips) Mid-span ____________ (L.V.D.T. x104 ______ (k-in) -- - Average 1 - - Average reading) (rad/in) 0.25 4.50 - - - 0.26 - - 0.26 0.002 0.000 0.02 0.75 13.50 - - -0.46 - - 0.46 0.004 0.000 0.07 1.50 27.00 - - -0.94 - - 0.94 0.021 0.001 0.15 (A) 2.00 36.00 - - -1.23 - - 1.23 0.029 0.001 0.21 2.50 45.00 - - - 1.56 - -- 1.56 0.037 0.003 0.27 3.00 54.00 - - - 1.90 - -1.90 0.046 *.0.003 0.33 3.50 63.00 - -- 2.33 - - 2.33 0.055 0.006 0.40 3.75 67.50 -- 2.72 - - 2.72 0.06 0.012 0.46 4.00d 72.00 - - - 5.03 - - 5.03 0.073 0.038 0.62 4.50 81.00 - - - 13.00 - -13.10 0.119 0.103 1.03 a) e 9 = Reading of one strain gage on each reinforcing bar, as numbered, at mid-sp'an. Adjusted to account for initial prestrain. b) e p = Average reading of two or three strain gages on each strand at mid span. c) In the non linear range, the stress is obtained directly from the actual stress strain curves of the tension reinforcemnent. d) Onset of cracking.

TABLE 1S (CONTINUED) Load Moment Stress in Reinforcing Bar Increase in stress in the prestressed Deflection Crack Curvature P at fs(ksi) Strand fps (ksi) (in) width (mm) (kips) Mid-span _________ (L.V.D.T. x0 ______ (k-in) -- -- Averae 1 -- -- Average ____reading) (rad/in) 4.75 85.50 - - - 17.46 - - 17.46 0.145 0.144 1.29 5.00 90.00 - - - 28.00 - - 28.00 0.184 0.256 1.97 5.50 99.00 - - - 42.80 -- - 42.80 0.292 0.464 3.19 6.00 108.00 - - - 54.50 - -- 54.50 0.405 0.683 4.46 6.50 117.00 - - - 66.30 66.30 0.556 0.885 5.65 7.00 126.00 - - - 73.40 - -- 73.40 0.706 1.084 6.85 7.40 133.20 - - - 82.80 - - 82.80 0.843 1.280 8.03 7.92 142.56 - -- - 90.40 - -90.40 1.258 1.920. 11.37 1 * 8.18 147.24 - - - 99.60 - - 99.60 1.560 2.360 13.58 f- Strain gage failed. N.A depth at ultimate 0.75" y- Yielding of Reinforcing steel.

TABLE 2S Beam Designation: PS2 Vc at time of loading = 5300 Psi I 2 w Type of Loadings Static Effective prestress, fpe - 137.0 Ksi 0 0 Reinforcing steel = -- Prestressing steel - 2 3/8*'-270 Ksi Stress in the Tension Reinforcementc) f " ElCa-4.0(E5.a29x103Ksi) (a) Note: 1.2,3, etc. are the locations of strain gages. fps EpC.p. (Ep28.6xIO Ksi) (b) Load Moment Stress in Reinforcing Bar Increase in stress in the prestressed Deflection Crack Curvature P at fa(ksi) Strand Afps (ksi) (in) width (mm) (kips) Mid-span _________ (L.V.D.T. xl04 (k-in) - - Average 1 2 Average _________ reading) (rad/in) 0.55 9.90 - - - 0.24 0.13 - 0.18 0.007 0.000 0.04 1.10 19.80 - - - 0.58 0.43 - 0.51 0.016 0.000 0.06 2.20 39.60 - - - 1.24 0.93 - 1.08 0.036 0.000 0.15 3.30 59.40 - - - 2.02 1.67 - 1.85 0.057 0.000 0.37 4.40 79.20 - - - 2.95 2.57 - 2.76 0.080 0.008. 0.57 5.50 99.00 - - - 4.50 3.98 - 4.24 0.108 "0.024 0.80 6.06 109.08 - - - 7.36 6.68 - 7.02 0.127 1.0.053 1.03 6.61d 118.98 - - - 11.53 10.83 -- 11.18 0.160 0.091 1.33 7.16 128.88 - - - 15.59 15.24. - 15.42 0.192 0.135 1.69 7.71 138.78 - - - 22.49 22.99 - 22.74 0.240 0.222 2.27 a) E. = Reading of one strain gage on each reinforcing bar, as numbered, at mid-span. Adjusted td account for initial E prestrain. b) p = Average reading of two or three strain gages on each strand at mid span. c) In the non linear range, the stress is obtained directly from the actual stress strain curves of the tension reinforcement. d) Onset of cracking.

TABLE 2S (CONTINUED) Load Moment Stress in Reinforcing Bar Increase in stress in the prestressed Deflection Crack Curvature P at fa(ksi) Strand Af's (ksi) (in) width (mm) (kips) Mid-span _______ (L.V.D.T. xl04 (k-in) Average 1 2 -- Average reading) /n 8.81 158.58 - - - 38.07 39.77 - 38.92 0.383 0.465 3.89 9.36 168.48 - - - 45.93 48.28 -- 47.10 0.477 0.592 4.77 10.46 188.28 - - - 60.60 63.50 - 62.10 0.674 0.909 6.55 11.01 198.18 - - - 68.20 70.60 - 69.40 0.784 1.069. 7.67 11.67 210.06 - - - 77.60 83.50 - 80.60 0.928 1.275 8.91 0n 12.66 227.88 - - - 94.10 98.80 -- 96.40 1.041 1.637 11.24 13.22 237.96 - - - 103.50 108.20 - 105.90 1.194 - 13.32 13.92 250.56 - - - 111.70 116.40 - 114.10 1.520 -- 15.30 f- Strain gage failed. N.A depth at ultimate - y- Yielding of Reinforcing steel.

TABLE 3S in C =l {n Beam Designations PS3 f'c at time of loading - 5730 Psi ol --- Type of Loadings Static Effective prestress, fpe - 136.0 Ksi 02 --- Reinforcing steel - -- 03 --------- Prestressing steel - 3 3/8"-270 Ksi Stress in the Tension Reinforcement(c), f, - ESa...(E,=29xl03 Ksi) (a) Notes 1,2,3, etc. are the locations of strain gages. fps - Ep p. (Ep=28.6x103 Ksi) (b) Load Moment Stress in Reinforcing Bar Increase in stress in the prestressed Deflection Crack Curvature P at fs(ksi) Strand A fps (ksi) (in) width (mm) (kips) Mid-span ____ (L.V.D.T. x0-4 _____ (k-in) -_ - Average 1 2 3 Average reading) (rad/in) 0.63 11.34 -- -- 0.09 0.27 0.51 0.29 0.007 0.001 0.02 2.50 45.00 - -- -- 0.09 1.30 2.43 1.27 0.034 0,.002 0.20 3.75 67.50 - - - 0.17 2.12 3.85 2.05 0.054 0.003 0.34 5.00 90.00 - -- - 0.31 2.87 5.26 2.81 0.073 0.005 0.49 6.25 112.50 - -- 0.37 3.69 6.75 3.60 0.094 0.006 0.04 7.50 135.00 -.. - 0.51 4.69 8.62 4.61 0.117 0.009 0.82 8.13 146.34.- - 0.69 5.73 10.50 5.64 0.131.b18 0.94 8.75d 157.50 - -- -- 1.20 8.22 14.24 7.89 0.150 0*,044 1.14 9.38 168.84 - -- -- 2.40 11.78 18.20 10.79 0.178 0.073 1.36 10.00 180.00 - - -- 4.75 17.13 23.18 15.02 0.213 0.114 1.66 a) E = Reading of one strain gage on each reinforcing bar, as numbered, at mid-span. Adjusted to account for initial prestrain. b) ~ p = Average reading of two or three strain gages on each strand at mid span. c) In the non linear range, the stress is obtained directly from the actual stress strain curves a& the tension reinforcement. d) Onset of cracking.

TABLE 3S (CONTINUED) Load Moment Stress in Reinforcing Bar Increase in stress in the prestressed Deflection Crack Curvature P at fs(ksi) Strand A fps (ksi) (in) width(mm) (Kips) Mid-span _ (L.V.D.T x0-4 (k-in) -- _ Average 1 2 3 Average ___reading) (rad/in) 10.63 191.34 -- -- -- 8.35 21.96 28.87 19.73 0.253 0.166 2.03 11.25 202.50 --- -- -- 11.55 26.97 34.76 23.43 0.300 0.222 2.44 12.50 225.00 - - --- 21.91 37.51 49.06 36.16 0.404 0.362 3.43 13.75 247.50 --- -- -- 32.32 47.76 64.00 48.03 0.522 Q. 506 4.41 15.00 270.00 -- -— _ -- 42.30 56.94 80.50 59.90 0.665 0.665 5.50 WJ 15.88 285.84 --- --- -- 48.93 65.18 88.70 67.60 0.771 0.780 6.31 16.25 292.50 --' -- 51.77 71.10 91.10 71.30 0.820 0.830 6.66 16.75 301.50 -- -- -- 54.60 75.80 96.40 75.60 0.892 0.901 717 18.18 327.24 -- -- -- 65.80 88.70 108.70 87.70 1.120 1.116 8.70 19.00 342.00 --- --- --- 71.10 96.90 114.60 94.20 1.372, —- 10.40 f- Strain gage failed. N.A depth at ultimate 2.0" y- Yielding of reinforcing steel.

TABLE 4S * a to Xoe oBeam Designations PP2S1 f'c at time of loading - 6576 Psi o3 — Type of Loadings Static Effective prestress, fpe a 165.0 Ksi * * -- - Reinforcing steel = 2#2-60 Ksi 1 2 Prestressing steel = 1 5/16"-250 Ksi Stress in the Tension Reinforcement(c): ffs = Eseas.. (Ea=29x10 J Ksi) (a) Note: 1,2,3, etc. are the locations of strain gages. fps = Epcp...(Ep=28.0 xl03 Ksi) (b) Load Moment Stress in Reinforcing Bar Increase in stress in the prestressed Deflection Crack Curvature P at fa(ksi) Strand A fps (ksi) (in) width (mm) (kips) Mid-span (L.V.D.T. x10-4 (k-in) 1 2 Average 3 -- Average _reading) (rad/in) 0.50 9.00 -5.51 -5.51 -5.51 0.18. 0.18 0.005 0.000 0.03 1.00 18.00 -4.84 -4.67 -4.76 0.49 --- -- 0.49 0.012..0.001 0.09 1.75 31.50 -3.19 -2.52 -2.87 1.12 --- -- 1.12 0.024 0.005 0.19 2.25 40.50 -1.67 -0.66 -1.17 1.57 -- -- 1.57 0.033 0.009 0.27 2.50 45.00 -0.72 0.41 -0.16 1.86. — --- 1.86 0.038 0.012 0.31 0D 3.00 54.00 3.48 5.46 4.47 3.07 --- -- 3.07 0.049 0.027 0.44 3.25d 58.50 11.28 14.01 12.65 5.83 —. -- 5.83 0.060 |.053 0.61 3.50 63.00 17.08 19.69 18.39 8.04 --- --- 8.04 0.069,-0.074 0.76.00 72.00 27.81 31.70 29.76 12.75 - _ __ 12.75 0.100 0.117 1.05 4.50 181.00 137.94 41.62 39.78 17.05. — --- 17.05 1 0.142 0.157 1.33 a) e s = Reading of one strain gage on each reinforcing bar, as numbered, at mid-span. Adjusted to account for initial prestrain. h) ~ p = Average reading of two or three strain gages on each strand at mid span. + c) In the non linear range, the stress is obtained directly from the actual stress strain curves Of the tension reinforcement. d) Onset of cracking.

TABLE 4S (CONTINUED) Load Moment Stress in Reinforcing Bar Increase in stress in the prestresaed Deflection Crack Curvature P at fs(ksi) Strand A fps (kai) (in) (Vidth(mm) (kips) Mid-span ___(L.V..T. xL*4 _____ (k-in) 1 2 Average a -- -- Average reading) (rad/in) 5.00 90.00 47.71 51442 49.57 20.96 ---- 20.96 0.187 0.195 1.59 5.50 99.00 58.76 62.73 60.75 25.59 --- --- 25.59 0.239 0.242 1.90 6.25Y 112.50 68.00 68.00 68.00 35.00 --- --- 35.00 0.354 0.351 3.34 6.50 117.00 78.00 f 78.00 55.70 --- -- 55.70 0.433 0.661 5.07 7.00 126.00 f - - 72.90 --- --- 72.90 0.696 1.046 7.24 7.90 142.20 -- - -- 92.90 --- -- 92.90 1.817 1.800 24.92 8.20 147.60 - -- 94.00 --- --- 94.00 2.700 --- 30.73 8.40 151.20 - - - 94.50 -- --- 94.50 4.000 --.. 35.24 f- Strain gage failed N.A depth at ultimate = 0.75" y- Yielding of reinforcing steel.

TABLE 5S in a cw ao dBeam Designation: PP2S2 f'c at time of loading = 5290 Psi o3 - Type of Loading Static Effective prestress, fpe - 167.0 Ksi 0 0 ---— ~- Reinforcing steel = 3#2-60 Ksi 1 2 Prestressing steel -e 1 3/8'-270 Ksi Stress in the Tension Reinforcement4c i f = Eaes... (E529x1O3 Ksi) (a) Note: 1.2.3. etc. are the locations of strain gages. fps =.Epcp*. (Ep.28.6xlO3 Ksi) (b) Load Moment Stress in Reinforcing Bar Increasein stress in the prestressed Deflection Crack Curvature P at f,(ksi) Strand A fp (ksi) (in) width (mnm) (kips) Mid-span _________(L.V.D.T. (k-in) 1 2 Average 3 Average reading)' (rad/in) 0.63 11.34 -9.87 -9.87 -9.87 0.30 --- -- 0.30 0.007 0.000 0.04 1.25 22.50 -8.74 -8.65 -8.70 0.72 -- -- 0.72 0.018 0.000, 0.12 1.88 33.84 -7.52 -7.41 -7.47 1.16 --- --- 1.16 0.029 0.002 0.21 3.13 56.34 -4.33 -4.19 -4.26 2.27 --- -- 2.27 0.053 0.011 0.41 3.75 67.50 0.08 1.03 0.56 3.92 -- -- 3.92 0.069 Q.029 0.57 4.38d 78.84 5.47 7.39 6.43 6.88 -- --- 6.88 0.090 0.054: 0.80 5.00 90.00 10.98 13.53 12.26 11.50 --- --- 11.50 0.122 *P.083 1.12 6.25 112.50 24.03 26.87 25.45 20.46 --- --- 20.46 0.219 0.150 2.09 7.50 135.00 38.97 40.85 39.91 28.97 -- -- 28.97 0.324 0.221 2.98 8.75 157.50 55.90 57.60 56.75 41.92 --- --- 41.92 0.453 0.350 4.12 a),s = Reading of one strain gage on each reinforcing bar, as numbered, at mid-span. Adjusted to'account for initial prestrain. 1) Ep = Average reading of two or three strain gages on each strand at mid span. c) In the non linear range, the stress is obtained directly from the actual stress strain curveS-`ef the tension reinforcement..) Onset of cracking.

TABLE 5S (CONTINUED) Load Moment Stress in Reinforcing Bar Increase in stress in the prestressed Deflection Crack Curvature P at fs(ksi) Strand A fps (ksi) (in) width(mm) (kips) Mid-span P (L.V.D.T. x10-4 (k-in) 1 2. Average 3 - — _ Average |.reading) (rad/in) 9.38Y 168.84 f 68.00 68.00 58.38 --- --- 58.38 0.568 0.590 5.75 10.08 181.44 --- f --- 72.50 --- -- 72.50 0.758 0.778' 7.48 10.83 194.94 --- --- --- 83.70 1 83.70, 1.006 0.996 9.74 11.23 202.14 -- -- --- 86.60 --- -- 86.60 1.162 1.153, 11.26 11.58 208.44 ---. ---. —- 91.30 ---- 91.30 1.447 1.424' 14.14 - 11.60 208.80 --- --- --- 94.80 --- --- 94.80 1.760 1.605 16.18, f- Strain gage failed N.A depth at ultimate = 2.50" y- Yielding of reinforcing steel.

TABLE 6S Q 3 4' oo Beam Designation: PP2S3 fc at time of loading = 6200 Psi o o -- Type of Loading: Static Effective prestress, fpe 133.0 Ksi * ---- Reinforcing steel = 2#3-60 Ksi 1 2 1 Prestressing steel = 2 3/8"-270 Ksi Stress in the Tension Reinforcement(c): fs =E Eg...(Es=29x103 Ksi) (a) Note: 1,2,3, etc. are the locations of strain gages. fps = Ep...(Ep=28.6x103 Ksi) (b) Load Moment Stress in Reinforcing Bar Increase in stress in the prestressed Deflection Crack Curvature P at fa(ksi) Strand A fps (ksi) (in) width (mm) (kips) Mid-span ____________ _______________ (L.V.D.T. x104 _____ (k-in) 1 2 Average 3 4 Average reading) (rad/in) 0.63 11.34 -12.81 -12.89 -12.85 0.00 0.37 -- 0.35 0.006 0.000 0.04 1.25 22.50 -11.97 -12.20 -12.09 0.66 0.61 -- 0.64 0.015 0.000 0.10 2.50 45.00 -10.14 -10.27 -10.27 1.42 1.33 -- 1.38 0.035 0.004 0.27 3.75 67.50 -7.88 -8.08 -7.98 2.20 2.16 --- 2.18 0.056 0.009 0.44 I GJ 5.00 90.00 -4.08 -4.60 -4.34 3.42 3.35 -- 3.39 0.079 0.020: 0.63 5.63 101.34 -0.13 -0.89 -0.51 4.72 4.73 -- 4.73 0.093 V0.034 0.77 6.25d 112.50 4.10 5.20 4.65 6.88 6.98 --- 6.93 0.111 0.052 0.95 7.50 135.00 10.50 11.44 10.97 11.31 11.90 -- 11.61 0.156 0.084 1.21 8.75 157.50 19.12 19.76 19.44 17.42 15.72 — 16.57 0.217 0.127 1.62 10.00 180.00 27.35 29.30 28.33 23.27 21.44 -- 22.36 0.297 0.162 2.35 a) cQ = Reading of one strain gage on each reinforcing bar, as numbered, at mid-span. Adjusted"'o account for initial prestrain. b) p = Average reading of two or three strain gages on each strand at mid span. c) In the non linear range, the stress is obtained directly from the actual stress strain curves of the tension reinforcement. d) Onset of cracking.

TABLE 6S (CONTINUED) Load Moment Stress in Reinforcing Bar Increase in stress in the prestressed Deflection Crack Curvature P at fs(ksi) Strand Afps (ksi) (in) width mm) (kips) Mid-span- L.V.D.T. xl0-4 l (k-in) 1 F 2 Average 4 i -- Averagel. reading) (rad/in) 12.50 225.00 47.28 50.88 49.08 35.98 34.38 --- 35.18 0.461 0.222 3.84 13.75 247.50 57.46 62.10 59.78 42.47 41.34 --- 41.91 0.545 0.254 4.52 15.00 270.00 68.37 73.57 70.97 49.44 48.19 --- 48.82 0.637 0.288 5.08 16.25Y 292.50 f f --- 59.90 53.40 --- 56.70 0.735 0.355 5.97 16.88 303.84 --- --- --- 68.70 66.40 --- 67.50 0.824 0.471 6.80 - 17.45 314.10 -- --- --- 80.50 78.10 --- 79.30 0.990 --- 8.16 18.60 334.80 --- --- -- 97.60 95.20 --- 96.40 1.156 --- 9.88 19.50 351.00 -- -- -- 110.50 110.80 --- 110.60 1.401 --- 11.84 20.00 360.00 --- -- 116.40 116.80 --- 116.60 1.580 |'- 13.26 f- Strain gage failed N.A depth at lultimate = 3.25" y- Yielding of reinforcing steel.

TABLE 7S * * 0 2#3 in 3 o 3 o Beam Designations PPlS1 f' at time of loading - 6040 Pat o --- Type of Loadings Static Effective prestress, fpe - 164.0 Ksi * * * ----- Reinforcing steel = 3#3-60 Ksi 1 2 Prestressing steel a 1 5/16"-2 50 Ksi Stress in the Tension Reinforcement(C): fs = Ee s... (Es=29xlOJ Ksi) (a) Note: 1,2,3, etc. are the locations of strain gages. fps - EpCp...(Ep"28.0x103 Ksi) (b) Load Moment Stress in Reinforcing Bar Increase in stress in the prestressed Deflection Crack Curvature P at fs(ksi) Strand A fps (ksi) (in) width (mm) (kips) Mid-span (L.V.D.T. x10-4 ____ (k-in) 1 2 Average 3 - - Average __reading) (rad/in) 0.63 11.34 -5.85 -5.70 -5.78 0.20 --- -- 0.20 0.007 0.001 0.05 1.88 33.84 -3.67 -3.50 -3.59 0.98 --- --- 0.98 0.026 0.005 0.19 3.13 56.34 -0.89 0.10 -0.40 2.14 --- -- 2.14 0.055 0.015 0.37 3.75 67.50 1.66 3.81 2.74 3.18 --- -- 3.18 0.064 0.028 0.48 4.38d 78.84 5.43 9.93 7.68 5.35 -- --- 5.35 0.084 0.044'. 0.70 U1 5.00 90.00 9.29 15.03 12.16 7.55 --- - 7.55 0.110 0.05 0.94 6.25 112.50 19.85 23.44 21.65 12.05 -- --- 12.05 0.184 0.088 1.64 7.50 135.00 29.62 33.21 31.42 16.28 --- --- 16.28 0.257 0.120 2.25 8.75 157.50 39.68 42.90 41.29 20.65 -- --- 20.65 0.333 0.150 2.77 10.00 180.00 49.77 52.35 51.06 24.93 --- -- 1 24.93 0.407 0.180. 3.32 a) Cs = Reading of one strain gage on each reinforcing bar, as numbered, at mid-span. Adjusted to account' for initial prestrain. h) ~p = Average reading of two or three strain gages on each strand at mid span. c) In the non linear range, the stress is obtained directly from the actual stress strain curves of the tension reinforcement. d) Onset of cracking.

TABLE 7S (CONTINUED) Load Moment Stress in Reinforcing Bar Increase in stress in the prestressed Deflection Crack Curvature P at f,(ksi) Strand A fps (ksi) (in) width(mm) (kips) Mid-span - pk (L.V.D.T. xlO-4 (k-in) 1 2 Average 3 4 -- Average reading) (rad/in) 11.25 202.50 59.72 61.40 60.56 27.38 --- -- 27.38 0.482 0.208 3.87 13.13Y 236.34 76.63 77.16 76.90 30.83 - --- 30.83 0.600 0.255 4.78 13.55 243.90 77.00 77.50 77.25 46.34 -- --- 46.34 0.661 0.480 6.22 14.18 255.24 80.00 80.00 80.00 60.14 --- -- 60.14 0.868 0.661 9.16 14.88 267.84 81.80 f 81.80 77.40 --- --- 77.40 1.489 0.861 16.11 I_ 15.27 274.86 83.20 --- 83.20 82.60 --- -- 82.60 2.060 0.955 20.42 15.68 282.24 f -- --- 86.00 --- --- 86.00 2.520 1.142 24.40 15.88 285.84 --- -- 89.10 89.10 2.880 --- 26.31 16.28 293.04 --- --- 92.40 -- -- 92.40 3.780- 32.84 [ I I I I J:21.401 1 1'-9 - 32.84 f-.Strain gage failed N.A depth at ultimate = 0.75" y- Yielding of reinforcing steel.

TABLE 8S N 3 o Beam Designation: PP1S2 f'c at time of loading - 5800 Psi o -Type of Loading: Static Effective prestress, fpe 160.0 Ksi - ---- Reinforcing steel = 2#4-60 Ksi 1I 2 Prestressing steel = 1 5/16"-250 Ksi Stress in the Tension Reinforcement(c): fs= EaCa"..(E5=29xl03 Ksi) (a) Note: 1,2.3, -etc. are the locations of strain gages. fps Epp... (Ep28.0xl03 Ksi) (b) Load Moment Stress in Reinforcing Bar Increase in stress in the prestressed Deflection Crack Curvature P at fs(ksi) Strand A fp (ksi) (in) width (mm,) (kips) Mid-span _______ (L.V.D.T. x104 (k-in) 1 2 Average 3 - -- Average reading) (rad/in) 0.63 11.34 -5.90 -5.46 -5.68 0.32 -- --- 0.32 0.001 0.000 0.06 1.25 22.50 -4.74 -4.52 -4.63 0.77 -- -- 0.77 0.003 0.003 0.14 2.50 45.00 -1.89 -1.63 -1.76 1.96 -- -- 1.96 0.021 0.014 0.33 3.75d 67.50 5.87 5.45 5.66 5.27 --- --- 5.27 0.060 0.043 0.63 5.00 90.00 13.21 12.50 12.85 9.35 -- --- 9.35 0.119 0.070 1.21 6.25 112.50 20.55 19.49 20.02 13.41 -- -- 13.41 0.187 0.097 1.75'^V 7.50 135.00 27.68 25.22 26.45 17.64 --- --- 17.64 0.252 0.121 2.28 8.75 157.50 33.46 32.10 32.78 22.15 -- -- 22.15 0.301 0.145 2.81 10.00 -— ~~~~~~~~~~~~~~9.6 043.9038 10.00 180.00 40.63 38.85 39.74 26.88 -- -- 26.88 0.366 0.168 3.34 11.25 202.50 47.80 45.18 46.49 28.00 -- -- 29.66 0.433 0.190 3.87 a) s = Reading of one strain gage on each reinforcing bar, as numbered, at mid-span. Adjusted to account f~r initial prestrain. b) p = Average reading of two or three strain gages on each strand at mid span. c) In the non linear range, the stress is obtained directly from the actual stress strain curves of the tension reinforcement. d) Onset of cracking.

TABLE 8S (CONTINUED) Load Moment Stress in Reinforcing Bar Increase in stress in the prestressed Deflection Crack Curvature P at fs(kei) Strand A fs (ksi) (in) yidth(mm) (kips) Mid-span _______- _______ (L.V.D.T. x104 ______ (k-in) I 2 Average 3 - -- Average reading) (rad/in) 12.50 225.00 58.33 56.17 57.25 31.38 -- -- 31.38 0.509 0.239 4.59 13.13 236.34 63.63 f 63.63 36.55 --- -- 36.55 0.540 0.281 5.03 14.18Y 255.24 72.40 -- 72.40 50.30 -- -- 50.30 0.661 0.486 6.72 14.50 261.00 f -- -- 53.80 -- -- 53.80 0.763 0.564 7.36 15.10 271.80 -- -- -- 64.10 -- -- 64.10 0.991 0,665 9.68 15.40 277.20 --- - -- --- 67.60 --- --- 67.60 1.134 0.725 10.86 15.75 283.50 -- --- -- -- -- -- -- 1.422 -- 13.25 f- Strain gage failed N.A depth at ultimate _ 1.75 v- Yieldina of reinforcing steel.

TABLE 9S 3 in (' 3 3. * Beam Designation: PP1S3 V* at time of loading = 5998 Psi o - Type of Loading: Static Effective prestress, fpe = 147.0 Ksi *. ------ Reinforcing steel = 3#4-60 Ksi 1 2 Prestressing steel - 1 3/8"-270 Ksi Stress in the Tension Reinforcementc: f5 ECe,.**(E,=29xlO3 Ksi) (a) Note: 1,2,3. etc. are the locations of strain gages. fps - Epvpe... (Ep28.6xl03 Ksi) (b) Load Moment Stress in Reinforcing Bar Increase in stress in the prestressed Deflection Crack Curvature P at fa(ksi) Strand Afps (ksi) (in) width (mm) (kips) Mid-span _______ _______ (L.V.D.T. xl04 (k-in) 1 2 Average 3 — Average reading) (rad/in) 0.55 9.90 -6.68 -6.56 -6.62 0.24 --- --- 0.24 0.007 0.000 0.01 1.10 19.80 -6.04 -5.81 -5.93 0.44 --- --- 0.44 0.016 0-.000 0.07 2.20 39.60 -4.42 -3.90. -4.16 1.17 -- -- 1.17 0.034 0.008 0.26 3.30 59.40 -2.01 -1.84 -1.93 2.17 --- --- 2.17 0.058 0.018 0.48 4.41 79.38 1.15 1.59 1.37 4.09 --- --- 4.09 0.087 0.031 0.76 5.51d 99.18 4.92 5.82 5.37 6.52 -- -- 6.52 0.121 0.046 1.11 6.61 118.98 9.30 10.02 9.66 9.41 --- --- 9.41 0.165 0.061 1.S1 7.71 138.78 13.79 14.75 14.27 13.03 --- --- 13.03 0.213 0.078 1.94 8.81 158.58 17.62 19.01 18.32 15.79 -- 15.79 0.260 0.092 2.37 10.46 188.28 23.86 25.86 24.86 20.25 } --- 20.25 0.332 0.113 2.91 a) cQ Reading of one strain gage on each reinforcing bar, as numbered, at mid-span, Adjusted to account fow initial prestrain. b) Ep = Average reading of two or three strain gaqes on each strand at mid span. c) In the non linear ranqe, the s.tress is obtained directly from the actual stress strain curves of the tension reinforcement. d) Onset of cracking.

TABLE 9S (CONTINUED) Load Moment Stress in Reinforcing Bar Increase in stress in the prestressed Deflection Crack Curvature P at fe(ksi) Strand A fp (ksi) (in) yidth(mm) (kips) Mid-span __(L__o.V.I *T0o4 (k-in) 1 -- 2 Average 3 — _ -- Average _________ reading) (rad/in) 12.66 227.88 32.91 35.78 34.35 26.11 --- -- 26.11 0.430 0.135 3.71 14.87 267.66 42.21 45.29 43.75 31.75 --- 31.75 0.535 0.158 4.56 16.52 297.37 49.03 51.49 50.26 35.74 -- -- 35.74 0.615 0.173 5.18 17.62 317.16 53.84 55.99 54.92 38.42 -- -- 38.42 0.674 0.183 5.64 18.72 336.96 58.51 60.60 59.56 41.17 --- --- 41.17 0.732 0.194 6.10 19.82Y 356.76 68.50 67.10 67.80 44.10 --- 44.10 0.799 0.211 7.76 20.92 376.56 68.50 67.10 67.80 66.40 --- -- 66.40 1.030 0.443 9.50 21.34 384.12 68.50 67.10 67.80 74.70 --- 74.70 1.217 --- 10.92 f- Strain gage failed N.A depth at ultimate --- y- Yielding of reinforcing steel.

TABLE 10S o |o a|p oBeam Designation: RS1 f'c at time of loading - 5940 Psi Type of Loadings Static Effective prestress, fpe --- Ksi * * * --- Reinforcing steel = 3#3-60 Ksi 1 2 1 Prestressing steel --- Stress in the Tension Reinforcement(c)s f E Eses... (Es=29xl0 Ksi) (a) Notes 1,2,3, etc. are the locations of strain gages. fps - Ep6p...(Ep=28.6x0O3 Ksi) (b) [Load Moment Stress in Reinforcing Bar Increase in stress in the prestressed Deflection Crack Curvature P at fs(ksi) Strand A fps (ksi) (in) width (mm) (kips) Mid-span (L.V.D.T. x10-4 ____ (k-in) 1 2 Average -- -- -- Average____ reading) (rad/in) 0.95 17.10 2.26 f 2.26 - -- --- -- 0.006 0.005 1.57 28.62 5.08 --- 5.08 --- --- - -- 0.026 0.013, d 2.26 40.68 8.90 --- 890 --- --- --- 0.056 0.032 2.67 48.06 11.46 --- 11.46 -- --- - -- 0.074 0.035 3.19 57.42 14.94 --- 14.94 -- -- - --- 0.091 0.044 -- 3.56 64.08 16.85 --- 16.85 --- -- ------ 0.114 0.051 4.45 80.10 21.98 --- 21.98 --- -- --- --- 0.156 f-.067 __ 5.33 95.94 27.00 -- 27.00 --- --- --- -- 0.198 0.083 0 6.00 108.00 31.46 --- 31.46 --- -- --- --- 0.231 0.102 6.61 118.98 35.00 --- 35.00 -- - --- --- 0.261 0.114 --- a) E, = Reading of one strain gage on each reinforcing bar, as numbered, at mid-span. Adjusted to account for initial prestrain. b) ~p = Average reading of two or three strain gages on each strand at mid span. c) In the non linear range, the stress is obtained directly from the actual stress strain curves'df the tension reinforcement. d) Onset of cracking.

TABLE 10S (CONTINUED) Load Moment Stress in Reinforcing Bar Increase in stress in the prestressed Deflection Crack Curvature P at fS(kti) Strand A fps (ksi) (in) Width(mm) (kips) Mid-span f(si (L.V.-.T. x104 ______ (k-in) 1 2 Average -- -- _ —Average _________ reading) (rad/in) 7.05 126.90 37.85 -- 37.85 --- --- - -- --- 0.291 0.127 7.93 142.74 43.82 --- 43.82 --- --- --- --- 0.337 0.145 8.46 152.28 47.45 -- 47.45 -- -- -- -- 0.369 0.152, 8.81 158.58 49.90 --- 49.90 --- -- - -- 0.392 0.165 9.91Y 178.40 f -- --- --- --- -- 0.584 --- -- 10.66 191.88 ---- - -- --- --- 1.605 10.79 194.22 -- - --- --- --- --- -- 2.135 -- 11.34 204.12 -- -- -- -- -- --- --- 2.707 ) -- f- Strain gage failed N.A depth at ultimate -- y- Yielding of reinforcing steel.

TABLE US co Tp aiBeam Designationt RS2 f'c at time of loading - 7000 Psi Type of Loading: Static Effective prestress, fpeKi * * * -Reinforcing steel = 3#4-60 Ksi 1 2 Prestressing steel S -- Stress in the Tension Reinforcement(c)i f= E.es...(E,=29xlO Ksi) (a) Note: 1.2,3, etc. are the locations of strain gages. fps Epep...(Ep=28.6x103 Ksi) (b) Load Moment Stress in Reinforcing Bar Increase in stress in the prestressed Deflection Crack Curvature P at fe(kai) Strand Afp (ksi) (in) width (mm) (kips) Mid-span ____________ (L.V.D.T. xl4 (k-in) 1 2 Average - - - Average reading)' (rad/in) 1.28 23.04 2.97 2.57 2.77 -- -- --- --- 0.021 0.006 0.17 2.31 41.58 4.92 4.37 4.65 - -- - -- - -- 0.039 0.013 0.30 3.63d 65.34 10.25 9.12 9.69 -- -- ----- 0.069 0.032 0.60 4.69 84.42 15.01 14.17 14.59 -- --- --- --- 0.113 0.051 0.97 01 5.64 101.42 19.27 18.34 18.81 --- -- --- --- 0.156 0.070 1.33 6.70 120.60 23.33 22.81 23.07 -- -- --- --- 0.202 0.083 1.70 8.00 144.00 28.55 28.49 28.52 --- --- --- -- 0.259 0-.102 2.16 10.35 186.30 38.38 38.85 38.62 --- --- --- --- 0.362.0.127 2.95 11.76 211.68 44.18 44.70 44.44 -- -- — 0.423 0.146 3.42 13.26 238.68 50.04 50.77 50.41 -- --- -- --- 0.489 0.165 3.91 a) E = Reading of one strain gage on each reinforcing bar, as numbered, at mid-span. Adjusted to account for initial prestrain. b) ~p - Average reading of two or three strain gages on each strand at mid span. c) In the non linear range, the stress is obtained directly from the actual stress strain curveS-bf the tension reinforcement. d) Onset of cracking.

TABLE US (CONTINUED) Load Moment Stress in Reinforcing Bar Increase in stress in the prestressed Deflection Crack Curvature P at fs(ksi) Strand A fps (kai) (in) Yidth(mmn) (kips) Mid-span L...T. xl04 (k-in) 1 2 Average A — -- Average reading) (rad/in) 14.67 264.06 55.78 56.51 56.15 --- 0 —- - -- 0.552 0.184 4.40 15.51 279.18 59.52 60.34 59.93 -- - --- -- 0.594 0.200 4.70 16.17Y 291.06 62.80 63.81 63.30 --- -- --- --- 0.620 0.211 4.89 16.39 295.02 62.80 63.81 63.30 -- -- --- --- 0.883 0.330'13.64 17.27 310.86 f f --- - -- --- --- 1.167 18.50 (1.rf. 18.00 324.00 -- --- --- --- --- --- --- 2.160 -- 22.00 f- Strain gage failed N.A depth at ultimate --- y- Yielding of reinforcing steel.

TABLE 12S oope ofBeam Designation: RS3 fc at time of loading = 7000 Psi Type of Loading: Static Effective prestress, fp Ksi * * * -- Reinforcing steel - 3#5-60 Ksi 1 _2 Prestressing steel - --- Stress in the Tension Reinforcement(c): fa Es Eae..*.(E=29x103 Ksi) (a) Notes 1,2,3, etc. are the locations of strain gages. fps pEp *(Ep.28.6xl03 Ksi) (b) Load Moment Stress in Reinforcing Bar Increase in stress in the prestressed Deflection Crack Curvature P at f5(ksi) Strand A fps (ksi) (in) width (mm) (kips) Mid-span _______(L.V.D.T. x04 (k-in) 1 2 Average -- - Average _________ reading) (rad/in) 1.32 23.76 -0.24 0.49 0.13 -- --- --- --- 0.018 0.003 0.12 2.42 43.56 0.17 1.07 0.62 -- -- -- -- 0.038 0.009 0.30 3.31 59.58 2.17 3.36 2.77 --- -- --- --- 0.058 0.019 0.47 I-i 4.18 75.24' 4.17 5.88 5.03 --- --- --- — 0.077 0.031 0.65 1 01 5.07d 91.26 7.07 8.67 7.87 -- -- -- -- 0.107 0.044 0.87 5.90 106.20 9.40 11.30 10.35 --- --- -- — 0.126' 0.054 1.07 7.53 135.54 15.14 16.09 15.62 -- -- -- -- 0.175 0.070 1.42 10.22 183.96 21.00 22.18 21.59 -- -- -- -- 0.250 0.095 2.00 11.54 207.72 25.87 24.56 25.22 --- --- --- 0.290 0.109 2.30 13.22 237.96 28.77 30.65 29.71 -- -- --- 0.336 0.127 2.68 a) e = Reading of one strain gage on each reinforcing bar, as numbered, at mid-span. Adjusteito account for initial prestrain. b) Ep = Average reading of two or three strain gages on each strand at mid span. c) In the non linear range, the stress is obtained directly from the actual stress strain curves of the tension reinforcement. d) Onset of cracking.

TABLE 12S (CONTINUED) Load Moment Stress in Reinforcing Bar Increase in stress in the prestressed Deflection Crack Curvature P at fs(ksi) Strand Afps (kai) (in) width(m) (kips) Mid-span ____.. _______- P.s (L.V.D.T. xl 0-4 (k-in) 1 2 Average -- Average g _ _ reading) (rad/in) 15.95 287.10 35.96 38.48 37.22 -- - -- I --- 0.421 0.152 3.35 17.62 317.16 40.42 43.18 41.80 --- --- --- --- 0.472 0.165 3.69 19.82 356.76 46.22 49.62 47.92 --- --- - -- 1- 0.546 0.191 4.24 22.03 396.54 52.31 56.40 54.36 --- --- --- --- 0.628 1 0.210' 4.86 23.26Y 418.68 65.00 65.00 65.00 --- - --- 0.783 0.343 7.17 0 24.00 432.00 65.00 65.00 65.00 --- -- -- --- 0.958 0.622 13.60 24.67 444.06 65.00 65.00 65.00 1 --- --- - 1.244 --- 17.70,. f- Strain gage failed N.A depth at ultimate - y- Yielding of reinforcing steel.

TABLE ID Beam Designation: PD1 Stress range in the prestressing strand I Afps(maxALfps~min) Type of Loading: Dynamic (cyclic) - apsma f'c at time of loading = 5570 Psi Stress range in the reinforcing bars - fe(max-'f(min) Effective prestress, fpe = 173.0 Ksi Note: See Table IS for more details. Afps at Pmin f. at Pmin Deflection at Pmin Crack width at Curvature at Pmin and Number of & Pmax (ksi) & max (ksi) and Pmax (in) Pmin & Pmax (mm) Pmax 10 (rad/in) Remarks Cycles ____ _ N mm mminmam maxx min mamax min maxx i W x min ma 1 2.30 18.78 - - 0.053 0.152 0.031 0.144 0.44 1.43 2 11.16 20.57 - - 0.109 0.164 0.098 0.163 1.02 1.55 = 0.14 3 11.10 21.11 -- -- 0.110 0.168 0.100 0.168 1.03 1.59 PPR =1 I 01 2500 11.35 25.38 - - 0.128 0.207 0.121 0.228 1.17 1.93 Pmin 3.3 Kips 104 11.35 26.17 0- -.140 0.222 0.131 0.245 1.23 2.04 ^ Pmx 49 Kips 5x104 12.21 28.16 - - 0.147 0.245 0.134 0.266 1.49 2.39 1.6x105 12.04 28.00 - - 0.163 0.261 0.144 0.280 1.55 2.48 5.0x105 f f - -- 0.189 0.299 0.147 0.282 1.66 2.57 7.5x105 - - - - 0.199 0.318 0.157 0.308 1.75 2.76 Beam failed at 106 - - - -- 0.229 0.356 0.165 0.316 1.81 2.82 1.212x106 cycles.xO6 -- - - - 0.297 0.431 0.193 0.348 1.97 3.00

TABLE 2D Beam Designation: PD2 Stress range in the prestressing strand - Afps(max)-fps(min) Type of Loading: Dynamic (cyclic) f'c at time of loading = 5660 Psi Stress range in the reinforcing bars - fr(max)fs(min) Effective prestress, fpe = 143.0 Ksi Note: See Table 2S for more details. Afps at Pmin fs at Pmin Deflection at Pmin Crack width at Curvature at Pmin and of Pma x (ksi) & Pmax (ksi) and max in) Pmin Pax ( max x 10 (rad/in) Remarks Cycles ______ ___________m N min max min max min max Win Wmax min max kU 1 3.81 25.94 -.- 0.096 0.257 0.023 0.254 Co 2 11.90 27.32 - - 0.174 0.270 0.134 0.273 0 =0.26 3 12.00 27.97 -- 0.176 0.277 0.144 0.283 PPR P 1 2500 12.70 29.77. 0.211 0.344 0.200 0.397 Pmin:' 5.5 Kips 5000 12.70 30.00 - - 0.211 0.345 0.196 0.397 Pmax 8.37 Kips 104 13.00 31.19 - -- 0.227 0.364 0.215 0.420' 5x104 15.67 34.27 - -- 0.244 0.395 0.240 0.466 7.5x104 17.80 35.41 - -- 0.246 0.403 0.243 0.472 105 17.27 36.60 - -- 0.254 0.410 0.246 0.491 2.5x105 f f -- 0.269 0.432 0.265 0.516 5x105. — -- - 0282 0.446 0.277 0.528'. ~........,........

TABLE 2D (CONTINUED) ^fp at Pmin fs at Pmin Deflection at Pmin Crack width at Curvature at Pmin and Number of & Pmax (ksi) & Pmax (ksi) and Pmax (in) Pmin & Pmax (mm) Pmax 1 (rad/in)emark Cycles.....m N min ax min max min max Wmin Wmax min max 7.5x105 f f - -- 0.293 0.457 0.288 0.541 106 - - - -| 0.302 0.463 0.295 0.542 Beam failed at l.5x106 - -- -- - 0.314 0.474 0.299 0.546 2.2x106 cycles 2.16x106 -- -- - - 0.481 0.700 0.575 0.929 2.17x10l6 - -- -- 0.677 0.900 0.983 1.269 1~~~~~~~~~~~~~~~~~~~~~~~~ X _

TABLE 3D Beam Designations PD3 Stress range in the prestressing strand - Afpa(max)`"ps(min) Type of Loading: Dynamic (cyclic) f c at time of loading = 5730 Psi Stress range in the reinforcing bars - fs(max)'fes(min) Effective prestress, fpe = 146.0 Ksi Note: See Table 3S for more details. N fP. at Pmin f. at Pmin Deflection at Pmin Crack width at Curvature at Pmin and Nu mber of & Pmax (ksi) & Pmax (ksi) and Pmax (in) Pmin & Pmax (m) Pmax x 10-4 (rad/in) Remarks Cycles N min max min max min max Wmin Wmax min max 1 4.70 20.26 - - 0.118 0.280 0.026 0.158 0.92 2.26 2 9.37 21.93 - - 0.182 0.300 0.071 0.178 1.47 2.42 5 = 0.37 3 9.38 21.66 - - 0.186 0.301 0.073 0.178 1.50 2.42 PPR = 1 2500 10.00 23.68 - - 0.198 0.329 0.084 0.205 1.73 2.63 Pin =.5 Kips 104 1 10.20 24.02 - - 0.202 0.337 0.088 0.214 1.76 2.68 Pmax 1.5 ips 5x104 10.90 25.24 -- - 0.218 0.356 0.095 0.227 1.85 2.81. 105 11.84 26.72 - - 0.224 0.365 0.100 0.241 1.92 2.93 2.5x105 10.36 30.44 - - 0.243 0.401 0.105 0.278 2.04 3.25 7.5x105 f f - - 0.269 0.412 0.134 0.285 2.29 3.34 1.1x106 - -- - - 0.290 0.435 0.153 0.305 2.50 3.57 1.25x10 - - -- - 0.308 0.456 0.170 0.325 2.66 3.74

TABLE 3D (CONTINUED) A fps at Pmin fs at Pmin Deflection at Pmin Crack width at Curvature at Pmin and Number of & Pmax (ksi) & Pmax (ksi) and Pmax (in) Pmin & Pmax (mm) Pmax x 10- (rad/in) Remarks Cycles______ N m min mIax m max Wmin max min ma i min max 1.38xl06 - - - - 0.319 0.470 0.184 0.338 2.75 3.85 1.68x106 - - - - 0.358 0.525 0.224 0.434 3.08 4.55 Beam failed at 1.75xl106 - - ( - -- 0.386 0.556 0.476 0.70 3.61 5.05 1.94x106 cycle 1.8x106 -- -- -- -- 0.399 0.580 0.504 0.738 3.77 5.38 1.89x10 - - - - 0.469 0.669 0.662 0.944 4.59 6.71 1.93x10 - - - - 0.557 0.771 0.780 1.121 5.61 7.83 1.94x10 - - - - 0.741 0.981 1.080 -- 7.54 10.12 (n

TABLE 4D Beam Designation: PP2D1 Stress range in the prestressing strand = Afps(max)fps(min) Type of Loading: Dynamic (cyclic) f'c at time of loading = 6576 Psi Stress range in the reinforcing bars f s(max)fs(min) Effective prestress, fpe = 165.0 Ksi Note: See Table 4S for more details. Nfps at Pmin f. at Pmin Deflection at Pmin Crack width at Curvature at Pmin and Number of & Pmax (ksi) & Pmax (ki) and Pmax (in) Pmn & Pmax (m) Pmax x 10 (rad/in) Remarks Cycles _____ N min max min max min max Wmig Wmax min max 1 4.44 17.79 7.20 38.63 0.055 0.159 0.058 0.158 0.27 1.42 2 12.90 18.72 22.14 40.35 0.125 0.173 0.122 0.167 1.08 1.50 = 0.1 3 13.20 18.98 22.62 40.73 0.128 0.176 0.125 0.171 1.11 1,53 PPR 0.62 2500 14.46 21.36 22.70 42.18 0.145 0.203 0.134 0.186 1.28 1.77 Pmin; 3.2 Kip 104 15.40 22.85 22.75 40.70 0.158 0.219 0.136 0.191 1.45 1.98 Pmax ^4.8 Kips 5x104 16.46 24.43 23.89 40.99 0.175 0.233 0.139 0.195 1.57 2.15 1.5x105 14.35 22.25 21.59 38.09 0.184 0.247 0.138 0.194 1.63 2.21 3.5x105 16.83 24.85 24.86 41.20 0.196 0.257 0.146 0.204 1.73 2.31 5x105 17.56 25.55 25.85 42.34 0.202 0.263 0.148 0.205 1.78 2.34 7.5x105 17.50 25.43 26.20 42.34 0.212 0.272 0.150 0.207 1.82 3.88 106 17.92 25.91 26.74 42.98 0.217 0.278 0.153 0.211 1.87. 2.44 -

TABLE 4D (CONTINUED) Aps at Pmin fs at Pmin Deflection at Pmin Crack width at Curvature at Pmin and Number of & Pmax (ksi) & Pmax (ksi) and Pmax (in) Pmin & Pmax (mnrks Cycles ______ _______ N min max min max min max Wmin Wmax min max 1.5x106 19.60 27.45 26.45 41.74 0.231 0.295 0.150 0.198 2.25 2.90 Beam was loaded 2x106 19.48 27.67 26.55 42.21 0.241 0.303 0.151 0.206 2.35 2.99 statically to 2.5x106 21.24 29.15 28.30 43.92 0.246 0.308 0.157 0.212 2.42 3.06 failure at 2.85x106 22.19 30.17 29.35 45.06 0.250 0.311 0.160 0.214 2.46 3.10 5x106 cycles 3.25x106 22.30 30.24 29.19 45.11 0.251 0.314 0.162 0.215 2.50 3.14 3.5x106 22.99 39.92 29.97 45.85 0.256 0.316 0.164 0.217 2.52 3.16 4x106 21.48 30.03 29.20 44.79 0.262 0.321 0.161 0.215 2.55 3.19 o 4.5x106 21.20 29.24 28.11 43.90 0.267 0.326 0.158 0.212 2.58 3.21 5x106 21.52 28.55 28.00 43.05 0.267 0.327 0.161 0.214 2.61 3.24' I 1< X1 1. _ ~.j~~~~~~~......~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~'* *

TABLE 5D Beam Designation: PP2D2 Stress range in the prestressing strand = Afps(max)fps(min) Type of Loading: Dynamic (cyclic) f'I at time of loading = 5290 Psi Stress range in the reinforcing bars fs(max)-fs(min) Effective prestress, fpe = 160.0 Ksi Note: See Table 5S for more details. Afps at Pmin f. at Pmin Deflection at Pmin Crack width at Curvature at Pmin and Number 1-4 of & Pmax (kSi) & Pmax (ksi) and Pmax (in) min & PPmax C Pmax x 104 (rad/in) Remarks Cycles mxam ma()_ N min max min max min max Wmin Wmax min max 1 9.44 27.35 9.64 35.00 0.109 0.337 0.077 0.199 1.08 3.38 1 -' 2 19.02 28.38 17.31 36.07 0.244 0.351 0.148 0.207 2.45 3.51 0 0.2 3 19.53 28.70 17.89 36.48 0.249 0.356 0.150 0.209 2.50 3.57 PPR = 0.68 2500 20.87 30.61 19.20 39.55 0.27 0.389 0.162 0.217 2.68 3.79 Pn.5 Kip 5000 21.08 31.03 19.25 40.13 0.273 0.395 0.163 0.220 2.72 3.85 Pmax =7.0 Kps 104 21.55 31.56 19.72 40.66 0.277 0.400 0.166 0.224 2.76 3.90. 5x104 22.75 33.10 20.82 41.47 0.296 0.417 0.170 0.228 2.87 4.03 105 23.14 33.36 21.23 41.61 0.304 0.424 0.171 0.229 2.93 4.08 2xl05 23.44 33.71 21.28 41.50 0.312 0.435 0.171 0.231 3.00 4.16 5x105 24.63 35.12 21.89 42.13 0.328 0.449 0.172 0.234 3.09 4.28 7.5x105 25.34 35.74 22.33 42.42 0.335 0.456 0.175 0.237 3.17 4.34'i

TABLE 5D (CONTINUED) Afps at Pmin fs at Pmin Deflection at Pmin Crack width at Curvature at Pmin and Number 104 (rad/in) Re~ of & Pmax (ksi) & Pmax (ksi) and Pmax (in) Pmin & P ( max ( x 1 (rad/inRemarks Cycles _____________ N min max min max min max Wmin Wmax min max 106 25.85 36.13 22.70 42.60 0.339 0.463 0.177 0.239 3.23 4.39 1.5x106 26.38 36.81 23.23 42.74 0.351 0.475 0.177 0.244 3.30 4.50 Beam was loaded 1.75xl0 26.48 36.79 23.49 42.54 0.360 0.481 0.177 0.241 3.38 4.55 statically to 2.25x106 27.35 37.74 24.04 43.32 0.363 0.486 0.179 0.244 3.44 4.61 failure at 2.75x106 26.68 37.16 23.23 42.37 0.372 0.492 0.178 0.241 3.51 4.65 5x106 cycles 3xl06 26.79 37.05 23.28 42.25 0.376 0.496 0.179 0.243 3.55 4.68 3.5x106 26.78 37.27 23.14 42.00 0.378 0.499 0.179 0.243 3.56. 4.69 4x,6 128.02 38.4 1 24.3%9 1 43.32 10.~382 10.502 1 0. 81 10.246 31 ~.61 1 4.74C1 4xl06 28.02 38.41 24.3~ 43.32 0.382 0.502 0.181 0.246 3.61 4.74 4.5x106 30.23 39.48 27.03 45.27 0.383 0.503 0.185 0.250 3.65 4.77 5x106 31.72 41.87 28.48 46.95 0.385 0.504 0.192 0.256 3.69 4.80.~~~~~~~~~~~*. **

TABLE 6D Beam Designation: PP203 Stress range in the prestressing strand = pa(fmax)pbfps(min) Type of Loadings Dynamic (cyclic) f'0 at time of loading = 6200 Psi Stress range in the reinforcing bars fs(max)-fs(min) Effective prestress, fpe = 131.0 Ksi Note: See Table 6S for more details. Afps at Pmin f at Pmin Deflection at Pmin Crack width at Curvature at Pmin and Number of & pmax (ksi) & pmax (ksi) and Pmax (in) pnin & Pmax Pnl) max x 10"4 (rad/in) Remarks Cycles N mi.n max min max mtn max Wmin Wmax min max 1 15.32 35.25 15.04 45.12 0.201 0.459 0.108 0.234 2 23.36 36.00 23.54 45.81 0.332 0.473 0.164 0.240 * =0.36 cm 3 23.60 36.39 23.86 46.36 0.338 0.481 0.165 0.243 PPR = 0.74 2500 24.52 39.33 24.96 49.06 0.355 0.525 0.169 0.259 Pin = 8.0 Kips 5000 24.78 39.61 25.37 49.29 0.362 0.529 0.171 0.259 Pmax 12,0 Kips 104 25.07 39.90 25.77 49.67 0.368 0,535 0.174 0.261. 5x104 25.50 40.32 27.00 50.51 0.381 0.547 0.178 0.265 105 25.94 40.97 27.80 51.38 0.388 0.556 0.179 0.268 2.5x105 27.29 42.15 29.57 53.12 0.406 0.568 0.185 0.273 5x105 27.33 41.88 30.09 53.18 0.418 0.581 0.188 0.274 7.5x105 27.37 41.61 30.61 53.58 0.421 0.584 0,190 0.275 - ~~~~~~~~~~~~~~ —c —c- -~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ — — ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~~~~~~~~~

TABLE 6D (CONTINUED) Afps at Pmin fs at Pmin Deflection at Pmin Crack width at Curvature at Pmin and Number of Pmmax (ksi) & Pmax (ksi) and Pmax (in) Pmin & Pmax (mm) max x 10-4 (rad/in) Remarks Cycles........... N min max min max min max Wmin Wmax min max 106 26.07 40.71 32.76 55.55 0.434 0.596 0.186 0.272 1.25x10 25.19 39.75 31;63 55.14 0.446 0.605 0.185 0.271 Beam was loaded 1.5xl06 25.83 40.12 f f 0.452 0.613 0.188 0.274 statically to 1.75x106 25.71 39.87 - - 0.457 0.618 0.186 0.272.failure at 2x106 25.68 41.43 -- | 0.461 0.623 0.191 0.275 5x106 cycles 2.5x106 27.74 42.19 - -_ 0.471 0.632 0.194 0.278 2.75x10 28.32 42.66.- - 0.474 0.636 0.196 0.280 oh 3x106 26.15 41.09 - -- 0.480 0.640 0.193 0.277 3.25xl0 26.52 41.30 - -- 0.480 0.642 0.240 0.327 7 3.75x106 27.37 42.24 - -- 0.485 0.649 0.242 0.329. 4.25x106 28.26 42.71 -- - 0.491 0.653 0.242 0.328 4.75x106 26.52 41.22 - -_ 0.494 0.658 0.242 0.328 5x106 28.54 43.02 - -- 0.497 0.660 0.246 0.332....................

TABLE.7D Beam Designation: PPlDI Stress range in the prestressing strand - Afps(max)~^ps(min) Type of Loading: Dynamic (cyclic) f'c at time of loading = 6040 Psi Stress range in the reinforcing bars fs(max)-f(in)l Effective prestress, fpe = 164.0 Ksi Note: See Table 75 for more details. Afps at min f5 at min Deflection at Pmin Crack width at Curvature at Pmin and Number P of & max (ksi) & Pmax (ksi) and Pmax (in) Pmin & Pmax (mm) Pmax x 104 (rad/in) Remarks Cycles mn a() a N min max min max min max Wmin Wmax min max 1 15.75 31.35 24.71 49.78 0.208 0.416 0.120 0.205 1.84 3.48' -' a~~~~~C\ 2 23.20 32.12 33.10 50.46 0.310 0.424 0.151 0.207 2.58 3.53 0.13 00 3 23.47 32.29 33.50 50.67 0.314 0.427 0.153 0.209 2.61 3.55 PPR = 0.33 2500 24.08 33.34 34.30 51.53 0.327 0.444 0.155 0.211 2.73 3.63 Pmin. 6.5 Kips / l04 24.15 33.97 34.54 52.25 0.340 0.453 0.156 0.213 2.76 3.71 Pmax 9.75 Kips 5x104 24.20 34.15 35.04 52.73 0.349 0.463 0.156 0.215 2.85 3.75 1.5x105 24.14 34.09 35.31 52.99 0.360 0.473 0.157 0.216 2.92 3.81 5x105 23.90 33.78 35.57 53.20 0.373 0.486 0.159 0.218 3.03 3.91 106 23.68 33.63 35.92 53.39 0.385 0.496 0.159 0.219 3.10 3.99 1.5x106 25.60 35.50 39.34 56.85 0.392 0.503 0.166 0.225 3.17 4.06 2x106 26.04 36.06 39.98 57.57 0.398 0.509 0.169 0.228 3.22 4.11

TABLE 7D (CONTINUED) Afp; at Pmin fs at Pmin Deflection at Pmin Crack width at Curvature at Pmin and Number of & max (ksi) & Pmax (ksi) and Pmax (in) Pmin & Pmax (mm) Pmax x 10 (rad/in) Remarks Cycles _ N min max min max min max Wmin Wmax min max 2.5x106 24.42 34.23 38.41 55.93 0.405 0.514 0.163 0.222 3.25 4.13 3xl06 24.60 34.34 38.96 56.33 0.408 0.518 0.164 0.223 3.27 4.17 Beam was loaded 3.5x106 25.00 34.82 38.99 56.36 0.413 0.522 0.165 0.224 3.31 4.19 statically to 4x106 26.70 36.46 40.90 58.25 0.413 0.523 0.173 0.230 3.36 4.23 failure at 4.5x106 25.60 35.52 40.00 57.46 0.419 0.527 0.169 0.226 3.37 4.24 5x106 cycles 5x106 25.54 35.34 40.15 57.46 0.422 0.533 0.167 0.226 3.38 4.26 ~-* cn

TABLE 8D Beam Designation: PPID2 Stress range in the prestressing strand = Afps(max)'^fps(min) Type of Loading: Dynamic (cyclic) f'c at time of loading = 5806 Psi Stress range in the reinforcing bars = fs(max)-f(min) Effective prestress, fpe - 138.0 Ksi Note: See Table 8S for more details. |ub Afps at Pmin fs at Pmin Deflection at Pmin Crack width at Curvature at Pmin and Number of & Pmax (kst) & Pmax (ksi) and Pmax (in) Pmin t Pmax (mm) Pmax 10 (ra/in) Remarks Cycles __ N min max min max min max Wmin Wmax min max 1 15.71 28.13 25.18 43.55 0.217 0.403 0.097 0.160 1.98 3.40, s 2 20.86 28.78 29.31 43.66 0.304 0.413 0.117 0.162 2.57 3.46 = 0.20 3 21.14 29.07 29.41 43.75 0.309 0.416 0.118 0.162 2.61 3.48 PPR = 0.33 1000 21.67 29.76 29.98 44.33 0.316 0.425 0.120 0.163 2.66 3.53 in 6.25 Kips 104 22.12 30.49 30.05 44.55 0.324 0.436 0.120 0.163 2.79 3.60 Pmax l9-5 Kip 5x104 22.36 31.07 29.87 44.75 0.339 0.448 0.121 0.164 2.84 3.66. l.5xl05 23.10 31.88 31.48 46.14 0.349 0.460 0.122 0.166 2.93 3.74 5xl05 22.16 30.88 31.79 *46.53 0.369 0.478 0.122 0.166 3.07 3.87 106 22.79 31.22 33.22 47.67 0.380 0.491 0.123 0.166 3.17 3.96 1.5x106 22.05 27.03 34.63 49.46 0.389 0.501 0.122 0.167 3.24 4.03 2x106 21.24 29.81 34.18 49.00 0.398 0.509 0.120 0.165 3.28 4.07

TABLE 8D (CONTINUED) Nfpue at Pmin fs at Pin Deflection at Pmin Crack width at Curvature at Pmin and Numbe P. mi inmn i of & Pmax (ksi) & Pmax (ksi) and Pmax (in) Pmin & Pmax (mm) Pmax x 10-4 (rad/in) Remarks Cycles N min max min max min max Wmin Wmax min max 2.5xl06 21.27 29.46 34.67 49.19 0.404 0.515 0.124 0.165 3.34 4.12 3x106 21.24 29.74 35.15 49.90 0.413 0.521 0.122 0.164 3.34 4.16 Beam was loaded 3.5x106 21.05 29.51 35.00 49.72 0.418 0.525 0.121 0.164 3.38 4.17 statically to 4x106 20.77 29.24 34.83 49.56 0.422 0.530 0.121 0.164 3.42 4.21 *,failure at 4.5x106 19.98 28.43 34.30 49.04 0.426 0.534 0.121 0.163 3.45 4.23 5x106 cycles 5x106 20.11 28.50 36.44 51.19 0.432 0.539 0.121 0.165 3.48 4.27 I-J

TABLE 9D Beam Designation: PPID3 Stress range in the prestressing strand = Afp(max)-Afps(min) Type of Loading: Dynamic (cyclic) S s(ma) ff at time of loading = 5998 Psi Stress range in the reinforcing bare - fs(max)-fs(i) Effective prestress, fpe = 150.0 Ksi Note: See Table 9S for more details. Afpa at Pmin f. at Pmin Deflection at Pmin Crack width at Curvature at Pmin and Number I of & max (ksi) & Pmax (kai) and Pmax (in) Pmin & Pmax (m) Pmax x 10 (rad/in) Remarks Cycles mn a() a N mmin max min max mn max Wmin Wax min max 1 13.45 24.57 17.86 36.76 0.213 0.397 0.082 0.138 2 17.67 24.58 24.47 36.97 0.297 0.400 0.104 0.138 C 0.3 3 17.84 24.74 24.93 37.34 0.302 0.401 0.105 0.138 PPR = 0.34 5000 16.93 24.04 24.80 37.29 0.314 0.416 0.111 0.137 Pmin 8.37 Kips 104 16.98 25.61 24.73 38.94 0.318 0.436 0.109 0.143 Pmax 1.55 Kips 105' 1 18.07 25.52 26.24 39.11 0.338 0.442 0.113 0.144 1 17.18 24.43 25.45 38.07 0.344 0.450 0.115 0.144 5.5x105 17.42 25.00 26.44 39.29 0.362 0.465 0.113 0.146 7.5xl05 17.32 24.82 26.35 39.14 0.365 0.470 0.113 0.145 106 17.07 22.92 27.13 40.91 0.389. 0.501 0.120 0.157 1.5x106 19.44 26.66 29.48 42.71 0.400 0.513 0.127 0.161

TABLE 9D (CONTINUED) ANme s at Pmin fs at Pin Deflection at Pmin Crack width at Curvature at Pmin and Number Ps m of & Pmax (ksi) & Pmax (ksi) and Pmax t(in) Pmin & Pmax (nm) Pmax x 10-4 (rad/in) Remarks Cycles ______ N min max min max min max Wmin Wmax min max 2xl06 18.70 26.57 31.05 42.88 0.414 0.523 0.126 0.162 2.5x106 18.94 26.91 30.12 43.32 0.424 0.529 0.125 0.161 Beam was loaded 3x106 19.57 27.40 30.93 44.04 0.428 0.534 0.127 0.163 statically to 3.5x106 20.69 28.38 32.01 44.97 0.429 0.538 0.131 0.167, failure at 3.85x106 21:18 28.95 32.64 45.43 0.434 0.541 0.133 0.168 5x106 cycles 4.25x10 21.66 29.25 33.05 45.87 0.436 0.545 0.134 0.169 4.75x10 19.71 27.17 31.08 43.84 0.445 0.549 0.128 0.163 24) 5x106 21.24 28.83 32.73 45.66 0.445 0.549 0.129 0.165

TABLE 10D Beam Designations RD1 Stress range in the prestressing strand iAfps(max) fps(min) Type of Loading: Dynamic (cyclic) - f'c at time of loading = 5940 Psi Stress range in the reinforcing bars - fs(max)-fs(min) Effective prestress, fpe -- Note: See Table 10S for more details. A fP at Pmin f. at Pmin Deflection at Pmin Crack width at Curvature at Pmin and Number of & max (ksi) & Pmax (kei) and Pmax (in) Pmin &Pmax (mm) Pmax x 10 (rad/in) Remarks Cycles _____________ N min max min max min max Wmin Wmax min max 1 -- - 28.46 46.70 0.221 0.386 0.123 0.185 2 - - 32.53 47.45 0.281 0.395 0.135 0.188 < ~ 0.12 104 - - 33.52 49.09 0.294 0.410 0.127 0.181 PPR = 0 2.5x104 - - 34.63 50.22 0.302 0.420 0.124 0.179 Pmin 44 Kips 5xl04 - - 34.74 50.47 0.306 0.423 0.125 0.178 Pmax t6.8 Kip 105 - - 35.64 51.41 0.306 0.426 0.127 0.180 1.5x105 - - 36.68 52.66 0.314 0.432 1 0.120 0.171 2x105 - -- _ 37.43 53.30 0.315 0.435 0.117 0.171 5x105 - - 38.01 53.69 0.349 0.474 0.121 0.174 7.5x105 - - 39.16 55.02 0.350 0.474 0.120 0.173 106 - - 41.36 57.12 0.357 0.475 0.123 0.174

TABLE 10D (CONTINUED) A fpA at Pmin fs at Pmin Deflection at Pmin Crack width at Curvature at Pmin and Number of & Pmax (ksi) & Pmax (ksi) and Pmax (in) Pmin Pmax (in) Pmax 10-4 (rad/in) Remarks Cycles N min max min max min max Wmin Wmax min max 1.5x106 - - 43.42 58.15 0.380 0.485 0.141 0.177 1.75x10 - - 39.96 54.41 0.383 0.486 0.134 0.167 Beamwas loaded 2x106 - - 43.90 58.59 0.384 0.490 0.142 0.176 statically to 2.5x106 - - 43.51 57.91 0.388 0.493 0.139 0.174 failure at 3x106 - - 45.63 60.20 0.392 0.497 0.150 0.184 3x106 cycles I~~~~ 01 11111 1 II I I g~.*

TABLE 11D Beam Designationi RD2 Stress range in the prestressing strand a Afps(max)-fps(min) Type of Loading: Dynamic (cyclic) f'c at time of loading = 5870 Psi Stress range in the reinforcing bars 3 fs(max)fs(min) Effective prestress, fpe -- Note: See Table 1lS for more details. ANumr fps at Pmin fs at Pmin Deflection at Pmin Crack width at Curvature at Pmin and Number Ps min a min min min of Pmax (ksi) & Pmax (ksi) and Pmax (in) Pmin & Pmax (mm max x 104 (rad/in) Rem Cycles...... N min max min max min max Wmin Wmax min max 1 - -_ 25.81 41.87 0.263 0.422 0.092 0.137 2 - - 31.06 42.59 0.312 0.430 0.105 0.137 = 8.20 ao 3 - - 31.74 43.00 0.330 0.434 0.106 0.138 PPR = 0 104 - - 32.82 45.04 0.350 0.455 0.108 0.135 Pmin " 7.27 Kips 2.5x104. 33.35 45.04 0.356 0.460 0.109 0.135 Pmax' 10.8 Kips 5x104 - -- 33.51 45.53 0.360 0.464 0.110 0.135 105 -_ - 33.63 45.71 0.366 0.470 0.111 0.136 2x105. -- 33.93 46.11 0.375 0.477 0.111 0.136 5x105 - _ - 31.12 43.27 0.376 0.485 0.104 0.131 7.5x105 -- - 32.31 44.23 0.387 0.492 0.107 0.141 106 -- - 30.96 42.81 0.391 0.497 0.106 0.140 _ _-............... ____ _

TABLE l1D (CONTINUED) Nfps at Pmin fs at Pmin Deflection at Pmin Crack width at Curvature at Pmin and Number of & Pmax (ksi) & Pmax (ksi) and Pmax (in) Pmin & Pmax (mm) Pmax x 4 (rad/in) Remarks Cycles ma x0-_ n N min ax max min max min max W 1.6x106 - -- 29.32 41.76 0.402 0.505 0.104 0.138 2x106 - -- 34.47 46.65 0.405 0.509 0.115 0.149 Beam was loaded 2.3x106 - -- 32.31 - 43.68 0.410 0.515 0.112 0.146 statically to 2.5x106 -- - 34.27 46.19 0.411 0.516 0.115 0.150 failure at 3x106 - - 32.37 44.27 0.420 0.525 0.112 0.145 5x106 cycles 3.5x106 - -- 35.04 46.90 0.423 0.527 0.119 0.153 4x106 - - 32.51 43.97 0.430 0.534 0.118 0.152.J.4.5x106 -- - 34.41 46.30 0.435 0.539 0.117 0.151 5x106 - - 34.93 46.89 0.440 0.540 0.117 0.151 i,`\

TABLE 12D Beam Designation: RD3 Stress range in the prestressing strand = Afpsmax)'^fps(min) Type of Loading: Dynamic (cyclic) fc at time of loading - 5553 Psi Stress range in the reinforcing bars = fs(max)fs(min) Effective prestress, fpe --- Note: See Table 12S for more details. Afps at Pmin fs at Pmin Deflection at Pmin Crack width at Curvature at Pmin and Number - R of s Pmax (ksi) & Pmax (ksi) and Pmax (in) Pmin L Pmax (mm) Pmax x 104 (ra/in) Rmarks Cycles I...... N min max min max min max Wmin Wmax min max 1 -. -. 24.92 38.64 0.252 0.405 0.095 0.136 1.93 2.99 2 - -_ 28.43 39.12 0.314 0.411 0.106 0.139 2.23 3.02 t= 0.29 o 3 - -_ 28.95 39.35 0.319 0.415 0.108 0.139 2.36 3.04 PPR = 0 2500 - - 29.71 40.45 0.330 0.428 0.110 0.142 2.41 3.09 Pin 10.0 Kip 104 -- - 30.19 40.74 0.334 0.433 0.113 0.143 2.43 3.12 Pmax -15.0 Kips 5x104 - -- 32.00 43.02 0.347 0.443 0.115 0.147 2.46 3.17. ~ 105 - - 33.03 43.96 0.352 0.447 0.118 0.150 2.50 3.20 2.5x105 - - 32.83 43.97 0.358 0.456 0.118 0.152 2.55 3.26 6x105 - -_ 29.18 39.50 0.369 0.467 0.102 0.136 2.57 3.28 7.5x105 -- - 28.98 40.09 0.374 0.471 0.096 0.132 2.59 3.30 1.25x10 -- -- 28.56 39.80 0.382 0.479 0.093 0.129 2.63 3.35 l I l I I I' l I_ I I I ~ ~~~~~~~~~~~~~~~~~~.- I

TABLE 12D (CONTINUED) Aps at min fs at Pmin Deflection at Pmin Crack width at Curvature at Pmin and Number of & Pmax (ksi) & Pmax (ksi) and Pmax (in) Pmin & Pmax (m) max x 104 (rad/in) Remarks Cycles max0 N min max min max min max Wmn mi max 1.5x106 -- - 29.42 40.50 0.384 0.482 0.095 0.130 2.66 3.38 2xl06 -- - 27.37 38.28 0.389 0.487 0.088 0.123 2.68 3.40 Beam was loaded 2.5x106 -- - 28.27 39.50 0.394 0.492 0.089 0.125 2.71 3.43 statically to 3x106 - - 28.53 39.61 0.396 0.495 0.091 0.125 2.74 3.45 failure at 3.5x106 - -- 29.82 41.00 0.400 0.498 0.095 0.130 2.76 3.48 5x106 cycles 3.75x106 - - 30.77 41.92 0.401 0.499 0.099 0.133 2.78 3.50 4.25x10 -- -- 31.04 41.80 0.401 0.501 0.102 0.136 2.81 3.52 - 4.5x106 -- 1 32.10 43.09 0.402 0.502 0.103 0.139 2.81 3.54 tD 5x106 - -- 28.13 39.22 0.406 0.506 0.085 0.120 2.82 3.54 \