THE FATIGUE BEHAVIOR OF PRESTRESSED CONCRETE MEMBERS Them gov fin Degree 0* M. S. E’EICHIGAN STATE UNIVERSITY Donaid E. Cochran 1964 TH ESlS This is to certify that the thesis entitled THE FATIGUE BEHAVIOR OF PRESTRESSED CONCRETE MEMBERS ‘ presented by Donald E. Cochran has been accepted towards fulfillment of the requirements for ' M S degree in Civil Engineering 663% Major professor Date Man; 8. 1964 0-169 LIBRARY Michigan S ta te Umvcrsi ty THE FATIGUE BEHAVIOR OF PRESTRESSED CONCRETE MEMBERS by Donald E. Cochran AN ABSTRACT OF A THESIS Submitted to Michigan State University in partial fulfillment of the requirements for the degree of MASTER OF SCIENCE Department of Civil and Sanitary Engineering 1964 / -w 45%” Approved (1?, ' ¢AQ£:, ABSTRACT THE FATIGUE BEHAVIOR OF PRESTRESSED CONCRETE MEMBERS by Donald E. Cochran The purpose of this study is to investigate the behavior of prestressed concrete when subjected to fatigue loadings. The principal objectives are: to determine what effect, if any, temperature has on the fatigue properties; to study the static strength behavior of members previously subjected to a fatigue loading; and to investigate the possibility of using sonic testing equipment to indicate fatigue damage. A total of fifteen 3" x 3" x 14 1/2" test beams were tested to fatigue failure in flexure. Four specimens were tested at 55°F, six at 73°F, and five at 90°F. The stress level of the tests varied from 34.1 to 61.0 percent of the ultimate static bending strength. Six other specimens were statically broken after a varying number of stress reversals at 45 percent of the ultimate static bending strength with the temperature held constant at 55°F. Five similar test beams were statically broken. All static tests were conducted using the third-point loading method. Temperature was found to affect the fatigue properties of prestressed concrete members. The lower the temperature, the more susceptible the member was to fatigue damage. Previous reversal loadings at a stress level sufficient to cause failure by fatigue were found to damage the static load-carrying capacity of the member after 95% of the reversals required to effect failure had been applied. It is shown that sonic testing equipment may be used to indicate ultimate strength, and that it may be used to indicate fatigue damage, but insufficient data is presented to determine the exact relationships. THE FATIGUE BEHAVIOR OF PRESTRESSED CONCRETE MEMBERS by Donald E. Cochran A THESIS Submitted to Michigan State University in partial fulfillment of the requirements for the degree of MASTER OF SCIENCE Department of Civil and Sanitary Engineering 1964 UN 'L. I O . . I;*( ‘5' 3 ACKNOWLEDGEMENTS The author wishes to express his sincere thanks to Dr. Charles E. Cutts, Chairman, Department of Civil Engineering, Michigan State University, for ‘his advice and guidance during this investigation. INDEX Chapter Page I INTRODUCTION.................. 1 II REVIEW or PREVIOUS INVESTIGATIONS. . . . . . . . 3 III SCOPE OF INVESTIGATION . . . . . . . . . . . . . 8 IV EXPERIMENTALPROGRAM.............. 11 V EXPERIMENTAL DATA AND RESULTS. . . . . . . . . . 24 VI DISCUSSION OF EXPERIMENTAL RESULTS . . . . . . . 47 VII CONCLUSIONS.................. 53 VIII RECOMMENDATIONS FOR PURTHER STUDY . . . . . . . 54 Ix BIuImMPHY O O O O O 0 C O O C O O O O O O O I 55 I. INTRODUCTION Perhaps one of the fastest growing uses of concrete is that of prestressed precast concrete. By using prestressed concrete, smaller members may be utilized, and by precasting the member, forming costs. may be reduced and the curing controlled to exacting specifications. In addition, the utilization of prestressed precast members reduces the required construction time. As in any other field, when a demand and a use for something exist, it may be put into use before complete testing has been performed. Many experiments on prestressed concrete have been made, but there seems to be little continuity in these experiments, and there is limited information as to the behavior of concrete when repeated loads are applied. Pretensioned prestressed concrete members are formed by tensioning the reinforcing steel, pouring the concrete, then releasing the tension in the reinforcing steel after the concrete has developed sufficient strength for the transfer. In this manner, the concrete is initially in compression, so that a transverse loading which would normally cause tension in the concrete will only cause a reduction in the compression already present. Since in present design practice, the concrete is assumed to carry no tension, a considerably smaller member may be used. The load is transmitted from the steel to the concrete entirely by bond. It is knownthat the load-carrying capacity of a member subjected to repetitive loads may be less than that of a member which is not subjected to repetitive loads due to the phenomenon known as fatigue. Fatigue failure may occur in the concrete, or the steel or in the bond between the two materials. II. REVIEW OF PREVIOUS INVESTIGATIONS GENERAL INFORMATION CONCERNING FATIGUE Fatigue is the result of repeatedly changing the stress in a material. It may be due to loading and unloading a member, loading and only partially unloading a member, loading and then reversing the load in a member or a combination of these conditions. Most materials will faily under a number of repeated loads, or fail in fatigue, if the loads are sufficiently high and the number Of applications sufficient to complete the failure. This type Of failure is krown as fatigue failure. Both the concrete and the steel used to reinforce concrete, both conventional and prestressed, exhibit the characterisitic of failing gradually under repetition Of loads. The two variables normally present in the fatigue of a material are stress level and number Of repetitions. Results Of fatigue tests and failure envelopes are generally presented in the form Of a S vs N plot. Here, 8 is the stress level, which may be expressed in a number Of ways, and N is the number of cycles required to cause failure plotted on a logarithmic scale. Metals possess an endurance limit. This means that any number Of load repetitions of a stress level lower than the endurance limit will not cause failure. In the normal S vs N plot the curve becomes asymptotic to the stress which represents the endurance limit. It does not appear that concrete has an endurance limit, that is, the S vs N plot does not become asymptotic, but continues downward and in fact is generally a straight line when plotted in terms Of S vs N. PLAIN CONCRETE Since concrete is assumed to carry only compressive stress in present design practice, it is important to concern one's self with the fatigue properties of concrete in compression alone. Fatigue limits for concrete in compression alone range from 40% to 55% of its virgin static compressive strength. Some (17) (6) of the available literature mentions an endurance limit for concrete in flexure. Kesler (10) states that concrete has no endurance limit, at least up to ten million cycles of loading. Rest periods appear to help resist failure due to fatigue, and previous loading at a low stress level also helps resist the damaging effects of fatigue. Nearly all papers state that the failure seems to be in the bond between the binding matrix and the aggregate. Kesler and Murdock (12) in their publication report that the initiation of the fatigue failure is due to progressive deterioration of the bond between the coarse aggregate and the binding matrix, reducing the section Of the specimen, and the final fracture is a result of the failure of the paste-fine aggregate bond. REINFORCED CONCRETE The majority of the fatigue failures Of reinforced beams, as in prestressed beams, occursin the reinforcing steel. Beams which are critical in longitudinal reinforcement seem to have a fatigue limit of 60-70% of the static ultimate strength at one million cycles. Occasionally, beams were noted to have failed in diagonal tension due to fatigue, but more generally in a combination of shear and bond. Beams failing in shear as low as 40% Of the static ultimate stress have been reported. In reinforced concrete, as niplain concrete, there is evidence that rest periods and initial fatiguing at a low stress level help resist fatigue failures. PRESTRESSED CONCRETE In prestressed concrete, the following types of fatigue failures are possible, as reported in Libby (14): 1. Failure of the concrete due to flexural compression. 2. Failure of the concrete due to diagonal tension or shear. 3. Failure of the prestressing steel due to flexural, or tensile stress variations. 4. Failure of pre-tensioned beams due to loss of bond stress. 5. Failure of the end anchorages of post-tensioned beams. As yet, fatigue failures due to diagonal tension or shear alone have not been Observed in prestressed concrete research. The majority of fatigue failures found in prestressed concrete testing have resulted from fatigue in the prestressed tendons. Several fatigue tests conducted abroad found individual wires contained in prestressing tendons failed by fatigue at points where they passed over spacers which were used to hold the wires in position. Bond failures have been noticed and reported, but principally in very short-span members. Many reports of fatigue have been made, but there seems to be little continuity in the available data. Some authors (Nordby 17) have attempted to condense the data, but have presented conflicting statements. It seems to be general belief, however, that prestressed beams are superior to conventionally reinforced beams as far as fatigue resistance is concerned. It is also general belief that the ultimate strength for beams which did not fail under repetitive loading is unimpaired by the repetitive loading. Nordby (17) and Patel (22). T. E. Stelson, (27) has presented the best review of the actual test data conducted to date. In this report he presents a method for predicting a safe design based on fatigue considerations. In no case, where tests have been made using conventionally prestressed members, has there been a report of failure of the concrete. For this reason, Mr. Vejubhai Gulababhai Patel submitted to Michigan State University in 1961 a Thesis concerned with the action of prestressed concrete under a flexural fatigue loading. By prestressing a test beam at the neutral axis, he was able to study the properties of the concrete itself, as the stress in the prestress wires was not affected by the loading. Mr. Patel concluded that: 1. The ultimate strength of prestressed beams under static loading was not affected by previous dynamic loading of 2.5 million cycles. 2. That the ratio of failure loads (reversal) in fatigue loadings to that in static ultimate loadings was approximately 45 percent. 3. That under fatigue loading in which the entire cross- section remained in compression, flexural compression failures occuned in the concrete. SONIC TESTING METHODS When a test prism supported at its nodal points is driven from the side at one end, the resulting vibration may be picked up at the top at the opposite end, as shown in figure three. By varying the driving frequency and using the equipment shown in figurethree, the resonant frequency of the prism may be obtained. It has been shown (19) that there is a relationship between the resonant frequency and the modulus of elasticity. This relationship is as follows: E : Can where E = Young's Modulus, C : a size constant, w = weight, and n = the resonant frequency. This method of non-destructive testing is now almost universally accepted. III. SCOPE OF INVESTIGATION QUESTIONS In reviewing the available current literature and reports of previous investigations, questions arose, and some inconsistencies became apparent. These questions are as follows: 1. Is the ultimate strength of prestressed beams under static loading affected by previous dynamic loading? 2. Will fatigue loading of less than 45% of the static ultimate stress cause failure of the member? 3. Does the temperature of the specimen affect the fatigue properties? 4. If fatigue impairs the static properties of a test specimen, is it possible to use sonic non-destructive testing procedures to indicate the damage? DISCUSSION OF QUESTIONS 1. It would appear that if a fatigue loading of 45% of the static ultimate load will ultimately cause failure of the specimen, then just before the specimen is destroyed by fatigue, its static properties will also be affected. 2. Since it is reported in many sources that plain concrete does not appear to have an endurance limit, (17) (27) is it not strange that some sources state that a loading of less than 45% will not cause failure? 3. From previous experience, it is knownthat properties of most materials vary somewhat with temperature. Temperature effects on the fatigue properties of prestressed concrete were not found in the literature. It appears that this is an area where information is lacking. 4. Previous studies (19) (5) have shown that there is a correlation between the sonic transverse resonant frequency of a specimen and the modulus of elasticity of the specimen. Will this equipment also indicate fatigue damage? What would be the outcome if one were to perform sonic tests on a reinforced specimen? Since it is known that the answers to these questions would require a much more rigorous and time consuming investigation than is now possible, and the questions are somewhat unrelated, complete answers will not be attempted. It is felt, however, that a general investigation would be of significant value in determining the course of future 'extensive research. Therefore, an investigation of the behavior of prestressed concrete members subjected to dynamic loading, completely reversed, will be made with the objective of providing partial answers to the above questions, and providing a beginning for future investigations. The size of the test specimen will be 3" x 3" x 14 1/2", since the available equipment is designed to use this size. Since one of the previous investigations (22) used this size, with two strands of steel wire at the neutral axis, (AS a 0.0342 in.2) With It uniform effective prestress of 473 psi, this investigation will attempt -10- to deal with that same basic specimen. Since the steel used in that investigation is not readily available, a single seven strand wire cable (JXS- 0.0356 in.2) will be used. The design effective prestress will be 473 psi. Experiments will be performed at three different temperatures. Some members will be destroyed by fatigue, others will be fatigued to various degrees and then statically destroyed. Applicable sonic resonant frequency measurements will be made in conjunction with these experiments. IV. EXPERIMENTAL PROGRAM SPECIMENS The test specimens used were pre-tensioned prestressed concrete beamm. The size of each beam was 3" x 3" x 14 1/2". Each beam was prestressed at the geometric center of the cross-section with a single cable. In Series One, sixteen beams were cast from a single concrete batch. In Series Two, eight beams were cast and in Series Three, ten beams were cast. Series One and Series Two were poured on the same day, and Series Three about five weeks later. The same concrete mix was used for all series. Six test cylinders of 4” diameter and 8" high were cast with each series. MATERIALS PRESTRESSING STEEL The prestressing steel used was seven strand. wire cable of nominal diameter : 0.25 inch. The area of steel given by the manufacturer (Roebling) is 0.0356 square inches. Three 10 inch gage lengths of cable were inspected and tested, and the following data obtained: Diameter of strand - 0.104” Area of cable - 0.0343 in.2. (As) Modulus of Elasticity - 22 x 106psi. (ES) Yielding load - 9800 lb. Ultimate load - 9900 lb. -11- -12- CONCRETE Natural sand and washed gravel were used as the fine and coarse aggregates, respectively. The maximum size of the aggregate was limited to 1/2 inch due to the small test specimens used. A sieve analysis (Table Eleven) showed the fineness modulus of the sand to be 2.97 and that of the coarse aggregate to be 6.01. The water-cement ratio was 0.400, the cement content was found by a yield test to be 7.0 sacks per cubic yard, and mix proportions of 1: 2.47 : 2.47 were used due to the high fineness moduli of the aggregate. The cement used was type 1 air-entrained. The cement, sand, and gravel were thoroughly mixed before the water was added, and final mixing time was 2 1/2 minutes in the Lancaster Laboratory Mixer. The concrete was placed in the forms in two equal layers, and each layer was rodded 25 times. The beams and cylinders were kept wet and covered for 7 days before the release of the prestress, and then moved to the moist room for the remainder of the standard curing. Design strength was 6000 psi, and the average 28 day strength was 5920 psi. -13- EFFECTIVE PRE STRF‘ SS The effective prestress is equal to the initial calculated prestress minus the prestress losses. Throughout the calculation of prestress losses, the "Tentative Recommendations For Prestressed Concrete," by the ACI-ASCE Joint Committee 323 (2) will be followed. In the calculations, the following terms will be used: E . = 1,800,000 7 500 times the cylinder strength at the C1 release of the wires. Modulus of eleasticity of the concrete. (Psi) E of = 1,800,000 ,4 500 times the cylinder strength at the . end of 28 days. Modulus of elasticity of the concrete. (Psi) E = Modulus of Elasticity of the steel used for prestressing the concrete. (Psi) = Strain in the steel. (in/in) .s 6c = Strain in the concrete. (in/in) Psi = Total load in the prestress wire before release. (lbs.) Psf = Total load in the prestress wire after release. (1bs.) PC = Total load in the concrete after release of the wires. (lbso) AS =. Area of the steel. (111.2) Ac = Area of the concrete. (in.2) Ag = Gross area : As. + AC. (in.2) fs = Stress in the prestress steel. (Psi) fC = Stress in the concrete. (Psi) f'C = Ultimate compressive stress in the 28 day old cylinder. (Psi) CC = Creep coefficient for the concrete. 5:3 .f Unit shrinkage strain for the concrete. Pt 3: Change in steel load due to A Es (1135.) PRESTRESS LOSSES -14- (Shown here for Series One and Series Two) (8) Elastic Shortening of the Concrete. Here, or, P transferred to the concrete = PS. - E: c After release of the wires, T’sf = and 6 = A6 . c F’ Sf 81 - I) P3 ES = 22 x 106 psi is initial (before release) 5’, = $1 5120 lb. S 1: 1,800,000 + 500 (3925) - 3 If we assume elastic conditions _P_ : E6 A PR - E2136 _ S S A8 A68 = EC ASES KcEc or, Psi PSf ASES Psf = PC 80) Psi " PC ASES from.which EN: = fc 2: 1EC and, P’ 1 .763 x 106 psi 144,000 psi P’ transferred to the concrete sf C -15- at release : 5120 . 9 o. 0356 ( 22 x _________6)1o6 -1 3. 763 x 10 = 563 psi. Therefore, fc since fc = Ec 6C, and CC = E: zdes, the loss of prestress in the steel is 6 A f = E fC = 22 X10 X 565) = 3274 Si S S E? 3.763 x10F p (b) Shrinkage of Concrete: 6 S = 0.0003 (as recommended) since Ace = A63 , A =AtE e 6 E , is c s s s so, Afs = 0.0003 (22 x 106) = 6600 psi. (c) Creep of the Concrete: ch = 1,800,000 + 500 (5980) = 4.790 x 105 psi. (ch sonic = 6.22 x 106 psi ) A maximum.concrete stress under loaded conditions will be assumed to be 563 psi + 0.5 fc ultlmate. =563+ 487 = 1050 psi. Cc = 2.5 (as adopted by the comittee ) for which, f = (c - 1) f ES 8 c c iEc 6 f8 = (2.5 -1) (1050) ( 22"” = 7234 psi 8, ° 4.79x10°) -15- (d) Relaxation of Steel Stress: The committee recommends 2-81 offS initial. Since the 7 day creep was found to be I'FZ, 4% was assumed for the computations. Therefore, f = 0.04 (144,000) = 5760 psi 8 TOTAL PRESTRESS LOSSES: Loss due to elastic shortening = 3274 psi Loss due to concrete shrinkage = 6600 psi Loss due to concrete creep = 7234 psi Loss due to relaxation of steel = _§Z§Q_ psi Total ' 22,868 psi Note: This should be compared to the 35,000 as recommended by the committee. The value of 35,000 is judged by many to be excessive, although if considered for a longer period of time than was required for the tests, the 22,868 would undoubtedly be revised upward. EFFECTIVE PRESTRESS: Since the steel prestress losses are 22,868 PSi or 15.88% f8 initial (say 16%), the effective concrete prestress must also be 161 less than the initial prestress, or 470 psi. For Series Three, a similar study with: EC at release = 3.738 x 106 fc =3850 psi and EC at 28 days = 4.730 x 106 f;: =5860 psi, yields an effective prestress of 462 psi. -17- CASTING OF SPECIMENS The equipment used to cast the specimens is shown in Figure Three. The prestressing force was applied by threading the end bolts into the gripping fixtures, as shown in Figure Four. A detail of the bolts and fixtures is shown in Figure Six. Due to the fact that the steel used was in the form of a cable, it was impossible to fix a strain gage directly to the cable. If a jack were used, the individual tension would have to be checked and adjusted. Since it was found that the required tension could be obtained without the use of jacks, they were not used. In order to check the load in each cable, a four inch section of 1 1/4" diameter standard pipe was machined to provide flat ends, and the two strain gages fixed to it, one on either side to eliminate influence due to bending. Since the area of the pipe was known, any indicated strain in the pipe could easily be converted to load in the cable. Each of the fabricated transducers was checked in a universal testing machine and found to be acceptable. These transducers are shown in Figure Seven. All three cables were loaded at once, and the indicated strain recorded. At the release of the prestress, the indicated strain was again recorded, and the difference between the first strain indication and the last was judged to be the relaxation of steel stress. This was found to be just over 1%. Lime-12.. General View of Preatress Bed 18. -19- Two SR-4 strain gages were fixed to one beam in each tog just prior to release of the C8b1€8,dud the actual initial concrete strain recorded. This indicated value was within 1 1/2 percent of that calculated in the section dealing with effective prestress, so the difference was neglected. During construction of the forms, it became evident that a certain amount of difficulty would be experienced in oiling the forms without getting any oil on the prestress cable. This problem was solved by drilling the holes in the forms to 1/2 inch diameter, oiling the forms, and then inserting a dry sleeve, 1/2 inch outside diameter and 1/4 inch inside diameter in the form before drawing the prestress cable through the forms. This arrangement is shown in Figure Six and Figure Seven Series One and Series Two were poured at the same time, so they were considered to have the same properties, since they possess identical histories. Series Three was poured at a later date, so the properties of this series were considered separately. About one day after the specimens were cast, the forms were removed by prying up the sides and chiseling out the blocks separating the beam ends. The beams were kept covered and thoroughly wetted throughout the remainder of the seven days before the prestress cables were released. At that time they were moved to the curing room. FATIGUE EQUIPMENT The fatigue testing machines used were Baldwin-Lima-Hamilton Sonntag Fatigue Testing Machines, which were equipped with SF-l-U F1 sure Three Apparatus for Obtaining Transverse Resonant Frequency Figure Tee Method of Preatreesing the Cables -21- bending fixtures. A typical view of this machine is shown in Figure Eight. Although the equipment was designed so that a preload could be applied to the specimen, none was applied. The specimen, therefore, was subjected to complete reversal of-stress. The stress was induced by an unbalanced rotating mass which was fixed to the center platen and so caused a vertical vibratory motion of this center platen. The outer platen was stationary, and due to the construction of the bending fixture, the vertical motion of the center platen imparted a constant bending moment to the center portion of the test beam. The frequency of the applied moment was 1800 cycles per minute and the counter, driven by a syncronous motor, recorded the number of reversals, each unit on the counter being 1000 cycles. The machine was equipped with a variable transformer which enabled the operator to control the rate of acceleration of the main drive synchronous motor. In this manner, the specimen was not over- stressed during either the starting or stopping of the test. 2 The machine was also equipped with limit switches which limit the vertical motion of the center platen. When a specimen failed during the test, the vertical motion of the center platen became excessive, tripping the limit switch, and stopping both the main driving motor and the counter. The applied moment was varied by varying the unbalance of the rotating mass. The machine was equipped with a scale so that the mass might be adjusted to give a particular force to the vibrating platen. 22. F1 ure Five Detail of Transducers eFo F1 Detail of Delta and Gripping Fixtures -23- Since this force was known, and since the dimensions of the bending fixture are known, (length of the bending arm.- 6") the required force to produce a particular stress in the specimen was calculated to be P :‘g crr' where 0" is the maximum stress in the specimen. 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B 8 1.3.3 . a 3 s .n o s .D o 3 m .1.u .l. .l 8 1.1.1. n w 1. n w 1. .3 a 1. e I. o o a e e on w e 1. s a e u u u u 1. a m o 3 o.s. a 3 a 3 u. up w 49.} m. .A .A a 0 ham 4.. 8 u ma oneseuHa oeueum ems u pace onwauum anus monn u onsumquEua mnoawoomm oonmuusm oohouumoo hHHmuwumum Beam same no humaanm umOH .w mHan -34- ousHumm NHm.o ounHHmm HoH.mH AxomaUV oomH oom.e man ooH.nH ownH coo.o Axumuov mnnH oo.nH nmoH onN.o mmoH omN.¢H onH ONm.m ooNH ono.¢H nme ooH.n ONNH owN.¢H ommH coo.¢ oan cam.MH owaH OMH.¢ nwwH omN.NH o¢ON NN¢.m mnaH omo.HH nNON ome.N ommH omn.oH owON omo.N nmaH Hmw.m / owON ¢n¢.H oo0N HmN.a mmoN Hom.o oNON mao.s ooHN see.o C) N P; OJ C) C) as F! N < comm ooo.eN s are mN o-m m HmN omen oNNm ooe.Ne s Nee N 01m m 1 me nanem Nee N .e>< omen ooo.me s are N m-m N omen SNNs ear... .3. N 4-... m onn con.NN : Nee wN N-N N oNNe ooo.pN : Nee mN u-N N comm ooo.eN s Nee eN e-N N omen ooN.ee s Nee N o-N N oHoe ooN.en : Nee N m-N N oNeN coo.ee sexes Nee N <-N N Hmm omen n Ne e He neHnsm Nee NN .s>< ones oom.mm : Nee mN N1H H - Hme nNeN - Ne e He nansm Nee N .s>¢ omen oom.Ne s Nee mN m-H H amen con.eN s Nee mN e-H H omen ooo.we s Nee N o-H H once ooe.on ._ Nee N m-H H ONwm Downhfi :wx:¢ %d6 5 oan . H. .— £13:me 2.00 O‘ O‘ H w 0‘ H N O‘ e-t (0 \D HA—O‘ mm 0 mm 1—4 N.H o o >>~1 00 1: ‘H n 0 o,_om mmouum mo .02 coca mugs illl. i _ _ 03mg omaummua noaga many now umooxo onau was hocoaroum auwuaaH "ouoz u 8.: S / S e .l. C v. no ( co: v. C n e w. n F 003 t n a n o a R 83 ooou M37: 0 mnwe 33 r ooaw Resonant Frequency Fig. B. vs. No. of Cycles @ 45% ult. T = 55°F -39- oo.~ mo.H mm.H mm.a om.~ ma.H N¢.H am.a om.H Ammauho mo maowaawav . mamwuo>mm «mouum mo .oz coma .III III Illl.|.| II... __ .7 OONH 82 3 II... III J...l...q I. J ”.3... m1 8.: z on”. :« 33.0.3033 mm 3032..» a \I . who: mum wood o>auoauumov .d 8: a ll 1 0.33... .3: 9.2. a wig. H302 m N L .u ”WI. coca 1 m w. i coma C t I.\ 1 "U m. n oowH w 002 a. e r n. It m oooN ooou m S e “n 03.0. I l l1®oo- ooqN Comparison of: Fig. C. Resonant Frequency Ultimate Static Destructive Load V8. No. of cycles @ 457. ult. c : 55°; VS. No. cycles @ 45% ult. t 55°F \ ( (------------—-----) -4o- \D H <- .4 cu q—l <3 v-O Q '31; -11 A _____ .g Q 0 Q u.4 o u > >~. o o :2 Q4 w o O o m as cooH 4° r-l “a: 8 00V :2 d‘ P on Resonant Frequency (cycles/sec.) I - 13.3.-. 1.11-0 2400 9" C xlg. D. 2200 2000 1800 1600 § No. of Cycles vs. Load - 43.68% ult. t Sonic Frequency 1200 Test Beam # T3-4 (Series #3) 90°F Q HA m m m o u.q o o > >. w o c: <3 <3 c> c> c: <3 <3 <3 c3 :3 :3 <3 <3 N H O 0" 00 l‘ Ln N N N H v-i H o—I P! Fig. E. No. of Cycles Test Beam # T3-1 (Series #3) vs. Load = 47.73% u1t. Temp. : 90°F -42- 48% 46% 4#% 42% ,\ u U .3: H 3 0 407. '3 a U U) 5 m 38% 36% 34% N (No. Cycles to failure) 1x106 2x106 3x106 5x106 Fig. F. S vs. N Temp. : 55°F Test Series #1 10x106 -43- 52% 50% 48% 46% S (2 static ultimate) 44% 421 40% 1x10 N (No. cycles to failure) 2x106 """3x106 ‘ Fig. G. S vs. N Test Series #2 5x10 6 1oi1o -44- 52% 50% 48% 46% 1? U 5 H 3 44% h.- 0 vi U 3 to $3 In 42% 40% N (No. cycles to failure) 1x106 2x106 3x106 5x106 101210 Fig. H. S vs. N Temp. : 73°F Test Series #3 3 Based on Ult. for Series #1 & #2 ......... = Based on Ult. for Series #3 -45- 48%-———- 444 S (1 static ultimate) 42% 40%”— 40% 38% N (No. cycles to failure) 6 6 5x106 10x10 20x106 —30x106 3x10 Fig. I. S vs. N Temp. : 90°F Test Series #3 : Based on Ult. For Series #1 & #2 -46- 567:. 527. -——— 48%— 447. — E E U H D U H U 407.— 3 m :5 U! 36% 327. N (No. cycles to failure) 1x10 5x10 10x106 205.10 Fig. J. S vs. N Temp. - Indicated Based on Respective Series VI. DISCUSSION OF EXPERIMENTAL RESULTS As seen from the data, eight tests have been disregarded. This is due to the fact that for specimen T2-3, the SF-l-U bending fixture broke, and it was impossible to know the exact history of the specimen. For specimens T1-4, and Tl-S, the preload equipment on the testing machine experienced a malfunction. For specimens Tl-Z, Tl-l, Tl-lO, and T1-13, the temperature was not constant. As is noted in Table Four, the average maximum stress for the specimens destroyed using the static third points loading was 980 psi for Series One and Series Two, while that for Series Three was 959 psi. Since the effective prestress was 470 psi and 462 psi respectively, the stress distribution at failure was as shown below. -980 psi -1450 psi Series #1 & #2 -470 psi {980 psi {510 psi -959 psi -1421 psi ‘6‘ II Series‘#3 -462 psi {959 psi {497 psi effective loading total prestress -47- -43- The results of the tests conducted at 55°F are summarized in Table Five, and the corresponding S vs N plot shown in Figure F. The results of the 73°F tests are summarized in Table Six, and the corresponding results plotted in Figures G and H. Note that in . Figure H the results are shown in two ways. One way with the stress level expressed as a percent of the static ultimate for Series One and Two, and the other way with the stress level expressed as a percent of the static ultimate for Series Three. The results of the 90°F test are summarized in Table Seven and the corresponding S vs N plot is shown in Figure I in a fashion similar to Figure B. Figure J is a consolidation of Figures F, G, H, and I utilizing a smaller scale. Here it is noted that there is indeed a temperature dependence for fatigue life of prestressed concrete. Table Eight summarizes the data collected from the portion of the tests in which members were subjected to a varying number of loadings at forty-five percent of the static ultimate stress, with the temperature held constant at 55°F. Here it is noted that when specimens T1-8 and T2-5 were statically broken using the third points loading method, the failure occurred outside the zone of maximum.moment, as shown in Figure 10. Therefore, the loads used for computations concerning these members have been reduced to an equivalent load which would have produced a moment in the center portion of the beam equal to that which actually caused failure. Figure A presents the data of Table Eight in graphical form. 49. Figure N13. . Typical static 1/3 Point Break m Break of Specimen 11-! under Static 1/3 Point Leading. (Typical of T2-5) -50- Table Eight also contains the resonant frequency data collected using these beams. This data is graphically presented in Figure 8. A comparison of the 'Ultimate Static Strength vs Number of Cycles at 45% Static Ultimate' and the 'Resonant Sonic Frequency vs Number of Cycles at 45% Static Ultimate' is made in Figure C. Here, the resonant sonic frequency is reduced so that the beginning and ending points of this curve will coincide with the respective points on the other curve. From this Figure, it is apparent that there is some relationship between decrease in resonant frequency and decrease in static ultimate load. No attempt has been made to determine this relationship, since it is felt that the available data is not sufficient to obtain this relationship. The actual relationship should be determined by future investigations. Table Nine presents resonant frequency data collected from specimens T3-1 and T3-4, for various numbers of cycles at 47% and 43% of the static ultimate load, respectively. Both tests were made at 90°F. Since Figure C shows there to be a relationship between resonant frequency and ultimate static strength, Figures D and E can also be interpreted to show decrease in static ultimate load. Table Ten contains the data from which the strength of the concrete was determined. As noted, the loading of the 4" diameter 8" long cylinders was at the rate of 35 psi/second, which is within the range recommended by the American Society for Testing Materials. Table Eleven contains the sieve analysis data from which the fineness modulii of the fine and coarse aggregates were determined. -51- From the data, it is apparent that a member loaded with sufficient load to eventually cause fatigue failure suffers eventual static load carrying damage. It does not appear, however, that this damage occurs until approximately 95% of the reversals required to cause failure by fatigue have been applied. It is also apparent that a reduction in resonant frequency corresponds to a reduction in ultimate static load- carrying capacity, and this fact has been used in the further data reduction. It is also apparent that the temperature of the fatigue tests affect the performance of the test beams. F1§2£° Twelve Typical Fatigue Fracture Figure Eleven Bending Fixture and Test Bea- VII. CONCLUSIONS From the observations made during the testing described, the following preliminary conclusions may be made: 1. The ultimate strength of prestressed concrete beams is adversely affected by a level of fatigue loading which would eventually cause failure. This phenomenon occurs only after approximately 95% of the total number of stress reversals to effect failure have been applied. 2. A fatigue loading of less than 45% of the static ultimate load will eventually cause failure of the member. 3. The temperature of the member must be considered when one is concerned with the fatigue performance of a prestressed concrete member. The lower the temperature, the more susceptible the member is to fatigue damage. - 4. Limited measurements tend to indicate that a relationship exists between the reduction in static load-carrying capacity of a prestressed member and the transverse resonant frequency of the member. -53- VIII. RECOMMENDATIONS FOR FURTHER STUDY It is recommended that further study by made in the following areas: TEMPERATURE It is suggested that tests be made at various temperatures and the data presented in a fashion similar to Figure J so that more exact fatigue considerations can be made with respect to temperature. TRANSVERSE RESONANT FREQUENCY vs ULTIMATE STRENGTH It is recommended that further investigations be made to determine the actual relationship between transverse resonant frequency, and ultimate static strength. Further consideration of the application of the sonic test to reinforced and prestressed members should be made. -54- 10. 11. 12. 13. 14. 15. -55- IX. BIBLIOGRAPHY AC1, "Fatigue of Concrete," ACI-Bibliography, No. 3, 1960. ACI-ASCE Joint Committee 323, "Tentative Recommendations for Prestressed Concrete," ACI Journal, V. 54, Jan., 1958. Abeles, P. W., "Fatigue Resistance of Prestressed Concrete Beams," Final Report, Fifth Congress, International Association for Bridge and Structural Engineering, Zurich, pp. 205-208, 1957. Assimacopoulos, B. M., Robert F. Warner, and Carl E. Ekberg, Jr., "High Speed Fatigue Tests on Small Specimens of Plain Concrete,” Prestressed Concrete Institute Journal, V. 4, No. 2, pp. 53-70, 1959. Carlin, Benson, ”Ultrasonics," McGraw-Hill Book Company, Inc., New York, 1949. Clemmer, H. F., "Fatigue of Concrete," Proceedings of the American Society for Testing Materials, V. 22, Part II, pp. 409-419, 1922. Connolly, William H., "Design of Prestressed Concrete Beams," F. W. Dodge Corp., New York, 1960. Ekberg, C. E. Jr., R. E. Walther, and R. G. Slutter, "Fatigue Resistance of Prestressed Concrete Beams in Bending," Proceedings, ASCE, V. 83, No. ST4, July, 1304-1--1306-17, 1957. Iomata, Shunji, "On a Fatigue Test of Prestressed Concrete," ACI Journal, V. 24, No. 8, April, pp. 766, 1953. Kesler, Clyde E., "Effect of Speed on Testing of Flexural Fatigue Strength of Plain Concrete," Proceedings, Highway Research Board, V. 32, pp. 251-258, 1953. Kesler, Clyde E., and John W. Murdock, "Effect of Range of Stress on Fatigue Strength of Plain Concrete Beams," ACI Journal, V. 30, No. 2, August, 1958 (Proceedings V. 55), pp. 222-231. Kesler, Clyde E., and John W. Murdock, "The Mechanism of Fatigue Failure in Concrete,” The Engineering Experiment Station, University of Illinois, 1960. Larnoch, W. J., Magazine of Concrete Research (London) V. 12, No. 36, November, pp. 171-176, 1960. libby, James R., "Prestressed Concrete," The Ronald Press Company, New York, 1960. Lin, T. Y., "Design of Prestressed Concrete Structures," John Wiley and Sons, Inc., New York, 1958. 16. 17. 18. 19. 20. 21. 22. 23. 24. 25. 26. 27. 28. ~56- McCall, John T., "Probability of Fatigue Failure of Plain Concrete," Journal of the American Concrete Institute, V. 30, pp. 233- 244, 1958. Nordby, Gene M., "Fatigue of Concrete-A Review of Research," ACI Journal, V. 30, No. 2, August, 1958 (Proceedings V. 55), pp. 191-220. Nordby, Gene M., and W. J. Venuti, "Fatigue and Static Tests of Steel Strand Prestressed Beams of Expanded Shale and Conventional Concrete," ACI Journal, V. 29, No. 2, August, 1957 (Proceedings V. 54), pp. 141-160. Oberst, Leonard, and Wilbut I. Duvall, ”Discussion of Dynamic Methods of Testing Concrete with Suggestions for Standardization," Proceedings American Society for Testing Materials, V. 41, p. 1053, 1941. Ozell, A. M., and E. Ardaman, "Fatigue Tests of Pre-tensioned Prestressed Beams," ACI Journal, V. 28, No. 4, October, 1956 (Proceedings V. 53), pp. 413-424. Ozell, A. M., and J. F. Diniz, "Fatigue Tests of Prestressed Concrete Beams Pretensioned with 1/2 in. Strands," Journal, Prestressed Concrete Institute, V. 3, No. 1, June, pp. 79-88, 1958. Patel, V. 6., "Fatigue of Prestressed Concrete Members," Thesis for the Degree M.S., Michigan State University, 1961. Preston, H. Kent, "Practical Prestressed Concrete," McGraw-Hill Book Company, Inc., New York, 1960. Ros, M. R. "Prestressed Concrete," Report No. 155, Swiss Material Testing Institute (EMPA), Zurich, pp. 17-26, 76-79, 1946. Rowe, R. E., "An Appreciation of Work Carried Out on Fatigue in Prestressed Concrete Structures," Magazine of Concrete Research (London), V. 9, No. 25, March, 1958, pp. 3-8. Stelson, Thomas E., and John R. Verna, "Repeated Loading Effect on Ultimate Static Strength of Concrete Beams," ACI Journal, Proceedings V. 60, No. 6, Part one, June, pp. 743-749, 1963. Stelson, T. E. "Fatigue of Concrete”, Proposal to ACI Committee 215, Unpublished, April 20, 1963. Thomas, F. 6., "Prestressed Concrete,” Proceedings, Conference at Institution of Civil Engineers (London), p. 33, 1949.