Full report

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lo0 INTRODUCTION The objective of this experiment was to determine the fatigue strength of reinforced concrete subjected to complete reversal loading The knowledge of these fatigue - . properties, which i s sparsely treated in the current literature, w i l l help in the design of reinforced concrete structure, subjected to a high intensity sound field or any form of severe vibration 2.0 TEST SPECIMEN Forty-five 3.25" x 1 I' x 25" reinforced concrete beams were cut out from three 24" x 1 " x 76 light weight concrete roof slabs. Manufactured by the Alabama Cement Tile Company. The slab manufacturer provides the following specifications Trade Name: Alaslab Density: 12 Ib/q ., ft. Allowable load: 60 Ib/sq.ft. Age: More than 90 days i n air Static Ultimate Tensile Strength: 730 psi, bending Reinforcement: 4 x 4 - 14 gage welded mesh fabric; placed at center of slab; not rusted. Aggregate: Light weight; high limestone content; maximum size not greater than 3/8". These beams were simply supported a t both ends i n a l l tests (see Figure 1 and 2) making the effective beam length, L, equal to 23 1/2". Metal film strain gages (8udd Company, type C6-161)were attached to the top and bottom surfaces of the beams, mid-span between the supports. These gages were first attached to small pieces of steel shim stock (3/1000" thick) which in turn were glued to the concrete surface by an epoxy cement of high bonding strength. Approximately 20 percent of the concrete specimens obtained from the three orig naI roof slabs were defective for one of the following: (i) non-uniform manufacturing process. (ii) initial crack. (iii) cutting fault, (iv) mishandling 3 .O TEST METHOD Seven beams were tested statically i n order to determine the tensile strength of the specimens,the rest were tested dynamically with complete reversal loading i n order to establish a stress-cycle (S-N) curve for the materia In the static test, a beam was loaded i n such a way that i t failed a t a section of

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constant bending moment. This was obtained by the use of a short piece of a 5" W channel placed at the middle position of the concrete beam (see Figure 2). The ultimate static strength i s calculated by the usual stress formula; tensile stress = Mc/l where M = L L Distance from neutral axis to the oute -most ''fibre'' = .5" c = c; : 4 I = Area moment of inertia = 3.25 x 1 /12 = 0.274 in P = Load required for failure of beam L = Length of beam between supports a = Half the depth of the W channel = 2.5" The strain recorded during both static and dynamic tests was quite low compared to the theoretical value. The measurements were greatly affected by localized internal and/or external cracks. The use of strain gages to measure the strain levels, experienced by the specimens unde: test, was therefore abolished. I n the dynamic test, a beam was simply supported at both ends. The supports were then secured to the table of an electromagnetic vibrator (an M B Model C-25 HH exciter). The test set-up and the equipment used are shown i n Figures 3 and 4. The inputs to the exciter, namely, the acceleration, frequency and wave form, can be controlled. The beam specimen vibrated in this fashion went through a tensile and compression stress cycle i n each vibration cycle. The maximum stress experienced by the test specimen was at the outer-most fibre of the specimen, and was a function only of the applied bending moment. The bending moment w i l l be shown to be a function of the relative acceleration of the beam with respect to i t s vibrating supports. Thus, any desirable stress level at the outer-most "fibre1' of the beam could be controlled by the sinusoidal input to the exciter. The data from actual test results show that the fundamental resonant frequency of most beams was 108 cps. tiowever, to avoid difficulties that were encountered i n resonant frequency testing, the beam specimens of this experiment were vibrated at a fixed frequency between 80 and 100 cps. A full report w i l l be issued i n the near future to show the validity O T t i t i s stress-controlling method and the off-resonant vibration technique. A beam thus vibrated i n the dynamic test possesses the same vibration characteristics, relative to i t s suppoiting foundation, as that of a pinned-pinned beam of fixed supports, subjected to forced vibration by an oscillatory, uniformly distributing load applied along the entire length of the beam. (This statement w i l l be proven i n the full report. Notice that in both cases, the generalized forces are the same). The deflection, y ( x,t ), of a beam with pinned-pinned supports, i n i t s fundamental mode, i s X y (x,t) = Y sin II- sin w t C L where Y = maximum deflection of beam C x = span wise coordinate w = 2 n f f - excitation frequency, cps.

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The acceleration can be expressed as 2 = - 0 y ( x , t) The maximum bending moment i s r 2 = - E I ($ y (x,t) max b e 4 f2 L 2 or y (x,t) max = M max E l where E = Young's modulus of elasticity 6 = 2 x 10 psi. It was found i n the static tests that the average tensita strength of the concrete specimens was 730 psi, with an average bending moment of 402 in-lb. The ultimate strength of these specimens, i n the dynamic tests was therefore assumed to be the same. However, since acceleration of the beam relative to i t s supports was to be controlled in the dynamic test, the ultimate strength of the specimen could be expressed in a more convenient form of acceleration, G which would produce a bending moment u l t of 402 in-lb a t the f i r s t half cycle of vibration. From equation (1) we have:

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2 4 x (f) (23.5)* x 12 1 -- x 2 x lo6 x 3,25 -3 2 I = 4.2 x 10 x (f) ,g's A t the test frequencies of 80, 90, 100 cps 402 (-) 386 G = 27.1 g's (peak, a t 8Ocps) ult G = 34,4 g's (peak, a t 9Ocps) ult G = 42.4 g's (peak, a t 100 cps) ult 4,O TEST RESULTS Static Tests: Run Number P L Thus, average moment =- (7-a ) 2 = 402 in-lb average stress =+ Load, P, a t failure, Ib 79 88 79 94 75 101 96 - 87.4 (average) = 730 psi , tension

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Dynamic Tests: Run Freq Acc .(peak) No CPS g's - - 27 100 27.5 32 98 23 33 80 19 34 80 17 35 80 22 36 80 20 38 80 20 39 80 26 % Modulus Time of No. of Cycles of Rupture * run, sec. a t Rupture 65 1 20 12,000 67 6 540 70 130 10,400 63 80 53I 400 81 2 160 74 230 23 I 000 74 235 23,400 96 ;5 40 * Ratio of applied stress to the ultimate stress Loth complited b y the formula Mc/I where M i s the failing bending moment. Figure 5 shows the plot of percent modulus of rupture vs fatigue life cycle from the above resuI ts Figures 6 - 10 show some typical visicorder records of the accelerations measured on the beam tested. CONCLUSION The stress-cycle (S-N) plot of the test results indicates that the endurance l i m i t of the specimen i s about 60 percent All specimens failed in concrete under tension. The reinforcing steel a t the middle of the beam appeared to add no tensile strength to the specimens, The resonant frequency of the beam specimens decreased continuously as the load cycles increased The decrease might be due to: (i) readjustment of end fixity (ii) the increase of internal damping (iii) internal and/or external cracks. The dynamic magnification factor, Q, and therefore the resonant response of the beam, decreased continuously as loa-i cycles increased. Q dropped from an initial value of 8 or 9 to 2 or 3 a t the ends of some longer tests. The Q measurements were conducted by low level resonant scans a t intervals during dynamic testing. The decreasing of Q indicated the increase of the internal damping of the material. The continuous changing of resonant frequency and Q, and the in-phase or outof-phase problems of response of beam to the excitation made resonant frequency

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fatigue vibration testing difficult. Off-resonant frequency testing i s therefore more suitable for this experiment. 6) The test specimens were not manufactured uniformly, and the material was not homogenous. Some beams, for example, failed i n static test a t a much lower Some of the tests, both static and dynamic, were therefore stress than expected. discarded i f there was a good reason to believe that the beams were abnormal e 7) It was very difficult to determine the exact load cycles of the specimens a t high percentage of modulus of rupture i n the dynamic tests. The acceleration of those tests could not be brought to the desired level i n a very short period of time. 8) Concrete beam specimens, eemile - reinforced a t the top and bottom of the specimens, are desirable for further study of the fatigue properties of concrete * 9) Random vibration testing should be included i n a further study. INSTRUMENTATION The instrumentation used for the tests i s listed below: One B and K Automatic Vibration Exciter Control, Model 1019. One M B Vibrator, Model C25 HH, Type A, MoB. Mfg. Company. One Electronic Counter, Hewlett Packard ., One Wyle lOKW Power Amplifier. One Honeywell Visicorder, Model 1508 One Oscilloscope, Type 545A, Tektronix, Inc One Strain Gate Indicator, Model W H 1, Strainsert Company. One Endevco Accelerometer, Model 2213 Three Endevco Accelerometers, Model 2226.

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REPORT NO. PAGE NO 3

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PAGE NO I 4 ' Fiaui-e 2: S i m p l y Suppolted Co:iciete Beam Uridei Static Test

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-'L- A c 'ON 3 5 V d 'ON l d O d 3 d

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I REPORT NO. PAGE NO Figui-e 4:

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r I I MODEL DATE 1 0 0 a .-

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• . t i g u l r 0 . Rut: N o , 34

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Figui-e 7. Run ;.lo. 38

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Figuie 9 . Low L e v t S,at) or Run N o . 34 A f t e r .j600Cycles

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