Predicting the Cyclic Behavior of Reinforced Concrete Beams
Hanks, David L.
McCabe, Steven L.
University of Kansas Center for Research, Inc.
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The effects of beam width on the cyclic behavior of reinforced concrete beamto-column connections are investigated. A new procedure, which takes into consideration the influence of a member's strength, stiffness, and load history on cyclic performance, is developed to predict the number of cycles to failure and energy dissipation capacity per cycle in terms of beam design and load parameters. A parametric investigation is performed to quantify and evaluate the effect of changes in flexural and shear strength and geometry on the predicted number of cycles to failure. Four lightly reinforced concrete cantilever beams, representing exterior beamto-column connections in a moment resistant frame, were tested and compared to earlier tests to evaluate the effect of beam width on member response under severe cyclic loading. The overall dimensions of the specimens and the design strength of the columns were identical. The flexural reinforcement ratios of the beams were 0.34 or 0.51% and the maximum applied shear stress varied from 64 to 105 psi. The ratio of positive to negative moment beam reinforcement at the column face was 0.5 or 1.0. The size and spacing of the transverse reinforcement did not vary between specimens and provided a nominal stirrup shear capacity of 79 psi. The nominal concrete strength was 4,000 psi. The ratio of beam width-to-effective depth remained constant at 0.95. Specimen response is evaluated based on the number of cycles to failure, energy dissipation capacity, and Energy Dissipation Index, D;. Test results from the current study are compared to previous research results for narrow beams fabricated with the same reinforcement and subjected to the same load history. A rational procedure, based on a physical interpretation of the load-deflection hysteresis response of reinforced concrete beams, is developed to predict the number of cycles to failure and the energy dissipation capacity per cycle in terms of a beam's design and loading parameters. A parametric investigation is perlormed to evaluate the effects of a change in flexural and shear strength and geometry on the preclicted number of cycles to failure. Based on the response of the beams investigated in the current study, an increase in the ratio of positive to negative moment reinforcement results in an increase in energy dissipated. For the wide beams with the same geometry and flexural and shear reinforcement, an increase in the clisplacement ductility factor decreases the number of cycles to failure and energy clissipation capacity. A comparison of wide and narrow beam test results shows that an increase in width increases the number of cycles to failure and energy dissipation capacity. An increase in the predicted number of cycles to failure is obtained with 1) a decrease in the maximum applied shear stress and root-mean-square clisplacement ductility factor, and 2) an increase in the nominal stirrup strength, ratio of positive to negative moment reinforcement, and ratio of beam width-to-stirrup spacing. The findings of the parametric investigation show that, for the beam used in the case study, the least improvement in cyclic perlormance is obtained through an increase in concrete strength. The most effective means available to increase cyclic perlorrnance is to increase the amount of positive moment reinforcement within the hinging regions.
Hanks, D.L., Darwin, D., McCabe, S.L., "Predicting the Cyclic Behavior of Reinforced Concrete Beams," SM Report No. 33, Research Grant PFR 79-24696, The National Science Foundation, March 1993, 250 pp.
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