Behavior of Reinforced Concrete Elements under Cyclic Shear. II: Theoretical Model

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Abstract
In order to design reinforced concrete (RC) structures in earthquake regions, a cyclic softened membrane model (CSMM) is presented to predict the load–deformation behavior of RC membrane elements subjected to reversed cyclic shear stresses. This model is an extension of the softened membrane model for monotonic shear behavior. Both models are rational because they satisfy Navier’s principles of mechanics of materials (stress equilibrium, strain compatibility, and constitutive laws of materials). Three new components of material laws were required in developing CSMM: the stress–strain relationships for concrete and steel in the unloading and reloading regions, the modifications of the envelope curve for compressive concrete, and the Hsu/Zhu ratios for cyclic loading. In order to verify the CSMM as a valid theoretical model, this study focused on comparing the predictions of CSMM with actual test results reported in the companion paper. We conclude from this comparison study that the CSMM can indeed predict the hysteretic loops and their pinched shapes, and that the “pinching effect” was the result of steel bar direction deviating from that of the principal stresses. The “pinching mechanism” and the “failure mechanism” are logically explained using Mohr’s circles of stresses and strains.

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