Authors: M. Gerin and P. Adebar
13th World Conference on Earthquake Engineering (WCEE), Vancouver, Canada, August 2004
Abstract
Techniques for modelling the seismic response of concrete structures are limited by the accuracy of the material models. Current models for reinforced concrete subjected to shear typically do not account for the effects of cracking and yielding. Diagonal cracking has a very pronounced effect on the shear stiffness of concrete structures, however, recommendations for cracked section shear stiffness are not readily available. The plastic strain of reinforcement is another important parameter that must be considered in the nonlinear seismic shear analysis of reinforced concrete. There is a strong relationship between plastic strain of reinforcement and plastic shear strain, e.g. yielding of the reinforcement results in yielding in shear of the element. Pinching of hysteresis loops is directly linked to the plastic strain in reinforcement, as is the deviation of principal compression stress and principal compression strain angles in concrete. The authors have recently developed a general model to predict the complete load-deformation response of reinforced concrete elements subjected to reverse-cyclic shear.
A unique feature of the model is that deformations at the cracks are separated from deformations of concrete between cracks, and crack deformations are assumed to be a consequence of strain compatibility between concrete and reinforcement. This paper presents simplified methods for modelling the non-linear seismic shear response of reinforced concrete based on the underlying principles of the general model. The methods include an effective cracked section shear stiffness determined from the shear strength and the shear strain at yield. The shear strain at yield is primarily a function of the yield strain of the horizontal reinforcement and strain of the vertical reinforcement. The cracked section shear stiffness can be used for linear analysis. For non-linear static analysis, a complete envelope is provided where the shear response is assumed to be elastic-plastic. The ultimate shear strain is determined from the shear strain at yield and the shear strain ductility.
The latter is a function of the ratio of shear stress to concrete compression strength. Simple hysteretic rules are also provided to define the complete reverse-cyclic shear response for non-linear dynamic analysis.
