Post-cracking shear modulus of reinforced concrete membrane elements

The shear modulus of reinforced concrete membrane elements subjected to monotonic in-plane shearing stresses is typically calculated using the elastic theory. Upon cracking, however, the elements suffer a significant loss in rigidity and hence the shear deformations at service load levels cannot be accurately calculated using the pre-cracking modulus. This paper presents a simple empirical equation for the calculation of the post-cracking shear modulus, given in the form of the tangent slope of the shear stress-strain curve. The proposed empirical equation is based on the experimental results from forty membrane specimens, and relates the cracked modulus to a "combined" index of the reinforcement in the orthogonal directions. In spite of its empirical nature and simplicity, the equation is capable of capturing the effect of different amounts of reinforcement and concrete strength. Hence it applies to both under-reinforced and over-reinforced membranes, and to normal and high strength concrete. (C) 2009 Elsevier Ltd. All rights reserved.