Truss modeling of reinforced concrete shear-flexure behavior

ABSTRACT

A reinforced concrete beam-column, assumed to possess a series of potential crack planes, is considered as a truss consisting of a finite number of differential truss elements and analyzed using the virtual work method to define the lateral force-deformation relationship. The differential truss is simplified using various numerical integration schemes, since the analytical integration involves the complexity. From such truss models the effects of the diagonal shear cracking can be reliably modeled and valuable information such as crack angles and the cracked elastic stiffness in both shear and flexure can be determined. An equation to estimate the theoretical crack angle is derived by considering the energy minimization on the virtual work done by shear and flexural components. Theoretical crack angles compare favorably with experimentally observed crack angles reported by previous researchers. It is postulated that the total shear strength can be found by combining three complementary mechanims that arise from truss action that incorporates the transverse hoop steel; truss action that incorporates the concrete tensile strength normal to the principal diagonal crack plane; and arch action that incorporates the axial load transferring mechanism. Displacement compatibility requirements are applied when combining the three mechanism to give the overall shear force-deformation behavior. The theory is also implemented computationally using cyclic non-linear truss elements. However, the present version of modeling technique cannot properly account for the cyclic loading effect due to the earthquake duration effect. If improved constitutive models were used to more faithfully represent concrete and steel behavior (under cyclic loading), then the overall predictions should also markedly improve