A MACRO-ELEMENT FOR THE NONLINEAR ANALYSIS OF DEEP BEAMS BASED ON A THREE-PARAMETER KINEMATIC MODEL

This paper presents a computationally-effective macro element for predicting the complete shear response of RC deep beams. The element stems from a three-parameter kinematic theory (3PKT) for the shear strength and deformation capacity of deep beams under double curvature. The macro element consists of two rotational springs and one transverse spring to simulate the nonlinear flexural and shear behaviour of deep shear spans. The element is applied to two deep beams tested to shear failure under three-point bending. The results are used to study the effect of unsymmetrical shear failures on the pre- and post-peak behaviour of nominally symmetrical members. It is found that the post-peak response is sensitive to the unloading path of the shear resisting mechanisms as well as to the global roughness of the critical diagonal cracks. Based on these analyses, modifications to the constitutive relationships of the shear mechanisms are proposed, and the macro element is applied to a continuous deep beam. It is shown that the model adequately captures the complete behaviour of the beam, including the redistribution of forces following the shear failure in the critical shear span.