A macro-element formulation and solution procedure for shear analysis of RC deep beams

This paper presents a computationally-effective macro element capable of predicting the complete shear response of RC deep beams in analogy with beam elements for slender beams. The element stems from a three-parameter kinematic theory (3PKT) for the shear strength and deformation capacity of deep beams subjected to double curvature. The macro element is composed of two rotational springs and one transverse spring to simulate the nonlinear flexural and shear behaviour of the shear span. The element has two nodes (end sections) with two DOFs per node, which enables it to be easily connected to other elements of the same or different types to model structures with deep beams. The numerical implementation of the element is based on the secant stiffness approach which provides robust convergence properties. Validation studies are performed by using thirteen tests from the literature showing excellent results for the complete shear response. The obtained peak load experimental-to-predicted ratios have an average of 1.10 with a coefficient of variation of 14.2%, while these values for the mid-span deflection are 1.16 and 17.0%.