Shear-Flexible Steel-Concrete Composite Beams in Partial Interaction: Closed-Form “Exact” Expression of the Stiffness Matrix

Abstract

This paper presents a theoretical model for analyzing shear-flexible steel-concrete composite beams in partial interaction. Both concrete slab and steel beam are modeled according to Timoshenko’s theory, and a continuous linear-behaving shear connection is considered between the two connected members. Simplified kinematic assumptions have been considered for the displacement fields of the two connected members to derive a model, which is at one time rather general, but even simple enough to be easily handled and actually solved in closed-form. The analytical formulation of both stiffness matrix and vector of equivalent nodal forces is the key achievement of the present paper. They completely define an “exact” finite element for the mentioned model and can be easily employed for carrying out computationally efficient analyses of steel-concrete composite beams looking after the effect of both shear flexibility of the structural members and slips occurring at the interface between the two connected members. Simple applications are finally proposed for demonstrating that the present “exact” finite element can be employed for analyzing shear-flexible steel-concrete composite beams by using just one element-per-member. Thus, it is more efficient than both alternative numerical solutions already available in the scientific literature and commercial finite element packages.