Second Order Nonlinear Inelastic Analysis of Composite Steel–Concrete Members. I: Theory

A total Lagrangian finite element (FE) model has been formulated for the nonlinear inelastic analysis of both composite beams and columns. An accurate rotation matrix is used in the position vector analysis and nonlinear strain derivations. The slip between the steel and concrete components due to the flexible shear connection at their interface is considered as an independent displacement in the formulation which makes it easier to assign the corresponding proper slip conditions at the connections between composite beams and columns. The effects of nonlinearities and slip on the deformations and strains in the steel and concrete components, and so on the stress resultants (i.e., internal forces), stiffness, and strength of the composite member are thus combined together in the formulation. The constitutive models for steel and concrete in this investigation are based on the longitudinal normal stress and the shear stress induced by the slip between the steel and concrete components. Hence, these models include the effects of the slip at the interface on the von Moses yield surface, associated flow rule and isotropic hardening rule. These constitutive models can be used in association with any type of uniaxial stress–strain curves for steel and concrete, including hot-rolled or cold-formed steel, and confined or unconfined concrete. The constitutive models are expressed in terms of engineering stresses and strains. The total Lagrangian formulation is applicable for these constitutive models directly, and most convenient for the slips at the interface between the steel and concrete components.