State space formulation for composite beam-columns with partial interaction

A state space formulation is established for analyzing static responses of composite members with partial shear interaction under the combined action of an arbitrary transverse load and a constant axial force. Three generalized displacements (deflection, rotation angle, and interface slip) and three generalized forces (bending moment, shear force, and axial force) are combined into a state vector, which satisfies a state equation whose solution is easily obtained using matrix theory. The interfacial normal contact stress between the two subelements of a composite member is derived in order to check the validity of the basic assumption of identical deflection (or curvature) possessed by the two subelements. We find that, when a concentrated load alone acts on clamped–clamped or clamped–free beam-columns, tensile normal contact stress does appear at certain part of the interface. The formulation is then readily extended to analyze continuous composite beam-columns and inhomogeneous composite beam-columns. In particular, a non-continuous model of slip stiffness along the interface with discrete rectangular pulses is incorporated into the analysis, and the numerical results indicate a significant effect of slip stiffness ununiformity on the critical axial load as well as internal actions of the composite members.