Analytical solution for a new higher order steel-concrete composite beam model

This paper presents an analytical solution of a composite beam model in which the constrained kinematics takes account of the overall shear deformability, warping of the slab cross section and of the steel beam, and partial shear interaction between slab and girder. The warping functions are obtained by considering the problem of unrestrained thin-walled members subjected to self-equilibrated elementary load schemes. The governing equations are derived from the balance condition imposed with the Virtual Work Theorem. The analytical solution of the governing differential equations is obtained exploiting exponential matrices. This method, furnishing the exact formulation of the solution without requiring any discretization of the beam, is used to determine the solution of the proposed applications according to the stiffness method, deriving the stiffness matrix and the reactions of fixed-end beams. Two case studies, i.e. a symmetric two span bridge deck subjected to a uniformly distributed load and to a point load, are presented; the comparisons with results obtained with a refined shell finite element model are very satisfactory.