Finite element formulation of a composite double T-beam subjected to torsion

Abstract

When a composite double T-beam is subjected to torsion, a pair of prestressing tendons resist torsional twisting due to the coupled restoring forces provided by the restoring action of the upward and downward displaced prestressing tendons. In addition, the composite action of the composite double T-beams provides an additional pure and warping torsional resistance. A three dimensional finite beam element for the composite double T-beam is formulated to account for the torsional stiffness due to the restoring action of a pair of prestressing tendons and the composite action. The finite element formulation is based on Vlasov’s hypothesis that considers the warping displacement in open sections. Strain energies stored in concrete, encasing steel, reinforcing bars, and a pair of prestressing tendons are included in the total potential energy of the composite double T-beam. Two-noded beam elements with seven-degrees of freedom per node approximate the axial, flexural, and torsional displacements. The torsional resistance due to the restoring action of the pair of prestressing tendons is discussed by comparing the two warping stiffness terms calculated with and without the consideration of their action. As numerical examples, two-span and three-span steel composite double T-beams are analyzed, and their bimoments and angles of twist are compared with those calculated from the conventional three dimensional finite element analysis and the analytical method of solving the governing differential equations.