Torsion of Box Girders with Deformable Cross Sections

Abstract

This paper studies thin‐walled trapezoidal cross‐section beams with lateral cantilevers subjected to a torsional load, considering the distortion of the cross section. Transverse and longitudinal displacements of the walls are governed by six shape functions, which describe bending in the horizontal plane, as well as torsion and distortion of the cross section; the shearing strain in the middle plane of the walls is considered; the shear center is not used. The theorem of minimum total potential energy is used to derive the governing equilibrium equations (and boundary conditions), whose solution is given in closed form. A wide set of constraints is studied (rigid or flexible transverse diaphragms, mixed kinematic and static boundary conditions), from a theoretical point of view and in numerical examples. The following results were obtained: (1) Torsion and distortion are a pair of coupled problems: distortion and warping stresses are always present; in particular, the longitudinal stress at the side cantilevers increases near “critical” loaded or constrained cross sections (the model detects this effect owing to the distinctive hypothesis of piecewise linear warping on the top flange for