GENERALIZED WARPING TORSION FORMULATION

A general formulation for torsional-flexural analysis of beams with ar bitrary cross section is presented in a general coordinate system. The theory maintains Vlasov's approach in terms of generalized strains an d stresses and yields the same system of differential equations. The c ommon hypothesis of transversely rigid cross section, which overestima tes the effective flexural and torsional section stiffness, is replace d by the assumption that stresses in the plane of the cross section ar e small. The resulting theory reduces to the exact solution of Timoshe nko when warping effects are neglected. Shear stresses due to shear fo rces, warping torsion, and Saint-Venant torsion are determined as the gradient components of a unique potential function. These equations ar e solved with the finite element method, which also provides the flexu ral and torsional section stiffness and the shear center. Numerical ex amples are presented and results are compared with full three-dimensio nal finite element analyses. The formulation is simple and, in spite o f the limitations of the simplifying hypotheses, sufficiently accurate for many engineering applications, bypassing costly three-dimensional finite element analyses.