Computational analysis of shear deformation effects on open thin-walled beams

When subjected to eccentric lateral or vertical loads, Open Thin-Walled Members (OTWMs) will suffer the risk of torsional failure for their relatively low torsional rigidity. The classic torsional theory, Vlasov's theory, was found to greatly underestimate the torsional rotation especially for OTWMs with lower span-depth ratio or lower shear modulus. Shear deformation along the middle line of cross section, which is neglected in Vlasov's theory, was considered and quantified in this paper. Two examples (U-beams and I-beams) were taken to be calculated by the proposed method, Vlasov's theory and finite element analysis. Results of average errors 2.90% and 1.77% guaranteed the applicability and accuracy of the proposed method. Besides, parametric analysis including different configurations, boundary conditions and span-height ratio were conducted to evaluate the effects of shear deformation on the torsional rotation of OTWMs. It was revealed that stronger boundary constraint and smaller span-depth ratio lead to greater effects of shear deformation, which cannot be neglected. The critical criteria to consider or ignore the shear effects under different boundary conditions were also defined.