Theoretical analysis of shear buckling stress in torsion of thin-walled square cross-section beams

Thin high-strength steel sheets are increasingly being applied to vehicle frames in order increase the strength and reduce weight. The thinner plate, more likely it is occur buckling. So important understand structural properties based on buckling theory efficiently design for early stages of development. authors have addressed issue theoretically determining shear stresses torsion thin-walled square cross-section beams. In previous paper (Budiansky, et al., 1948) infinitely long beams, two adjacent plates were treated collectively, modes expressed as an infinite series width direction a single sinusoidal wave length direction, then, method Lagrange multiplier was used consider constraint condition center line, finally stress obtained by energy method. However, this process cannot be finite-length beams because satisfy boundary conditions at both ends longitudinal direction. So, purpose determine beam finite length. First, process, considered mode represented Fourier plate. method, taking into account line plate multiplier. validity derived values compared with FEM results, results good agreement.