Nihon Kikai Gakkai ronbunshu (Mar 2023)
Theoretical analysis of shear buckling stress in torsion of thin-walled square cross-section beams
Abstract
Thin high-strength steel sheets are increasingly being applied to vehicle frames in order to increase the strength and reduce the weight. The thinner the plate, the more likely it is to occur buckling. So it is important to understand the structural properties based on buckling theory in order to efficiently design for buckling in the early stages of vehicle development. The authors have addressed the issue of theoretically determining the shear buckling stresses in torsion of thin-walled square cross-section beams. In the previous paper (Budiansky, et al., 1948) for determining shear buckling stresses in torsion of infinitely long thin-walled square beams, two adjacent plates were treated collectively, the buckling modes were expressed as an infinite series in the width direction and a single sinusoidal wave in the infinite length direction, then, the method of Lagrange multiplier was used to consider the constraint condition in the center line, finally the shear buckling stress was obtained by the energy method. However, this process cannot be applied to finite-length beams because a single sinusoidal wave cannot satisfy the boundary conditions at both ends in the longitudinal direction. So, the purpose of this paper is to theoretically determine the shear buckling stress in torsion of a thin-walled square beam of finite length. First, based on the previous process, two adjacent plates are considered to be a single plate, and the buckling mode is represented by an infinite Fourier series as in the shear buckling of a single plate. The shear buckling stress in torsion is obtained by the energy method, taking into account the constraint condition in the center line of the width direction of the plate by the method of Lagrange multiplier. The validity of the derived values is compared with the FEM results, and the results are in good agreement.
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