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Recently, high strength steel is used increasingly for plates which constitute the frame structures of vehicles. Since these plates become thinner, the buckling on the plates has been recognized as an important issue for automotive industries. For this issue, various methods have been proposed and are currently in practical use. In this paper, the buckling stress relation equations of the plate are discussed which is the basis of buckling analysis of a structure, and on the basis of the buckling stress relation equation of a single plate, the relation equation of compression and shear is shown under axis compression force and twisting torque on the box beam composed by thin plates. And, the approximate expression for the compression buckling stress is proposed by the knowledge of the buckling eigenvalue equation by the energy method and the approximate expression of the twisting. The accuracy of the approximate expression and relation equation is investigated as compared with the results from the buckling eigenvalue analysis by FEM. As the results, well-known relation equations of the plates can be obtained by approximating the buckling eigenequations by the energy method assuming the deformed shape function with low-order terms. Also the compression buckling stress of the box beam determined by a single plate theory does not have enough accuracy, and it is necessary to consider the coupling with adjacent plates. The difference between the proposed expression and results by FEM is less than about 6% for the aspect ratio of the cross section between 0.3 and 1.0. And then, the shown buckling stress relation equation of compression and torsion has up to 12% difference from the results by FEM.

Buckling stress relation equations of box beam under compression and torsion