Closed-form solution for crushing response of three-dimensional thin-walled “S” frames with rectangular cross-sections

The crushing behavior of thin-walled rectangular cross-section “S” shaped frames subjected to complex loading cases was analyzed. The results of the biaxial bending collapse of prismatic beams and the collapse under combined bending and compression developed earlier by the present authors were applied to a practical problem of a three-dimensional S frame. The analytical solution of the crushing resistance was derived and the two types of deformation modes were identified using the analysis of the fully plastic bending moment with different orientation angle of bending axis. It was shown that the critical aspect ratio of the rectangular cross-section separating the two deformation modes is 1.366. The analytically derived crushing force gave excellent correlation with the finite element results. The simplified calculation routines derived through this study can be applied to an early design stage of a car body.