A relationship between progressive collapse and initial buckling for tubular structures under axial loading

• Windowed and conventional triangular, square and pentagonal tubes under axial loading were simulated.
• Two buckling modes, symmetric and anti-symmetric, were observed in the windowed tube.
• There exists a critical symmetric buckling mode in the windowed tube.
• At critical buckling mode, the mean crushing force of windowed tube matches well with that of the corresponding conventional tube.

The progressive collapse of tubular structures under axial loading is a challenging problem in mechanics. Due to the nonlinearities in large plastic deformation, such a problem can only be solved case by case under the assumption of an appropriate collapse mechanism. In this paper, a relationship between the progressive collapse of an axially loaded tube and the initial buckling of its windowed counterpart is presented. Numerical investigation was performed on the axial crushing of triangular, square and pentagonal tubes and the initial buckling modes of the corresponding windowed tubes. Results show that at the critical symmetric buckling mode, the theoretical mean crushing force of the angle-shaped column in the windowed tube matches very well with the actual mean crushing force of the conventional one. This relationship is crucial to the development of a generalized method for progressive collapse without assuming collapse mechanism. Based on it, an empirical equation on the mean crushing force of axially loaded square tubes is presented. The mean crushing forces predicted by this equation are in good agreement with the experimental results and theoretical values.