Interactive Plastic Local Buckling of Box-shaped Aluminium Members under Uniform Compression

A theoretical approach for predicting the ultimate resistance of aluminium alloy members subjected to local buckling under uniform compression is presented focusing the attention on box sections. Starting from the J2 deformation theory of plasticity, the theory of plastic buckling of plates is presented including, as an original contribution, also the variability of the Poisson's ratio depending on the stress levels. The differential equation of the plates at the onset of buckling is developed and the corresponding solution is provided. Starting from the obtained closed-form solution, the interactive buckling either in the elastic or in the plastic range is analysed. The interaction between the plate elements constituting the member section is explicitly accounted for using a completely theoretical approach where the evaluation of the critical stress leading to local buckling in the plastic range is derived as the value corresponding to the existence of a non-trivial solution for which the determinant of the matrix of the equation system is equal to zero. The accuracy of the plastic buckling theory is pointed out by comparing the buckling resistance obtained by the theoretical approach with the values of the ultimate resistance provided by stub column tests. Finally, some advances concerning the use of the effective thickness approach, currently adopted by Eurocode 9, are also proposed and herein presented for the first time and compared with test results.

Automated summary

This paper presents a theoretical approach for predicting the ultimate resistance of aluminium alloy members subjected to local buckling under uniform compression, focusing on box sections. The theory considers the variability of Poisson's ratio, develops the differential equation of plates at the onset of buckling, and analyses the interactive buckling in the elastic or plastic range. The accuracy of the plastic buckling theory is validated by comparing theoretical predictions with values from stub column tests and proposing advances in the effective thickness approach.