A voxels-based Rayleigh-Ritz method for the post-buckling elasto-plastic analysis of restrained steel columns in fire

Abstract

The paper presents a novel numerical strategy to analyse steel columns in fire, based on the concept of voxel. The material obeys to an elasto-plastic constitutive law that degrades with temperature. The member's internal strain energy is computed through an original methodology: the column is considered to be a grid of small and perfectly packed parallelepipeds, denominated as voxels. Any quantity is constant along any voxel and equal to its value at the voxel's geometric centre. The coordinates of each voxel's geometric centre are inferred by the voxel's ordering in the global grid, and its constitutive law depends solely on the strains and on the temperature at the voxel's geometrical centre, and is independent of the neighbouring voxels. The total internal strain energy is given by the sum of all internal energies along the grid and depends solely on the temperature and of the degrees of freedom. The strategy is able to deal with complex behaviours, such as snap-back and spread of plasticity, and requires a smaller number of degrees of freedom to a given accuracy, when compared to alternative methodologies. It enables new and transformative insights on the behaviour of columns in fire and can be incorporated in other methodologies.