Modal decomposition of thin-walled member collapse mechanisms

• GBT-based modal decomposition of elastic–plastic equilibrium configurations and collapse modes.
• First-order elastic–plastic GBT formulation to assess the structural behaviour of thin-walled beams.
• Illustration: 5 elastic–plastic thin-walled beams with different cross-sections and support conditions.
• Most of the GBT-based results effectively validated against ABAQUS shell finite element values.
• Novel concept with great potential relevance for the improvement or development of design methods.

Following recent investigations on the decomposition of elastic buckling modes into combinations of structurally meaningful deformation modes, this work presents a novel extension of the above procedure to elastic–plastic collapse mechanisms and highlights the relevant role that this concept may play in the mechanical knowledge/interpretation of thin-walled member failures. In order to achieve the sought decomposition, a code based on a Generalised Beam Theory (GBT) formulation developed to perform first-order elastic–plastic analyses of thin-walled members is employed. Five illustrative examples are presented and discussed, and the results displayed, namely load-deflection curves, deformed configurations and stress contours, are validated through the comparison with values provided by shell finite element analyses. The most relevant modal results addressed consist of (i) load-deflection curves determined on the basis of pre-selected deformation mode sets, (ii) modal participation diagrams and (iii) modal amplitude functions. These results make it easy to characterise and interpret the mechanics associated with the thin-walled member elastic–plastic failures (as well as with the various loading stages), which may be of great importance in the improvement/development of existing/new design methods (e.g, yield-line theory, direct strength method).