Modelling stability of reinforced concrete walls applying convex optimization

Due to time constraints on structural design processes, modelling and computational complexityis often a key concern in limit state analysis of reinforced concrete (RC) structures, causing practitioners tochoose efficient but inaccurate methods of analysis over more advanced ones. Recently, a framework usingconvex optimization for elasto-plastic, geometrically linear analysis of RC walls was proposed, enabling analysisof models with more than 10,000 finite elements within minutes on a standard PC. In order to improve theapplicability and relevance of the framework as a design tool, this paper proposes an extension that enablesthe determination of the critical buckling load. Based on the nonlinear solution obtained from the elasto-plasticoptimization problem, the cracked tangent stiffness of the RC sections is determined, and a linearized bucklingproblem is posed and solved as a linear eigenvalue problem. This allows the actual critical buckling load tobe determined by solving a sequence of optimization and eigenvalue problems. The accuracy of the proposedmethod is assessed, and its applicability to practical design scenarios is demonstrated by an analysis of an RCwall with a door hole, showing an average solution time of approximately 30 seconds per load step.