Analysis of stability and mechanism of frames with partially rigid connections

Abstract

A method is presented for stability analysis and finding mechanisms of frames with partially rigid connections. Equilibrium equations are formulated with respect to the reduced vector of member-end forces, for which linear constraints are assigned. The modes of self-equilibrium forces and unstable mechanisms are found using singular value decomposition of the matrix representing equilibrium equations and constraints. An infinitesimal mechanism with small degree of kinematic indeterminacy can be found using limit analysis for an artificial proportional loading condition. The effectiveness of proposed method is demonstrated through examples of frames with rectangular and hexagonal grids.