Geometric and material non‐linear analysis of beam‐columns and frames using the minimum residual displacement method

A geometric and material non‐linear analysis procedure for framed structures is presented, using a solution algorithm of minimizing the residual displacements. This new non‐linear solution technique is believed to be the optimum in the Newton–Raphson scheme since it follows the shortest path to achieve convergence. The concept of the effective tangent stiffness matrix is introduced and is found to be efficient, simple and logical in handling the non‐linear analysis of frames with braced members and in separating multiple bifurcation points.