Nonlinear Analysis of Structures

This lecture covers the flexibility-based fiber beam-column element and force-based beam-column elements for nonlinear analysis of structures. It delves into element displacement increments, force-displacement relations, section flexibilities, stiffness matrices, residual deformations, and residual forces. The lecture also discusses the analysis of a tapered member, integration points, weights, and section flexibility. The instructor, Prof. Dimitrios Lignos from RESSLab EPFL, explains the deformation updates, residual displacements, and transformation of residuals to resisting forces. The lecture concludes with examples of tapered members, axial forces, and tangent section flexibilities.