Nonlinear Modal Analysis of Structures with Rigid-End Offsets

The nonlinear modal analysis (NMA) methodology for analyzing moment-resisting framed structures is here extended to include frame elements with rigid-end offsets. Four key components of the NMA methodology for conducting dynamic analysis of nonlinear framed structures include: (1) the force analogy method for material nonlinearity; (2) stability functions for geometric nonlinearity; (3) the state space method for dynamic analysis; and (4) modal superposition for computational efficiency. Under this NMA methodology, the nonlinear stiffness matrices capturing full panel zone rigidities and centroidal locations of plastic hinges in moment-resisting frames are completely derived in conjunction with satisfying global equilibrium, joint compatibility, and element force-displacement relationship. Nonlinear dynamic analysis of a 10-story steel frame with rigid-end offsets is then performed and results are compared with those obtained using Perform-3D (P3D) commercial software. Good agreement between NMA and P3D results indicate accuracy of the proposed methodology even though it is based on different assumptions.