A force analogy method (FAM) assessment on different static condensation procedures for frames with full Rayleigh damping

In this paper, influence of different static condensation methods on nonlinear time history response of structures in presence of full Rayleigh damping matrix has been studied. Equation of motion is derived in details for 2 newly introduced cases; Full Static Condensation Model and Reduced Static Condensation Model (RSCM or RSCM‐1). Nonlinear analyses are performed with state‐space form of equation of motion along with force analogy method. A novel aspect of this study in comparison with previous researches is to consider full Rayleigh damping in formulations for static condensation in nonlinear structural analysis. Numerical examples are presented for the proposed methods. In addition, the same structure was modeled in finite element method and analyzed by the OpenSEES program. Comparisons demonstrate that results, which are obtained from introduced methods in this article, are in good agreement with the finite element method results. In addition to explaining the equation derivations in main article, proofs for some equations have been demonstrated in appendices. The comparisons show that both RSCM and Full Static Condensation Model lead to almost the same results but in case of using RSCM‐1, the responses have some deviation from other condensation methods.