Displacement estimation of nonlinear structures using the force analogy method

Significant effort has gone toward developing accurate and efficient displacement estimation procedures for the nonlinear multi-degree-of-freedom (MDOF) system. Although the dynamic nonlinear analysis is capable of providing the high computational precision through the step-by-step time integration method, the simplified method is still expected and imperative for seismic design practices. The work presented in this paper focuses on the implementation of using the modal superposition method to estimate displacement responses of the nonlinear MDOF system based on the force analogy method (FAM). The current research demonstrated that the equation of motion for the nonlinear MDOF system can be decoupled, but other two governing equations in the FAM about the internal force, such as the moment and force of structural members, are not decomposable. Thus, the FAM is incorporated with the modal pushover analysis (MPA) method to determine the basic parameters of each mode such that the modal superposition method can be suitable for the solution of the nonlinear MDOF system. The procedure presented here is an approximately estimation method due to the application of MPA method. However, the value and potential for the maximum displacement estimation of the nonlinear MDOF system were demonstrated through the application in a framed structure. Copyright (c) 2014 John Wiley & Sons, Ltd.