Civil Engineering Reference
In-Depth Information
8
Application of the Force
Analogy Method in Modal
Superposition
The conventional modal superposition method (MSM) has been validated as a fast and simple
way to calculate responses of multi-degree-of-freedom (MDOF) systems under environmental
loads. Significant effort has been spent towards extending the usage of MSM in linear dynamic
analysis to nonlinear dynamic analysis. In this chapter, the MSM for decoupling governing
equation of motions in the force analogy method (FAM) is implemented. The main feasible
reason is that the nonlinear deformation of the MDOF system can be separated to the elastic
and plastic displacement so that the left-hand side of the equation of motion of nonlinear sys-
tems retains the linear properties of corresponding elastic system in the FAM. The nonlinear
static pushover analysis (NSPA) procedure in the FAM is established and some examples are
presented to demonstrate it. In addition, it is validated that the equation of motion for the
MDOF systems in the FAM can be decoupled and two others for solving the force and moment
of structural members cannot be decomposed directly. However, the NSPA procedure in the
FAM provides a way to determine each equivalent single-degree-of-freedom (SDOF) system
corresponding to various models such that the decomposition of these two equations can be
achieved.
This chapter consists of three parts: Nonlinear static pushover analysis, modal decomposi-
tion method and response summation. They are presented in Section 8.1, 8.2 and 8.3,
respectively.
