Civil Engineering Reference
In-Depth Information
1
Introduction
1.1 History of the Force Analogy Method
The force analogy method (FAM) is an analytical tool for solving structural analysis problems
with material nonlinearity. It uses the concept of “inelastic displacement”, or more commonly
known as the “residual displacement” in the formulation, where the nonlinear stiffness force
due to material nonlinearity is represented by a change in displacement instead of a change
in stiffness. The original concept of FAM was first introduced by Lin (1968), where the pro-
posed method was actually applied to stress and strain in continuum mechanics with the ine-
lastic behavior defined by plastic strain. Unfortunately, this concept only found limited
acceptance because it was developed at approximately the same time as researchers were focus-
ing their attention on studying the deformation of solids using numerical simulation methods,
such as the finite element method with the inelastic behavior defined by changing stiffness.
Although the finite element method is a powerful tool and widely used, the procedure of
the step-by-step numerical integration is unavoidable, time consuming, cumbersome, and
costly for practical design in 1980s and even today.
Recognizing that nonlinear finite element method of analysis is a time-consuming process,
many structural engineers are constantly seeking a simplified dynamic analysis approach for
analyzing nonlinear multi-degree-of-freedom (MDOF) systems to carry out their structural
designs. One simplified approach is to represent the nonlinear MDOF system as an elastic sys-
tem, in which structural response can be estimated by response spectra analysis of using the
convenient and efficient modal superposition method. Newmark (1970) proposed a well-
known method of extending the elastic response spectra analysis to engineering design of non-
linear systems through the use of inelastic response spectra. However, the method is strictly
valid for single-degree-of-freedom (SDOF) systems and thus is inadequate for the analysis
