# fema-440:6.Improved Procedures for Equivalent Linearization

## fema-440:6.等效线性化的改进方法

Posted by JS on March 1, 2021

## 6.1 Introduction

This chapter presents an improved equivalent linearization procedure as a modification to the Capacity-Spectmm Method (CSM) of ATC-40. The CSM is a form of equivalent linearization briefly summarized in Sections 2.4 and 3.3.1. Detailed information on equivalent linearization in general and the derivation of the improved procedures are included in Appendix D.

When equivalent linearization is used as a part of a nonlinear static procedure that models the nonlinear response of a building with a SDOF oscillator, the objective is to estimate the maximum displacement response of the nonlinear system with an “equivalent” linear system using an effective period, Teff, and effective damping,$\beta$eff, Aff (see Figure 6-1). The global force-deformation relationship shown in Figure 6-1 for a SDOF oscillator in acceleration-displacement response spectrum (ADRS) format is termed a capacity curve. The capacity curve shown in Figure 6-1 is developed using the conventional procedures of FEMA 356 or ATC-40. The effective linear parameters are ftnctions of the characteristics of the capacity curve, the corresponding initial period and damping, and the ductility demand, g, as specified in the following sections.

Recommendations for the improved equivalent linearization procedures rely on the previous procedures in ATC-40, and much of the process remains the same. This chapter focuses on the parts that change. The following section presents new expressions to determine effective period and effective damping. It also includes a technique to modify the resulting demand spectrum to coincide with the familiar CSM technique of using the intersection of the modified demand with thvapacity curve to generate a performance point for the structural model. The reduction in the initial demand spectrum resulting from the effective damping may be determined using conventional techniques outlined in Section 6.3. The previous limits on effective damping of ATC-40 should not be applied to these new procedures. However, the user must recognize that the results are an estimate of median response and imply no factor of safety for structures that may exhibit poor performance and/or large uncertainty in behavior. The effective parameters for equivalent linearization are functions of ductility. Since ductility (the ratio of maximum displacement to yield displacement) is the object of the analysis, the solution must be found using iterative or graphical techniques. Three of these are presented in Section 6.4. They have been developed to be similar to those of ATC-40.

Finally, it should be noted that these procedures may not be reliable for extremely high ductilities (e.g., greater than 10 to 12).