Earthquake analysis of linear systems

Earthquake analysis of linear systems

Abstract: In this chapter procedures for earthquake analysis of structures idealized as a lumped mass system are developed. This chapter also describes the calculation of structural response as a function of time when the structure is subjected to earthquake ground motion. Discussion will be with respect to multi-storey buildings with symmetric plan using response history analysis (RHA). Then response spectrum analysis (RSA) is applied to compute the peak response of a structure during the earthquake from the earthquake response. Analysis of buildings with an unsymmetric plan is also discussed.

Key words: response spectrum, response history, modal contribution factor, earthquake analysis, linear systems, CQC rule, SRSS rule.

Introduction

The earthquake excitation of structures is defined in terms of ground motion which varies from site to site. Hence, defining the appropriate ground motion of a particular site has been the subject of research. The irregular slippage among faults succeeded by multiple random reflections, refractions and attenuations within the ground earth formation through which they pass produce earthquakes responsible for ground shaking. Hence, stochastic modelling of strong ground motion seems appropriate and this has led to the development of procedures to generate synthetic accelerograms. For very important structures like nuclear reactors and nuclear power plants located in a zone of high seismic activity, it is desirable to carry out a stochastic seismic analysis that describes the response in probabilistic terms. However, for most of the structures deterministic seismic analysis is sufficient. This chapter discusses the deterministic earthquake response of structures; that is, the response of structures to prescribed earthquake loadings. There are two commonly used deterministic procedures for specifying seismic design loads:

1.     dynamic analysis

2.     the equivalent static procedure.

The dynamic analysis can be either a response spectrum analysis (RSA) or a complete time history analysis (THA). The equivalent static force procedure (which will be discussed in the next chapter) detailed in most seismic design codes of various countries, specifies earthquake induced inertial force in the structure as equivalent static loads by the use of empirical formulae. This chapter provides an introduction to the deterministic earthquake response of structures.