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.

Earthquake analysis of
linear systems

**Abstract: **In this chapter procedures for
earthquake analysis of structures** **idealized as a *lumped ma*ss
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.

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Civil : Structural dynamics of earthquake engineering : Earthquake analysis of linear systems |

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