Advances in Seismic Design Methodologies - Earthquake Engineering for Structural Design - page 422

422 Earthquake Engineering for Structural Design

close to the first vibration of the structure). Contrary, the results of this procedure can
by very inaccurate when applied to a building with a highly irregular structure system,
unless the building is capable of response to seismic loads in a nearly elastic manner.
When the contribution of higher modes of vibration is significant, this method is not
conservative. In these cases, a complete dynamic response spectrum analysis is
advisable (ESDEP, 2008).

9.5.4 Response SpectrumAnalysis: Modal Response Method

The response spectrum analysis is the standard procedure of the modern seismic design
codes. It aims to directly give the maximum effects of earthquake in various elements
of the structure. The general method, called also the multi-modal method, consists on
computing the various modes of vibration of the structure (Fig. 9.24a) and the
maximum response of each mode with reference to a response spectrum (Fig .9.24b),
by determining the lateral distribution of seismic forces for each mode and the
corresponding internal forces. The structure response can be defined as a combination
of many modes. A rule is then used to combine the responses of these different modes.
For this reason the method is also known as the superposition of modal response
method. For the combination of these modal responses, three methods are available
(Wikipedia, nd):
- The sum of absolute values of the modal response. This is the most conservative
method, because it assumes that the maximum modal values, for all modes, occur
at the same time.
- The square root of the sum of the squares (SRSS) of forces and displacements.
This method assumes that all of the maximum modal values are statistically
independent. For three-dimensional structures, in which a large number of
frequencies are almost identical, this assumption is not justified.
- The complete quadratic combination (CQC) of modal responses, which is based on
random vibration theories in order to minimize the introduction of avoidable
errors. This method has been incorporated as an option in most modern computer
programs for seismic analysis.
There are computational advantages in using the response spectrum method of
seismic analysis for the prediction of member forces and displacements in structural
systems. But the use of the response spectrum method has some limitations, being only
an approximate method. The first approximation refers to the use of spectra given for a
single degree of freedom system, valuable only for the first vibration mode, to
determine the structural response for the superior vibration modes. The second one is
that it is restricted to linear elastic analysis, in which the damping properties can only
be estimated with low degree of confidence. The third one refers to the procedure of
superposition of different response modes, in which, due to the sum of square values,
the sign of the values disappears.