Response Evaluation - Fundamentals of Earthquake Engineering - page 243

(j) Perform a static structural analysis to evaluate the response quantities, as those described in Section
4.8. For 3D models it is necessary to apply the static horizontal distribution of forces along the
principal directions of the plan layout fulfi lling the combination rules outlined in Section 4.4 .
(k) Scale the horizontal displacements computed in (j) by using an amplifi cation factor, which is
often assumed equal to the force reduction factor in (b), or a proportion of it. The estimated dis-
placements are those generated by earthquake loading.

Seismic design codes allow the use of the equivalent lateral force procedure for relatively regular
structures with fundamental periods not greater than 1.5-2.0 seconds. For irregular or long- period
structures, more refi ned dynamic analyses such as modal spectral or inelastic response history analysis
should be used. Recently, to permit performance-based assessment of structural systems, inelastic static
pushovers and incremental dynamic analyses have also been recommended in seismic codes worldwide.
Table 4.8 summarizes commonly used methods of analysis included in international seismic codes and
their range of applicability.
In code application of modal spectral analysis, design spectra are scaled by using the all-embracing
force reduction factor ( R or q ), and the elastic response of the structural system is computed using the
response spectrum analysis, as detailed in Section 4.6.1.1. All signifi cant modes are required in
the combined response. This condition is satisfi ed by having the total effective modal mass included
in the analysis equal to at least 85% to 90% of the total mass of the structure. Although calibrated for
buildings, the latter rule is useful also for bridge structures. As with the static load procedure, 5%
accidental eccentricity should be included in spatial pushover analysis. Methods of structural analysis
presented in Sections 4.6.1, 4.6.2 and 4.6.3 are compared in Table 4.9, which complements Table 4.1
in Section 4.3. The comparison is expressed in terms of type of input, material inelasticity and geometric
non - linearity, and accuracy.
Methods of analysis are often a compromise between accuracy and complexity. The simplest method
that provides the desired information with reasonable accuracy is usually the preferred method. Unfor-
tunately, the ideal solution is seldom available. For example, as shown in Table 4.9, inelastic dynamic
response analysis is the most accurate and realistic method for seismic assessment because it can
accommodate material inelasticity and geometric non-linearity. It is, however, also highly complex and
time-consuming. Conversely, the equivalent static analysis is very simple to use but could be rather
poor in accuracy. Its applicability is limited to the subclass of regular and short-period structures.
Whereas inelastic static (or pushover) analysis is currently used extensively in the design offi ce, its
dynamic counterpart remains a challenge. To bridge the gap between research and application, it is
necessary to provide training to civil engineers in advanced structural dynamics and inelastic behaviour,
and create more user-friendly advanced software for inelastic dynamic analysis.

Table 4.8 Methods of analysis implemented in seismic design codes and their applicability.

Type of structure Static analysis Dynamic analysis

ELF NSP RSA LRH NRH

Regular ✓ ✓ ✓ ✓ ✓

Irregular ✗ ✗ ✓ ✓ ✓

Key : ELF = equivalent lateral force; NSP = non - linear static pushover; RSA = response spectrum analysis;
LRH = linear response history; NRH = non - linear response history; ✓ = applicable; ✗ = not applicable.