Advances in Seismic Design Methodologies - Earthquake Engineering for Structural Design - page 431

Advances in Seismic Design Methodologies 431

mode alone, which is the basis for push-over procedures currently used in engineering
practice, does not adequately estimate the seismic demands. If two or three vibration
modes are included in analysis, the height-wise variation of story drifts determined
using modal push-over procedure is generally similar to the “exact” results from non-
linear response history analysis. For low-rise to mid-rise buildings, it is sufficient to
include, beside the first mode, only the second vibration mode. The third vibration
mode contribution should be included only for taller frames.
The criticisms of this procedure refer to the used quadratic modal combination rules
(SRSS or CQC) used in computing the results. These rules inevitably lead to
monotonically increase the obtained values, since the possibility of sign changing is
precluded, whilst it may be needed to represent the uneven redistribution of forces after
an inelastic mechanism is triggered at some location (Pinho et al, 2005).
Adaptive push-over procedure considers the changing of both characteristics which
determine the structural response, the load pattern and the structural rigidity. When
plastic hinges form in the structure, constant distribution of lateral forces cannot be any
longer used. In this procedure, the dynamic analysis is transformed into a static
analysis, which is repeated many times as soon as the stiffness changes due to the
formation of new plastic hinges (Fig. 9.29a). For each step, a new distribution of lateral
loads is changed according to the mode shapes of the structure. So, these loadings are
updated at each analysis step, reflecting progressive damage accumulation and
resulting modification of modal parameters (Fig. 9.29b), which characterize the
structural response at increasing loading levels.
According to the procedure developed by Papanikolaou (Papanikolaou et al, 2005),
the lateral load pattern is not kept constant during the analysis, but it is continuously
updated, based on a combination of the instantaneous mode shapes and spectral
amplifications corresponding to the inelastic periods of the structure (Fig. 9.30). One
can see that for each step, the structural periods are changed (especially for the first
mode) and, correspondingly, the configuration of lateral loads is modified, this change
being obtained from the response spectra. After defining the lateral profiles for all
different modes, a modal combination (SRSS or CQC) is carried out. The base shear
remains independent of the load pattern, being controlled by the current loading level
only. Thus, the magnitude of the push-over load is still applied incrementally, as
formed in the conventional push-over approach. The main criticisms regarding this
procedure refer to the same quadratic modal combination rules (SRSS, CQC), as has
been discussed for the modal push-over procedure.
Within the adaptive push-over procedure, the application of a displacement method,
as opposed to the force method used in the previous procedure, seems to be more
attractive, being in line with the present tendency for the development and code
implementation of deformation-based design and assessment methods. Further, such a
displacement-based design procedure seems to lead to superior response predictions,