Civil Engineering Reference
In-Depth Information
where the scaling factor
S
n
can be assumed as follows:
V
NV
B
s
S
=
(4.33.2)
n
in which
V
B
is the estimate of the total base shear of the structure and
N
s
the number of steps
utilized to apply the base shear, e.g.
N
s
= 100.
(h) Perform a static pushover of the structure subjected to the scaled incremental storey forces
computed in step (g) and corresponding to each mode independently. Different formulations can
be used to describe the force variation, which is considered for the incremental updating of the
force vector, during the pushover analysis (e.g. Bracci
et al
., 1997; Gupta and Kunnath, 2000 ;
Elnashai, 2002 ).
(i) Estimate element (or local) and structure (or global) forces and displacements by means of SRSS
combinations of each modal quantity for the
k
th step of analysis. Add the above quantities, i.e.
forces and displacements, to the relevant quantity of the (
k
- 1)th step.
(j) Compare the values established in step (i) to the limiting values for the specifi ed performance
goals at both local and global levels, as provided, for example, in Section 4.7. Return to step (b)
until the target performance is achieved.
In the above adaptive procedures there are, however, a number of controversial issues, e.g. issue of
force distribution and updating. Research to refi ne adaptive pushover methods is still ongoing for both
buildings (e.g. Antoniou and Pinho, 2004a,b; Chopra and Chintanapakdee, 2004; Goel and Chopra,
2004, among many others) and bridges (e.g. Aydinoglu, 2004; Kappos
et al
., 2005 , among others).
Comparisons between conventional and adaptive pushover curves for regular and irregular structural
systems are provided in Figure 4.38. The adaptive pushovers were performed by utilizing the scaling
of acceleration spectrum. Two load patterns were employed for the conventional pushovers, i.e. uniform
and triangular. The results of response history analyses are also included in Figure 4.38 as a
benchmark.
It is observed from this simple comparison that the uniform distribution provides an upper bound
of the lateral capacity in the inelastic range only for the regular model. In the case of irregular systems,
the conventional PA is often inadequate to capture the dynamic behaviour, thus proving how misleading
fi xed patterns can be. In several cases, adaptive pushover is superior to the conventional variant, but
this is by no means guaranteed. A wide-ranging comparison between conventional and adaptive push-
over methods is available in Papanikolaou
et al
. (2006) .
1,000
1,000
800
800
600
600
400
400
Triangular
Uniform
Triangular
Uniform
200
200
Adaptive
Dynamic
Adaptive
Dynamic
0
0
0.0
1.0
2.0
3.0
0.0
1.0
2.0
3.0
Total Drift (%)
Total Drift (%)
Figure 4.38
Conventional, adaptive and dynamic pushover curves for different structural models: regular (
left
)
and irregular (
right
) systems
