Civil Engineering Reference
In-Depth Information
when more than 85% of the total mass participates in the fundamental mode in the direction under
consideration. Alternatively, a lateral distribution proportional to the storey inertia forces consistent
with the storey shear distribution calculated by combination of modal responses, as illustrated in Sec-
tions 4.6.1.1 and 4.6.3, may be used. In so doing, it is necessary to fi rst perform a response spectrum
analysis as described in Section 4.6.1.1 including a suffi cient number of modes to capture at least 85%
to 90% of the total mass and use the appropriate design ground-motion spectrum. The choice of at least
two load distributions along the main axis of the structure is a practical and viable solution to partly
overcome the limitations of using a static analysis method to solve an inherently dynamic problem.
(ii) Adaptive Pushover Analysis
Adaptive pushover is a method by which possible changes to the distribution of inertial forces, as shown
for example in Figure 4.37, can be taken into account during static analysis. As such, it responds to the
main shortcoming of conventional pushover, where a constant forcing function has to be used. The
time-invariant pattern of horizontal forces and displacements used in conventional pushover may indeed
not refl ect adequately the inelastic response characteristics of the structure (Elnashai, 2002 ). Several
attempts at adapting the force distribution to the state of inelasticity are provided in the literature (e.g.
Bracci
et al
., 1997; Gupta and Kunnath, 2000). Consequently, a new method of analysis, referred to as
' adaptive pushover ' was formulated.
The steps required to perform adaptive pushover analysis for structural systems are summarized as
follows:
(a) Apply the gravity loads in a single step.
(b) Perform an eigenvalue analysis of the structure at the current stiffness state. The elastic stiffness
can be used for the initial step. Eigenvalues and eigenvectors are computed.
(c) Determine the modal participation factors Γ
j
for the
j
th mode using equation (4.17.5) in Section
4.6.1.1 .
(d) Compute the modal storey forces at each fl oor level for the
N
modes deemed to satisfy mass
participation of about 85-90% of the total mass. These forces
F
i,j
are estimated at the
i
th level
for the
j
th mode (being 1 ≤
j
≤
N
) as given below:
F
=Γ
M
Φ
g
(4.29)
ij
,
j
i
ij
,
1,000
3.0% Drift
2.0% Drift
800
1.0% Drift
600
0.9% Drift
400
Initial
200
0
0.0
0.5
1.0
1.5
2.0
2.5
3.0
Total Drift (%)
Figure 4.37
Changes of the distribution of inertial forces in a regular framed building (
adaptive force
distribution
)
