Life Cycle Cost Considerations in Seismic Design Optimization of Structures - Structural Seismic Design Optimization and Earthquake Engineering - page 11

Figure 5. Recommended rehabilitation objectives for buildings in FEMA 273 (Adapted from FEMA, 1997)

demand imposed on the structure. The capacity
varies during the strong ground shaking which
also influences the seismic forces acting on the
structure. The most elegant way of evaluating
the failure probabilities is through the joint prob-
ability density function of capacity and demand
which can be derived by Monte Carlo simulation
(MCS). However, there are various sources of
uncertainty in evaluation of the failure probabili-
ties including the inherent variability of ground
motions and randomness in material properties.
Accounting for all the variability through MCS
requires a large number of structural analyses. At
the same time, accurate prediction of structural
capacity and earthquake demand is critical for
seismic design, and it is required to use analysis
methods that yield reliable estimates. Performing
MCS becomes infeasible when computationally
demanding methods such as inelastic dynamic
time history analysis is used. Therefore, here it
is assumed that structural capacity is independent
from earthquake demand and pushover analysis is
used to evaluate the former while the latter is ob-
tained by inelastic dynamic time history analysis.

Finite element model (based on distributed
inelasticity) of the structure under consideration
is built and pushover analysis is conducted. In
order to establish the limit state threshold values
that define the structural capacity, the response
metrics obtained from the analysis such as stresses,
strains, and interstory drifts are correlated to
previously mentioned performance levels. Here
only structural damage is considered; however,
nonstructural damage could also be incorporated
into the performance level definitions as suggested
by Vision 2000 (SEAOC, 1995). Local (e.g.
stresses and strains) and global (e.g. interstory
drift) response measures could be combined to
define different performance levels. Here, only the
strains in longitudinal reinforcement and the core
concrete are used as the criterion and the threshold
values are represented in terms of interstory drift
by mapping the strains onto the pushover curves.
A typical pushover curve is shown in Figure 6(a)
alongside the limit state points based on strains
in the longitudinal reinforcement and the core
concrete.