Incremental dynamic analysis (IDA) applied to seismic risk assessment of bridges - Seismic Risk Analysis and Management of Civil Infrastructure Systems - page 555

21.2 Incrementaldynamicanalysis(IDA)
21.2.1 Damage measures (DMs) and IMs
The IDA results are commonly presented using an IM versus a damage
measure (DM) of interest. IM is a non-negative scalable quantity, which is
obtained from accelerograms. In IDA, it is monotonically increased with a
scale factor to attain various seismic excitation levels (Vamvatsikos and
Cornell, 2002). Examples of scalable IMs which are commonly used in the
IDA include the PGA, peak ground velocity (PGV) and the 5% damped
spectral acceleration at the structure's fi rst-mode period T 1 ( S a ( T 1 )). The
use of S a ( T 1 ) as IM is often recommended and used in different studies and
guidelines (ATC-63, 2008; Vamvatsikos and Cornell, 2002).
DM is defi ned as a non-negative scalar quantity that characterizes the
response of the structure to seismic excitations and can be evaluated from
the output of the nonlinear dynamic analysis. Selecting an appropriate DM
depends on the objective of the analyses and the characteristics of the
structure. Some of the common choices include the maximum base shear,
maximum column ductility demands, global cumulative hysteretic energy
and maximum column drift ratio. For bridges, the maximum drift ratio of
the critical columns is typically used for the DM parameter.
21.2.2 IDA curves
An IDA curve is the plot of the DM variable versus the IM parameter.
These curves demonstrate the state of the DM parameter at different IM
levels of the input records. This enables the study of the seismic demand
parameters from low seismic intensity levels prior to yielding of the struc-
ture up to ultimate performance levels, such as dynamic instability of the
structure (i.e., collapse), buckling or fracture of the steel bars, shear failure,
etc. Each non-linear dynamic analysis performed at each seismic intensity
level is presented by a point in the IDA curve. This point demonstrates the
maximum seismic demand (in terms of the DM parameter) obtained at the
corresponding IM level of the ground motion record. The full IDA curve
then can be developed by fi tting a curve through the points computed for
different IM levels. Various types of IDA responses, including hardening
behaviour, softening behaviour, waving behaviour and structural resurrec-
tion, may be observed (Vamvatsikos and Cornell, 2002).
21.2.3 Summarizing IDA results
Different ground motion records in IDA often result in different response
predictions which are quite dissimilar, due to complex structural behaviour
and large record-to-record variability. Therefore, it is essential to summarize