Using a performance-based earthquake engineering (PBEE) approach to estimate structural performance targets for bridges - Seismic Risk Analysis and Management of Civil Infrastructure Systems - page 539

et al. , 2008). Since the primary objective of the study was to address the
effect of vertical ground motions, more near-fault recordings with either
large or small vertical components compared to the horizontal component
were added to the dataset. The resulting set of 114 ground motions (228
horizontal and 114 vertical components) were used in the nonlinear dynamic
and regression analyses (Step 1 in Fig. 20.2).
Kunnath et al. (2008) used a portion of the widening project of the
Camino Del Norte Bridge located in California as a typical ordinary stan-
dard highway bridge and representative of the class of structures. The
prototype was a single bent bridge with two spans of 30.95 m and 30.52 m
in length and many confi gurations were generated by changing the dimen-
sion of the bridge model without violating the code specifi cations on allowed
dimensional and balanced stiffness requirements. The nonlinear dynamic
analyses were carried out in two stages (Gülerce et al. , 2012): in Stage 1,
only horizontal components of the motion were applied as a base case, while
in Stage 2, both horizontal and vertical components were applied simultane-
ously to monitor the increase in the response due to the inclusion of the
vertical component (Step 2 in Fig. 20.2). Analysis results of the bridge con-
fi guration with horizontal fi rst-mode fundamental periods of 0.27 and 0.46
seconds (in longitudinal and transverse directions, respectively) and vertical
fi rst-mode fundamental period of 0.12 seconds are presented in the follow-
ing sections.
Results of the nonlinear dynamic analyses showed that some structural
response parameters were amplifi ed signifi cantly when the vertical accel-
erations were incorporated, such as the axial force demand in the column
and moment demands in the girder both at the mid-span and at the face of
the bent cap (Kunnath et al. , 2008). On the other hand, some commonly
examined structural response parameters such as lateral displacements of
the deck, were not infl uenced signifi cantly by the inclusion of vertical
motions (Gülerce et al. , 2012). The parameters that were affected signifi -
cantly due to vertical accelerations were selected as the structural response
measures to be used in the PBEE framework. Similar to the previous prac-
tice (Mackie and Stojadinovic, 2003), peak values of the response history
were chosen as EDPs (after normalizing with the dead load values to offer
a rational basis for comparison of different bridge confi gurations). Type
1-EDPs were defi ned using positive peaks of the axial load in the column,
moments at the mid-span and at the support as:

= (

) max,Stage Demand

DL

1

Type 1 − EDP [20.12]

where ( Demand ) max, Stage1 is the positive extreme value of the demand time
history at the base case (without the vertical accelerations) and DL is the
corresponding dead load value as shown in Fig. 20.3(a).