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 545

Span
moment
demand

1

0.1

Span
moment
capacity

0.01

Support
moment
demand

0.001

0.0001

Support
moment
capacity

0.00001

0.000001

0.1 1 10

Type 2-EDP

20.9 Structural demand hazard curves at Stage 1 for an example near
fault site for Type 2-EDPs.

20.8 shows the structural demand hazard curves for Type 1-EDPs (axial
load demand and positive moment demands at the mid-span and at the
support) for a near-fault site. Similarly, Fig. 20.9 presents the structural
demand hazard curves for Type 2-EDPs (negative moment demands at the
mid-span and at the support) for the same site. The broken lines in both
fi gures indicate the capacity defi ned as the onset of inelastic deformation/
yielding recalling that the girders in a highway bridge are designed to
remain elastic under seismic action (Kunnath et al. , 2008) for each EDP.
Details of the analysis, fault system, and source characteristics used for
the assessment were explained in Gülerce and Abrahamson (2010). Acc-
ording to Figs 20.8 and 20.9, none of the Type 1-EDPs exceed the corre-
sponding capacities at Stage 1. There is a chance of exceeding the capacity
for Type 2-EDPs, but these probabilities are small (less than 0.0001 annual
probabilities).

20.5.3 Vector-valued PSDMs and vector-valued PSHA

The increase in the EDPs (defi ned by Equations 20.12 and 20.13) when the
vertical ground motions were included in the nonlinear dynamic analyses
(Stage 2) can be described by vertical factor (VF) (Gülerce et al. , 2012).
Similar to the EDPs at Stage 1, two types of vertical factors were defi ned
and normalized as shown in Equations 20.17 and 20.18. Type 1-VF repre-
sents the amplifi cation for Type 1-EDPs, while Type 2-VF is for Type 2-EDPs: