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 548

Axial load
demand

1

Axial load
capacity

0.1

Span moment
demand

0.01

Span moment
capacity

0.001

Support
moment
demand
Support
moment
capacity

0.0001

1 10

Type 1-EDP

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

where v ( EDP _ Stage2 > z ) represents the annual rate of exceeding the
specifi ed value of EDP including the vertical accelerations, S aH is the hori-
zontal S a at the horizontal period of the structure, S aV is the vertical S a at
the vertical period of the structure, ε H is the epsilon for horizontal ground

motion model, ε

V is the epsilon for the vertical ground motion model, f εH (

ε

H )

is the probability density function for ε H , and f εV ( ε V | ε H ) is the probability

density function for

H . The structural demand hazard
curves for Type 1-EDPs and Type 2-EDPs for the same site at Stage 2 are
presented in Figs 20.12 and 20.13, respectively.
Figure 20.12 shows that the probability of exceeding the axial load capac-
ity at the column and the positive mid-span moment capacity increased
signifi cantly, but these EDPs still remained below the capacity. Annual
probability of exceeding the support moment capacity (for both Type1- and
Type 2-EDPs) was computed as 0.001 at this stage (Figs 20.12 and 20.13).
Negative mid-span moment demand was identifi ed as the most critical
parameter under the infl uence of vertical accelerations and the annual
probability of exceeding the negative mid-span moment capacity was sub-
stantial (equal to 0.01) at Stage 2 (Fig. 20.13).

ε

V conditioned on

ε

20.6 Future trends

Recent research results and ongoing discussions on the main components
of the PBEE framework including the PSHA, development of PSDMs, use