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 546

( )

Demand
DL

max,Stage 2

Type 1 −= VF [20.17]

Type 1 − EDP

( )

Demand − DL

min,Stage 2

DL

Type 2 −= VF [20.18]

Type 2 − EDP

where ( Demand ) max,Stage2 and ( Demand ) min,Stage2 are the positive and negative
extremes of the demand versus time history at Stage 2. Since both horizon-
tal and vertical ground motion components have impact on the structural
response at this stage, distribution of the vertical factors with respect to the
vertical and horizontal S a was checked to investigate the trends of the
data as shown in Figs 20.10 and 20.11 for Type 1-VFs and Type 2-VFs,
respectively.
Figures 20.10 and 20.11 reveal that both types of vertical factors increase
as the vertical S a increases. The structural response is also dependent on the
horizontal S a , but this dependence is weaker than the dependence on the
vertical S a . The PSDMs were constructed using different functional forms
for Type 1- and Type 2-VFs by including two IMs instead of one; the hori-
zontal S a at the horizontal (either transverse or longitudinal) period of the
bridge ( S aH ) and the vertical S a at the vertical period of the bridge ( S aV ).
The PSDMs for the Type 1-VFs and Type 2-VFs are given in Equations
20.19 and 20.20, respectively.

2.0 2.0

1.5 1.5

1.0 1.0

0.5 0.5

0 0

-0.5 -0.5

3 2 10123 -3 -2 -1 0 1 2 3

ln (IM2= S a V)

ln (IM1= S a H)

(a) (b)

20.10 Distribution of Type 1-VF with respect to (a) horizontal spectral
accelerations and (b) vertical spectral acceleration.