Van Nuys Sensitivity Study
Keith Porter
PEER Building Testbed Progress Meeting
Richmond Field Station
23 May 2002
Objectives
• Assess gross sensitivity of damage factor
(DF) to uncertainty in basic random
variables (X)
• Assess variability in each Xi
• Assess sensitivity of DF to uncertainty in Xi
• Illustrate with the Van Nuys testbed
Methodology, 1/3
• Identify basic variables XT = [X1, X2,…XN] in
repair cost C = f(X)
• Assess E[Xi], Var[Xi] for i = 1, 2, … N
• Assess Xi,50 = 50th percentile of Xi
• Assess Xi,10 = 10th percentile of Xi
• Assess Xi,90 = 90th percentile of Xi
Methodology, 2/3
1.
2.
3.
4.
5.
Describe facility B as a collection of
standard assembly types j = 1, 2, … Nj with possible
damage states d = 1, 2, … Nj,d, each with
uncertain capacity Fj,d, and
uncertain repair costs Cj,d
Structural analysis : EDP = g(GM, B)
Damage analysis: for each assembly k,
if EDPk > Fi,d, then DMk ≥ d
Loss analysis: C = (1 + COP)SjSdNj,dCj,d
Damage factor DF = C/RCN
(RCN: replacement cost, new)
Methodology, 3/3
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Calculate baseline C0 = f(X1,50, X2,50, … XN,50)
Ci,10= f(X1,50, X2,50,…Xi,10,… XN,50): i = 1…N
Ci,90= f(X1,50, X2,50,…Xi,90,… XN,50): i = 1…N
Swingi = |Ci,90 – Ci,10|
Sort Xi by swingi & plot in a “tornado diagram”
Results: Xi
Xi
Xi,10
X i,50
X i,90
0.11
(LA50, 0.52)
0.27
(LA50, 1.28)
0.58
(LA50, 2.74)
LA45, 1.10
LA50, 1.28
LA49, 1.26
0.87Mn
Mn
1.13Mn
Damping
2.4%
5.0%
7.6%
Force-def. multiplier
0.90
1.00
1.10
Assembly capacity
e lnxm 1.28
xm
e lnxm 1.28
xm and  from Table 4
Costs: unit cost
e lnxm 1.28
xm
e lnxm 1.28
xm and  from Table 5
0.15
0.175
0.20
Sa (g)
Ground motion
Mass
O&P
Comment
Spectral acceleration
(Record, scaling factor)
Record, scaling factor
Mn: nominal mass
Constant stiffness
CO&P of Equation 11
Results: Tornado Diagram
Assembly capacity
Sa
Ground motion record
Unit cost
Damping
F-d multiplier
Mass
O&P
0.00
0.25
0.50
Damage factor
0.75
1.00
Conclusions
• For this model & this building, assembly capacity
and shaking intensity swamp other uncertainties
• Important uncertainties omitted, need study:
– F-d model selection, R/C joint capacity, difference
between field & lab fragility, repair method | damage
state, nonunion vs. union, demand surge, …
• Tornado diagram depicts important RVs
• Model for UC Science Building? Bridges?
• Report: www.peertestbeds.net/Crosscutting.htm