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 X i Assess sensitivity of DF to uncertainty in X i Illustrate with the Van Nuys testbed

Methodology, 1/3 Identify basic variables X T = [X 1, X 2,…X N ] in repair cost C = f(X) Assess E[X i ], Var[X i ] for i = 1, 2, … N Assess X i,50 = 50 th percentile of X i Assess X i,10 = 10 th percentile of X i Assess X i,90 = 90 th percentile of X i

Methodology, 2/3 1.Describe facility B as a collection of standard assembly types j = 1, 2, … N j with possible damage states d = 1, 2, … N j,d, each with uncertain capacity F j,d, and uncertain repair costs C j,d 2.Structural analysis : EDP = g(GM, B) 3.Damage analysis: for each assembly k, if EDP k > F i,d, then DM k ≥ d 4.Loss analysis: C = (1 + C OP )  j  d N j,d C j,d 5.Damage factor DF = C/RCN (RCN: replacement cost, new)

Methodology, 3/3 Calculate baseline C 0 = f(X 1,50, X 2,50, … X N,50 ) C i,10 = f(X 1,50, X 2,50,…X i,10,… X N,50 ): i = 1…N C i,90 = f(X 1,50, X 2,50,…X i,90,… X N,50 ): i = 1…N Swing i = |C i,90 – C i,10 | Sort X i by swing i & plot in a “tornado diagram”

Results: X i

Results: Tornado Diagram

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: