Performance-based Earthquake Engineering – A Very Short

Introduction(why taking Dynamics of Structures)

Dr. ZhiQiang ChenUMKC

Spring,2011

Conventional Design Philosophies

• ASD (allowable strength design)• LRFD (load and resistance factor design)– Both feature comparing required strength with

nominal strength of individual structural membersASD: Ru ≤Rn/Ω, Ω is called safety factorLRFD: Ru ≤ φRn, φ is called resistant factor

– Results: safe v.s. not save; sufficient v.s. not sufficient; ok v.s. not ok…for individual members

• LRFD is superior to ASD: LRFD seeks to assure performance in terms of failure probability

Issues of LRFD

• LRFD lacks– a system-level quantification of structural

behavior (structural response indices) at different hazard levels (to structural engineers)

– a system-level quantification of structural performance at different hazard levels (to clients)

Earlier Efforts of PBEE (1st generation PBEE)

• SEAOC’s vision 2000 (1995); FEMA 273 (1997)– Relate structural response indices (inter-story

drift, local ductility…) with some performance measures (e.g. immediate occupancy, life safety, collapse

prevention), yet with no rigorous/explicit formulation• Given a prescribed level of earthquake, one computes

the maximum inter-story drift, then how we relate this value with the system performance?• The performance measures are too descriptive but

quantifiable.

SEAOC Vision 2000 recommended seismic performance objectives for buildings

PEER’s PBEE Framework – 2nd Generation PBEE

(Pacific Earthquake Engineering Research)

• Explicitly define four categories of design variables– Intensity Measures (IM), e.g. Peak Ground

Acceleration)– Demand Parameter (DP), e.g. Peak Inter-Story

Drift Ratio)– Damage Measures (DM), e.g. Physical Condition– Decision Variables (DV), e.g. $loss, downtime,

life-safety

How to obtain and relate DV, DM, DP and IM?

HazardAnalysis

(HA)

Structural Analysis

(SA)

Fragility Analysis (FA)

LossAnalysis (LA)

1. Analysis steps are conducted in a successive way2. The most challenging factor – UNCERTAINTIES!

All the analysis has to be conducted statistically! One session of Structural Analysis is deterministic … needs to conduct

many many times (statistically), and obtain DPs given different IMs

PEER’s Probabilistic Methodology

• Based on total probability theorem• G<a|b> reads as the probability of

exceedance (a > ao) given b

• Needs to define each component statistically• Structural Analysis component: G<EDP | IM>

The State-of-the-Art• Currently being implemented in ATC-58, ATC-

63, Tall Building Initiative of PEER)• Lots of debate though…many active research

projects and many research needs exist• PBEE will, as many believe, transform the

next-generation engineering design• PBEE derivatives: PB

wind/hurricane/tsunami/blast/fire …if you characterize the hazard (hazard analysis) well probabilistically.

More reflection…• We are used to saying (as SE) we are conservative

– This makes sense since we are doing LRFD design, which is either safe or not. To be safe (enough), we tend to be conservative (since we don’t have more refined and quantifiable performance measures)

• The PBEE philosophy seeks to achieve specified performance targets (e.g. the annual mean probability of downtime more than 1 day is 0.1%) under the stated level of seismic hazard.

• This means that accurate Structural Analysis is essential – no more being less or more conservative. The analysis must be sufficiently accurate!– Some mechanisms, such as Soil-Structure-Interaction (SSI), are often

beneficial towards reducing seismic demands. Traditionally, SSI is ignored in the seismic design community. In the PBEE framework, SSI should be included in the modeling.

– Plus, SSI sometimes is detrimental!

To obtain DP accurately given IM

• To achieve accurate analysis– The ground input– The soil-foundation-structure

interaction– The damping mechanism– The material/member properties – The structural configuration and

simplification– Nonstructural/structural

components …

<DP | IM>n<DP | IM>nG<DP | IM>G<DP | IM>

Definition of DP

IMIM

DPDP

How to obtain this analytically?

• Solve the dynamic governing equation of the soil-foundation-structure system!

• How to solve it? what if [K] is not constant? what are the invariant features given different P(t) of the system? what if the frequency contents of P(t) are close to the ‘mode’ of the structure?

• We will address these question marks in this class!

ሾ𝑀ሿ𝑥''ሺ𝑡ሻ+ሾ𝐶ሿ𝑥′ሺ𝑡ሻ+ሾ𝐾ሿ𝑥ሺ𝑡ሻ= 𝑃ሺ𝑡ሻ

References

• SEAOC 2000 (1995)• FEMA 273 (1997)• G.G. Deierlein, H. Krawinkler, & C.A. Cornell, A framework for

performance-based earthquake engineering, 2003 Pacific Conference in Earthquake Engineering

• Krawinkler, H., and Miranda, E. (2004). Performance-based earthquake engineering, Chapter 9 of Earthquake engineering: from engineering seismology to performance-based engineering, Y. Bozorgnia and V.V. Bertero, Editors, CRC Pres

• ATC-58, 50% finished report, Guidelines for Seismic Performance Assessment of Buildings, 2009