# Performance-based Earthquake Engineering – A primer

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Performance-based Earthquake Engineering – A primerDr. ZhiQiang
Chen

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

nominal strength of individual structural members ASD: Ru ≤Rn/Ω, Ω is called safety factor

LRFD: 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

– 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?

Hazard Analysis

Fragility Analysis (FA)

Loss Analysis (LA)

1. Analysis steps are conducted in a successive way 2. 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

– Nonstructural/structural components …

Definition of DP

• 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!

'' + ′ + =

References

• 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

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

nominal strength of individual structural members ASD: Ru ≤Rn/Ω, Ω is called safety factor

LRFD: 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

– 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?

Hazard Analysis

Fragility Analysis (FA)

Loss Analysis (LA)

1. Analysis steps are conducted in a successive way 2. 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

– Nonstructural/structural components …

Definition of DP

• 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!

'' + ′ + =

References

• 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