introduction to PBEE

Performance-based Earthquake
Engineering – A Very Short
(why taking Dynamics of Structures)
Dr. ZhiQiang Chen
Conventional Design Philosophies
• ASD (allowable strength design)
• 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
• 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
• 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
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
– Intensity Measures (IM), e.g. Peak Ground
– Demand Parameter (DP), e.g. Peak Inter-Story
Drift Ratio)
– Damage Measures (DM), e.g. Physical Condition
– Decision Variables (DV), e.g. $loss, downtime,
How to obtain and relate DV, DM, DP and IM?
Analysis (LA)
Analysis (FA)
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, ATC63, 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
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
– The ground input
– The soil-foundation-structure
– The damping mechanism
– The material/member properties
– The structural configuration and
– Nonstructural/structural
components …
<DP | IM>n
G<DP | IM>
Definition of DP
How to obtain this analytically?
• Solve the dynamic governing equation of the soilfoundation-structure system!
𝑀 𝑥'' 𝑡 + 𝐶 𝑥 ′ 𝑡 + 𝐾 𝑥 𝑡 = 𝑃 𝑡
• 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!
• 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 performancebased engineering, Y. Bozorgnia and V.V. Bertero, Editors, CRC
• ATC-58, 50% finished report, Guidelines for Seismic
Performance Assessment of Buildings, 2009