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CEE 227 - Earthquake Engineering

U.C. Berkeley Spring 2003 ©UC Regents 1-1

Basic Concepts: Performance-based Earthquake Engineering

Seismic Performance

�What are our goals?

�A design framework for expressing performance goals

�Performance vs. Engineering Response parameters

�Nonlinear response - Is it desirable feature or a problem to overcome?

�Some engineering approaches to improve performance

�Quantifying performance



Performance Expectations

� Current codes - What are their stated

objectives?

� Ideal situation - A simple limit states

framework for design.

� Current directions - Vision 2000

(SEAOC), SAC LRFD approach, etc.

� Future directions - reliability based

approaches, PEER performance-based

evaluation strategy

� References

Model codes

Vision 2000

FEMA 273/356

FEMA 350-353

PEER PBEE

FEMA PBEE

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References: Performance-Based Design Codes�Hamburger, R.O., Performance-Based Analysis and Design Procedure for Moment Resisting Steel Frames, Background Document, SAC Steel Project, Sept. 1998.

�SEAOC, Vision 2000: Performance Based Seismic Engineering of Buildings, San Francisco, April 1995.

�Recommended Seismic Design Criteria for New Steel Moment-Frame Buildings, FEMA 350, Federal Emergency Management Agency, Washington DC, July 2000

� FEMA, Guidelines for Seismic Rehabilitation of Buildings, Vol. 1: Guidelines, FEMA 356, Washington DC, 2002 (formerly FEMA 273).

�Earthquake Engineering Research Center, Performance-based Seismic Design of Buildings: An Action Plan , U.C., Berkeley, 1995.

�FEMA/EERI, Action Plan for Performance -Based Seismic Design, FEMA 349, Washington DC, 2000.

�ATC, Development of Performance-based Earthquake Design Guidelines, ATC-58, Redwood City, 2002.



Current Model Codes

CBC, IBC and UBC

� Stated purpose:

�Provide minimum provisions

for design and construction of

structures to resist effects of

seismic ground motions

�“…to safeguard against major structural failures and loss of

life, not to limit damage or

maintain function.”(UBC, 1997 ed., Section 1626)

Structurally undamaged building astride fault

Shear failures in short “captive” columns

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SEAOC “Blue Book” Recommendations

EarthquakeIntensity

Frequency ofOccurrence

DesiredPerformance

1 Minor Several timesduring service

life

No damage tostructure or

nonstructuralcontents

2 Moderate One or moretimes duringservice live

Limited damage tononstructural

components andno significantdamage tostructure

3 Major(Catastrophic)

(10%exceedencein 50 years)

Rare andunusual eventas large as anyexperienced invicinity of site.

No collapse ofstructure or other

damage thatwould create a life

safety hazard.

(After: Lateral Force Recommendations and Commentary, SEAOC.)

Commentary states:

Three

Tiers



Current code goals are ambiguous

� Definitions are non-

quantitative (e.g., limited

damage, one or more times,

etc.)

� Three tiers, but…�Only one design earthquake

� Provisions not specifically

associated with any particular

performance level.

� Leads to wide variation in

interpretation and

performance.

EarthquakeIntensity

Frequency ofOccurrence

DesiredPerformance

1 Minor Several timesduring service

life

No damage tostructure or

nonstructuralcontents

2 Moderate One or moretimes duringservice live

Limited damage tononstructural

components andno significantdamage tostructure

3 Major(Catastrophic)

(10%exceedencein 50 years)

Rare andunusual eventas large as anyexperienced invicinity of site.

No collapse ofstructure or other

damage thatwould create a life

safety hazard.

(After: Lateral Force Recommendations and Commentary, SEAOC.)

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Vision 2000 - Trends toward

Performance-Based Seismic Engineering

of Buildings

Seminal Document - some powerful new concepts

� The definitions of performance states developed are:

� incorporated in the appendices of the SEAOC “Recommended

Lateral Force Requirements and Commentary”

� Refined by other groups in later documents

� Focuses on:

� defining what constitutes a frequent, rare or very rare

earthquake, and

� describing in detail what are the performance states that one

wants for different types of events and structures.



Vision 2000 - Basic Approach

Relationship developed

between:

� Performance objective

� Type of facility

� Probability of earthquake

and

Response parameters related

to each performance

objective.

� Specific demand parameters identified, and

� Initial acceptance criteria are established.

Performance objective

increases (i.e., less damage):� for a high probability earthquake

(one that may occur several times during the life of a structure), or

� for an important structure or dangerous occupancy (i.e., a hospital or dynamite plant)

Conversely, more damage is

acceptable:� for a rare, severe earthquake,

� for less critical or temporary facilities.

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Vision 2000 - Performance States

� Fully operational Continuous service. Negligible structural and non-structural damage.

�Operational Most operations and functions can resume immediately. Structure safe for occupancy. Essential operations protected, non-essential operations disrupted. Repair required to restore some non-essential services. Damage is light.

� Life Safe Damage is moderate, but structure remains stable. Selected building systems, features or contents may be protected from damage. Life safety is generally protected. Building may be evacuated following earthquake. Repair possible, but may be economically impractical.

�Near Collapse Damage severe, but structural collapse prevented. Non-structural elements may fall.



Occupancy or Use of Building Considered

Three occupancy types considered in Vision

2000.

� Safety Critical Facilities:� Large quantities of hazardous materials (toxins, radioactive

materials, explosives) with significant external effects of damage to building.

� Essential/Hazardous Facilities� Critical post-earthquake facilities (hospitals, communications

centers, police, fire stations, etc.)� Hazardous materials with limited impact outside of immediate

vicinity of building. (Refineries, etc.)

� Basic Facilities � All other structures.

One can argue withor adapt these definitions.

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Quantitative Indexing of Earthquake

The earthquake intensity is now described quantitatively

in probabilistic terms for Vision 2000.

EarthquakeClaassification

Recurrance Interval Probability of Occurance

Frequent 43 years 50% in 30 years

Occasional 72 years 50% in 50 years

Rare 475 years 10% in 50 years

Very Rare 970 years* 10% in 100 years

* need not exceed mean + 1 standard deviationfor the maximum deterministic event



Schematic Relation Between Performance

Objective and Earthquake Probability

Performance ObjectiveEarthquakeProbability

FullyOperational Operational Life Safe Near Collapse

Frequent

Occasional

Rare

Very Rare

adapted from Vision 2000, SEAOC

Basic Facilities

Essential/Hazardous Facilities

Safety Critical Facilities

UnacceptablePerformance

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Comments on Relationship

� Thus, a building would be expected to suffer more damage if it were subjected to a more severe, less likely earthquake.

� A more critical building would be expected to have less damage for the same earthquake probability.

Performance ObjectiveEarthquakeProbability

FullyOperational Operational Life Safe Near Collapse

Frequent

Occasional

Rare

Very Rare

adapted from Vision 2000, SEAOC

Basic Facilities

Essential/Hazardous Facilities

Safety Critical Facilities

UnacceptablePerformance



Comments on Approach.

A basic structure would be expected to:

�have essentially no damage if subjected to an

earthquake with a 30% probability of occurrence in 30 years, whereas it would be

�be near collapse if subjected to an event with a

10% probability within 100 years.

One can substitute more appropriate numbers for a

particular project, or upgrade the characterization of

the structure (to an essential facility, for instance,

where the structure would be designed to remain

life safe during the very rare event.)

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Some More Comments

� This method removes some of the ambiguity from

current recommendations.

� Geotechnical engineers (seismologists and structural

engineers) are able to and do regularly develop

estimates of peak ground motion parameters

(acceleration, velocity, etc.), elastic response spectrum

and even time histories corresponding to:

x% probability of occurrence in “y” years

We will look at how this is done later in the course.



Quantification of Earthquake Hazard

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Acceptance Criteria

� Vision 2000 introduces engineering response parameters to consider (drift, stress, plastic hinge rotation angle, acceleration, etc.) and what limits are acceptable for a particular performance objective.

� These criteria were for the most part based on consensus, rather than on test data or quantitative field observation.

For example, ...



Drift Limits in Vision 2000

Permissible MaximumDrift, %

Permissible PermanentDrift, %

Fully Opera tiona l 0.2 negligible

Opera tiona l 0.5 negligible

Life Safe 1.5 0 .5

Near Collapse 2.5 2 .5

After, Vision 2000, SEAOC

Vision 2000 does not describe acceptable analysis methods. So,how do we calculate the maximum drift (or maximum permanentdrift) and prove we satisfy these criteria?

Why are these criteria selected? Will a building at 2.6% driftcollapse? Can all buildings with drifts of 0.4% remain operational?

NEW

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Damage to Steel Moment Frames

Damage Description

Fully Operational Negligible

Operational Minor local yielding at a few places. Noobservable fractures. Minor buckling orobservable permanent distortion ofmembers.

Life Safe Hinges form. Local buckling of somebeam elements. Severe joint distortion.Isolated connection failures. A fewelements may experience fracture.

Near Collapse Extensive distortion of beams andcolumn panels. Many fractures inconnections.

Big jump

May need to add intermediate limit state related to reparability wheredamage is limited to make repair quick and/or economically feasible.Since damage difficult to quantify and economics issues are owner-sensitive, these intermediate states are difficult to incorporate in a code.



Extending the Vision 2000 approach� The Vision 2000 approach does not suggest analytical

approaches nor methods to assure reliability of structure.

� Intermediate limit states difficult to quantify.

� The Vision 2000 is an uncoupled approach. That is, we end up

with a deterministic procedure based on a probabilistically

determined spectrum. Load and resistance factors still remain

to be determined to provide desired reliability.

� Identification of limit states by subjective name (continued

operation) may lead to legal problems if goal is not realized

following an earthquake. Some codes use a letter system (i.e.,

performance objective A, B, C, etc.). Probabilistic specification

of response parameters may be better.

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Several Major Advances in FEMA-273/356Guidelines for Seismic Rehabilitation of Buildings

� Four Performance Goals:� Collapse Prevention, Life Safe, Continued Occupancy, Operational

� National Seismic Hazard Maps developed by USGS� Spectral ordinants (5% damping) for

different probabilities of occurrence and soil conditions at T= 0.2sec and T=1sec.

� Displacement-Based Approach with subjective factors to

assess uncertainty

� droof = C0C1C2C3C4Sdelastic

� Defines Nonlinear Dynamic and Static Pushover methods

in addition to conventional elastic methods

Sa

SDS

SD1/T

T



Severity of Damage

Joe’s

Beer!Beer!Food!Food!

Joe’s


Operational LifeSafety

CollapsePrevention

Joe’s


ImmediateOccupancy

Damage0% 99%(R. Hamburger)

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Structural/Nonstructural/Element Criteria

From FEMA 356



Damage related to demand parameters

Structural Displacement ∆∆∆∆

Lat

eral

Res

ista

nce

Joe’s



Joe’s


Joe’s

Member Capacity

Force

Deformation

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Relate Probabilities of Exceedence to Damage States

0.01

0.1

1

10

0.00010.0010.010.1

Annual Probability of Exceedance

Pe

ak

Gro

un

dA

cce

lera

tio

n-

g

Joe’s


Frequent(25 years)

Very Rare(2500 years)


Joe’s

Rare(500 years)


Joe’s

Occasional

(72 years)



Some limitations of FEMA 356

� While ground motion is defined in probabilistic terms,

uncertainty and randomness not considered related to:

�structural demands, and

�capacities.

� Evaluation is made on a member by member basis…the

failure of a few elements might not lead to the failure of

the system.

� Performance goals are defined in absolute, but

subjective terms. Structure is either life safe or it is not.

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Extending the FEMA 356 concept

Basic Limit States Design Format

Common format in Europe and in other industries.

� Explicit list of performance goals, criteria, and usually, a acceptable probability of reaching or exceeding the goal;

� Direct relation between goal and what engineering demand parameter is checked (and acceptance criteria).

� Explicit recognition and consideration of randomness and uncertainty (e.g., LRFD format implementation)

Limit State Performance Objective Evaluation Criteria forEngineering Parameters

Probability ofExceeding

Performance Criteria

NameGoal you are trying to

achieveResponse

parameter(s) measuredand acceptance criteria

x1 % iny1 years Many



For each limit state:

Need to recognize and

manage randomness and

uncertainty.

�Not adequate to say

Dmedian

< Cmedian

�Need probability of failure

less than a specified

amount.

X% probability in y years (often, y is the assumed service life)

In LRFD format

γγγγ Dmedian< φ φ φ φ C

median

Demand Capacity

Frequency of Occurrence

FailureProbability

Response Parameter

Dmedian Cmedian

Cmedian

Dmedian

>γγγγφφφφ

For a givenprobability of failurein ‘y’ years

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Large randomness and uncertainty in

earthquake-resistant design

�Randomness in both demand and capacity.� Earthquake motions inherently random. Even with increased knowledge there will

be large randomness in excitation and response.

� Structural behavior effected by random variations in material properties, deterioration and construction quality. Capacity is also affected by loading history and duration which are influenced by randomness of excitation.

�Uncertainty in demand has components related to:� Seismology (what earthquake intensity is expected during a given interval of time) -

various methods available to improve estimates

� Ground motion characteristics (what response spectrum corresponds to an earthquake motion corresponding to a given intensity and soil conditions)

� Structural characteristics (what is the structure’s actual mass, stiffness, strength, damping, foundation condition, etc.?)

�Modeling (have we accurately modeled the structures: completeness, etc.)

� Structural Analysis Method (Elastic, Inelastic; dynamic, static?)



Uncertainty and randomness in capacityIn the past, strength was

generally primary criterion

related to capacity

Now, focus is increasingly on

strain, deformation and energy

dissipation (fatigue) capacities.

From Marc Eberhard, UW

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Capacity estimates may be a problem�Even for flexural strength, there are difficulties:

� Slab contributions (composite action)� Connections (panel zone deformations, welds, bar pull out, etc.)� Shear (in members, connections and structural walls)� Non-compliant or marginally ductile elements (existing structures).

� Inconsistent development of capacity equations� In complete tests or inadequate documentation�Non-structural components (cladding and other architectural features may actually behave like structural elements, or alter the behavior of structural elements)

�Both strength & deformation capacity sensitive to:�Loading history (low-cycle fatigue)�Rate of loading effects (effects on strength and deformability)

�Ultimately, seismic capacity is related to dynamic aspects of response of a complete structural system



Probabilistic PBE Approaches

In general one would want to state the problem as:

w% chance of exceeding performance objective in ‘y’years (life of structure)

This is complex, computationally intensive reliability problem.

�Solve rigorously as a reliability problem.

�Results tend to be dominated by uncertainty in ground motions

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Seismic Hazard and Performance Level

Now more common to uncouple the problem, as:

x% chance of exceeding performance level for an earthquakewith an z% probability of occurrence in ‘y’ years

� Treat ground motion and structure separately:� Probabilistic response spectrum used with deterministic “conservative” selection of

seismic hazard for design.

� Develop calibrated load and resistance factors using reliability analysis or Monte Carlo

simulation to have appropriate overall reliability.

Thus, Performance Objective has three parts:�Definition of Performance Level

� Statement of associated Seismic Hazard

� Statement of desired confidence



Significance of Confidence Level

Now, engineer can state:

We have a high, moderate, or low confidence that the performance objective can be met for an earthquake

with a “x”% probability of occurring in “y” years

We would say, for instance: there is a 90% (10%)

confidence that a structure will remain stable in earth-

quakes having a median probability of exceedence of 2% in

50 years.

Powerful evaluation tool, and one that is understandable by

clients and other professionals

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FEMA/SAC Steel Project� Builds on FEMA 273/356, but covers new & existing buildings

� Two Performance Objectives � Continued Occupancy - damage permitted, so long as it does not reduce future

confidence in building’s ability to achieved performance objectives

� Collapse Prevention - local plastic rotations, global instability, avoid premature failure modes

� NEHRP seismic hazard data: 50%, 10% and 2% in 50 years

� Consistent system-level reliability approach used. Treats randomness and uncertainty to focus on confidence of achieving performance goal during specified period.� Designer/owner can select confidence level.

� Rational load, resistance and analysis bias factors developed for various forms of uncertainties.

� Extensive Monte Carlo simulation used.



Performance-based Design: SAC Approach

LRFD-type format often utilized

�Demand uncertainty divided into several parts; �Ground motion (randomness and uncertainty treated using probabilistically-based response spectrum and load factors corresponding to geographical location and soil conditions),�Structural response -- Even for a family of ground motions with “similar” characteristics, structural response will have large variations.�Analysis method - ESP, EDP, NSP, NDP

�Modeling --Variations in mechanical and dynamic characteristics will make these uncertainties in response demand larger.

�Seismic capacity related to three main components:�Element level effects (stress, plastic hinge rotations)

�Global behavior (drifts, static and dynamic instability)

�Brittle failure modes (premature column fracture or buckling)

See: R. Hamburger, Performance-Based Analysis and Design Procedure for Moment-Resisting Steel Frames, SAC Background Report

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SAC Approach

�Basic approach

or, combining terms and adding confidence level:

� Multi-level design approach� Standard default code approach with specified demand, capacity

and confidence values� 90% confidence for global instability response parameters

� 50% confidence for local stability and continued occupancy

� Explicit methods allowing nonlinear analysis and testing to develop demand and capacity values, or to specify different target confidence levels

γ γ γ γ φφ φ φ1 2 3 1 2 3. .. .. .n nD C≤

γ γ φcon D C≤



SAC Approach for New Buildings

1. Select performance objective, confidence levels and earthquake hazard, e.g. Collapse Prevention, 90% confidence and 2% in 50 year hazard.

2. Determine design seismic earthquake for hazard, e.g. spectral displacement at the fundamental periods of the building, time histories...

3. Develop a mathematical model of the building.

4. Analyze mathematical model to determine the values of the key design parameters: maximum and permanent inter-story drift; column load.

5. Apply demand and bias factors to the computed response parameter values to compensate for the various biases and uncertainties inherent in the predictive methodology as well as the randomness inherent in seismic structural response . Apply additional demand factor to achieve desired confidence level.

6. Compare the factored demand against the factored acceptance criteria value for the response parameter. γ γ φcon D C≤

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0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 20

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Sa/SaARS

Pro

babi

lity

Dcol = 60", ar = 6, Pr = 0.2

Spalling Park Ang > 0.4 Park Ang > 1.0 Fatigue Index> 0.5Fatigue Index> 1.0

Fragility curves describe reliability of structure

Spalling

FatigueFailure

SignificantDamage

(Park&Ang)

MinorDamage

(Park&Ang)



Rapid Evolution of Performance-oriented

Codes and Guidelines expected.

� These PBEE guidelines (FEMA 273, SAC, etc.) are being

routinely used for many new and existing buildings.

� These are only first steps in developing Performance

Based Codes. Much work is needed to evaluate and

validate methodologies. Lots of changes will be made in

the next few years.

� Improved tools needed for analysis and design.

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Structural Engineering Tools Improve

Greater demands for quantitative

design and evaluation methods

that realistically and explicitly

account for performance

� Improving analysis tools

� Improving characterization of

performance

� Improved proportioning strategies

� Improved earthquake characterization

� Improving control of uncertainties

� Improved assessment of losses

CapacityDesign

Sd

Probability

HazardModel

δ

DemandCapacity Reliability

Model

Probability

Fails

LossModels

$

AnalysisEngine

DamageModels



Drift is not ... performance

�Engineers must use quantitative engineering demand

parameters (such as drift, plastic rotation, stress) as a

measure of performance.

�These are generally not performance indices of interest

to an owner who is concerned about repair cost, loss of

revenue, injuries to occupants, down time, etc.

�Many intermediate performance objectives related to

reparable damage or minimization of economic or social

impacts.

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Structural Engineering Tools Improve

Greater demands for quantitative

design and evaluation methods

that realistically and explicitly

account for performance

� Improving analysis tools

� Improving characterization of

performance

� Improved proportioning strategies

� Improved earthquake characterization

� Improving control of uncertainties

� Improved assessment of losses

CapacityDesign

Sd

Probability

HazardModel

δ


Model

Probability

Fails

LossModels

$

AnalysisEngine

DamageModels



Economic, social & operational impacts

� In general, we need to consider economic and related

impacts as well. Initial costs need to be compared with

“life cycle” costs to determine the design that performs

best. Evaluation of economic costs also depend on who pays for damage (owner, insurance, government).

� Perspective varies

* Developer * Large institutional owner

* Insurance company * Government decision makers

* Engineer

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Performance-Based Design Approaches

Sd

Probability

HazardModel

CapacityDesign

AnalysisEngine

LossModels $

DamageModels

δ


Model

Probability

Fails?



( ) ∫∫∫= )(||| IMdIMEDPdGEDPDMdGDMDVGDVv λ

PEER – Probability Framework Equation

Performance (Loss) Models and Simulation HazardImpact

IM – Intensity Measure

EDP – Engineering Demand Parameter

DM – Damage Measure

DV – Decision Variable

ν(DV) – Probabilistic Description of Decision Variable

(e.g., Mean Annual Probability $ Loss > 50% Replacement Cost)

Implementation Through

LRFD-like Format:

CD CSS|D fPa

a⋅φ≤⋅γ

0

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FUTURE of PBEE

� FEMA is funding a new project to implement a PBEE framework for all structural systems, not just retrofit or steel… ATC-58 project

� PBEE is currently being implemented on many conventional and important structures

� Answers need for more reliable, quantitative information on performance, utilizing modern capabilities for characterizing seismic hazard, simulating seismic response, and assessing impact of response on owner and society

� Validation and refinement needed

� How do we design a structure to attain our objectives reliably? NEXT….

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