h5. pbsd_presentation.pdf

8/17/2019 h5. PBSD_Presentation.pdf

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Performance Performance - - Based Seismic Design Based Seismic Design


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Outline

• General concepts of PBD

• FEMA-350 in building design: Step-by Step

1. Performance definition2. Evaluation approach

3. Analysis4. Mathematical modeling 5. Acceptance criteria


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Basic Design Approach

• Prescriptive design• Prescribed

strength• Prescriptive

details.


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Basic Design Approach

• Structural system type and frame

configuration• Frame member sizes

• Design force levels• Perform a structural analysis

• Revise specifications• Complete the design (detailing requirements)


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Expected Performance


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Why Performance-Based Design?

• Evaluate the probable seismic performance of

steel moment-frame buildings.

• Design steel moment-frame buildings foralternative performance capabilities and also toquantify the ability of a specific design to achieve

desired performance objectives.


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PB methodology in simple words…

Design for the achievement of specifiedresults rather than adherence to

prescribed means.


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PB Methodology

Earthquake professionals quantify seismic risk

in terms that are meaningful to the decisionmakers.

Decision-makers make informed decisions thatdefine a rational course of action for theearthquake professionals.


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Applying FEMA-350 in Design

A Step by Step Description


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PBSD Steps:

1. Performance definition2. Evaluation approach3. Analysis4. Mathematical modeling 5. Acceptance criteria


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I. Performance Definition

A Performance Objective has two

components:

• Hazard Level• Performance Level (limiting damage state)

Association of a performance level (damagestate) to a hazard level is called a performanceobjective .


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Hazard Level

• Characterized by a hazard curve, whichindicates the probability that a given value ofa ground motion parameter, for examplepeak ground acceleration, will be exceededover a certain period of time.

• For example: – 2% POE in 50 years or 2500 years return period – 50% POE in 50 years or 100 years return period


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Performance Level

Performance levels are discrete damage states

selected among all possible damage statesthat a building could experience as a result ofearthquake response.

• For example: – Collapse Prevention (CP) – Immediate Occupancy (IO)


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Performance Level


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Uncertainties

• Behavior and response of the structure• Accuracy of analysis procedures

• Ground motions

Therefore the performance objective isexpressed in terms of confidence levels.


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Performance Objective

Therefore a performance objective for a design

should more correctly be stated as:

• A certain level of confidence (i.e. 95%)that thestructure will provide Collapse Prevention orbetter performance for earthquake hazards

with 2% probability of exceedance in 50 years


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PBSD Steps:

Performance definition2. Evaluation approach3. Analysis4. Mathematical modeling 5. Acceptance criteria


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II. Evaluation

• The structural analysis is used to predict the valueof various structural response parameters: – Interstory drift: – Axial force

• Predicted demands are adjusted by two factors: – Analytical uncertainty factor, γa – Demand variability factor, γ

• Structural capacities are adjusted by resistantfactors, φ• Level of confidence is calculated based on the ratio

of factored demand to factored capacity.


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III. Analysis Method

1. Linear static procedure

2. Linear dynamic procedure

3. Nonlinear static procedure

4. Nonlinear dynamic procedure


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III. Analysis Method


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Linear Static Procedure

• It is an equivalent lateral force technique

• Has inherently more uncertainty because it accountsless accurately the dynamic characteristics of thestructures

• Applied lateral forces follow a pattern thatresembles the distribution of inertial forces in aregular structure responding linearly to the ground

excitations• It is assumed that the structure’s response isdominated by the fundamental mode


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LSP Steps

• Calculate the fundamental period for each of

the two orthogonal directions, from: – Eigenvalue analysis of the mathematical model

– Apoximate period formula (4-1):

• Calculate Pseudo Lateral Load for each ofthe two orthogonal directions, from:

( )2 0n n K M ω ϕ − =0.8

t nT C h=

1 2 3 aV C C C S W =


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C 1

A modification factor to relate expected maximum inelasticdisplacements to displacements calculated for linear elasticresponse:


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C 1

S a ,g

T, sec

1 1.0C =1 1.5C =

T s0.2T s


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C 2

• A modification factor to represent the effect

of hysteretic pinching on the maximumdisplacement response, for steel momentframes:

2 1.0C =


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C 3

• A modification factor to represent increased

dynamic displacements due to P-delta effects andstiffness degradation:


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Base Shear- 1 2 3 aV C C C S W =

• S a : Response spectrum acceleration at the

fundamental period and damping ratio of thebuilding in the direction under consideration, for thehazard level corresponding to the performanceobjective being evaluated (I.e., probability ofexceedance.)

• W: Total dead load and anticipated live load


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Nonlinear Dynamic Procedure

Response calculations are carried out usingnonlinear response-history analysis

An estimate of median response parameterof interest will be obtained by performingthe analyses over a set of minimum sevenpairs of strong ground motion records

The mathematical model of the buildingstructures should incorporate the inelasticmaterial and nonlinear geometric behavior


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IV. Mathematical Modeling

1. Frame configuration2. Connection modeling

• Fully-restrained (FR)• Partially-restrained (PR)• Simple shear tab

• Panel zone stiffness3. Horizontal torsion4. Foundation5. Diaphragms6. P-Delta effects7. Multidimensional excitation effects8. Vertical ground motion


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PBSD Steps:

Performance definitionEvaluation approach

AnalysisMathematical modeling

5. Acceptance criteria


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V. Acceptance Criteria

Acceptability of building performance should

be evaluated by determining a level ofconfidence in the building’s ability to meetthe desired performance objective(s).

1. Factored-Demand-to-Capacity Ratio• For interstory drift• For column axial load• For column splice tension

2. Confidence-level computations


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V. Acceptance Criteria


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Analysis Uncertainty Factor


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Demand Variability Factor


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Structural Capacity and Capacity Factor


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Uncertainty Coefficient


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Confidence Levels


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Classroom activity…

• Problem 1: Find how much confidence a designer h

on his/her design against collapse for a 10-storySMF (with post-Northridge partially retrainedconnection) that has a median interstory drift demanof 5% under a set of seven earthquake input motionrecords with 2% probability of exceedance in 50

years? Nonlinear dynamic analysis is used.


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Conclusions

1. PBD can be seen as an approach for managingseismic risk, where by:


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Conclusions

Infrequent Rare Very Rare Frequency of DesignGround Shaking Level

l


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Conclusions

0 25% 50% 100%$, % Replacement

0 1 7 30 180Downtime, days

C l i


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Conclusions

2. Simplified analytical performanceevaluation methodology. (Chapter 4)

Applicable only to well-configured,

regular structures.3. Detailed procedures for performance

evaluation. (Appendix A) Applicableto irregular structures.

C l i


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Conclusions

4. Increased confidence in a building’s ability

to provide specific performance can beobtained by:• Providing greater earthquake resistance,• Reducing some of the uncertainties in the

performance evaluation process,• Using more exact procedures of Appendix

A.


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Thank you!

Any Questions?

C fid L l


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Confidence Levels

exp2

UT x UT k

K b

λ β β ⎧ ⎫⎛ ⎞= − −⎨ ⎬

⎜ ⎟⎝ ⎠⎩ ⎭== Uncertainty measure equal to the vector sum (SRSS) of theUncertainty measure equal to the vector sum (SRSS) of the

logarithmic standard deviation of the variations in demand andlogarithmic standard deviation of the variations in demand andcapacity resulting from uncertainty;capacity resulting from uncertainty;

== Slope of the hazard curve inSlope of the hazard curve in lnln--lnln coordinates at the hazard levelcoordinates at the hazard levelof interest;of interest;

== Coefficient relating the incremental change in demand to anCoefficient relating the incremental change in demand to anincremental change in ground motion intensity (usually taken asincremental change in ground motion intensity (usually taken as 1.0).1.0).

== Standard GaussianStandard Gaussian variate variate associated with the probability ofassociated with the probability of x x notnotbeing exceeded as a function of the number of standard deviationbeing exceeded as a function of the number of standard deviation ssabove or below the mean found in standard probability tables.above or below the mean found in standard probability tables.

K K x x

b b kk

UT

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