Pushover Point

5/24/2018 Pushover Point

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Static Pushover Analysis

Performance Based Design

Modeling for Pushover Analysis

Use of the Pushover Curve

M. Iqbal Suharwardy

Computers and Structures, Inc.

Static Pushover Analysis for Seismic Design

March 22, 1999


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Performance Check of Structures

Purpose

How will a structure perform when subjected toa given level of earthquake?

Definition of structural performance

Definition of earthquake level

Determination of performance level


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Performance Check of Structures

Process

Recently released guidelines for SeismicRehabilitation of Buildings:

ATC-40

FEMA 273 (ATC-33)


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Types of Performance Checks

Linear Static Analysis

Linear Dynamic Analysis

Nonlinear Static Analysis

(Pushover Analysis)

Nonlinear Dynamic Analysis


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Performance Check Using Pushover

Deformation Measure

ForceMeas

ure

Performance Limits

(IO, LS, CP)

Expected Performance Point

for given Earthquake

Goal is to predict peak response of building

and components for a given earthquake


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Why Do Pushover Analysis?

Design Earthquakes cause nonlinear

behavior

Better understand building behavior- Identify weak elements

- Realistic prediction of element demands

Less conservative acceptance criteria can beused with consequences understood


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Steps in Performance Check

Construct Pushover curve

Select earthquake level(s) to check

Select performance level(s) to check

Select acceptance criteria for each

performance level

Verify acceptance

Capacity Spectrum Method (ATC-40)

Displacement Coefficient Method (FEMA 273)


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Constructing Pushover Curve

Define Structural ModelElements (components)

Strength - deformation properties

Define LoadsGravity

Lateral load pattern

Select Control Displacements or Drifts Perform Pushover Analysis


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Pushover Modeling

Definition of Structural Model3D or 2D

Primary and Secondary Elements (components)

Non structural Elements

Foundation flexibility

P-Delta effects


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Pushover Modeling (Elements)

TypesTruss - yielding and buckling

3D Beam - major direction flexural and shear hinging

3D Column - P-M-M interactionand shear hinging

Panel zone - Shear yielding

In-fill panel - Shear failure

Shear wall - P-M-Shear interaction!

Spring - for foundation modeling


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Pushover Modeling (Properties)

Force-Deformation Relationship

B

A

C

D E

Force

Deformation


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Pushover Modeling (Properties)

Force-Deformation (Back bone Curve)

Force

Deformation


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Pushover Modeling (Beam Element)

Three dimensional Beam Element

Plastic Hinge Rigid Zone

Span LoadsFlexibleConnection Shear Hinge


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Pushover Modeling (Column Element)

Three dimensional Column Element


Shear Hinge


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Axial Load - Moment Interaction (Concrete)

P

M


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Axial Load - Moment Interaction (Steel)

yeyeCE PPFZM /118.1


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Pushover Modeling (Loads)

Start with Gravity LoadsDead Load

Some portion of Live Load

Select Lateral Load PatternLateral Load Patterns (Vertical Distribution)

Lateral Load Horizontal DistributionTorsional Effects

Orthogonal Effects


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Pushover Modeling (Loads)

Lateral Load Patterns (Vertical Distribution)

Uniform Code Lateral Mode 1


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Pushover Analysis (Control)

Force controlled analysis

Deformation controlled analysisRoof Displacement

Generalized Displacement Definitions

Limit of analysisInstability - loss of gravity load carrying capacity

Excessive distortions


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Pushover Analysis (Solution Schemes)

Event by Event StrategiesManual

Newton-Raphson Type StrategiesConstant stiffness iterationsTangent stiffness iterations

Problem of degradation of strength

Ritz Modes (Reduced Space) Strategies


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Event by Event Strategy

Roof Displacement

BaseShear


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Problem of Degradation of Strength

Roof Displacement

Ba

seShear


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Pushover Analysis (Results)

Deformation Measure

ForceMeasure


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Pushover Analysis (Results)


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Use of Pushover Curve

Capacity Spectrum Method

- detailed in ATC-40

- and as alternate method in FEMA-273 Displacement Coefficient Method

- detailed in FEMA-273


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Use of Pushover Curve (ATC-40)

Construct Capacity Spectrum

Estimate Equivalent Damping

Determine Demand Spectrum

Determine Performance Point

Verify Acceptance


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Constructing Capacity Spectrum

Roof Displacement

Ba

seShear

Spectral Displacement

Spec

tralAcceleration


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MDOF Equivalent SDOF

The displaced shape at any point

on the pushover curve is used to

obtain an equivalent SDOF

system.

ais the mass participation and

relates the base shears

PF is the participation factor and

relates the roof displacement to

the SDOF displacement


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Spectral

Acceleration


roofroofd

a

PFS

WVS

,1

1

1*/

//

a


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Estimation of Equivalent Viscous Damping

Spectral

Acceleration


factor

EE soD

eq

)/(*)4/1(05.0

0

0


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Estimation of Equivalent Damping

Ed

Eso


Spectra

l

Acceleration


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Response Spectrum (5% damping)

Spectral

Acceleration

Time Period

2.5CA

CV/T


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Response Spectrum (5% damping)

CAand CVdepend on:- Seismic zone (0.075 to 0.4)

- Nearness to fault and source type (1 to 2)

- Soil Type (1 to 2.5)

- Level of Earthquake (0.5 to 1.5)


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Reduced Spectrum (Effective damping)

Spectral

Acceleration

Time Period

2.5CA/Bs

CV/(T BL)


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Acceleration-Displacement Response Spectrum

Spectral

Acceleration

Time Period

T0Spectral

Acceleration


T0Sd

= Sa

T2/42


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Performance Point

Spectral

Acceleration


Demand Spectrum for effective

damping at performance point

Capacity Spectrum


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Performance Point

Spec

tralAcceleration



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Verification of Acceptance

Deformation Measure

Fo

rceMeasure

Performance Limits

(IO, LS, CP)

Expected Performance Point



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Use of Pushover Curve (FEMA-273)

(Displacement Coefficient Method)

Estimate Target Displacement

Verify Acceptance


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Estimation of Target Displacement

Estimate effective elastic stiffness, KeEstimate post yield stiffness, Ks

Estimate effective fundamental period, Te

Calculate target roof displacement as

)4/( 223210 eaTSCCCC


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Estimation of Target Displacement

C0 Relates spectral to roof displacementC1Modifier for inelastic displacement

C2Modifier for hysteresis loop shape

C3Modifier for second order effects


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Estimation of Effective Elastic Period, Te

BaseShe

ar

Roof Displacement

Vy

.6Vy

Ke

aKe = Ks

Estimate Te using Ke

Estimate Elastic Spectral Displacement

)4/( 22 ea

TS


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Calculation of C0Relates spectral to roof displacement

- use modal participation factor for controlnode from first mode

- or use modal participation factor for

control node from deflected shape at the

target displacement

- or use tables based on number of stories

and varies from 1 to 1.5


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Calculation of C1Modifier for inelastic displacement

Sp

ectral

Acceleration

Time Period

C1= 1

T0

C1= [1 +(R-1)T0/Te]/R

R is elastic strength

demand to yield

strength


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Calculation of C2Modifier for hysteresis loop shape

- from Tables- depends on Framing Type

(degrading strength)

- depends on Performance Level

- depends on Effective Period

- varies from 1.0 to 1.5


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Calculation of C3Modifier for dynamic second order effects

C3= 1 if post yield slope, ais positive

else

C3= 1 +[ |a|(R-1)3/2]/T

e


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Verification of Acceptance

Deformation Measure

Fo

rceMeasure

Performance Limits

(IO, LS, CP)

Target Displacement (or

corresponding deformation)



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Use of Pushover Curve

Do these methods work?

Comparisons with:

- Nonlinear time history analysis- Single degree of freedom systems

- Multi-degree of freedom systems

- Observed damageHow do they compare with each other?


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SAP2000/ETABS Pushover Options

SAP2000 released September, 1998

Full 3D implementation

Single model for- linear static analysis

- linear response spectrum analysis

- linear time history analysis- nonlinear time history analysis

- nonlinear static pushover analysis

- steel and concrete design


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Generally follows ATC-40 & FEMA 273

Available Pushover Element Types

- 3D truss (axial hinge)- 3D beam (moment and shear hinges)

- 3D column (P-M-M and shear hinges)

- Shells, Solids, etc. considered linear

- Panel zone (later)- 3D column (Fiber hinge) (later)

- Shear wall (plasticity model) (later)

- Nonlinear springs (later)


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Force-Deformation Relationship

B

C D

E F

Deformation

Force

A


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Three dimensional Beam Element


Span LoadsFlexible

Connection Shear Hinge


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Strength - deformation and P-M-M curves

can be calculated by program for:

- steel beams (FEMA 273)

- steel columns (FEMA 273)

- shear hinges in EBF Links (FEMA 273)

- concrete beams (ATC-40)

- concrete columns (ATC-40)

- shear hinges in coupling beams (ATC-40)


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Gravity Load Analysis- Nodal Loads

- Element Loads- Load controlled Analysis

Pushover analysis- Starts from gravity loads- Nodal Load Patterns (user, modal, mass)

- Multi-step Displacement or Drift controlled


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Available Results for each step of loading- Base Shear

- Element Forces- Section Forces

- Joint Displacements

- Drifts

- Element Hinge Deformations- Limit Points (acceptance criteria) reached


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Pushover Curve Postprocessing (ATC-40)- Conversion to Capacity Spectrum

- Calculation of Effective Period (per step)- Calculation of Effective Damping (per step)

- Calculation of Demand Spectrum (per step)

- Location of Performance Point

- Limit Points (acceptance criteria) reached


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Visual Display for each step- Deformed Shape- Member Force Diagrams- Hinge Locations and Stages

Graphs

- Base Shear vs Roof Displacement- Capacity Curve- Demand Curve- Demand Spectra at different dampings- Effective period lines

Documents

Pushover Point