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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
Plastic Hinge Rigid Zone
Shear Hinge
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Pushover Modeling (Column Element)
Axial Load - Moment Interaction (Concrete)
P
M
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Pushover Modeling (Column Element)
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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Pushover Analysis (Solution Schemes)
Event by Event Strategy
Roof Displacement
BaseShear
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Pushover Analysis (Solution Schemes)
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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Use of Pushover Curve (ATC-40)
Constructing Capacity Spectrum
Roof Displacement
Ba
seShear
Spectral Displacement
Spec
tralAcceleration
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Use of Pushover Curve (ATC-40)
Constructing Capacity Spectrum
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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Use of Pushover Curve (ATC-40)
Constructing Capacity Spectrum
Spectral
Acceleration
Spectral Displacement
roofroofd
a
PFS
WVS
,1
1
1*/
//
a
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Use of Pushover Curve (ATC-40)
Estimation of Equivalent Viscous Damping
Spectral
Acceleration
Spectral Displacement
factor
EE soD
eq
)/(*)4/1(05.0
0
0
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Use of Pushover Curve (ATC-40)
Estimation of Equivalent Damping
Ed
Eso
Spectral Displacement
Spectra
l
Acceleration
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Use of Pushover Curve (ATC-40)
Response Spectrum (5% damping)
Spectral
Acceleration
Time Period
2.5CA
CV/T
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Use of Pushover Curve (ATC-40)
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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Use of Pushover Curve (ATC-40)
Reduced Spectrum (Effective damping)
Spectral
Acceleration
Time Period
2.5CA/Bs
CV/(T BL)
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Use of Pushover Curve (ATC-40)
Acceleration-Displacement Response Spectrum
Spectral
Acceleration
Time Period
T0Spectral
Acceleration
Spectral Displacement
T0Sd
= Sa
T2/42
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Use of Pushover Curve (ATC-40)
Performance Point
Spectral
Acceleration
Spectral Displacement
Demand Spectrum for effective
damping at performance point
Capacity Spectrum
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Use of Pushover Curve (ATC-40)
Performance Point
Spec
tralAcceleration
Spectral Displacement
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Use of Pushover Curve (ATC-40)
Verification of Acceptance
Deformation Measure
Fo
rceMeasure
Performance Limits
(IO, LS, CP)
Expected Performance Point
for given Earthquake
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Use of Pushover Curve (ATC-40)
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Use of Pushover Curve (FEMA-273)
(Displacement Coefficient Method)
Estimate Target Displacement
Verify Acceptance
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Use of Pushover Curve (FEMA-273)
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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Use of Pushover Curve (FEMA-273)
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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Use of Pushover Curve (ATC-40)
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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Use of Pushover Curve (FEMA-273)
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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Use of Pushover Curve (FEMA-273)
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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Use of Pushover Curve (FEMA-273)
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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Use of Pushover Curve (FEMA-273)
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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Use of Pushover Curve (FEMA-273)
Verification of Acceptance
Deformation Measure
Fo
rceMeasure
Performance Limits
(IO, LS, CP)
Target Displacement (or
corresponding deformation)
for given Earthquake
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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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SAP2000/ETABS Pushover Options
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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SAP2000/ETABS Pushover Options
Force-Deformation Relationship
B
C D
E F
Deformation
Force
A
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SAP2000/ETABS Pushover Options
Three dimensional Beam Element
Plastic Hinge Rigid Zone
Span LoadsFlexible
Connection Shear Hinge
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SAP2000/ETABS Pushover Options
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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SAP2000/ETABS Pushover Options
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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SAP2000/ETABS Pushover Options
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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SAP2000/ETABS Pushover Options
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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SAP2000/ETABS Pushover Options
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
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