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
Performance Check of Structures
Purpose
How will a structure perform when subjected to a given level of earthquake?
–Definition of structural performance
–Definition of earthquake level
–Determination of performance level
Performance Check of Structures
Process
Recently released guidelines for Seismic
Rehabilitation of Buildings:
–ATC-40
– FEMA 273 (ATC-33)
Types of Performance Checks
Linear Static Analysis
Linear Dynamic Analysis
Nonlinear Static Analysis
(Pushover Analysis)
Nonlinear Dynamic Analysis
Performance Check Using Pushover
Deformation Measure
Fo
rce
Me
asu
re
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
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 be
used with consequences understood
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)
Constructing Pushover Curve
Define Structural Model Elements (components)
Strength - deformation properties
Define Loads Gravity
Lateral load pattern
Select Control Displacements or Drifts
Perform Pushover Analysis
Pushover Modeling
Definition of Structural Model 3D or 2D
Primary and Secondary Elements (components)
Non structural Elements
Foundation flexibility
P-Delta effects
Pushover Modeling (Elements)
Types Truss - yielding and buckling
3D Beam - major direction flexural and shear hinging
3D Column - P-M-M interaction and shear hinging
Panel zone - Shear yielding
In-fill panel - Shear failure
Shear wall - P-M-Shear interaction!
Spring - for foundation modeling
Pushover Modeling (Properties)
Force-Deformation Relationship
B
A
C
D E
Forc
e
Deformation
Pushover Modeling (Properties)
Force-Deformation (Back bone Curve)
Fo
rce
Deformation
Pushover Modeling (Beam Element)
Three dimensional Beam Element
Plastic Hinge Rigid Zone
Span Loads Flexible
Connection Shear Hinge
Pushover Modeling (Column Element)
Three dimensional Column Element
Plastic Hinge Rigid Zone
Shear Hinge
Pushover Modeling (Column Element)
Axial Load - Moment Interaction (Concrete)
P
M
Pushover Modeling (Column Element)
Axial Load - Moment Interaction (Steel)
yeyeCE PPFZM /118.1
Pushover Modeling (Loads)
Start with Gravity Loads Dead Load
Some portion of Live Load
Select Lateral Load Pattern Lateral Load Patterns (Vertical Distribution)
Lateral Load Horizontal Distribution
Torsional Effects
Orthogonal Effects
Pushover Modeling (Loads)
Lateral Load Patterns (Vertical Distribution)
Uniform Code Lateral Mode 1
Pushover Analysis (Control)
Force controlled analysis
Deformation controlled analysis Roof Displacement
Generalized Displacement Definitions
Limit of analysis Instability - loss of gravity load carrying capacity
Excessive distortions
Pushover Analysis (Solution Schemes)
Event by Event Strategies Manual
Newton-Raphson Type Strategies Constant stiffness iterations
Tangent stiffness iterations
Problem of degradation of strength
Ritz Modes (Reduced Space) Strategies
Pushover Analysis (Solution Schemes)
Event by Event Strategy
Roof Displacement
Ba
se
Sh
ea
r
Pushover Analysis (Solution Schemes)
Problem of Degradation of Strength
Roof Displacement
Ba
se
Sh
ea
r
Pushover Analysis (Results)
Deformation Measure
Fo
rce
Me
asu
re
Pushover Analysis (Results)
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
Use of Pushover Curve (ATC-40)
Construct Capacity Spectrum
Estimate Equivalent Damping
Determine Demand Spectrum
Determine Performance Point
Verify Acceptance
Use of Pushover Curve (ATC-40)
Constructing Capacity Spectrum
Roof Displacement
Ba
se
Sh
ea
r
Spectral Displacement
Sp
ectr
al A
cce
lera
tio
n
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.
a is the mass participation and
relates the base shears
PF is the participation factor and
relates the roof displacement to
the SDOF displacement
Use of Pushover Curve (ATC-40)
Constructing Capacity Spectrum S
pectr
al
Accele
ration
Spectral Displacement
roofroofd
a
PFS
WVS
,1
1
1*/
//
a
Use of Pushover Curve (ATC-40)
Estimation of Equivalent Viscous Damping S
pectr
al
Accele
ration
Spectral Displacement
factor
EE soD
eq
)/(*)4/1(
05.0
0
0
Use of Pushover Curve (ATC-40)
Estimation of Equivalent Damping
Ed
Eso
Spectral Displacement
S
pectr
al
Accele
ration
Use of Pushover Curve (ATC-40)
Response Spectrum (5% damping) S
pectr
al
Accele
ration
Time Period
2.5CA
CV/T
Use of Pushover Curve (ATC-40)
Response Spectrum (5% damping)
CA and CV depend 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)
Use of Pushover Curve (ATC-40)
Reduced Spectrum (Effective damping) S
pectr
al
Accele
ration
Time Period
2.5CA/Bs
CV/(T BL)
Use of Pushover Curve (ATC-40)
Acceleration-Displacement Response Spectrum
S
pectr
al
Accele
ratio
n
Time Period
T0 S
pectr
al
Accele
ration
Spectral Displacement
T0 Sd = SaT2/42
Use of Pushover Curve (ATC-40)
Performance Point S
pectr
al
Accele
ration
Spectral Displacement
Demand Spectrum for effective
damping at performance point
Capacity Spectrum
Use of Pushover Curve (ATC-40)
Performance Point S
pectr
al A
ccele
ration
Spectral Displacement
Use of Pushover Curve (ATC-40)
Verification of Acceptance
Deformation Measure
Fo
rce
Me
asu
re
Performance Limits
(IO, LS, CP)
Expected Performance Point
for given Earthquake
Use of Pushover Curve (ATC-40)
Use of Pushover Curve (FEMA-273)
(Displacement Coefficient Method)
Estimate Target Displacement
Verify Acceptance
Use of Pushover Curve (FEMA-273)
Estimation of Target Displacement
Estimate effective elastic stiffness, Ke
Estimate post yield stiffness, Ks
Estimate effective fundamental period, Te
Calculate target roof displacement as
)4/( 223210 ea TSCCCC
Use of Pushover Curve (FEMA-273)
Estimation of Target Displacement
C0 Relates spectral to roof displacement
C1 Modifier for inelastic displacement
C2 Modifier for hysteresis loop shape
C3 Modifier for second order effects
Use of Pushover Curve (ATC-40)
Estimation of Effective Elastic Period, Te
B
ase
She
ar
Roof Displacement
Vy
.6Vy
Ke
aKe = Ks
Estimate Te using Ke
Estimate Elastic Spectral Displacement
)4/( 22 ea TS
Use of Pushover Curve (FEMA-273)
Calculation of C0 Relates spectral to roof displacement
- use modal participation factor for control
node 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
Use of Pushover Curve (FEMA-273)
Calculation of C1 Modifier for inelastic displacement
S
pectr
al
Accele
ration
Time Period
C1 = 1
T0
C1 = [1 +(R-1)T0/Te]/R
R is elastic strength
demand to yield
strength
Use of Pushover Curve (FEMA-273)
Calculation of C2 Modifier 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
Use of Pushover Curve (FEMA-273)
Calculation of C3 Modifier for dynamic second order effects
C3 = 1 if post yield slope, a is positive
else
C3 = 1 +[ |a|(R-1)3/2 ]/Te
Use of Pushover Curve (FEMA-273)
Verification of Acceptance
Deformation Measure
Fo
rce
Me
asu
re
Performance Limits
(IO, LS, CP)
Target Displacement (or
corresponding deformation)
for given Earthquake
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 damage
How do they compare with each other?
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
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)
SAP2000/ETABS Pushover Options
Force-Deformation Relationship
B
C D
E F
Deformation
Forc
e
A
SAP2000/ETABS Pushover Options
Three dimensional Beam Element
Plastic Hinge Rigid Zone
Span Loads Flexible
Connection Shear Hinge
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)
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
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
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
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
