Download - Static Pushover Analysis
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Static Pushover Analysis
Performance Based Design
Modeling for Pushover Analysis
Use of the Pushover Curve
Thoudam Jagat Singh
Static Pushover Analysis for Seismic DesignMarch 22, 1999
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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
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Performance Check of Structures
Process
Recently released guidelines for Seismic
Rehabilitation 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
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
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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 be
used 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 Model Elements (components) Strength - deformation properties
Define Loads Gravity Lateral load pattern
Select Control Displacements or Drifts Perform Pushover Analysis
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Pushover Modeling
Definition of Structural Model 3D or 2D Primary and Secondary Elements (components) Non structural Elements Foundation flexibility P-Delta effects
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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
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Pushover Modeling (Properties)
Force-Deformation Relationship
B
A
C
D E
For
ce
Deformation
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Pushover Modeling (Properties)
Force-Deformation (Back bone Curve)
For
ce
Deformation
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Pushover Modeling (Beam Element)
Three dimensional Beam Element
Plastic Hinge Rigid Zone
Span LoadsFlexible Connection 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 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
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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 analysis Roof Displacement Generalized Displacement Definitions
Limit of analysis Instability - loss of gravity load carrying capacity Excessive distortions
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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
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Pushover Analysis (Solution Schemes)
Event by Event Strategy
Roof Displacement
Ba
se S
hea
r
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Pushover Analysis (Solution Schemes)
Problem of Degradation of Strength
Roof Displacement
Ba
se S
hea
r
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Pushover Analysis (Results)
Deformation Measure
Fo
rce
Me
asu
re
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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
se S
hea
r
Spectral Displacement
Sp
ectr
al A
cce
lera
tion
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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.
is 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
Spe
ctra
l A
ccel
erat
ion
Spectral Displacement
roofroofd
a
PFS
WVS
,1
1
1*/
//
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Use of Pushover Curve (ATC-40)
Estimation of Equivalent Viscous Damping
Spe
ctra
l A
ccel
erat
ion
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
S
pect
ral
Acc
eler
atio
n
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Use of Pushover Curve (ATC-40)
Response Spectrum (5% damping)
Spe
ctra
l A
ccel
erat
ion
Time Period
2.5CA
CV/T
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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)
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Use of Pushover Curve (ATC-40)
Reduced Spectrum (Effective damping)
Spe
ctra
l A
ccel
erat
ion
Time Period
2.5CA/Bs
CV/(T BL)
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Use of Pushover Curve (ATC-40)
Acceleration-Displacement Response Spectrum
S
pect
ral
Acc
eler
atio
n
Time Period
T0 S
pect
ral
Acc
eler
atio
nSpectral Displacement
T0Sd = SaT2/42
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Use of Pushover Curve (ATC-40)
Performance Point
Spe
ctra
l A
ccel
erat
ion
Spectral Displacement
Demand Spectrum for effectivedamping at performance point
Capacity Spectrum
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Use of Pushover Curve (ATC-40)
Performance Point
Spe
ctra
l Acc
eler
atio
n
Spectral Displacement
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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
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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, Ke Estimate post yield stiffness, Ks Estimate effective fundamental period, Te Calculate target roof displacement as
)4/( 223210 ea TSCCCC
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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
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Use of Pushover Curve (ATC-40)
Estimation of Effective Elastic Period, Te
Bas
e S
hear
Roof Displacement
Vy
.6Vy
Ke
Ke = 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 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
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Use of Pushover Curve (FEMA-273) Calculation of C1
Modifier for inelastic displacement
S
pect
ral
Acc
eler
atio
n
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 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
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Use of Pushover Curve (FEMA-273) Calculation of C3
Modifier for dynamic second order effects
C3 = 1 if post yield slope, is positive
else C3 = 1 +[ ||(R-1)3/2 ]/Te
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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
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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 damage How 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
For
ce
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