Download - 1223989 static pushover analysis
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Static Pushover Analysis
Performance Based Design
Modeling for Pushover Analysis
Use of the Pushover Curve
M. Iqbal SuharwardyComputers and Structures, Inc.
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
For
ce M
ea
sure
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
For
ce M
ea
sure
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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
Bas
e S
hea
r
Spectral Displacement
Spe
ctra
l Acc
ele
ratio
n
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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.
α 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*/
//
ϕα
∆==
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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
κπβ
κββ)/(*)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
pec
tra
l A
cce
lera
tion
Spectral Displacement
T0Sd = SaT2/4π2
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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
ele
ratio
n
Spectral Displacement
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Use of Pushover Curve (ATC-40)
Verification of Acceptance
Deformation Measure
For
ce M
ea
sure
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 πδ 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
Ba
se S
hear
Roof Displacement
Vy
.6Vy
Ke
αKe = Ks
Estimate Te using Ke
Estimate Elastic Spectral Displacement
)4/( 22 πδ 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, α is positive
else
C3 = 1 +[ |α|(R-1)3/2 ]/Te
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Use of Pushover Curve (FEMA-273)
Verification of Acceptance
Deformation Measure
For
ce M
ea
sure
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