Pushover analysis

1
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

2
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

3
Performance Check of Structures

• Process
• Recently released guidelines for Seismic
  Rehabilitation of Buildings
• ATC-40
• FEMA 273 (ATC-33)

4
Types of Performance Checks

• Linear Static Analysis
• Linear Dynamic Analysis
• Nonlinear Static Analysis(Pushover Analysis)
• Nonlinear Dynamic Analysis

5
Performance Check Using Pushover
Expected Performance Point for given Earthquake
Force Measure
Performance Limits (IO, LS, CP)
Deformation Measure
Goal is to predict peak response of building and
components for a given earthquake
6
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

7
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)

8
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

9
Pushover Modeling

• Definition of Structural Model
• 3D or 2D
• Primary and Secondary Elements (components)
• Non structural Elements
• Foundation flexibility
• P-Delta effects

10
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

11
Pushover Modeling (Properties)

• Force-Deformation Relationship

C
B
Force
D
E
A
Deformation
12
Pushover Modeling (Properties)

• Force-Deformation (Back bone Curve)

Force
Deformation
13
Pushover Modeling (Beam Element)

• Three dimensional Beam Element

Span Loads
Flexible Connection
Shear Hinge
Plastic Hinge
Rigid Zone
14
Pushover Modeling (Column Element)

• Three dimensional Column Element

Shear Hinge
Plastic Hinge
Rigid Zone
15
Pushover Modeling (Column Element)

• Axial Load - Moment Interaction (Concrete)

P
M
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Pushover Modeling (Column Element)

• Axial Load - Moment Interaction (Steel)

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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

18
Pushover Modeling (Loads)

• Lateral Load Patterns (Vertical Distribution)

Mode 1
Code Lateral
Uniform
19
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

20
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

21
Pushover Analysis (Solution Schemes)

• Event by Event Strategy

Base Shear
Roof Displacement
22
Pushover Analysis (Solution Schemes)

• Problem of Degradation of Strength

Base Shear
Roof Displacement
23
Pushover Analysis (Results)
Force Measure
Deformation Measure
24
Pushover Analysis (Results)
25
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

26
Use of Pushover Curve (ATC-40)

• Construct Capacity Spectrum
• Estimate Equivalent Damping
• Determine Demand Spectrum
• Determine Performance Point
• Verify Acceptance

27
Use of Pushover Curve (ATC-40)

• Constructing Capacity Spectrum

Spectral Acceleration
Base Shear
Roof Displacement
Spectral Displacement
28
Use of Pushover Curve (ATC-40)

• Constructing Capacity Spectrum

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
Equivalent SDOF
MDOF
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Use of Pushover Curve (ATC-40)

• Constructing Capacity Spectrum

Spectral Acceleration
Spectral Displacement
30
Use of Pushover Curve (ATC-40)

• Estimation of Equivalent Viscous Damping

Spectral Acceleration
Spectral Displacement
31
Use of Pushover Curve (ATC-40)

• Estimation of Equivalent Damping

Spectral Acceleration
Eso
Spectral Displacement
Ed
32
Use of Pushover Curve (ATC-40)

• Response Spectrum (5 damping)

2.5CA
CV/T
Spectral Acceleration
Time Period
33
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)

34
Use of Pushover Curve (ATC-40)

• Reduced Spectrum (Effective damping)

2.5CA/Bs
Spectral Acceleration
CV/(T BL)
Time Period
35
Use of Pushover Curve (ATC-40)

• Acceleration-Displacement Response Spectrum

T0
Sd SaT2/4p2
Spectral Acceleration
Spectral Acceleration
T0
Spectral Displacement
Time Period
36
Use of Pushover Curve (ATC-40)

• Performance Point

Demand Spectrum for effectivedamping at
performance point
Spectral Acceleration
Capacity Spectrum
Spectral Displacement
37
Use of Pushover Curve (ATC-40)

• Performance Point

Spectral Acceleration
Spectral Displacement
38
Use of Pushover Curve (ATC-40)

• Verification of Acceptance

Expected Performance Point for given Earthquake
Force Measure
Performance Limits (IO, LS, CP)
Deformation Measure
39
Use of Pushover Curve (ATC-40)
40
Use of Pushover Curve (FEMA-273)

• (Displacement Coefficient Method)
• Estimate Target Displacement
• Verify Acceptance

41
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

42
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

43
Use of Pushover Curve (ATC-40)

• Estimation of Effective Elastic Period, Te

Vy
aKe Ks
Estimate Te using Ke Estimate Elastic Spectral
Displacement
.6Vy
Base Shear
Ke
Roof Displacement
44
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

45
Use of Pushover Curve (FEMA-273)

• Calculation of C1
• Modifier for inelastic displacement

C1 1 (R-1)T0/Te/R
R is elastic strength demand to yield strength
Spectral Acceleration
C1 1
T0
Time Period
46
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

47
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

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Use of Pushover Curve (FEMA-273)

• Verification of Acceptance

Target Displacement (or corresponding
deformation) for given Earthquake
Force Measure
Performance Limits (IO, LS, CP)
Deformation Measure
49
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?

50
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

51
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)

52
SAP2000/ETABS Pushover Options

• Force-Deformation Relationship

D
C
B
Force
E
F
A
Deformation
53
SAP2000/ETABS Pushover Options

• Three dimensional Beam Element

Span Loads
Flexible Connection
Shear Hinge
Plastic Hinge
Rigid Zone
54
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)

55
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