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
Flexible Connection
Span Loads
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

16. Pushover Modeling (Column Element)
Axial Load - Moment Interaction (Steel)

17. 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)
Uniform
Code Lateral
Mode 1

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 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
Base Shear
Spectral Acceleration
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
MDOF
Equivalent SDOF

29. 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
Time Period
Spectral Displacement

36. Use of Pushover Curve (ATC-40)
Performance Point
Demand Spectrum for effective damping 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

48. 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 C D B
Force E F A
Deformation

53. SAP2000/ETABS Pushover Options
Three dimensional Beam Element
Flexible Connection
Span Loads
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

56. 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

57. 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

58. 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