This document discusses static pushover analysis for seismic design performance assessment. It describes how to construct a pushover curve by defining a structural model and loads, and performing an analysis while controlling displacements. Two main methods are presented for using the pushover curve: the Capacity Spectrum Method (ATC-40) which constructs a capacity spectrum and determines a performance point, and the Displacement Coefficient Method (FEMA 273) which estimates a target displacement. The document also provides examples of modeling elements and their force-deformation properties for the 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
Deformation Measure
Force Measure
Performance Limits
(IO, LS, CP)
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
B
A
C
D E Force
Deformation

12. Pushover Modeling (Properties)
Force-Deformation (Back bone Curve)
Force
Deformation

13. Pushover Modeling (Beam Element)
Three dimensional Beam Element
Flexible Span Loads
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

16. Pushover Modeling (Column Element)
Axial Load - Moment Interaction (Steel)
CE ye ( ye ) M =1.18Z F 1- P / P

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
Roof Displacement
Base Shear

22. Pushover Analysis (Solution Schemes)
Problem of Degradation of Strength
Roof Displacement
Base Shear

23. Pushover Analysis (Results)
Deformation Measure
Force 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
Roof Displacement
Base Shear
Spectral Displacement
Spectral Acceleration

28. 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

29. Use of Pushover Curve (ATC-40)
Constructing Capacity Spectrum
Spectral
Acceleration
( )
S =
V W
a
S PF
1
d roof ( roof )
1 / *
Spectral Displacement
1 ,
/ /
j
a
= D

30. Use of Pushover Curve (ATC-40)
Estimation of Equivalent Viscous Damping
Spectral
Acceleration
b kb
= +
b p
factor
0.05
Spectral Displacement
ED Eso
eq
k
(1/ 4 )*( / )
0
0
=

31. Use of Pushover Curve (ATC-40)
Estimation of Equivalent Damping
Ed
Eso
Spectral Displacement
Spectral
Acceleration

32. Use of Pushover Curve (ATC-40)
Response Spectrum (5% damping)
Spectral
Acceleration
Time Period
2.5CA
CV/T

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)
Spectral
Acceleration
Time Period
2.5CA/Bs
CV/(T BL)

35. Use of Pushover Curve (ATC-40)
Acceleration-Displacement Response Spectrum
Spectral
Acceleration
T0
S T0 d = SaT2/4p2
Time Period
Spectral
Acceleration
Spectral Displacement

36. Use of Pushover Curve (ATC-40)
Performance Point
Spectral
Acceleration
Demand Spectrum for effective
damping at performance point
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
Deformation Measure
Force Measure
Performance Limits
(IO, LS, CP)

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
2 /(4 2 )
d = C0 C1C2 C3 Sa Te p

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
.6Vy
Base Shear Roof Displacement
Ke
aKe = Ks
Estimate Te using Ke
Estimate Elastic Spectral Displacement
d =Sa Te2 /(4p 2 )

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
Spectral
Acceleration
C1 = [1 +(R-1)T0/Te]/R
C1 = 1
T0
Time Period
R is elastic strength
demand to yield
strength

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
Deformation Measure
Force Measure
Performance Limits
(IO, LS, CP)

49. How do they compare with each other?
- Observed damage
- Multi-degree of freedom systems
- Single degree of freedom systems
- Nonlinear time history analysis
Comparisons with:
Do these methods work?
Use of Pushover Curve

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
B
C D
E F
Deformation
Force A

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

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