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Static Pushover Analysis

Static Pushover Analysis

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Static Pushover Analysis

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  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 interactionand 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) 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

  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 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

  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