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

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

Performance Check of Structures Process Recently released guidelines for Seismic Rehabilitation of Buildings: ATC-40 FEMA 273 (ATC-33)

Types of Performance Checks Linear Static Analysis Linear Dynamic Analysis Nonlinear Static Analysis (Pushover Analysis) Nonlinear Dynamic Analysis

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

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

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)

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

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

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

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

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

Pushover Modeling (Beam Element) Three dimensional Beam Element Flexible Connection Span Loads Shear Hinge Plastic Hinge Rigid Zone

Pushover Modeling (Column Element) Three dimensional Column Element Shear Hinge Plastic Hinge Rigid Zone

Pushover Modeling (Column Element) Axial Load - Moment Interaction (Concrete) P M

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

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

Pushover Modeling (Loads) Lateral Load Patterns (Vertical Distribution) Uniform Code Lateral Mode 1

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

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

Pushover Analysis (Solution Schemes) Event by Event Strategy Base Shear Roof Displacement

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

Pushover Analysis (Results) Force Measure Deformation Measure

Pushover Analysis (Results)

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

Use of Pushover Curve (ATC-40) Construct Capacity Spectrum Estimate Equivalent Damping Determine Demand Spectrum Determine Performance Point Verify Acceptance

Use of Pushover Curve (ATC-40) Constructing Capacity Spectrum Base Shear Spectral Acceleration Roof Displacement Spectral Displacement

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

Use of Pushover Curve (ATC-40) Constructing Capacity Spectrum Spectral Acceleration Spectral Displacement

Use of Pushover Curve (ATC-40) Estimation of Equivalent Viscous Damping Spectral Acceleration Spectral Displacement

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

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

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)

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

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

Use of Pushover Curve (ATC-40) Performance Point Demand Spectrum for effective damping at performance point Spectral Acceleration Capacity Spectrum Spectral Displacement

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

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

Use of Pushover Curve (ATC-40)

Use of Pushover Curve (FEMA-273) (Displacement Coefficient Method) Estimate Target Displacement Verify Acceptance

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

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

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

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

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

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

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

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

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?

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

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)

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

SAP2000/ETABS Pushover Options Three dimensional Beam Element Flexible Connection Span Loads Shear Hinge Plastic Hinge Rigid Zone

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)

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

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

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

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