Static Pushover AnalysisPerformance Based DesignModeling for Pushover AnalysisUse of the Pushover Curve

M. Iqbal SuharwardyComputers and Structures, Inc.

Static Pushover Analysis for Seismic DesignMarch 22, 1999

Performance Check of StructuresPurpose

How will a structure perform when subjected to a given level of earthquake? Definition of structural performanceDefinition of earthquake levelDetermination of performance level

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

Types of Performance ChecksLinear Static AnalysisLinear Dynamic AnalysisNonlinear Static Analysis (Pushover Analysis)Nonlinear Dynamic Analysis

Performance Check Using PushoverDeformation MeasureForce MeasurePerformance Limits (IO, LS, CP)Expected Performance Point for given EarthquakeGoal is to predict peak response of building and components for a given earthquake

Why Do Pushover Analysis?Design Earthquakes cause nonlinear behaviorBetter understand building behavior - Identify weak elements - Realistic prediction of element demands Less conservative acceptance criteria can be used with consequences understood

Steps in Performance CheckConstruct Pushover curveSelect earthquake level(s) to checkSelect performance level(s) to checkSelect acceptance criteria for each performance levelVerify acceptanceCapacity Spectrum Method (ATC-40)Displacement Coefficient Method (FEMA 273)

Constructing Pushover CurveDefine Structural ModelElements (components)Strength - deformation propertiesDefine LoadsGravityLateral load patternSelect Control Displacements or DriftsPerform Pushover Analysis

Pushover ModelingDefinition of Structural Model3D or 2DPrimary and Secondary Elements (components)Non structural ElementsFoundation flexibilityP-Delta effects

Pushover Modeling (Elements)TypesTruss - yielding and buckling3D Beam - major direction flexural and shear hinging3D Column - P-M-M interaction and shear hingingPanel zone - Shear yieldingIn-fill panel - Shear failureShear wall - P-M-Shear interaction!Spring - for foundation modeling

Pushover Modeling (Properties)Force-Deformation RelationshipBACDEForceDeformation

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

Pushover Modeling (Beam Element)Three dimensional Beam ElementPlastic HingeRigid ZoneSpan LoadsFlexible ConnectionShear Hinge

Pushover Modeling (Column Element)Three dimensional Column ElementPlastic HingeRigid ZoneShear Hinge

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

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

Pushover Modeling (Loads)Start with Gravity LoadsDead LoadSome portion of Live Load Select Lateral Load PatternLateral Load Patterns (Vertical Distribution)Lateral Load Horizontal DistributionTorsional EffectsOrthogonal Effects

Pushover Modeling (Loads)Lateral Load Patterns (Vertical Distribution)UniformCode LateralMode 1

Pushover Analysis (Control)Force controlled analysis Deformation controlled analysisRoof DisplacementGeneralized Displacement Definitions

Limit of analysisInstability - loss of gravity load carrying capacityExcessive distortions

Pushover Analysis (Solution Schemes)Event by Event StrategiesManualNewton-Raphson Type StrategiesConstant stiffness iterationsTangent stiffness iterations Problem of degradation of strengthRitz Modes (Reduced Space) Strategies

Pushover Analysis (Solution Schemes)Event by Event Strategy

Roof DisplacementBase Shear

Pushover Analysis (Solution Schemes)Problem of Degradation of Strength

Roof DisplacementBase Shear

Pushover Analysis (Results)Deformation MeasureForce Measure

Pushover Analysis (Results)

Use of Pushover CurveCapacity Spectrum Method - detailed in ATC-40 - and as alternate method in FEMA-273Displacement Coefficient Method - detailed in FEMA-273

Use of Pushover Curve (ATC-40)Construct Capacity SpectrumEstimate Equivalent DampingDetermine Demand SpectrumDetermine Performance PointVerify Acceptance

Use of Pushover Curve (ATC-40) Constructing Capacity SpectrumRoof DisplacementBase ShearSpectral DisplacementSpectral Acceleration

Use of Pushover Curve (ATC-40) Constructing Capacity SpectrumMDOFEquivalent SDOFThe 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 shearsPF is the participation factor and relates the roof displacement to the SDOF displacement

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

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

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

Use of Pushover Curve (ATC-40)Response Spectrum (5% damping) Spectral AccelerationTime Period2.5CACV/T

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) Spectral AccelerationTime Period2.5CA/BsCV/(T BL)

Use of Pushover Curve (ATC-40)Acceleration-Displacement Response Spectrum Spectral AccelerationTime PeriodT0 Spectral AccelerationSpectral DisplacementT0Sd = SaT2/4p2

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

Demand Spectrum for effective damping at performance pointCapacity Spectrum

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

Use of Pushover Curve (ATC-40)Verification of AcceptanceDeformation MeasureForce MeasurePerformance Limits (IO, LS, CP)Expected Performance Point for given Earthquake

Use of Pushover Curve (ATC-40)

Use of Pushover Curve (FEMA-273) (Displacement Coefficient Method)

Estimate Target DisplacementVerify Acceptance

Use of Pushover Curve (FEMA-273) Estimation of Target Displacement

Estimate effective elastic stiffness, KeEstimate post yield stiffness, KsEstimate effective fundamental period, TeCalculate target roof displacement as

Use of Pushover Curve (FEMA-273) Estimation of Target Displacement

C0 Relates spectral to roof displacementC1 Modifier for inelastic displacementC2 Modifier for hysteresis loop shapeC3 Modifier for second order effects

Use of Pushover Curve (ATC-40)Estimation of Effective Elastic Period, Te Base ShearRoof DisplacementVy.6VyKeaKe = KsEstimate Te using KeEstimate Elastic Spectral Displacement

Use of Pushover Curve (FEMA-273) Calculation of C0Relates 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 C1Modifier for inelastic displacement

Spectral AccelerationTime PeriodC1 = 1T0C1 = [1 +(R-1)T0/Te]/RR is elastic strength demand to yield strength

Use of Pushover Curve (FEMA-273) Calculation of C2Modifier 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 C3Modifier for dynamic second order effects

C3 = 1 if post yield slope, a is positive elseC3 = 1 +[ |a|(R-1)3/2 ]/Te

Use of Pushover Curve (FEMA-273)Verification of AcceptanceDeformation MeasureForce MeasurePerformance Limits (IO, LS, CP)Target Displacement (or corresponding deformation) for given Earthquake

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 damageHow do they compare with each other?

SAP2000/ETABS Pushover OptionsSAP2000 released September, 1998 Full 3D implementationSingle 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 OptionsGenerally follows ATC-40 & FEMA 273Available 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 OptionsForce-Deformation RelationshipBCDEFDeformationForceA

SAP2000/ETABS Pushover OptionsThree dimensional Beam ElementPlastic HingeRigid ZoneSpan LoadsFlexible ConnectionShear Hinge

SAP2000/ETABS Pushover OptionsStrength - 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 OptionsGravity 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 OptionsAvailable 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 OptionsPushover 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 OptionsVisual 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