Static Pushover Analysis

Static Pushover Analysis

Performance Based Design

Modeling for Pushover Analysis

Use of the Pushover Curve

Thoudam Jagat Singh

Static Pushover Analysis for Seismic DesignMarch 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

Deformation Measure

Fo

rce

Me

asu

re

Performance Limits (IO, LS, CP)

Expected Performance Point for given Earthquake

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

B

A

C

D E

For

ce

Deformation

Pushover Modeling (Properties)

Force-Deformation (Back bone Curve)

For

ce

Deformation

Pushover Modeling (Beam Element)

Three dimensional Beam Element

Plastic Hinge Rigid Zone

Span LoadsFlexible Connection Shear Hinge

Pushover Modeling (Column Element)

Three dimensional Column Element


Shear Hinge


Axial Load - Moment Interaction (Concrete)

P

M


Axial Load - Moment Interaction (Steel)

yeyeCE PPFZM /118.1

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


Event by Event Strategy

Roof Displacement

Ba

se S

hea

r


Problem of Degradation of Strength

Roof Displacement

Ba

se S

hea

r

Pushover Analysis (Results)

Deformation Measure

Fo

rce

Me

asu

re

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


Constructing Capacity Spectrum

Roof Displacement

Ba

se S

hea

r

Spectral Displacement

Sp

ectr

al A

cce

lera

tion



MDOF Equivalent SDOF

The displaced shape at any point on the pushover curve is used to obtain an equivalent SDOF system.

is the mass participation and relates the base shears

PF is the participation factor and relates the roof displacement to the SDOF displacement



Spe

ctra

l A

ccel

erat

ion


roofroofd

a

PFS

WVS

,1

1

1*/

//


Estimation of Equivalent Viscous Damping

Spe

ctra

l A

ccel

erat

ion


factor

EE soD

eq

)/(*)4/1(

05.0

0

0


Estimation of Equivalent Damping

Ed

Eso


S

pect

ral

Acc

eler

atio

n


Response Spectrum (5% damping)

Spe

ctra

l A

ccel

erat

ion

Time Period

2.5CA

CV/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)


Reduced Spectrum (Effective damping)

Spe

ctra

l A

ccel

erat

ion

Time Period

2.5CA/Bs

CV/(T BL)


Acceleration-Displacement Response Spectrum

S

pect

ral

Acc

eler

atio

n

Time Period

T0 S

pect

ral

Acc

eler

atio

nSpectral Displacement

T0Sd = SaT2/42


Performance Point

Spe

ctra

l A

ccel

erat

ion


Demand Spectrum for effectivedamping at performance point

Capacity Spectrum


Performance Point

Spe

ctra

l Acc

eler

atio

n



Verification of Acceptance

Deformation Measure

Fo

rce

Me

asu

re


Expected Performance Point for given Earthquake


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

)4/( 223210 ea TSCCCC

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


Estimation of Effective Elastic Period, Te

Bas

e S

hear

Roof Displacement

Vy

.6Vy

Ke

Ke = Ks

Estimate Te using Ke

Estimate Elastic Spectral Displacement

)4/( 22 ea TS

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


Modifier for inelastic displacement

S

pect

ral

Acc

eler

atio

n

Time Period

C1 = 1

T0

C1 = [1 +(R-1)T0/Te]/R

R is elastic strength demand to yield strength


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


Modifier for dynamic second order effects

C3 = 1 if post yield slope, is positive

else C3 = 1 +[ ||(R-1)3/2 ]/Te

Use of Pushover Curve (FEMA-273)

Verification of Acceptance

Deformation Measure

Fo

rce

Me

asu

re


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 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


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)


Force-Deformation Relationship

B

C D

E F

Deformation

For

ce

A


Three dimensional Beam Element


Span LoadsFlexible Connection Shear Hinge


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)


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


Available Results for each step of loading - Base Shear - Element Forces - Section Forces - Joint Displacements - Drifts - Element Hinge Deformations - Limit Points (acceptance criteria) reached


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


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

Documents

Static Pushover Analysis