1223989 static pushover analysis

Static Pushover Analysis

Performance Based Design

Modeling for Pushover Analysis

Use of the Pushover Curve

M. Iqbal SuharwardyComputers and Structures, Inc.

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

For

ce M

ea

sure

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

For

ce M

ea

sure

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

Bas

e S

hea

r

Spectral Displacement

Spe

ctra

l Acc

ele

ratio

n



MDOF Equivalent SDOF

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

α 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*/

//

ϕα

∆==


Estimation of Equivalent Viscous Damping

Spe

ctra

l A

ccel

erat

ion


factor

EE soD

eq

κπβ

κββ)/(*)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

pec

tra

l A

cce

lera

tion


T0Sd = SaT2/4π2


Performance Point

Spe

ctra

l A

ccel

erat

ion


Demand Spectrum for effectivedamping at performance point

Capacity Spectrum


Performance Point

Spe

ctra

l Acc

ele

ratio

n



Verification of Acceptance

Deformation Measure

For

ce M

ea

sure


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 πδ 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

Ba

se S

hear

Roof Displacement

Vy

.6Vy

Ke

αKe = Ks

Estimate Te using Ke

Estimate Elastic Spectral Displacement

)4/( 22 πδ 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, α is positive

else

C3 = 1 +[ |α|(R-1)3/2 ]/Te

Use of Pushover Curve (FEMA-273)

Verification of Acceptance

Deformation Measure

For

ce M

ea

sure


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

Engineering

1223989 static pushover analysis