Asep4A Pushover Analysis

PUSHOVER ANALYSIS OF BUILDINGSASEP SUMMIT 2012JUNE 8-9, 2012LA BREZA HOTEL, QUEZON CITY

ULPIANO P. IGNACIO, JR., M.Sc., F.ASEP, PICE

PROFESSOR OF CIVIL ENGINEERINGUNIVERSITY OF THE PHILIPPINES DILIMAN

Seminar on WIND & EARTHQUAKE ENGINEERINGMarch 23-24, 2012Regalia Tower Hotel Suites, Cubao, Quezon CityPUSHOVER ANALYSIS OF BUILDINGS

To introduce the basic concept of Pushover Analysis ofBuildings

To discuss the uses of a pushover analysis and a pushovercurve

To describe the different procedures for structural analysis

To present the general procedure in performing a pushoveranalysis

Objectives

Outline:

Types of Structural Analysis Procedures

What is Pushover Analysis?

How is a Pushover Curve constructed?

What are the uses of Pushover Analysis?

Types of Structural Analysis

ANALYSIS RESPONSEACTION

STRUCTURE (MODEL)

ACTION : DEAD LOAD, LIVE LOAD, WIND LOAD, SEISMIC, BLAST, ETC.

STRUCTURE: MATERIALS, COMPONENTS, GEOMETRY, SUPPORTS, ETC.

RESPONSE: DISPLACEMENTS, STRESSES, MOMENTS, SHEARS, ETC.

STRUCTURAL ANALYSIS – determination of the RESPONSEof a STRUCTURE due to external ACTIONS.

STRUCTURE(MODEL)

Materials may be ELASTIC or INELASTIC

ACTION (FORCE OR EXCITATION) may be:

STATIC – constant, slowly applied loadorDYNAMIC – time varying loads

STRUCTURE – consists of elements or componentsmade of materials and connected ina specific geometric arrangement.

RESPONSE may be LINEAR or NONLINEAR

Types of Material and Geometric Response Behavior

STRUCTURE(MODEL)

STRUCTURE: MATERIALS, GEOMETRY

NONLINEAR- ELASTIC

LINEAR- ELASTICLINEAR - INELASTIC

NONLINEAR- INELASTIC

Figures from ACECOMS, AIT

STRUCTURE: MATERIALS, GEOMETRY

Of the four combinations, the LINEAR-INELASTIC and the NONLINEAR-ELASTIC behavior are unlikely tohappen in practical structural cases.

Hence, only the LINEAR-ELASTIC andthe NONLINEAR-INELASTIC cases areentertained. They will simply be calledLINEAR AND NONLINEAR behavior,respectively.

Types of Structural Analysis Procedures

Together with the nature of the ACTION,whether STATIC or DYNAMIC, we have thefollowing four types of structural analysis

procedures:

NONLINEAR STATIC PROCEDURE

NONLINEAR DYNAMIC PROCEDURE

LINEAR STATIC PROCEDURE

LINEAR DYNAMIC PROCEDURE

LINEAR STATIC PROCEDURE (LSP)

An example of an LSP is the Static Force Procedureof Sec. 208.5.2 of the NSCP. In this procedure, theeffect of the ground motion on the building isconverted to a Design Base Shear, V. This V isconverted into a set of equivalent static lateralforces applied at the floor levels.

The structure is modeled and its properties aregiven by its stiffness matrix, [K]. In this procedure,the [K] remains constant.

LINEAR DYNAMIC PROCEDURE (LDP)

An example of an LDP is the DynamicAnalysis Procedure of Sec. 208.6 of theNSCP. In this procedure, an elastic dynamicanalysis utilizing the peak modal responsebased on the response spectrum for allsignificant modes is made.

To obtain the total response, the maximummodal contribution of significant modes arecombined in a prescribed manner, e.g. SRSSor CQC method.

NONLINEAR STATIC PROCEDURE (NSP)

An example of a NONLINEAR STATICPROCEDURE is a PUSHOVER ANALYSIS.

Oftentimes the Nonlinear Static Procedureis called Pushover Analysis

NONLINEAR DYNAMIC PROCEDURE (NDP)

• nonlinear dynamic procedures consider the timehistory of the ground shaking

• they incorporate inelastic member behavior undercyclic earthquake ground motions

• they explicitly simulate hysteretic energydissipation in the nonlinear range

• being more rigorous they require more time andcomputational effort and resources to perform

• Nonlinear Dynamic Procedure is also calledNonlinear Time History Analysis.

Outline:

Types of Structural Analysis √

■ Pushover Analysis is an incremental staticanalysis used to determine the force-displacement relationship for a structure orstructural element.

■ The analysis involves applying horizontalloads, in a prescribed pattern, to a computermodel of the structure incrementally, andplotting the total applied shear force andassociated lateral displacement at eachincrement, until the structure reaches a limit

state or collapse condition.

As individual components of a structure yield orfail, the earthquake forces on the building areshifted to other components.

A pushover analysis simulates this phenomenon byapplying loads until the weak link in the structure isfound and then revising the model to incorporatethe changes in the structure caused by the yieldingor failing of the weak link.

A second iteration is then performed to study howthe loads are redistributed in the structure. Thestructure is “pushed” again until the second weaklink is discovered.

This process continues until the yield patternfor the whole structure under seismic loadingis identified.

The plot of the total lateral force (base shear)vs. the displacement of a reference point(usually the center of mass of the roof level) isthe pushover curve or capacity curve.

A pushover analysis is an approximationof the more accurate and morecomplicated Nonlinear Dynamic Procedure

A pushover analysis is only useful forevaluating nonlinear structures for whichthe fundamental mode dominates and isnot suitable for certain irregular ordynamically complex structures.

Adapted from a presentation presentationpresentation made by Ron Ham burger atat Earth arth quake Anal ysis Methods : Predicting Building Behavior Behavior , a FEMA-SponsoredEERI Technical Seminar , 1999

Outline:

What is Pushover Analysis? √

How is a Pushover Curve constructed ?

2 types of pushover analysis:

FORCE CONTROLLED - the force is incrementallyincreased

DISPLACEMENT-CONTROLLED – the displacementof the reference point isincrementally increased

The displacement controlled pushover analysis isgenerally preferred over the force controlled onebecause the analysis could be carried out up to thedesired level of the displacement.

Pushover Analysis is carried out using computersoftware.

CreateMathematical

Apply gravity load todetermine

initial nodaldisplacements and

member forces

Apply increment oflateral load

Update nodaldisplacements and

member forces

Modify structuralstiffness to

represent yielding

Δ < Δ < Δlimit

Plot F vs. Δ

Flowchart of Procedure (Force-Controlled)

CreateMathematical

Apply gravity load todetermine

initial nodaldisplacements and

member forces

Apply increment ofdisplacement pattern

Update nodaldisplacements and

member forces

Modify structuralstiffness to

represent yielding

Δ < Δ < Δlimit

Plot F vs. Δ

Flowchart of Procedure (Displacement-Controlled)

Create Mathematical Model of the Structure

Geometry

Element Types – limit states Truss – yielding/buckling Beam – major axis bending and shear (M,V) Column – Axial, bending in 2 axes, shear

(P-M1-M2 and V) Panel zone – shear yielding In-fill panel – shear failure Shear Wall – P-M-V interaction Spring – for support modeling

Potential Plastic HingeLocation(must be predicted andrevised as needed)

Define Material Propertiesconcrete, steel, reinforcing bars, etc.density, strength, yield point, modulus ofelasticity, poisson’s ratio, shear modulus, etc.

Define Section PropertiesBeam Properties (dimensions, reinforcement,

steel section, etc.)Column Properties (dimensions,reinforcement,

steel section, etc.)

Define Element and Hinge Properties

General Force-Deformation Relationship

Deformation

Plastic Hinge Rigid Zone

Span LoadsFlexibleConnection Shear Hinge

Modeling Beam Element

Plastic Hinge Rigid Zone

Shear Hinge

Modeling Column Element

Modeling Column ElementAxial Load – Moment Interaction (RC)

• 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

Modeling Loads

Uniform Code Lateral Mode 1

Modeling Loads

Lateral Load Pattern

Plotting the Pushover Curve

Results of Analysis

RESULTS - CAPACITY SPECTRUM

Plot showing Hinge Location

Plot of Moment Diagram

Outline:

What is Pushover Analysis? √

Uses of Pushover Analysis

Assessment and Rehabilitation of Existing Buildings

1. Performance Check of Structures

Published Guidelines for Seismic Rehabilitation ofBuildings:

ATC-40 – Seismic Evaluation and Retrofit ofConcrete Buildings (1996)

FEMA 273 – NEHRP Guidelines for the SeismicRehabilitation of Buildings (1997)

FEMA 356 – Prestandard and Commentary forthe Seismic Rehabilitation of Buildings (2000)

FEMA 440 (ATC-55) - Improvement of Nonlinear StaticSeismic Analysis Procedures

Capacity Spectrum Method of ATC 40

Roof Displacement

Spectral Displacement

Convert Pushover Curve to Capacity Spectrum

Pushover Curve Capacity Spectrum

Time Period

Response Spectrum ( at effective damping)

Time Period

T0Sd = SaT2/4p2

Convert the Response Spectrum to Acceleration-Displacement Response Spectrum Format(Demand Spectrum)

Demand Spectrum for effectivedamping at performance point

Capacity Spectrum

Determine the Performance Point

Deformation Measure

Performance Limits(IO, LS, CP)

Expected Performance Pointfor given Earthquake

Verification of Acceptance

IO – Immediate OccupancyLS – Life SafetyCP – Collapse Prevention

Displacement Coefficient Method- described in FEMA-273

The performance point of the structure is obtained by thedetermination of a “target displacement” using the “CoefficientMethod” outlined in FEMA 273.

Where:

2. Performance Based Design (PBD)

PBD is similar to assessment and rehabilitationof buildings, except that we are dealing with newbuildings instead of existing ones.

In PBD, we design buildings so that they willperform according to pre-determined standardslike IO, LS, and CP at corresponding levels ofseismic shaking.

Therefore, pushover analysis is a necessarycomponent of PBD.

3. Development of Fragility and Vulnerability Curves

FRAGILITY CURVE (FUNCTION) - a curve (function)that shows the relationship between structuralperformance and ground motion. Specifically, it givesthe probability that a structure is in, or exceeding, agiven damage state due to a given ground motionintensity. If given in a tabular form, it is called a DamageProbability Matrix (DPM)

VULNERABILITY – the degree of loss to a given element atrisk resulting from a given level of hazard (e.g. groundmotion intensity). It is defined as the ratio of theexpected loss to the maximum possible loss, on a scaleof 0 to 1 (or 0 to 100%)

There are three methods used in developingfragility curves. These are:

1. Empirical Method (observed data)2. Analytical Method3. Heuristic Method (Based on experts’ opinion)

The analytical method relies heavily on the use ofpushover analysis

Typical example of a Damage Probability Matrix

Damage State V VI VII VIII IX X XI XII

No Damage 90 20 5 0 0 0 0 0

Slight 10 35 40 15 0 0 0 0

Moderate 0 30 35 30 20 10 0 0

Extensive 0 5 20 30 40 50 20 0

Complete 0 0 0 25 40 40 80 100

(Damage in percent of building population)

Seminar on WIND & EARTHQUAKE ENGINEERINGMarch 23-24, 2012Regalia Tower Hotel Suites, Cubao, Quezon City

Ground Motion Intensity

PUSHOVER ANALYSIS OF BUILDINGS

Fragility Curves

Example Vulnerability curve for a given type ofbuilding

Ground Motion Intensity

Damage

Summary

Pushover Analysis gives us a better idea how a structure willperform when subjected to a given level of earthquake.

Design Earthquakes cause nonlinear behavior which cannotbe handled by linear static procedures.

Pushover analysis gives a better understanding of thebuilding behavior well into the inelastic region.

Pushover analysis Identifies weak elements with plastic hingeformation and their order of formation. It gives realisticprediction of element demands.

It is a good substitute for the more accurate NonlinearDynamic Analysis for buildings where the fundamentalmode of vibration dominates. For buildings with morethan one significant mode and buildings with irregularfeatures, nonlinear static pushover analysis may not beaccurate.

Thank Youfor listening!

Asep4A Pushover Analysis

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