Pushover Analysis Guide Final

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SaroshH.LodiAslamF.MohammedRashidA.KhanNEDUniversityofEngineeringandTechnologyM.SelimGunayUniversityofCalifornia,Berkeley

SupportedbythePakistanUSScienceandTechnologyCooperationProgram

ofReinforced

ConcreteBuildings

with

Masonry

Infill

Walls

APracticalGuidetoNonlinearStaticAnalysis


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A Practical Guide to Nonlinear Static Analysis

Preface

Reinforced concrete (RC) frames with unreinforced masonry (URM) infill walls arecommonly used as the structural system for buildings in many seismically active regions

around the world. Structural engineers recognize that many buildings of this type have

performed poorly during earthquakes. URM infill walls used in Pakistan and adjoining

regions comprise of either burnt clay bricks or cement concrete block masonry. These URM

infill walls are generally treated as non-structural elements, because they are used mainly for

architectural purposes, and structural engineers often ignore them during structural design.

During earthquakes, infill walls affect the response of the structure, and may either beneficial

or detrimental effects. Infill walls contribute to the lateral force resisting capacity and

damping of the structure up to a certain level of ground motion. Infill walls increase the

initial stiffness and decrease the fundamental period of the structure, which might bebeneficial or detrimental, depending on the frequency content of the ground motion.

URM infill walls are prone to early brittle failure, and infill wall failures may lead to the

formation of a weak story, which can cause the building to collapse. Infill walls interact with

the surrounding frame in such a way that column shear failure is made more likely. In

addition, an unequal spatial distribution of infill walls for functional reasons for example,

windows and open commercial spaces on the street frontage and full walls adjacent to

neighbouring buildings can create torsion that places additional demands on columns and

may cause them to fail.

Because of the potentially dire consequences of ignoring the structural role of URM infillwalls, proper consideration of infill walls is essential in any structural analysis of RC frame

buildings with infill walls. This document provides engineers with guidance on how to model

infill walls and include them in structural analyses. Because the consequences of ignoring

infill walls are not region related but exist throughout the world, the authors anticipate that

the guide will be useful for practicing engineers in Pakistan as well as in other countries with

many similar buildings.

This document discusses and illustrates how to analyze infill building with an example in

ETABS building analysis and design software by Computers and Structures, Inc. of a 2-D

nonlinear static pushover analysis of a six storey RC building with URM infill walls, based

on guidelines and modeling procedures given in the ATC-40 and FEMA-356 documents. Theprocedures for defining the strength and stiffness of equivalent strut members used to model

infill walls are also applicable for linear analyses.

This manual was developed as part of a project that NED University of Engineering (NED)

and Technology and GeoHazards International (GHI), a California based non-profit

organization that improves global earthquake safety, conducted together to assess and design

seismic retrofits for existing buildings typical of the local building stock, such as the one

described in this report. The project was funded by the Pakistan Higher Education

Commission (HEC) and The National Academies through a grant from the United States

Agency for International Development (USAID).

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A Practical Guide to Nonlinear Static Analysis of Reinforced Concrete Buildings with

Masonry Infill Walls

Copyright 2011 NED University of Engineering and Technology, and GeoHazards

International. All rights reserved, with the exception that Computers and Structures, Inc.

retains copyright to all material pertaining to their ETABS building analysis and design

software.

Developed by:

Sarosh H. Lodi, Professor and Dean, Faculty of Civil Engineering and Architecture, NED

University of Engineering and Technology, KarachiAslam F. Mohammed, Assistant Professor, NED University of Engineering and Technology,

Karachi

Rashid A. Khan, Professor, NED University of Engineering and Technology, Karachi

M. Selim Gunay, Post-doctoral Researcher, University of California, Berkeley

Technical reviewers:

Khalid M. Mosalam, Professor, University of California, Berkeley

Gregory G. Deierlein, Professor, Stanford University

David Mar, Principal, Tipping Mar, Berkeley California

Sahibzada F. A. Rafeeqi, Professor and Pro-Vice Chancellor, NED University of Engineering

and Technology, Karachi

Technical editing:

Janise Rodgers, GeoHazards International

Justin Moresco, GeoHazards International

Acknowledgments:

The project team wishes to thank Computers and Structures, Inc. of Berkeley, California for

their generous donation of ETABS building analysis and design software, which was used

to perform the analyses in this guide.

Disclaimer: All parties, including but not limited to NED University of Engineering and

Technology, GeoHazards International, Higher Education Commission, The National

Academies, the United States Agency for International Development, and Computers and

Structures, Inc., are not responsible for any damage or harm that may occur despite or

because of the application of measures and techniques described in this guide. In addition,

users of this guide are solely responsible for the accuracy of structural models, analyses, and

results and for their subsequent usage in any structural design or construction works.


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Contents

Chapter 1 Introduction..........................................................................................................7Chapter 2 Masonry Infill Walls are Important .....................................................................8

An Example of the Effects of Unreinforced Masonry Infill................................................10Chapter 3 Performance Based Analysis .............................................................................12

3.1 Nonlinear Static Procedures in Current Standards.........................................................123.1.1 Displacement Coefficient Method from FEMA 356 / ASCE 41...........................133.1.2 Capacity Spectrum Method from ATC-40 ............................................................14

3.2 Modelling Infill Walls as Struts....................................................................................15Chapter 4 Pushover Analysis Using ETABS .....................................................................18

4.1 Defining how nonlinearity is considered .....................................................................184.2 Determining Analysis Cases ........................................................................................194.3 Defining Loading.........................................................................................................194.4 Selecting the Type of Load Control.............................................................................204.5 Analysis Results...........................................................................................................204.6 Procedure .....................................................................................................................214.7 Important Considerations.............................................................................................21

Chapter 5 Example of Pushover Analysis Using ETABS .......................................................225.1 Modelling.....................................................................................................................225.2 Defining and Assigning Loads on Structure .............................................................305.3 Analysis.....................................................................................................................34

5.3.2 Non-Linear Static Analysis................................................................................365.4 Results .......................................................................................................................53

Sources of Additional Information ..........................................................................................58References................................................................................................................................59

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Chapter1 Introduction

The 2005 Kashmir earthquake dramatically demonstrated the lethal combination ofvulnerable buildings and strong ground shaking. But the earthquake-affected areas arent the

only places at risk earthquake faults underlie many parts of Pakistan. The countrys cities,

including Karachi (see sidebar) have many reinforced concrete (RC) frame buildings with

masonry infill walls that are at risk of earthquake damage. There is a growing need for

engineers to evaluate these buildings to determine their potential performance in a major

earthquake. This guide will show you how to use a simple yet powerful analysis technique

called nonlinear static analysis, or pushover analysis, to determine what type and extent of

earthquake damage may occur in these buildings, and the effects of potential strengthening

measures that you can apply to reduce damage.

The recent advent of structural design for a particularlevel of earthquake performance, such as immediate

post-earthquake occupancy, (termed performance

based earthquake engineering), has resulted in

guidelines such as ATC-40 (1996), FEMA-273 (1996)

and FEMA-356 (2000) and standards such as ASCE-

41 (2006), among others. New Zealands building

code is performance-based. Among the different types

of analyses described in these documents, pushover

analysis comes forward because of its optimal

accuracy, efficiency and ease of use.

Pushover analysis gives necessary insight into

nonlinear behaviour without the additional

complexities of nonlinear dynamic analysis. Pushover

analysis is a static, nonlinear procedure in which the

magnitude of the structural loading is incrementally

increased in accordance with a certain predefined

pattern. As the load increases, the structure begins to

yield and become damaged, and the structural

deficiencies and failure modes of the building become

apparent. The loading is monotonic (i.e., in a single direction) with the effects of the loadreversals that occur during a real earthquake being estimated by using modified monotonic

force-deformation criteria and with damping approximations. The goal of static pushover

analysis is to evaluate the real strength of the existing structure, rather than to give the lower

bound strength for design.

The city of Karachi, with more

than 14 million inhabitants, sits

close to a tectonic plate boundary

and within reach of earthquakes

on numerous faults surrounding

the city. Karachis buildings are

at risk due to the combination of

seismic hazard and structural

vulnerability.

Due to the reasons mentioned above, this document focuses on nonlinear static analysis with

an emphasis on RC frame buildings with masonry infill walls. Pushover analysis is

demonstrated using the computer software ETABS, which was developed by Berkeley,

California-based Computers and Structures Inc. and is one of several available software

programs with the capability to conduct pushover analysis. ETABS is an integrated building

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analysis and design software that incorporates linear, nonlinear, static and dynamic analysis

capabilities with the building design features.

Chapter2 MasonryInfillWallsareImportant

Reinforced concrete (RC) frame buildings with unreinforced masonry (URM) infill walls are

commonly built throughout the world, including in seismically active regions. URM infill

walls are widely used as partitions throughout Pakistan, and despite often being considered as

non-structural elements, they affect both the structural and non-structural performance of RC

buildings. Structural engineers recognize that many buildings of this type have performed

poorly and have even collapsed during recent earthquakes in Turkey, Taiwan, India, Algeria,

Pakistan, China, Italy and Haiti, as Figure 1shows.

a)

b)

d)c)

f)e)


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Figure 1. Masonry infill-related damage in recent

earthquakes

9

However, contrary to the experience gathered from

these earthquakes, these buildings continue to be built

in many seismic regions around the world.

Particularly in countries with emerging economies,

vulnerable infilled frame buildings continue to be

built at a rapid rate in order to keep up with urban

population growth and contribute greatly to increased

global earthquake risk. When the seismic

vulnerabilities present in the RC system (such as lack

of confinement at the beam and column ends and the

beam column joints, strong beam-weak column

proportions, and presence of shear-critical columns)

are combined with the complexity due to the

interaction of the infill walls and the surroundingframe and the brittleness of the URM materials, non-

ductile RC frames with URM infill walls may be

considered as one of the worlds most common types

of seismically vulnerable buildings. Therefore, it is

essential to apply existing knowledge on the

behaviour of this complex structural system to

develop proper modelling techniques and adequate

retrofit methods.

URM infill walls are generally treated as non-

structural elements which are used mainly forarchitectural purposes. However, many researchers

(e.g., Humar et al., 2001; Saatcioglu et al., 2001;

Korkmaz et al., 2007; Mondal and Jain, 2008; Taher,

et al., 2008) and the experiences in past earthquakes

have shown that the presence of URM walls changes

the seismic response of framed building. The URM

walls function as structural elements, and they may

have beneficial or detrimental effects. Infill walls contribute to the lateral force resisting

capacity and damping of the structure up to a certain level of structural response. They

increase the initial stiffness and decrease the initial period of the structure, which might be

beneficial or detrimental depending on the frequency content of the experienced groundmotion. URM infill walls are prone to early brittle failure. Infill walls interacting with frames

tend to alter the buildings overall strength and stiffness distribution. This may be despite the

design intent of the engineer, because infill walls are typically considered as non-structural

and therefore neglected in the frame design. Many buildings have a soft storey created by

commercial space (shops) or parking at the ground floor (Figure 1a and b). Even in buildings

without open spaces at the ground floor, brittle infill wall failure may lead to the formation of

a weak and soft storey during ground shaking in buildings that would have otherwise not had

one (Figure 1c and d). In addition, infill walls interact with the surrounding frame in such a

way that column shear failure is made more likely (Figure 1e). Infill walls can also induce

torsion when some sides of the building have solid infill walls and the other sides have either

infill walls with openings or no infill walls for architectural or usage purposes (Figure 1f).

Most of the damage to reinforced

concrete buildings observed after

the 2005 Kashmir earthquake was

attributed to poor materialquality, inadequate reinforcement

details and poor construction

practices. Many URM infill walls

were damaged themselves, and

led to soft storey collapses in

medium to high rise buildings

with commercial space (shops) or

parking at the ground floor and a

large concentration of heavy, stiff

infill walls in the stories above.

These vulnerabilities in RCbuildings exist throughout

Pakistan.


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Considering the severity of the detrimental effects of infill they can cause collapse proper

modelling of URM infill walls within RC frames is essentialfor seismic evaluation and

consequently for the selection of adequate retrofit solutions to reduce damage and its

consequences.

AnExampleoftheEffectsofUnreinforcedMasonryInfill

Before moving ahead, it is instructive to see how infill alters the behaviour of a bare RC

frame. Using pushover analysis, we compare here the differences in behaviour between a

bare frame and the same frame with infill walls in all the stories except the first, shown in

Figure 2 below. The effect of the infill is emulated by a single diagonal compression strut in

each bay.

Figure 2. Bare frame (left) and the same frame with infill in all stories except ground (right)

The pushover curves are compared in Figure 3. The strength and stiffness of the infilled

frame is significantly increased due to the presence of infill, but the displacement capacity

decreases and a soft story develops, which is evident from the displacement profiles in Figure

4. The deformation accumulates in the bottom story the true behaviour during an

earthquake when infill is considered in the analysis, rather than being distributed evenly

over all stories when the designer ignores the infill and incorrectly models the building as a

bare frame.

So, based on these results, infill walls can be beneficial as long as they are properly taken into

consideration in the design process and the failure mechanism is controlled (i.e., no weak

story is allowed to occur).However, this example also shows that failing to consider infill

walls during structural design can lead to deadly weak-story collapses.


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Figure 3. Pushover curve comparison for the bare and infilled frames

Figure 4. Displacement profile comparison for the bare and infilled frames

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Chapter3 PerformanceBasedAnalysis

The guidelines and standards mentioned in the introduction include modelling procedures,

acceptance criteria and analysis procedures for pushover analysis. These documents define

force-deformation criteria for potential locations of lumped inelastic behaviour, designated as

plastic hingesused in pushover analysis. As shown in Figure 5 below, five points labelled A,B, C, D, and E are used to define the force deformation behaviour of the plastic hinge, and

three points labelled IO (Immediate Occupancy), LS (Life Safety) and CP (Collapse

Prevention) are used to define the acceptance criteria for the hinge. In these documents, if all

the members meet the acceptance criteria for a particular performance level, such as Life

Safety, then the entire structure is expected to achieve the Life Safety level of performance.

The values assigned to each of these points vary depending on the type of member as well as

many other parameters, such as the expected type of failure, the level of stresses with respect

to the strength, or code compliance.

Figure 5. Force-Deformation Relation for Plastic Hinge in Pushover Analysis

Both the ATC-40 and FEMA 356 documents present similar performance-based engineering

methods that rely on nonlinear static analysis procedures for prediction of structural demands.

While procedures in both documents involve generation of a pushover curve to predict the

inelastic force-deformation behaviour of the structure, they differ in the technique used to

calculate the global inelastic displacement demand for a given ground motion. The FEMA

356 document uses the Coefficient Method, whereby displacement demand is calculated by

modifying elastic predictions of displacement demand. The ATC-40 Report details the

Capacity-Spectrum Method, whereby modal displacement demand is determined from theintersection of a capacity curve, derived from the pushover curve, with a demand curve that

consists of the smoothed response spectrum representing the design ground motion, modified

to account for hysteretic damping effects.

3.1NonlinearStaticProceduresinCurrentStandards

Current standards such as ASCE 41 provide two alternate methods of estimating the peak

displacement demand for use in nonlinear static procedures: the displacement coefficient

method and the capacity spectrum method. Both methods rely on an equivalent linearization

approach. The basic assumption in equivalent linearization techniques is that the maximum

inelastic deformation of a nonlinear single degree of freedom (SDOF) system isapproximately equal to the maximum deformation of a linear elastic SDOF system, provided


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that the linear elastic system has a period and a damping ratio that are larger than the initial

values of those for the nonlinear system.

The displacement coefficient method is conceptually simpler and easier to use, and is not

prone to the graphical misinterpretations that can occur with the capacity spectrum method.

The authors recommend using the displacement coefficient method, either alone or to checkresults obtained by using the automated capacity spectrum method capabilities in ETABS.

3.1.1 DisplacementCoefficientMethodfromFEMA356/ASCE41

The displacement coefficient method (simply called the coefficient method in FEMA 356) is

the primary method of estimating displacement for the nonlinear static procedure in ASCE

41, and its pre-standard FEMA 356. The displacement coefficient method generates an

estimate of the maximum global displacement, called the target displacement, by modifying

the linear elastic response of an equivalent SDOF system. This is accomplished by

multiplying the SDOF spectral displacement by a series of coefficients, C0through C3. Figure

6 shows the process used to calculate the target displacement.

Figure 6. Schematic illustration of the process of estimating target displacement using the

displacement coefficient method, for a given response spectrum and effective period, Te(reproduced from FEMA 440, Figure 2-12, a public domain document).

First an effective period, Te, is generated from the initial period, Ti,by a graphical procedure

using an idealized force-deformation curve (i.e., pushover curve) relating base shear to roof

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displacement, which accounts for some stiffness loss as the system begins to behave

inelastically. The effective period represents the linear stiffness of the equivalent SDOF

system. The effective period is used to determine the equivalent SDOF systems spectral

acceleration, Sa, using an elastic response spectrum. The procedure assumes that the damping

(usually 5%) is appropriate for a structure in the elastic range.

Then, the peak elastic spectral displacement is determined from the spectral acceleration

using the following equation:

aeff

d ST

S2

2

4 (1)

The Displacement Coefficient Method then uses four coefficients to convert the peak elastic

spectral displacement first to elastic displacement at the roof and then to inelastic

displacement at the roof. FEMA 440, Improvement of Nonlinear Static Seismic Analysis

Procedures, explains each of the coefficients C0through C3as follows:

The coefficient C0is a shape factor (often taken as the first mode participation factor) that

simply converts the spectral displacement to the displacement at the roof. The other

coefficients each account for a separate inelastic effect. The coefficient C1is the ratio of

expected displacement for a bilinear inelastic oscillator to the displacement for a linear

oscillator. C1 depends on the ratio of elastic force, calculated as the spectral acceleration

multiplied by the mass, to the yield strength, the period of the SDOF system, Teand thecharacteristic period of the spectrum. The coefficient C2accounts for the effect of pinching in

load-deformation relationships due to degradation in stiffness and strength. Finally, the

coefficient C3adjusts for second-order geometric nonlinearity (P-) effects. The coefficients

are empirical and derived primarily from statistical studies of the nonlinear response-history

analyses of SDOF oscillators and adjusted using engineering judgment.

3.1.2 CapacitySpectrumMethodfromATC40

The initial step in the capacity spectrum method (as used in ATC-40) is the same as in thedisplacement coefficient method: generate a pushover curve for the structure. However, in the

capacity spectrum method, the results are plotted in acceleration-displacement response

spectrum (ADRS) format, shown in Figure 7. To plot the pushover in ADRS format (called a

capacity curve), the base shear versus roof displacement relationship must be converted using

the dynamic properties of the system. The ground motion acceleration response spectrum,

representing the seismic demand, is also converted to ADRS format, so that the capacity

curve can be plotted on the same axes as the seismic demand. It is important to note that in

ADRS format, period is represented by radial lines emanating from the origin.


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Figure 7. Graphical representation of the Capacity Spectrum Method, as presented in ATC-

40 (reproduced from FEMA 440, a public-domain document).

Once the pushover curve and response spectrum are plotted together in ADRS format,

iteration is required to determine the maximum inelastic displacement, called the

performance point. FEMA 440 explains why:

The capacity spectrum method assumes that the equivalent damping of the system is

proportional to the area enclosed by the capacity curve. The equivalent period, Teq, is

assumed to be the secant period at which the seismic ground motion demand, reduced for the

equivalent damping, intersects the capacity curve. Since the equivalent period and damping

are both a function of the displacement, the solution to determine the maximum inelastic

displacement (i.e., performance point) is iterative. ATC-40 imposes limits on the equivalent

damping to account for strength and stiffness degradation.

3.2 ModellingInfillWallsasStruts

The most common method of modelling infill walls is to use equivalent diagonal

compression struts (Figure 8).

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Figure 8. Equivalent diagonal compression strut modelling of infill walls (reproduced from

FEMA 356, a public domain document)

The axial stiffness of an equivalent strut can be calculated with Equation 2 according to

Section 7.5.2 of FEMA-356.

250

14

2.

infcolfe

infm

hIE

)sin(tE (2a)

diagcol Lha40

11750.

. (2b)

diag

infminf

L

tEak

(2c)

In these equations,EmandEfeare the elastic moduli of the infill and the frame material,

respectively, tinfis the thickness of the infill wall, hcol andIcolare the height and moment of

inertia of the section of the column of the surrounding frame, hinfis the height of the infill

wall panel andLdiagis the length of the diagonal strut. The strength of the compression strut is

calculated with Equation 3.


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cos

fsAN

infinfcomp

(3)

In Equation 3,Ainfis the cross sectional area of the infill wall,fsinfis the shear strength of

masonry and is the angle of the diagonal strut with the horizontal.

As a special case, it is also possible to model an infill wall retrofitted with mesh

reinforcement and concrete by using two diagonal struts, one of which is a compression

member and the other is a tension member. In this case, stiffness is calculated with Equation

4 and distributed equally to the struts.

25.0

inf

inf1

4

2sin

hIE

tEtE

colfe

ccm (4a)

diagcol Lha 1175.0 4.0

(4b)

diag

ccm

Lk infinf

tEtEa (4c)

In Equation 4,Em,EcandEfeare the elasticity moduli of the infill, concrete used for retrofit

and the frame material, respectively. The other terms in the equation are defined as follows: tfis the thickness of the infill wall, tcis the thickness of the concrete, is the angle of the

diagonal strut with the horizontal, hcolandIcolare the height and moment of inertia of the

section of the column of the surrounding frame, hinfis the height of the infill wall panel and

Ldiagis the length of the diagonal strut. The strengths of compression and tension members

are calculated with Equations 5 and 6, respectively.

cos

3.3infinf cc fAfsANcomp (5)

cos

infNtens

yss sLfA(6)

In Equations 5 and 6,AinfandAc(in2) are the cross sectional area of the infill wall and

concrete, respectively,fsinfis the shear strength of masonry,fcis concrete strength (psi), and

is the angle of the diagonal strut with the horizontal.Asis the total cross sectional area of

horizontal mesh reinforcement with spacing s,fysis the strength of steel, andLinfis the wall

length.

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Chapter4 PushoverAnalysisUsingETABS

Pushover analysis is a very powerful feature offered only in the non-linear version of

ETABS. In addition to performing pushover analyses for performance-based seismic design,

this feature can be used to perform general static nonlinear analysis and the analysis of staged

(incremental) construction. ETABS menus and documentation refer to pushover analysis asstatic nonlinear analysis.

Performing any nonlinear analysis takes time and requires patience. Please read the following

information carefully before performing pushover analysis. Make sure to pay special

attention to the Important Considerations section later in this guide. The key points for

conducting pushover analysis can be summarized as follows:

1. Defining how nonlinearity is considered

2. Determining analysis cases

3. Defining loading

4. Selecting the type of load control5. Analysis Results

6. Procedure for conducting pushover analysis

7. Important Considerations

Information in the sections 4.1 through 4.7 has been adapted for Pakistan conditions from

user documentation for ETABS software, prepared by Computers and Structures, Inc.

4.1 Defininghownonlinearityisconsidered

Properly modelling the nonlinear behaviour that the structure is expected to undergo is very

important for obtaining credible analysis results. However, more complicated models are notnecessarily more accurate. When developing a model, keep in mind that pushover analysis

contains inherent simplifications regarding the dynamic behaviour of the building, and select

the level of model complexity accordingly. Several types of nonlinear behaviour can be

considered in a pushover analysis:

1. Material nonlinearity at discrete, user-defined hinges in frame/line

elements. Plastic hinges can be assigned at any number of locations along the

length of any frame element (see Frame Nonlinear Hinge Assignments to Line

Objects in ETABS documentation for details), wherever yielding or other

inelastic behaviour is expected. Uncoupled moment, torsion, axial force and

shear hinges are available. There is also a coupled P-M2-M3 hinge thatconsiders the interaction of axial force and bending moments at the hinge

location. More than one type of hinge can exist at the same location. For

example, you might assign both an M3 (moment) and a V2 (shear) hinge to

the same end of a frame element. Default hinge properties are provided based

on ATC-40 and FEMA-356 criteria.

For reinforced concrete frame buildings, use coupled P-M hinges when

modelling columns and uncoupled moment hinges for beams. Separate shear

hinges are recommended. To reduce the size and complexity of the model, a

number of analysts check shear forces in each member against that members

shear capacity rather than using shear hinges.


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2. Material nonlinearity in the link elements. The available nonlinear

behaviour includes gap (compression only), hook (tension only), uniaxial

plasticity along any degree of freedom, and two types of base isolators (biaxial

plasticity and biaxial friction/pendulum). The link damper property has no

effect in a static nonlinear analysis.

3. Geometric nonlinearity in all elements. You can choose between

considering only P-delta effects or considering P-delta effects plus large

displacements. Large displacement effects consider equilibrium in the

deformed configuration and allow for large translations and rotations.

However, the strains within each element are assumed to remain small. The P-

Delta effects option (without large deformations) is recommended.

4. Adding or removing elements. Members can be added or removed in a

sequence of stages during each analysis case.

4.2Determining

Analysis

Cases

Static nonlinear analysis can consist of any number of cases. Each static nonlinear case can

have a different distribution of load on the structure. For example, a typical static nonlinear

analysis might consist of three cases. The first would apply gravity load to the structure, the

second would apply one distribution of lateral load over the height of the structure, and the

third would apply another distribution of lateral load over the height of the structure.

A static nonlinear case may start from zero initial conditions, or it may start from the results

at the end of a previous case. In the previous example, the gravity case would start from zero

initial conditions, and each of the two lateral cases could start from the end of the gravity

case.

Static nonlinear analysis cases are completely independent of all other analysis types in

ETABS. In particular, any initial P-delta analysis performed for linear and dynamic analysis

has no effect upon static nonlinear analysis cases. The only interaction is that linear mode

shapes can be used for loading in static nonlinear cases.

Static nonlinear analysis cases can be used for design. Generally it does not make sense to

combine linear and nonlinear results, so static nonlinear cases that are to be used for design

should include all loads, appropriately scaled, that are to be combined for the design check.

4.3Defining

Loading

The distribution of load applied on the structure for a given static nonlinear case is defined as

a scaled combination of one or more of the following:

Any static load case.

A uniform acceleration acting in any of the three global directions. The force at

each joint is proportional to the mass assigned to that joint (i.e., that calculated from

the tributary area) and acts in the specified direction.

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A modal load for any eigen or Ritz mode. The force at each joint is proportional to

the product of the modal displacement (eigenvector), and the mass tributary to that

joint, and it acts in the direction of the modal displacement.

The load combination for each static nonlinear case is incremental, meaning it acts in

addition to the load already on the structure if starting from a previous static nonlinear case.

Floor slabs in reinforced concrete frame buildings are generally modelled as rigid

diaphragms. The rigid diaphragm causes the joints connected to the same floor slab to

displace the same amount horizontally. You will need to consider diaphragm deformations,

and model the diaphragms as flexible, in the following cases:

Concrete slab is thinner than 100 mm (4 inches); Diaphragm has span to depth ratio of 4:1 or greater, where span is defined as the span

between lines of lateral resistance; and

Diaphragm has large opening (30% or more of floor area is a good rule of thumb).

4.4Selecting

the

Type

of

Load

Control

ETABS has two distinctly different types of control available for applying the load. Each

analysis case can use a different type of load control. The choice generally depends on the

physical nature of the load and the behaviour expected from the structure:

Force control.The full load combination is applied as specified. Force control

should be used when the load is known (such as gravity load), and the

structure is expected to be able to support the load in the elastic range.

Displacement control.A single Monitored Displacement component (or the

Conjugate Displacement) in the structure is controlled. The magnitude of theload combination is increased or decreased as necessary until the control

displacement reaches a value that you specify. Displacement control should be

used when specified drifts are sought (such as in seismic loading), where the

magnitude of the applied load is not known in advance, or when the structure

can be expected to lose strength or become unstable.

4.5 AnalysisResults

ETABS provides several types of output that can be obtained from the static nonlinear

analysis:

1. Base Reaction versus Monitored Displacement can be plotted.

2. Tabulated values of Base Reaction versus Monitored Displacement at each

point along the pushover curve, along with tabulations of the number of hinges

beyond certain control points on their hinge property force-displacement curve

can be viewed on the screen, printed, or saved to a file.

3. Base Reaction versus Monitored Displacement can be plotted in the ADRS

format where the vertical axis is spectral acceleration and the horizontal axis is

spectral displacement. The demand spectra can be superimposed on this plot.

4. Tabulated values of the capacity spectrum (ADRS capacity and demand

curves), the effective period and the effective damping can be viewed on thescreen, printed, or saved to a file.


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5. The sequence of hinge formation and the color-coded state of each hinge can

be viewed graphically, on a step-by-step basis, for each step of the static

nonlinear case.

6. The member forces and stresses can be viewed graphically, on a step-by-step

basis, for each step of the static nonlinear case.

7. Member forces and hinge results for selected members can be written to a file

in spreadsheet format for subsequent processing in a spreadsheet program.

8. Member forces and hinge results for selected members can be written to a file

in Access database format.

4.6 Procedure

The following general sequence of steps is involved in performing a static nonlinear analysis:

1. Create a model just like you would for any other analysis. Note that material

nonlinearity is restricted to frame and link elements, although other elementtypes may be present in the model.

2. Define the static load cases, if any, that are needed for use in the static

nonlinear analysis (Define > Static Load Cases command). Define any other

static and dynamic analysis cases that may be needed for steel or concrete

design of frame elements.

3. Define hinge properties, if any (Define > Frame Nonlinear Hinge Properties

command).

4. Assign hinge properties, if any, to frame/line elements (Assign > Frame/Line

> Frame Nonlinear Hinges command).5. Define nonlinear link properties, if any (Define > Link Properties command).

6. Assign link properties, if any, to frame/line elements (Assign > Frame/Line >

Link Properties command).

7. Run the basic linear and dynamic analyses (Analyze > Run command).

8. Define the static nonlinear load cases (Define > Static Nonlinear/Pushover

Cases command).

9. Run the static nonlinear analysis (Analyze > Run Static Nonlinear Analysis

command).

10. Review the static nonlinear results (Display > Show Static Pushover Curve

command), (Display > Show Deformed Shape command), (Display > Show

Member Forces/Stress Diagram command), and (File > Print Tables >

Analysis Output command).

11. Perform any design checks that utilize static nonlinear cases.

12. Revise the model as necessary and repeat.

4.7 ImportantConsiderations

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Nonlinear analysis takes time and patience. Each nonlinear problem is different. Expect to

spend a certain amount of time to learn the best way to approach each new problem. Start


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simple and build up gradually. Make sure the model performs as expected under linear static

loads and modal analysis. Rather than starting with hinges everywhere, add them gradually

beginning with the areas where you expect the most nonlinearity. Start with hinge models

that do not lose strength for primary members; modify the hinge models later or redesign the

structure.

Perform your initial analyses without geometric nonlinearity. Add P-delta effects, and

possibly large deformations later. Start with modest target displacements and a limited

number of steps. In the beginning, the goal should be to perform the analyses quickly so that

you can gain experience with your model. As your confidence grows with a particular model,

you can push it further and consider more extreme nonlinear behaviour.

Mathematically, pushover analysis does not always guarantee a unique solution. Inertial

effects in dynamic analysis and in the real world limit the path a structure can follow. But this

is not true for static analysis, particularly in unstable cases where strength is lost due to

material or geometric nonlinearity.

Small changes in properties or loading can cause large changes in nonlinear response. For

this reason, it is extremely important that you consider different loading patterns, and that you

perform sensitivity studies on the effect of varying the properties of the structure. At

minimum, the recommended lateral load patterns include a uniform load distribution and a

triangular load distribution representing the fundamental vibration mode.

Chapter5ExampleofPushoverAnalysisUsingETABS

5.1 Modelling

Define the grid system according to your structure.

a. After opening ETABS, the first window to appear is shown here.


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b. Click on FILE followed by DEFAULT.EDB or NO, using the latter

option for a new model.

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c. If your structure has one of the available structural systems, click the

desired one. Otherwise, click the GRID ONLY option. When you click the

GRID ONLY, the following grids appear.

In ETABS, the regular order of 1) defining materials, 2) defining sections and assigning the

defined materials to member sections and, 3) defining members and assigning the defined

sections to members is used similarly to most other structural analysis software. Nodes are

automatically created while defining members through the graphical user interface.


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Define the materials (e.g., concrete, masonry, etc.) used in the model.

1. Click on DEFINE then MATERIAL PROPERTIES.

2. Define the necessary materials according to your model.

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Define the frame sections for beams, columns, struts, etc. For masonry struts, usethe actual masonry properties, if known, to calculate the equivalent strut capacity.

If the actual properties are not known, use the low values in ASCE-41. Parametric

studies, where the analyst conducts a series of analyses that vary one property of

interest, such as a material strength, while leaving the others fixed, are very useful

in bounding the potential response when the masonry properties are not known.Using lower masonry strengths is not necessarily conservative, because stronger

infill panels can cause shear failures in the adjacent columns.

a. Click on DEFINE, then FRAME SECTIONS.


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b. The following window appears after clicking on FRAME SECTIONS.

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c. In the previous window, click on the type of section that you want to use.

For example, the following window appears after selecting a rectangular

section. Section dimensions can be input in this window as well as the

reinforcement data in case of reinforced concrete. The material that will beassigned to the section can also be selected from the list of previously

defined materials.

Define the members of the structure such as beams, columns, walls, slabs, etc. Thegraphical user interface is a powerful and efficient tool at this stage.

a. Members can be defined by using the highlighted tool bar shown in the

following image.


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b. For modelling of beams and columns, you can use line the element tool

bar. When you click on this, the following window appears, from which a

desired section can be selected.

c. For modelling an RCC wall, an area element tool bar can be used. When

you click on this, the following window appears.

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5.2 DefiningandAssigningLoadsonStructure

Apply gravity loads

Dead load and live load factors should be based on the expected gravity loads for the

building. For most pushover analyses, use the total dead load and 50% of the live load(1.0 DL + 0.5 LL). You should also check the case of total dead load and zero live

load (1.0 DL + 0 LL).

All dead loads in the building (structural components, partitions, architectural finishes

and more) should be included in in defining the total dead load. The live load per unit

area is accepted as 40, 60 and 100 psf for office buildings, residential buildings and

mosques, respectively, per UBC-97, ASCE 7 and many other building design codes.

In this example, the partition load, live load and architectural finishes load are

assumed to be 50 psf, 40 psf and 24 psf, respectively. Masonry infill walls should be

considered as dead loads, because the infill walls are structural elements.

a. The next step is to apply the gravity loads on the structure. Use the

DEFINE option and click on STATIC LOAD CASES.

b. When you click on STATIC LOAD CASES, the following window

appears. In this window you can add the different types of load you wantto assign to your structure. Here is an example of a STATIC LOAD CASE


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DEFINITION window. Self Weight Multiplier is a scale factor which

multiplies the distributed gravity forces calculated by using the specific

weight of a material and the area of a section. It is typically 1 for dead

loads and 0 for other loads.

After defining the static load cases, the loads on the members

corresponding to each load case can be defined. For this purpose, select

any frame member, click on ASSIGN and then click on FRAME/LINE

LOADS. The following window appears.

If you want to apply a uniform load, click on the DISTRIBUTED option in

this window, which causes the following window to appear.

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c. In this window, you can enter the magnitude of loading, its direction and

specify the load type.

Define load combination as per design code.

a. The loads from individual static load cases can be combined using a load

combination. Click DEFINE and then LOAD COMBINATION.


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b. When you click on load combination, the following window appears. In

this window, click on ADD NEW COMBO

c. When you click on ADD NEW COMBO, the following window appears in

which you can define the load combination as per design code.

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5.3 Analysis

Linear static analysis can be used as a way to validate the model since anything wrong in the

model will show itself in the response. These errors can be easily viewed through the user

interface. To conduct a linear static analysis, click on ANALYZE followed by RUN

ANALYSIS.

ETABS has tools that use the results of linear static analysis to size members and select

reinforcement for RCC members. While these tools can be used to estimate approximatereinforcing if the reinforcement in an existing structure is not known, it is much more

reliable to conduct field investigations, especially in critical locations such as the ground

storey frame.

To design a structure:

a. Click on PREFERENCES < CONCRETE FRAME DESIGN.


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b. The desired design code can be assigned in the window that appears.

c. Click on ANALYZE in the main menu and then RUN ANALYSIS.

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d. After the analysis, you should design the structure by selecting member

sizes and reinforcement. To do that, click on DESIGN < CONCRETE

FRAME DESIGN


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a. To define a hinge, use DEFINE < FRAME NONLINEAR HINGE

PROPERTIES

b. When you click on FRAME NONLINEAR HINGE PROPERTIES, the

following window appears. In this window, click on ADD NEWPROPERTY

c. After clicking on ADD NEW PROPERTY, the following window appears.

There are options available through which you can define any type of

hinge.

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d. To define the flexural hinge for beam, click on MODIFY/SHOW FOR M3

in the preceding window. The following window appears.


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Define the hinges using the criteria in ASCE 41. The hinge properties

should properly consider the likely as-built conditions, rather that only the

design drawings or code provisions. Many buildings in Pakistan and the

region will have columns with poor confinement and inadequate ties.

Model the hinges conservatively, assuming that the strength and

deformation capacity are on the low end of the possible range.

Assign the hinges in the columns, beams, struts and other structural members.

a. After defining the hinges, the next step is to assign the hinge in the frame

elements. Click on ASSIGN < FRAME/LINE < FRAME NONLINEAR

HINGES.

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b. After clicking on FRAME NONLINEAR HINGES, the desired type of

hinge can be assigned to the selected member from the list of defined

hinges.

Define the non-linear static analysis.

a. After assigning hinges, click on STATIC NONLINEAR PUSHOVER

CASES.


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b. Click on ADD NEW CASE in the window that appears.

c. Two nonlinear cases are basically defined. One for gravity and one for

lateral forces. When ADD NEW CASE is clicked, the window that

appears is where the static nonlinear cases are defined.

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Before proceeding further, there are several terms that need to be defined in the nonlinear

static case definition window. The description of the options below is reprinted from the

ETABS software documentation.

A. Options

1. Force Control.Choose the type of analysis, force controlled or displacement

controlled, by checking the appropriate check box:

a. Load Level Defined By Pattern.Check the Load Level Defined By

Pattern check box to perform a force-controlled analysis. The analysis

applies the full load value defined by the sum of all loads specified in

the Load Pattern box (unless it fails to converge at a lower force

value). This option is useful for applying gravity load to the structure.

b. Push To Displ. Magnitude.Check the Push To Displ. Magnitude

check box to perform a displacement-controlled analysis. The loadcombination specified in the Load Pattern area of the form is applied,

but its magnitude is increased or decreased as necessary to keep the

control displacement increasing in magnitude. This option is useful for

applying lateral load to the structure, or for any case where the

magnitude of the applied load is not known in advance, or when the

structure can be expected to lose strength or become unstable.

Review the target Displacement Magnitude (i.e., the value in

the edit box opposite the Push to Disp. Magnitude check box)

and check the check box if you want to use the Conjugate

Displacement for control (recommended). If the box is notchecked, the Monitored Displacement is used for control.

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Use Conjugate Displ. for Control

The conjugate displacement is a generalized displacement

measure that is defined as the work conjugate of the applied

Load Pattern. It is a weighted sum of all displacement degrees

of freedom in the structure: each displacement component is

multiplied by the load applied at that degree of freedom, and

the results are summed.

The conjugate displacement is usually the most sensitive

measure of displacement in the structure under a given

specified load. It is usually recommended that you use the

conjugate displacement unless you can identify a displacement

in the structure that monotonically increases during the

analysis.

When you use the conjugate displacement to control the

analysis, the load increments are adjusted in an attempt to reach

the specified monitored displacement. However, the analysis

will usually only approximately satisfy the targeted


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displacement, particularly if the monitored displacement is in a

different direction than the conjugate displacement.

Monitor

Define the Monitored Displacement by selecting thedisplacement degree of freedom, and by entering the label and

selecting the story level of the point to be monitored. The

Monitored Displacement is used to plot the pushover curve and

also for displacement control when the Push To Displ.

Magnitude option is used.

The Monitored Displacement is a single displacement

component at a single point that is monitored during a static

nonlinear analysis. When plotting the pushover curve, the

program always uses the monitored displacement for the

horizontal axis. The monitored displacement is also used todetermine when to terminate a displacement-controlled

analysis.

The monitored degree of freedom and the monitored point

location are all given default values by ETABS; you can easily

replace those default values. The default value for the

monitored point is a point located at the top of the structure; use

this point for infill frame buildings. The default monitored

degree of freedom is UX; other available directions are UY,

UZ, RX, RY, and RZ.

For the most meaningful pushover curve, it is important that

you choose a monitored displacement that is sensitive to the

applied load pattern. For example, you should not typically

monitor degree of freedom UX when the load is applied in

direction UY. Likewise you should not monitor joints that are

close to the restraints.

The same considerations apply when choosing a monitored

displacement for the purposes of displacement control. Choose

a displacement that is sensitive to the applied load and, ifpossible, one that increases monotonically during the analysis.

You may use the monitored displacement or the conjugate

displacement for displacement control, but it is the magnitude

of the monitored displacement that is used to determine when

to terminate a displacement-controlled analysis.

When you use the conjugate displacement to control the

analysis, the load increments are adjusted in an attempt to reach

the specified monitored displacement. However, the analysis

will usually only approximately satisfy the targeteddisplacement, particularly if the monitored displacement is in a


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best. If the Member Unloading Method is set to Restart Using Secant

Stiffness, a value of 1 is also recommended.

Maximum Null Steps

The Maximum Null Steps is used, if necessary, to declare failure (i.e.,

non-convergence) in a run before it reaches the specified force or

displacement goal. The program may be unable to converge on a step

when catastrophic failure occurs in the structure, or when the load

cannot be increased in a load-controlled analysis. There may also be

instances where it is unable to converge in a step because of numerical

sensitivity in the solution.

There are four types of null steps.

1. When an event in one hinge changes the stiffness of the

structure such that another hinge has an immediate event. This

shows up as zero-length step.

2. When the Member Unloading Method is set to Unload Entire

Structure and the unloading of a hinge causes a reversal in the

direction of load applied to the structure. This shows up as

zero-length step.

3. When the Member Unloading Method is set to Apply Local

Redistribution and the unloading of a hinge causes the

application and removal of an internal local redistribution load.

This shows up as multiple zero-length steps.

4. When a step fails to converge within the Maximum

Iteration/Step and the step size is halved. This is not a zero-

length step.

Null steps are to be expected in any analysis; they are not necessarily

bad. However, an excessive number of them may indicate failure of the

analysis.

Typically the Maximum Null Steps should be set to about 25% of theMaximum Total Steps (e.g., the default is 50 Maximum Null Steps for

200 Maximum Total Steps), but you may need at least twice as many

when the Member Unloading Method is set to Apply Local

Redistribution. Significant Large Displacement effects may also

require more null steps.

Maximum Total Steps

The Maximum Total Steps limits the total time the analysis will be

allowed to run.


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ETABS attempts to apply as much of the specified load pattern as

possible but may be restricted by the occurrence of an event, failure to

converge within the Maximum Iterations/Step, or a limit on the

maximum step size from the Minimum Number of Saved Steps. As a

result, a typical static nonlinear analysis may consist of a large number

of steps. Additional steps may be required by some Member UnloadingMethods to redistribute load.

An event occurs whenever a hinge reaches a new point on its stress-

strain curve or elastically unloads. Thus the number of steps required

to reach a specified target load or displacement will increase with the

number of hinges in the model.

Each step takes about the same amount of computer time. As you gain

experience with a particular model, you will be able to set the

Maximum Total Steps to limit the time the static nonlinear analysis is

allowed to run. You should start small and gradually build up to largernumbers of steps.

If your analysis does not reach its target within the Maximum Total

Steps, you can run it again with a larger number of steps, but first

examine the results to see whether the structure is still stable enough to

be worth pushing it any farther.

Only steps resulting in significant changes in the shape of the pushover

curve are saved for output.

5. Review the following analysis control parameters, changing them if necessary.

In most cases, the default values are adequate.

Maximum Iterations/Step and Iteration Tolerance

Static equilibrium is checked at the end of each step in a static

nonlinear analysis. The unbalanced load is calculated as the difference

between the externally applied loads and the internal forces in the

elements. If the ratio of the unbalanced-load magnitude to the applied-

load magnitude exceeds the Iteration Tolerance, the unbalanced load is

applied to the structure in a second iteration for that step. These

iterations continue until the unbalanced load satisfies the Iteration

Tolerance or the Maximum Iterations/Step is reached. In the latter

case, the step size is halved and the load is applied again from the

beginning of the step.

If necessary, the step size is continuously halved until equilibrium is

finally achieved. Each halving of the step size counts as a null step. For

the next step after convergence, the program repeatedly doubles the

step size until it finds the largest size that will converge or until an

event occurs.

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Iteration is primarily activated by nonlinear link properties and by

geometric nonlinearity, especially for large-displacement analysis.

Iteration is not usually required for material nonlinearity in the frame

hinges because of the event-to-event strategy used.

Event Tolerance

The Event Tolerance is a ratio used to determine the lumping together

of events. When ETABS determines that one hinge has experienced an

event, it checks for other hinges that are close (within the Event

Tolerance) to experiencing an event. For all hinges within the Event

Tolerance, the program will modify their states to cause these nearby

events to occur.

Larger event tolerances can shorten analysis time by reducing the

number of steps caused by events, but can increase equilibrium errors

within the elements due to the modification of the hinge states. Smallerevent tolerances give more accurate results at the expense of more

computational time. The default value of 0.01 works well for most

cases.

Consider the figure, which shows the location of two hinges on their

force-displacement plots. Hinge 1 has reached an event location. For

hinge 2, if the Event Tolerance is met it too will be treated as part of

the event. In the figure, if the Force Tolerance divided by the Yield

Force is less than the Event Tolerance, and the Displacement

Tolerance divided by the horizontal distance from B to C is less than

the Event Tolerance, then hinge 2 will be treated as part of the event.When determining the Force Tolerance Ratio, the denominator is

always the yield force. When determining the Displacement Tolerance

Ratio, the denominator is the horizontal length of the portion of the

force-displacement curve that the hinge is currently on. In the figure,

hinge 2 is on the B-C portion of the curve, thus we used the B-C

horizontal length in the denominator of the Displacement Tolerance

Ratio.

B. Member Unloading Method

1. Select the method to be used to handle hinges that drop load. This may affectthe number of steps you allow for the analysis.

When a hinge unloads, the program must find a way to remove the load that

the hinge was carrying and possibly redistribute it to the rest of the structure.

Hinge unloading occurs whenever the stress-strain (force-deformation or

moment-rotation) curve shows a drop in capacity, such as is often assumed

from point C to point D, or from point E to point F (complete rupture).

Such unloading along a negative slope is unstable in a static analysis, and a

unique solution is not always mathematically guaranteed. In dynamic analysis

(and the real world) inertia provides stability and a unique solution.


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Because ETABS is performing a static analysis, special methods are needed to

solve this unstable problem. Some methods may work better with some

problems. Different methods may produce different results for the same

problem.

ETABS provides three different methods to solve this problem of hingeunloading, which are described next.

If all stress-strain slopes are positive or zero, these methods are not used

unless the hinge passes point E and ruptures. Instability caused by geometric

effects is not handled by these methods.

Unload Entire Structure

When a hinge reaches a negative-sloped portion of the stress-strain

curve, the program continues to try to increase the applied load. If this

results in increased strain (decreased stress) the analysis proceeds. Ifthe strain tries to reverse, the program instead reverses the load on the

whole structure until the hinge is fully unloaded to the next segment on

the stress-strain curve. At this point the program reverts to increasing

the load on the structure. Other parts of the structure may now pick up

the load that was removed from the unloading hinge.

Whether the load must be reversed or not to unload the hinge depends

on the relative flexibility of the unloading hinge compared with other

parts of the structure that act in series with the hinge. This is very

problem-dependent, but it is automatically detected by the program.

This method is the most efficient of the three methods available, and is

usually the first method you should try. It generally works well if hinge

unloading does not require large reductions in the load applied to the

structure. It will fail if two hinges compete to unload, such as where

one hinge requires the applied load to increase while the other requires

the load to decrease. In this case, the analysis will stop with the

message UNABLE TO FIND A SOLUTION, in which case you

should try one of the other two methods.

This method uses a moderate number of null steps.

Apply Local Redistribution

This method is similar to the Unload Entire Section method, except

that instead of unloading the entire structure, only the element

containing the hinge is unloaded. When a hinge is on a negative-sloped

portion of the stress-strain curve and the applied load causes the strain

to reverse, the program applies a temporary, localized, self-

equilibrating, internal load that unloads the element. This causes the

hinge to unload. After the hinge has unloaded, the temporary load is

reversed, transferring the removed load to neighbouring elements. This

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process is intended to imitate how local inertia forces might stabilize a

rapidly unloading element.

This method is often the most effective of the three methods available,

but usually requires more steps than the first method, including a lot of

very small steps and a lot of null steps. The limit on null steps shouldusually be set between 40% and 70% of the total steps allowed.

This method will fail if two hinges in the same element compete to

unload, such as where one hinge requires the temporary load to

increase while the other requires the load to decrease. In this case, the

analysis will stop with the message UNABLE TO FIND A

SOLUTION, after which you should divide the element so the hinges

are separated and try again. Check the .LOG file to see which elements

are having problems. Caution: the element length may affect default

hinge properties that are automatically calculated by the program, so

fixed hinge properties should be assigned to any elements that are to bedivided.

Restart Using Secant Stiffness

This method is quite different from the other two. Whenever any hinge

reaches a negative-sloped portion of the stress-strain curve, all hinges

that have become nonlinear are reformed using secant stiffness

properties, and the analysis is restarted.

The secant stiffness for each hinge is determined as the secant from

point O to point X on the stress strain curve, where: Point O is thestress-stain point at the beginning of the static nonlinear case (which

usually includes the stress due to gravity load); and Point X is the

current point on the stress-strain curve if the slope is zero or positive,

or else it is the point at the bottom end of a negatively-sloping segment

of the stress-strain curve.

When the load is re-applied from the beginning of the analysis, each

hinge moves along the secant until it reaches point X, after which the

hinge resumes using the given stress-strain curve.

This method is similar to the approach suggested by the FEMA 273guidelines, and makes sense when performing pushover analysis where

the static nonlinear analysis represents cyclic loading of increasing

amplitude rather than a monotonic static push.

This method is the least efficient of the three, with the number of steps

required increasing as the square of the target displacement. It is also

the most robust (least likely to fail) provided that the gravity load is not

too large. This method may fail when the stress in a hinge under

gravity load is large enough that the secant from O to X is negative. On

the other hand, this method may also give solutions where the other

two fail due to hinges with small (nearly horizontal) negative slopes.


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C. Geometric Nonlinearity Effects

1. Select the Geometric Nonlinearity Effects to be included. Geometric

nonlinearity effects are considered on all elements in the structure. The

following options are available:

The large displacement option should be used for cable structures undergoing

significant deformation; and for buckling analysis, particularly for snap-

through buckling and post-buckling behaviour. Cables (modelled by frame

elements) and other elements that undergo significant relative rotations within

the element should be divided into smaller elements to satisfy the requirement

that the strains and rotations within an element are small.

For most other structures, the P-delta option is adequate, particularly when

material nonlinearity dominates. If reasonable, it is recommended that the

analysis be performed first without P-delta (i.e., use None), adding geometric

nonlinearity effects later.

None

All equilibrium equations are considered in the undeformed

configuration of the structure.

P-Delta

The equilibrium equations take into partial account the deformed

configuration of the structure. Tensile forces tend to resist the rotation

of elements and stiffen the structure, and compressive forces tend to

enhance the rotation of elements and destabilize the structure. This

may require a moderate amount of iteration.

P-Delta and Large Displacements

All equilibrium equations are written in the deformed configuration of

the structure. This may require a large amount of iteration.

D. Load Pattern

One of the most difficult issues for pushover analysis is choosing the pushover load

distribution. During an actual earthquake, the effective loads on a structure change

continuously in magnitude, distribution and direction. The distribution of story shears

over the height of a building can thus change substantially with time, especially fortaller buildings where higher modes of vibration can have significant effects. In a

static pushover analysis, the distribution and direction of the loads are fixed, and only

the magnitude varies. Hence, the distribution of story shears stays constant. To

account for different story shear distributions, it is necessary to consider a number of

different pushover load distributions.

One option in FEMA 356 is to use uniform and triangular distributions over the

building height. Note that a uniform distribution usually corresponds to a uniform

acceleration over the building height, so that the load at any floor level is proportional

to the mass at the floor. Similarly, a triangular distribution usually corresponds to a

linearly increasing acceleration over the building height.

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In ETABS the distribution of load applied on the structure for a given static nonlinear

case is defined as a scaled combination of one or more of the following:

Any static load case.

A uniform acceleration acting in any of the three global directions. The force

at each joint is proportional to the mass tributary to that joint and acts in thespecified direction.

A modal load for any eigen or Ritz mode. The force at each joint is

proportional to the product of the modal displacement, the modal circular

frequency squared ( 2), and the mass tributary to that joint, and it acts in the

direction of the modal displacement.

The load combination for each static nonlinear case is incremental, meaning it acts in

addition to the load already on the structure if starting from a previous static nonlinear

case.

Add, modify or delete a Load Pattern for the static nonlinear case using the followingbuttons.

Add button. To add a Load to the Load Pattern definition, select the load

from the Load drop down box, type in the appropriate scale factor in Scale

Factor edit box, and click the Add button. If the selected load is a mode (only

available if mode shapes have been requested for the analysis), input the mode

shape in the resulting form and click the OK button.

Modify button. To modify the scale factor for a load specified as part of the

load pattern, highlight the load in the Load/Scale Factor list box, edit the scale

factor in the Scale Factor edit box, and click the Modify button.Delete button.To delete a load specified as part of the load pattern, highlight the load in the

Load/Scale Factor list box and click the Delete button.

Click the OK button to accept all of the changes made in the Static Nonlinear Case

Data form. Clicking the Cancel button means that none of the changes will be

accepted. Note that you must also click the OK button in the Define Static Nonlinear

Cases form to accept the changes.

Run the non-linear static analysis. Click the ANALYZE option, RUN STATIC

NONLINEAR ANALYSIS. During the analysis, sometimes there is a warning in

nonlinear analysis. You should stop the analysis and increase the number of null stepsand total steps in nonlinear static data form and again run the analysis.


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5.4 Results

Check the pushover curve and capacity curve.

a. After the analysis, check the results by clicking on DISPLAY < SHOW

STATIC PUSHOVER CURVE.

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b. When we click on SHOW STATIC PUSHOVER CURVE, the following

window appears.


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b. When we click on SHOW DEFORMED SHAPE, the following window

appears.


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c. In the previous window, set the case and step number and the following

window appears.

Check the status of the internal hinges

Check the status of hinges to see if the structure can meet the demand or not.

Based on the hinge states and the failure mechanisms, the need for retrofit and the

type of retrofit can be determined.

The colour of hinges defines the status of hinges.

This building needs a retrofit to prevent the soft story from forming. Once

you have created a model, it is straightforward to modify it by adding new

elements in different places to test out potential retrofit solutions.

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Sources of Additional Information

As the example in the previous chapter shows, nonlinear analysis is a powerful tool toexamine the expected behaviour of a building during a strong earthquake. The building

shown in the example needed a seismic retrofit, and a retrofit solution was selected by testing

a number of different retrofit options in ETABS. FEMA 547, Techniques for the Seismic

Rehabilitation of Buildings, which is available free of charge from www.fema.gov, provides

detailed information on potential retrofit solutions and how to select them. Also, the reports

on buildings analyzed as case studies during the Pakistan-US cooperative project provide

detailed examples of retrofit solutions for typical Pakistani buildings. These reports can be

downloaded from the GeoHazards International website at www.geohaz.org. Additional

detailed information about nonlinear analysis can be found in the NEHRP Seismic Design

Technical Brief No. 4,Nonlinear Structural Analysis for Seismic Design: A Guide for

Practicing Engineers, available free of charge from www.nehrp.gov.


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References

1. ETABS, User Interface Reference Manual. 2002, Computers & Structures (CSi):California.

2. Federal Emergency Management Agency, FEMA-356: Prestandard and Commentary

for the Seismic Rehabilitation of Buildings. 2000: Washington DC.

3. American Society of Civil Engineers, ASCE-41: Seismic Rehabilitation of Existing

Buildings. 2006: Virginia.

4. Applied Technology Council, ATC-40: Seismic Evaluation and Retrofit of Concrete

Buildings. 1996: California.

5. Humar, J.M., D. Lau, and J.-R. Pierre, Performance of buildings during the 2001 Bhuj

earthquake.Canadian Journal of Civil Engineering, 2001. 28(6): p. 979-991.

6. Korkmaz, K.A., F. Demir, and M. Sivri, Earthquake Assessment of R / C Structures

with Masonry Infill Walls.International Journal of Science and Technology, 2007. 2:

p. 155-164.

7. Mondal, G. and S.K. Jain, Lateral Stiffness of Masonry Infilled Reinforced Concrete

(RC) Frames with Central Opening.Earthquake Spectra, 2008. 24(3): p. 701.

8. Saatcioglu, M., et al., The August 17, 1999, Kocaeli (Turkey) earthquake damage

to structures.Canadian Journal of Civil Engineering, 2001. 28(4): p. 715-737.

9. Taher, S.E.-D.F. and H.M.E.-D. Afefy, ROLE OF MASONRY INFILL IN SEISMIC

RESISTANCE OF RC STRUCTURES. The Arabian Journal for Science and

Engineering, 2008. 33: p. 291-306.

12. Murty, C.V.R., et al., AT RISK : The Seismic Performance of Reinforced Concrete

Frame Buildings with Masonry Infill Walls. 2006, Earthquake Engineering Research

Institute and the International Association for Earthquake Engineering: Oakland. p.

83.

13. Kodur, V.K.R., M.A. Erki, and J.H.P. Quenneville, Seismic design and analysis of

masonry-infilled frames.Canadian Journal of Civil Engineering, 1995. 22(3): p. 576-

587.

Documents

Pushover Analysis Guide Final