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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
2
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
Seminar on WIND & EARTHQUAKE ENGINEERINGMarch 23-24, 2012Regalia Tower Hotel Suites, Cubao, Quezon CityPUSHOVER ANALYSIS OF BUILDINGS
3
Outline:
Types of Structural Analysis Procedures
What is Pushover Analysis?
How is a Pushover Curve constructed?
What are the uses of Pushover Analysis?
Seminar on WIND & EARTHQUAKE ENGINEERINGMarch 23-24, 2012Regalia Tower Hotel Suites, Cubao, Quezon CityPUSHOVER ANALYSIS OF BUILDINGS
4
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.
Seminar on WIND & EARTHQUAKE ENGINEERINGMarch 23-24, 2012Regalia Tower Hotel Suites, Cubao, Quezon CityPUSHOVER ANALYSIS OF BUILDINGS
Types of Structural Analysis
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
Seminar on WIND & EARTHQUAKE ENGINEERINGMarch 23-24, 2012Regalia Tower Hotel Suites, Cubao, Quezon CityPUSHOVER ANALYSIS OF BUILDINGS
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Types of Material and Geometric Response Behavior
STRUCTURE(MODEL)
STRUCTURE: MATERIALS, GEOMETRY
NONLINEAR- ELASTIC
LINEAR- ELASTICLINEAR - INELASTIC
NONLINEAR- INELASTIC
Figures from ACECOMS, AIT
Seminar on WIND & EARTHQUAKE ENGINEERINGMarch 23-24, 2012Regalia Tower Hotel Suites, Cubao, Quezon CityPUSHOVER ANALYSIS OF BUILDINGS
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Types of Structural Analysis
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.
Seminar on WIND & EARTHQUAKE ENGINEERINGMarch 23-24, 2012Regalia Tower Hotel Suites, Cubao, Quezon CityPUSHOVER ANALYSIS OF BUILDINGS
8
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
Seminar on WIND & EARTHQUAKE ENGINEERINGMarch 23-24, 2012Regalia Tower Hotel Suites, Cubao, Quezon CityPUSHOVER ANALYSIS OF BUILDINGS
9
Types of Structural Analysis
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.
Seminar on WIND & EARTHQUAKE ENGINEERINGMarch 23-24, 2012Regalia Tower Hotel Suites, Cubao, Quezon CityPUSHOVER ANALYSIS OF BUILDINGS
10
Types of Structural Analysis
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.
Seminar on WIND & EARTHQUAKE ENGINEERINGMarch 23-24, 2012Regalia Tower Hotel Suites, Cubao, Quezon CityPUSHOVER ANALYSIS OF BUILDINGS
11
Types of Structural Analysis
NONLINEAR STATIC PROCEDURE (NSP)
An example of a NONLINEAR STATICPROCEDURE is a PUSHOVER ANALYSIS.
Oftentimes the Nonlinear Static Procedureis called Pushover Analysis
Seminar on WIND & EARTHQUAKE ENGINEERINGMarch 23-24, 2012Regalia Tower Hotel Suites, Cubao, Quezon CityPUSHOVER ANALYSIS OF BUILDINGS
12
Types of Structural 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.
Seminar on WIND & EARTHQUAKE ENGINEERINGMarch 23-24, 2012Regalia Tower Hotel Suites, Cubao, Quezon CityPUSHOVER ANALYSIS OF BUILDINGS
13
Outline:
Types of Structural Analysis √
What is Pushover Analysis?
How is a Pushover Curve constructed?
What are the uses of Pushover Analysis?
Seminar on WIND & EARTHQUAKE ENGINEERINGMarch 23-24, 2012Regalia Tower Hotel Suites, Cubao, Quezon CityPUSHOVER ANALYSIS OF BUILDINGS
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What is Pushover 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.
Seminar on WIND & EARTHQUAKE ENGINEERINGMarch 23-24, 2012Regalia Tower Hotel Suites, Cubao, Quezon CityPUSHOVER ANALYSIS OF BUILDINGS
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What is Pushover Analysis?
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.
Seminar on WIND & EARTHQUAKE ENGINEERINGMarch 23-24, 2012Regalia Tower Hotel Suites, Cubao, Quezon CityPUSHOVER ANALYSIS OF BUILDINGS
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What is Pushover Analysis?
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.
Seminar on WIND & EARTHQUAKE ENGINEERINGMarch 23-24, 2012Regalia Tower Hotel Suites, Cubao, Quezon CityPUSHOVER ANALYSIS OF BUILDINGS
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What is Pushover Analysis?
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.
Seminar on WIND & EARTHQUAKE ENGINEERINGMarch 23-24, 2012Regalia Tower Hotel Suites, Cubao, Quezon CityPUSHOVER ANALYSIS OF BUILDINGS
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What is Pushover Analysis?
Seminar on WIND & EARTHQUAKE ENGINEERINGMarch 23-24, 2012Regalia Tower Hotel Suites, Cubao, Quezon CityPUSHOVER ANALYSIS OF BUILDINGS
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
Seminar on WIND & EARTHQUAKE ENGINEERINGMarch 23-24, 2012Regalia Tower Hotel Suites, Cubao, Quezon CityPUSHOVER ANALYSIS OF BUILDINGS
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What is Pushover Analysis?
1
2
4
6 8
10
Seminar on WIND & EARTHQUAKE ENGINEERINGMarch 23-24, 2012Regalia Tower Hotel Suites, Cubao, Quezon CityPUSHOVER ANALYSIS OF BUILDINGS
21
Outline:
Types of Structural Analysis √
What is Pushover Analysis? √
How is a Pushover Curve constructed?
What are the uses of Pushover Analysis?
Seminar on WIND & EARTHQUAKE ENGINEERINGMarch 23-24, 2012Regalia Tower Hotel Suites, Cubao, Quezon CityPUSHOVER ANALYSIS OF BUILDINGS
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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.
Seminar on WIND & EARTHQUAKE ENGINEERINGMarch 23-24, 2012Regalia Tower Hotel Suites, Cubao, Quezon CityPUSHOVER ANALYSIS OF BUILDINGS
CreateMathematical
Model
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
YES
NO
Plot F vs. Δ
Flowchart of Procedure (Force-Controlled)
Seminar on WIND & EARTHQUAKE ENGINEERINGMarch 23-24, 2012Regalia Tower Hotel Suites, Cubao, Quezon CityPUSHOVER ANALYSIS OF BUILDINGS
CreateMathematical
Model
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
YES
NO
Plot F vs. Δ
Flowchart of Procedure (Displacement-Controlled)
Seminar on WIND & EARTHQUAKE ENGINEERINGMarch 23-24, 2012Regalia Tower Hotel Suites, Cubao, Quezon CityPUSHOVER ANALYSIS OF BUILDINGS
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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)
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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.)
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Define Element and Hinge Properties
General Force-Deformation Relationship
B
A
C
D E
Fo
rce
Deformation
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Plastic Hinge Rigid Zone
Span LoadsFlexibleConnection Shear Hinge
Modeling Beam Element
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Plastic Hinge Rigid Zone
Shear Hinge
Modeling Column Element
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P
M
Modeling Column ElementAxial Load – Moment Interaction (RC)
Seminar on WIND & EARTHQUAKE ENGINEERINGMarch 23-24, 2012Regalia Tower Hotel Suites, Cubao, Quezon CityPUSHOVER ANALYSIS OF BUILDINGS
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• 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
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Uniform Code Lateral Mode 1
Modeling Loads
Lateral Load Pattern
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F1
F2
F3
ib FV
Vb
E
S
Plotting the Pushover Curve
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Results of Analysis
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RESULTS - CAPACITY SPECTRUM
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Plot showing Hinge Location
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Plot of Moment Diagram
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Outline:
Types of Structural Analysis √
What is Pushover Analysis? √
How is a Pushover Curve constructed?
What are the uses of Pushover Analysis?
√
Seminar on WIND & EARTHQUAKE ENGINEERINGMarch 23-24, 2012Regalia Tower Hotel Suites, Cubao, Quezon CityPUSHOVER ANALYSIS OF BUILDINGS
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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
Seminar on WIND & EARTHQUAKE ENGINEERINGMarch 23-24, 2012Regalia Tower Hotel Suites, Cubao, Quezon CityPUSHOVER ANALYSIS OF BUILDINGS
Capacity Spectrum Method of ATC 40
Roof Displacement
Ba
se
Sh
ea
r
Spectral Displacement
Sp
ectr
alA
cce
lera
tion
Convert Pushover Curve to Capacity Spectrum
Pushover Curve Capacity Spectrum
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Sp
ectr
al
Acce
lera
tion
Time Period
2.5CA
CV/T
Response Spectrum ( at effective damping)
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Sp
ectr
al
Acce
lera
tion
Time Period
T0S
pe
ctr
al
Acce
lera
tion
Spectral Displacement
T0Sd = SaT2/4p2
Convert the Response Spectrum to Acceleration-Displacement Response Spectrum Format(Demand Spectrum)
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Sp
ectr
al
Acce
lera
tion
Spectral Displacement
Demand Spectrum for effectivedamping at performance point
Capacity Spectrum
Determine the Performance Point
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Deformation Measure
Fo
rce
Me
asu
re
Performance Limits(IO, LS, CP)
Expected Performance Pointfor given Earthquake
Verification of Acceptance
IO – Immediate OccupancyLS – Life SafetyCP – Collapse Prevention
Seminar on WIND & EARTHQUAKE ENGINEERINGMarch 23-24, 2012Regalia Tower Hotel Suites, Cubao, Quezon CityPUSHOVER ANALYSIS OF BUILDINGS
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.
Seminar on WIND & EARTHQUAKE ENGINEERINGMarch 23-24, 2012Regalia Tower Hotel Suites, Cubao, Quezon CityPUSHOVER ANALYSIS OF BUILDINGS
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Where:
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Uses of Pushover Analysis
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.
Seminar on WIND & EARTHQUAKE ENGINEERINGMarch 23-24, 2012Regalia Tower Hotel Suites, Cubao, Quezon CityPUSHOVER ANALYSIS OF BUILDINGS
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Uses of Pushover Analysis
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%)
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Uses of Pushover Analysis
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
Seminar on WIND & EARTHQUAKE ENGINEERINGMarch 23-24, 2012Regalia Tower Hotel Suites, Cubao, Quezon CityPUSHOVER ANALYSIS OF BUILDINGS
50
Uses of Pushover Analysis
Typical example of a Damage Probability Matrix
MMI
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)
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Ground Motion Intensity
PUSHOVER ANALYSIS OF BUILDINGS
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Uses of Pushover Analysis
Fragility Curves
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Uses of Pushover Analysis
Example Vulnerability curve for a given type ofbuilding
1.0
0.5
0.
Ground Motion Intensity
Damage
Ratio
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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.
Seminar on WIND & EARTHQUAKE ENGINEERINGMarch 23-24, 2012Regalia Tower Hotel Suites, Cubao, Quezon CityPUSHOVER ANALYSIS OF BUILDINGS
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Uses of Pushover Analysis
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.
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Thank Youfor listening!