Asep4A Pushover Analysis

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

ULPIANO P. IGNACIO IGNACIO,, JR., M.Sc., F.ASEP, PICE PROFESSOR PROFESSO R OF CIVIL ENGINEERING UNIVERSITY OF THE PHILIPPINES DILIMAN 1

March 23-24, 2012 Regalia Tower Hotel Suites, Cubao, Quezon City

PUSHOVER ANALYSIS OF BUILDINGS

Semina Sem inarr on WIN WIND D & EAR EARTHQ THQUAK UAKE E ENG ENGINE INEER ERING ING

Objectives To describe the different different procedures for structural structural analysis

To introduce introduce the basic concept concept of Pushover Analysis of Buildings

To present the general general procedure in performing a pushover pushover analysis

To discuss the uses of a pushover analysis and a pushover curve 2




Objectives To describe the different different procedures for structural structural analysis

To introduce introduce the basic concept concept of Pushover Analysis of Buildings

To present the general general procedure in performing a pushover pushover analysis

To discuss the uses of a pushover analysis and a pushover curve 2




Outline: 

Types of Structural Analysis Analysis Procedures



What is Pushover Analysis?



How is a Pushove Pushoverr Curve construc constructed? ted?



What are the uses uses of Pushover Pushover Analy Analysis? sis?

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Types of Structu Structural ral Analy Analysis sis

ANALYSIS

ACTION

STRUC STR UCTUR TURE E

RESPONSE

(MODEL (MO DEL))

ACTION : ACTION : DEAD LOAD, LIVE LOAD, WIND LOAD, SEISMIC, BLAST, ETC. STRUCTURE:: MA STRUCTURE MATERIALS, TERIALS, COMPONENTS, GEOMETRY GEOMETRY,, SUPPORTS, S UPPORTS, ETC. RESPONSE:: DISPLACEMENTS, STRESSES, MOMENTS, SHEARS, ETC. RESPONSE STRUCTURAL ANAL ANALYSIS YSIS – determination of the RESPONSE of a STRUCTURE STRUCTURE due due to external ACTIONS external ACTIONS..

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Types of Structural Analysis ACTION ACT ION (FOR (FORCE CE OR EX EXCIT CITA ATION TION)) may be: STATIC – constant, slowly applied load STATIC – or DYNAMIC – DYNAMIC – time varying loads STRUCTURE – consists of elements or components made of materials and connected in a specific geometric arrangement. STRUCTURE (MODEL)

Materials may be ELASTIC or INELASTIC

RESPONSE may be LINEAR or NONLINEAR



Seminar on WIND & EARTHQUAKE ENGINEERING

Types of Material and Geometric Response Behavior

LINEAR- ELASTIC

LINEAR - INELASTIC

STRUCTURE (MODEL)

NONLINEAR- ELASTIC

NONLINEAR- INELASTIC

STRUCTURE: MATERIALS, GEOMETRY

Figures from ACECOMS, AIT

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Types of Structural Analysis Of the four combinations, the LINEARINELASTIC and the NONLINEARELASTIC behavior are unlikely to happen in practical structural cases. Hence, only the LINEAR-ELASTIC and the NONLINEAR-INELASTIC cases are entertained. They will simply be called STRUCTURE: MATERIALS, GEOMETRY LINEAR AND NONLINEAR behavior, respectively. 7




Types of Structural Analysis Procedures Together with the nature of the ACTION, whether STATIC or DYNAMIC, we have the following four types of structural analysis procedures: LINEAR STATIC PROCEDURE

LINEAR DYNAMIC PROCEDURE

NONLINEAR STATIC PROCEDURE

NONLINEAR DYNAMIC PROCEDURE 8




Types of Structural Analysis LINEAR STATIC PROCEDURE (LSP)

An example of an LSP is the Static Force Procedure of Sec. 208.5.2 of the NSCP. In this procedure, the effect of the ground motion on the building is converted to a Design Base Shear, V. This V is converted into a set of equivalent static lateral forces applied at the floor levels. The structure is modeled and its properties are given by its stiffness matrix, [K]. In this procedure, the [K] remains constant. 9




Types of Structural Analysis LINEAR DYNAMIC PROCEDURE (LDP)

An example of an LDP is the Dynamic Analysis Procedure of Sec. 208.6 of the NSCP. In this procedure, an elastic dynamic analysis utilizing the peak modal response based on the response spectrum for all significant modes is made. To obtain the total response, the maximum modal contribution of significant modes are combined in a prescribed manner, e.g. SRSS or CQC method.

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Types of Structural Analysis NONLINEAR STATIC PROCEDURE (NSP)

An example of a NONLINEAR STATIC PROCEDURE is a PUSHOVER ANALYSIS. Oftentimes the Nonlinear Static Procedure is called Pushover Analysis

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Types of Structural Analysis NONLINEAR DYNAMIC PROCEDURE (NDP)

• nonlinear dynamic procedures consider the time history of the ground shaking

• they incorporate inelastic member behavior under cyclic earthquake ground motions

• they explicitly simulate hysteretic energy dissipation in the nonlinear range

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

• Nonlinear Dynamic Procedure is also called Nonlinear Time History Analysis.

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Outline: 

Types of Structural Analysis

√






How is a Pushover Curve constructed?



What are the uses of Pushover Analysis?

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■ Pushover Analysis is an incremental static analysis used to determine the forcedisplacement relationship for a structure or structural element.

■ The analysis involves applying horizontal loads, in a prescribed pattern, to a computer model of the structure incrementally, and plotting the total applied shear force and associated lateral displacement at each increment, until the structure reaches a limit state or collapse condition. 14




What is Pushover Analysis? 

As individual components of a structure yield or fail, the earthquake forces on the building are shifted to other components.



A pushover analysis simulates this phenomenon by applying loads until the weak link in the structure is found and then revising the model to incorporate the changes in the structure caused by the yielding or failing of the weak link.



A second iteration is then performed to study how the loads are redistributed in the structure. The structure is “pushed” again until the second weak link is discovered. 15





This process continues until the yield pattern for the whole structure under seismic loading is 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) is the pushover curve or capacity curve.

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A pushover analysis is an approximation of the more accurate and more complicated Nonlinear Dynamic Procedure



A pushover analysis is only useful for evaluating nonlinear structures for which the fundamental mode dominates and is not suitable for certain irregular or dynamically complex structures.

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





4 6 2

8 10

1

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Outline: Types of Structural Analysis

√


√

How is a Pushover Curve constructed? What are the uses of Pushover Analysis?

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How is a Pushover Curve constructed ? 2 types of pushover analysis: FORCE CONTROLLED - the force is incrementally increased DISPLACEMENT-CONTROLLED – the displacement of the reference point is incrementally increased The displacement controlled pushover analysis is generally preferred over the force controlled one because the analysis could be carried out up to the desired level of the displacement. Pushover Analysis is carried out using computer software.

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Flowchart of Procedure (Force-Controlled) Create Mathematical Model

Apply gravity load to determine initial nodal displacements and member forces

Update nodal displacements and member forces

Δ< Δlimit YES

Apply increment of lateral load

Modify structural stiffness to represent yielding

NO

Plot F vs. Δ




Flowchart of Procedure (Displacement-Controlled) Create Mathematical Model

Apply gravity load to determine initial nodal displacements and member forces

Update nodal displacements and member forces

Δ<

NO

Δlimit YES

Apply increment of displacement pattern

Modify structural stiffness to represent yielding

Plot F vs. Δ






Create Mathematical Model of the Structure Geometry Potential Plastic Hinge Location (must be predicted and revised as needed)

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

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

Define Material Properties concrete, steel, reinforcing bars, etc. density, strength, yield point, modulus of elasticity, poisson’s ratio, shear modulus, etc.



Define Section Properties Beam 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

C B e c r o F

D

A

E

Deformation

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Modeling Beam Element

Flexible Connection

Span Loads Shear Hinge

Plastic Hinge

Rigid Zone

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Modeling Column Element

Shear Hinge

Plastic Hinge

Rigid Zone

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Modeling Column Element Axial Load – Moment Interaction (RC) P

M




Modeling Loads • Start with Gravity Loads – Dead Load – Some portion of Live Load – • Select Lateral Load Pattern – Lateral Load Patterns (Vertical Distribution) – Lateral Load Horizontal Distribution – Torsional Effects – Orthogonal Effects

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Modeling Loads Lateral Load Pattern

Uniform

Code Lateral

Mode 1 32




Plotting the Pushover Curve V b E

F 3

F 2 F 1

S

V b   F i



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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

√


√

How is a Pushover Curve constructed?

√

What are the uses of Pushover Analysis?

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

Uses of Pushover Analysis 1. Performance Check of Structures Assessment and Rehabilitation of Existing Buildings Published Guidelines for Seismic Rehabilitation of Buildings: ATC-40 – Seismic Evaluation and Retrofit of Concrete Buildings (1996) FEMA 273 – NEHRP Guidelines for the Seismic Rehabilitation of Buildings (1997) FEMA 356 – Prestandard and Commentary for the Seismic Rehabilitation of Buildings (2000) FEMA 440 (ATC-55) - Improvement of Nonlinear Static Seismic Analysis Procedures 39




Capacity Spectrum Method of ATC 40

Pushover Curve

r a e h S e s a B

Roof Displacement

n o i t a r e l e c c A l a r t c e p S

Capacity Spectrum

Spectral Displacement

Convert Pushover Curve to Capacity Spectrum




Response Spectrum ( at effective damping)

2.5CA n o l i t a r a t r c l e e e p S c c A

CV/T

Time Period

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Convert the Response Spectrum to AccelerationDisplacement Response Spectrum Format (Demand Spectrum)

T0

Sd = SaT2/4p2 n o l i t a r a t r c l e e e p S c c A

T0

Time Period

n o l i t a r a t r c l e e e p S c c A


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Determine the Performance Point

Demand Spectrum for effective damping at performance point n o l i t a r a t r c l e e e p S c c A

Capacity Spectrum


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Verification of Acceptance Expected Performance Point for given Earthquake e r u s a e M e c r o F

Performance Limits (IO, LS, CP)

Deformation Measure IO – Immediate Occupancy LS – Life Safety CP – Collapse Prevention 44




Displacement Coefficient Method - described in FEMA-273 The performance point of the structure is obtained by the determination of a “target displacement” using the “Coefficient Method” outlined in FEMA 273.




Where:

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

Uses of Pushover Analysis

2. Performance Based Design (PBD) PBD is similar to assessment and rehabilitation of buildings, except that we are dealing with new buildings instead of existing ones. In PBD, we design buildings so that they will perform according to pre-determined standards like IO, LS, and CP at corresponding levels of seismic shaking. Therefore, pushover analysis is a necessary component of PBD. 47







3. Development of Fragility and Vulnerability Curves FRAGILITY CURVE (FUNCTION) - a curve (function) that shows the relationship between structural performance and ground motion. Specifically, it gives the probability that a structure is in, or exceeding, a given damage state due to a given ground motion intensity. If given in a tabular form, it is called a Damage Probability Matrix (DPM) VULNERABILITY – the degree of loss to a given element at risk resulting from a given level of hazard (e.g. ground motion intensity). It is defined as the ratio of the expected loss to the maximum possible loss, on a scale of 0 to 1 (or 0 to 100%) 48







There are three methods used in developing fragility curves. These are: 1. Empirical Method (observed data) 2. Analytical Method 3. Heuristic Method (Based on experts’ opinion) The analytical method relies heavily on the use of pushover analysis

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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 Fragility Curves 51







D a m a g e

R a t i o

1.0

0.5

0 .

Ground Motion Intensity

Example Vulnerability curve for a given type of building 52




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Summary

Pushover Analysis gives us a better idea how a structure will perform when subjected to a given level of earthquake. Design Earthquakes cause nonlinear behavior which cannot be handled by linear static procedures. Pushover analysis gives a better understanding of the building behavior well into the inelastic region. Pushover analysis Identifies weak elements with plastic hinge formation and their order of formation. It gives realistic prediction of element demands.

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Uses of Pushover Analysis It is a good substitute for the more accurate Nonlinear Dynamic Analysis for buildings where the fundamental mode of vibration dominates. For buildings with more than one significant mode and buildings with irregular features, nonlinear static pushover analysis may not be accurate.

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Asep4A Pushover Analysis

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