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Response Spectrum MethodAs Per IS 1893 (Part 1):2002

Satish A. Annigeri

Civil Engineering DepartmentB.V.B. College of Engineering & Technology

Hubli 580 [email protected]

10 May, 2007

Satish A. Annigeri (BVBCET, Hubli) Response Spectrum Method 10 May, 2007 1 / 27
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Objectives

Discuss thephilosophy of design of Earthquake Resistant Structures

Understand the concept of Response Spectrum Method

Understand thegeneral provisions of IS 1893(Part 1):2002

Understand the procedure for implementing Response SpectrumMethod as per IS 1893 (Part 1):2002

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Objectives





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Introduction

Categories of Earthquake Resistant Structures

Engineered Structuress

Structures which are explicitly analysed and designed to ensure thatthey are earthquake resistant

Examples of Engineered Structures

Multistorey buildings

BridgesTowers, Water tanksNuclear reactors

Non-engineered Structuress

Structures which arenotexplicitly analysed and designed to ensure

that they are earthquake resistant

Earthquake resistance is ensured throughgood materials ofconstructionandgood construction practices

Examples of Non-engineered Structures

Masonry structuresSatish A. Annigeri (BVBCET, Hubli) Response Spectrum Method 10 May, 2007 3 / 27

Introduction
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Indian Standard Codes for Engineered Structures

Engineered Structures

IS 1893- Criteria for Earthquake Resistant Design of Structures

Part 1: IS 1893(Part 1):2002General Provisions and BuildingsPart 2: Liquid retaining tanks - Not yet publishedPart 3: Bridges and Retaining Walls - Not yet publishedPart 4: IS 1893(Part 4):2005Industrial structures including stack like

structuresPart 5: Dams and embankments -Not yet published

IS 13920:1993- Ductile Detailing of Reinforced Concrete StructuresSubjected to Seismic Forces - Code of Practice

Important NoteUntil Parts 2, 3 and 5 are ready, design of such structures is governed bythe relevant clauses ofIS 1893:1984


Introduction
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IS 1893- Criteria for Earthquake Resistant Design of Structures

Part 1: IS 1893(Part 1):2002General Provisions and BuildingsPart 2: Liquid retaining tanks - Not yet publishedPart 3: Bridges and Retaining Walls - Not yet publishedPart 4: IS 1893(Part 4):2005Industrial structures including stack like





Introduction
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IS 1893- Criteria for Earthquake Resistant Design of StructuresPart 1: IS 1893(Part 1):2002General Provisions and BuildingsPart 2: Liquid retaining tanks - Not yet publishedPart 3: Bridges and Retaining Walls - Not yet publishedPart 4: IS 1893(Part 4):2005Industrial structures including stack like





Introduction
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IS 1893- Criteria for Earthquake Resistant Design of StructuresPart 1: IS 1893(Part 1):2002General Provisions and BuildingsPart 2: Liquid retaining tanks - Not yet publishedPart 3: Bridges and Retaining Walls - Not yet publishedPart 4: IS 1893(Part 4):2005Industrial structures including stack like





Introduction


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Indian Standard Codes for Non-engineered Structures

Non-engineered Structures

IS 4326:1993Earthquake Resistant Design & Construction ofBuildings - Code of Practice

IS 4326:1993deals with Masonry buildings

Size and location ofopenings

Size, location and details ofhorizontal bandsVertical reinforcementin masonry construction


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Indian Standard Codes for Non-engineered Structures

Non-engineered Structures

IS 4326:1993Earthquake Resistant Design & Construction ofBuildings - Code of Practice

IS 4326:1993deals with Masonry buildings

Size and location ofopenings

Size, location and details ofhorizontal bandsVertical reinforcementin masonry construction


Introduction
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Philosophy of Design of Earthquake Resistant Structures

Characteristics of Earthquake Resistant Structures

1 During amild earthquakeno damage to any structural elements (that is, structure shouldrespond elastically),non-structural elements (such as glazing, infill walls, ceiling) may bedamaged

2 During amoderate earthquake

Structural elements may suffer(repairable) damage, but . . .It must be possible torehabilitate the structureand make it fit for itsintended use

3

During asevere earthquakeStructural elements may suffer irrepairable damage, but . . .The structure shouldnot collapsewithout giving adequate time for theoccupants of the structure to escape with their life


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Implications of the Design Philosophy

How can we achieve all three goals simultaneously?

Correctly estimatethe seismic force on the structure

Analyze the structure for acombination of loads- Dead Load, LiveLoad, Earthquake Load

Design the components of the struture for the most severe load

combinationDetailthe structure for ductility

Understimatingthe seismic force will result in the collapse of thestructure during even a moderate earthquake

Overstimatingthe seismic force will result in an uneconomicalstructure (no damage even during a severe earthquake)

Strengthalone is not enough. Ductility is necessary to satisfy thethird requirement


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IS 1893 (Part 1):2002

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IS 1893 (Part 1)- General Provisions and Buildings

Load combinations

Seismic Zoning of India (Z)

Design SpectrumSag

Regular and Irregular configuration of buildings

Importance Factor (I

)Response Reduction Factor (R)

Design Imposed Loads for earthquake force calculation

Seismic Weight of Buildings (W)

Methods of estimating seismic design force1 Static Analysis (Equivalent Static Analysis)2 Dynamic Analysis

Response Spectrum AnalysisTime History Analysis


IS 1893 (Part 1):2002

C
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Load Combinations

Plastic Design of Steel Structures

1 1.7(Dead Load + Imposed Load)2 1.7(Dead Load Earthquake Load)

3 1.3(Dead Load + Imposed Load Earthquake Load)

Limit State Design of Reinforced and Prestressed Concrete Structures

1 1.5(Dead Load + Imposed Load)


3 1.5(Dead Load Earthquake Load)

4

0.9 Dead Load

1.9 Earthquake Load


IS 1893 (Part 1):2002

L d C bi i
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Load Combinations

Plastic Design of Steel Structures

1 1.7(Dead Load + Imposed Load)2 1.7(Dead Load Earthquake Load)


Limit State Design of Reinforced and Prestressed Concrete Structures

1 1.5(Dead Load + Imposed Load)


3 1.5(Dead Load Earthquake Load)

4

0.9 Dead Load

1.9 Earthquake Load


IS 1893 (Part 1):2002

D i E h k L d
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Design Earthquake Load

Design Horizontal Earthquake Load

Lateral Load Resisting Elements in Orthogonal DirectionsStructure must be designed for the effects due to full design earthquakeload in one direction at a timeLateral Load Resisting Elements Not in Orthogonal DirectionsStructure must be designed for the effects due to full design earthquake

load in one direction plus 30% of the design earthquake load in theother direction

Design Vertical Earthquake Load

Design acceleration spectrum in vertical direction may be taken as 23 ofthe design horizontal acceleration


IS 1893 (Part 1):2002

S i i Z i f I di


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Seismic Zoning of India

India is divided into4 seismic zones, Zone II to Zone V

Zone II is the least severe seismic zone andZone V is the most severe

Seismic zoning is based on geological investigationsandhistory ofpast earthquakesexperienced by the the location

Seismic zoning is given in Fig. 1 (page 5) of IS 1893(Part 1):2002

Coastal Karnatakalies in Zone III and therest of Karnatakalies inZone II

Zone III: Dharwad, Belgaum, Bijapur, Karwar, Mangalore

Zone II: Bangalore, Mysore, Chitradurga, Gulbarga (See Annexure E,

page 35-36)


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Seismic Zones of India


IS 1893 (Part 1):2002

Z F t f Diff t S is i Z s


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Zone Fator for Different Seismic Zones

Table: Table 2 Zone Factor Z (page 16)

SeismicZone II III IV V

Seismic

Intensity Low Moderate Severe VerySevere

Z 0.10 0.16 0.24 0.36


IS 1893 (Part 1):2002

Response Spectra for Rock and Soil Sites for 5% Damping
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Response Spectra for Rock and Soil Sites for 5% Damping


IS 1893 (Part 1):2002

Response Spectra from Equations


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Response Spectra from Equations

Type I - Rock or Hard Soil

Sa

g =

1 + 15 T 0s T 0.1s

2.50 0.1s T 0.4s

1.00/T 0.4s T 4.0s

Type II - Medium Soil

Sa

g =

1 + 15 T 0s T 0.1s

2.50 0.1s T 0.55s

1.36/T 0.55s T 4.0s

Type III - Soft Soil

Sa

g =

1 + 15 T 0s T 0.1s

2.50 0.1s T 0.67s

1.67/T 0.67s T 4.0s


IS 1893 (Part 1):2002

Design Spectrum
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Design Spectrum

Design Spectrumis a graph of Spectral Acceleration CoefficientSag

versus Period of Vibration (T)There arethreediffrent Spectra, for three differentSoil types

The design spectrum is for5% damping, and must besuitably scaledif the damping ratio is not 5% (See Table 3, page 17)

Design Spectrum has three distinct phases (See Fig. 2, page 16)Linearlry increasingportion from T= 0s upto T = 0.1sConstant portionfrom T = 0.1s to T = 0.4/0.55/0.67sDecreasing curved portionfrom T= 0.4/0.55/0.67s to T= 4s

Maximum Spectral Acceleration is Sa = 2.5g

From the Design Spectrum, we get theMaximum Accelerationexperienced by a SDOF system with a given Natural Period

Design Spectrum gives theDesign Elastic Force


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Response Reduction Factor
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p

Designing your structure as per theDesign Spectrumof the code will

ensure that the structure will remain elastic during a severeearthquake

But the structurecost will increaseif we design it to remain elasticeven during a severe earthquake

If we reduce the design force in theright way, we can satisfy the threerequirements for earthquake resistant structures

The proportion by which we can reduce the elastic design force, andstill satisfy the third requirement for earthquake resistant structures iswhat the code callsResponse Reduction Factor (R)


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Response Reduction Factor in IS 1893 (Part 1):2002
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( )

Response Reduction Factor depends on two factors

The type ofLateral Load Resisting SystemThe degree ofDuctility detailing

R varies

From3.0 to 5.0forFrame StructuresandFrom1.5 to 3.0forMasonry Wall Buildings

It is greater if properductility detailingis planned to be doneIt is greater ifadditional lateral load resisting systems, such as, bracesare provided

Guidelines for choosing R for RC frame structures

Ductility Detailing Nomenlature R

IS 456:2000 OMRF 3

IS 13920:1993 SMRF 5


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R varies





IS 456:2000 OMRF 3

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IS 1893 (Part 1):2002

Importance Factor (I)
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Important structureswhich mustcontinue to function even after

occurrence of a severe earthquakemust be made stronger than theordinary structures

Design force for such structures is made more than for ordinarystructures

Importance factor (I) is given in Table 6, page 18

Importance factor for buildings is

1.5forlifeline building structures, and1.0forordinary building structures

Importance factor for structures other than buildings is not given in

IS 1893 (Part 1):2002Importance factor fordamsis3.0, and forcontainers of inflammableliquids, it is2.0, as given inIS 1893:1984(Table 4, page 19)


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Design Imposed Loads for Earthquake Force Calculation
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The imposed loads to be considered for design of buildings are taken

as perIS 875 (Part 2):1987The natural period of vibration of a building depends on its

Massdue to(i)Dead Loads- Do not vary, and(ii)Imposed Loads- Do vary

Lateral Stiffness- Does not varyIt is therefore important that we correctly estimate theImposed Loadexisting on the buildingduring the earthquake

Thisreduction in the Imposed Loadis only for the purpose ofcomputing the vibration properties of the structure

ForGravity Load calculation,full Imposed Loadmust be considered


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Seismic Weight (W) of a Building
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Seismic Weight (W)

Seismic weight is the sum ofDead Load, andan appropriate part of Imposed Load, that part which islikelyto bepresent during an earthquake

Part of the Imposed Load to be considered while calculating the

Seismic Weight isFloors

25% of Imposed Loadif Imposed Load 3.0 kN/m2

50% of Imposed Loadif Imposed Load > 3.0 kN/m2

Roof

Nil, as the likelihood of Imposed Load being present on the roofat the time of an earthquake is considered to be extremely low(7.3.2, page 17)


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Seismic Weight (W)






Roof



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Seismic Weight (W)






Roof



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Methods of Estimating Seismic Forces
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If Dynamic Analysis isnotrequired as per the code, Equivalent Static

Methodcan be usedDynamic Analysismustbe performed under the followingcircumstances

Dynamic Analysismustbe used in the following cases(7.8.1, page 25)

Zones II, III Zones IV, VRegular Buildings h>90m h>40m

Irregular Buildings h>40m h>12m

Dynamic analysis, when required, must be performed either by the

Time History Analysisor by theResponse Spectrum Method (7.8.2,page 25)WhenTime History Analysisis used, the designer must

Choose anappropriate ground motion, andUseaccepted principles of dynamicsfor theanalysis(7.8.3,page23)


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If Dynamic Analysis isnotrequired as per the code, Equivalent StaticMethodcan be usedDynamic Analysismustbe performed under the followingcircumstances








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Equivalent Static Method
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Design Sesimic Base Shear, VB=AhW (7.5.3, page 24)

Distribute VB to different floor levels, Qi =VBWih

2

i

nj=1Wjh

2j (7.7.1,

page 24)

Apply the floor loads Qialong one directionand compute the seismicdesign forces

Apply the same floor loads Qiin a direction perpendicular to the firstCombine the seismic design forces with other design forces, as per theload combinations required

Design the structural membersfor the most severe load combination


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2

i

nj=1Wjh

2j (7.7.1,

page 24)





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2

i

nj=1Wjh

2j (7.7.1,

page 24)





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2

i

nj=1Wjh

2j (7.7.1,

page 24)





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D i S i i B Sh V A W ( 3 2 )
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2i

nj=1Wjh

2j (7.7.1,

page 24)





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2i

nj=1Wjh

2j (7.7.1,

page 24)





IS 1893 (Part 1):2002

Steps for Equivalent Static Procedure

Z F t (Z ) (T bl 2 16)
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Zone Factor (Z)(Table 2, page 16)

Height of building, hCheck if Equivalent Static Method can be usedClause 7.8.1, page 25

Importance Factor (I),(Table 6, page 18)

Response Reduction Factor (R),(Table 7, page 23)

Soil Type - One of Type I(Rock or Hard Soil), Type II(Medium Soil)or type III(Soft Soil)

Damping Ratio - Usually 5% for Reinforced Concrete and 2% forSteel(7.8.2.1, page 25)

Multiplying Factor for

Sa

g for damping ratios other than 5%(Table 3,page 17)


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Z F t (Z ) (T bl 2 16)
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Multiplying Factor for

Sa

g for damping ratios other than 5%(Table 3,page 17)


IS 1893 (Part 1):2002


Zone Factor (Z ) (Table 2 page 16)
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Multiplying Factor for Sag

for damping ratios other than 5%(Table 3,page 17)


IS 1893 (Part 1):2002

Steps for Equivalent Static Procedure contd...

Fundamental Natural Period (7 6 page 24)
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Fundamental Natural Period(7.6, page 24)

Ta = 0.075h

0.75

RC frames without brick infill panelsTa = 0.085h0.75 Steel frames without bracings

Ta = 0.09h

d All other buildings

Average Response Acceleration CoefficientSag

(Fig. 2, page 16)

using (i) Soil type, (ii) Fundamental Natural Period and (iii) DampingRatio

Design Horizontal Seismic Coefficient Ah = ZI2R

Sag

Design Seismic Base Shear VB=AhW (7.5.3, page 24)

Design lateral load at Floor i, Qi=VBWih

2

inj=1Wjh

2j (7.7.1, page 24)

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Ta = 0.075

h0.75


Ta = 0.09h



(Fig. 2, page 16)



Sag



2

inj=1Wjh

2j (7.7.1, page 24)

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Ta = 0.075

h0.75


Ta = 0.09h



(Fig. 2, page 16)



Sag



2

i

nj=1Wjh

2j (7.7.1, page 24)

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Ta = 0.075

h0.75


Ta = 0.09h



(Fig. 2, page 16)



Sag



2

i

nj=1Wjh

2j (7.7.1, page 24)



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Ta

= 0.075h0.75 RC frames without brick infill panelsTa = 0.085h

0.

75 Steel frames without bracings

Ta = 0.09h



(Fig. 2, page 16)



Sag



2

i

nj=1Wjh

2j (7.7.1, page 24)


Response Spectrum Method (7.8.4, page 25)

Undamped free vibration of the entire building using established
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Undamped free vibration of the entire building using establishedmethods of mechanics

Number of modes to be considered must be such that thesum totalof modal masses of all modes considered is at least 90% of the totalseismic massPeak response quantities, such as, member design forces,

displacements, storey forces, storey shears and base reactions shall becombined as perComplete Quadratic Combination (CQC)methodModal Mass Mkof mode kis given as follows

Mk=[n

i=1 Wiik]2

gni=1 Wi

2ik

Implementing Response Spectrum Method by hand is tedious anderror prone as thecomputations required are complexIt is better to use a computer program for Response SpectrumMethod

Satish A Annigeri (BVBCET Hubli) Response Spectrum Method 10 May 2007 26 / 27 IS 1893 (Part 1):2002


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p g gmethods of mechanics



Mk=[n

i=1 Wiik]2

gni=1 Wi

2ik




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i=1 Wiik]2

gni=1 Wi

2ik




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Mk=[n

i=1 Wiik]2

gni=1 Wi

2ik




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methods of mechanics



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gni=1 Wi

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methods of mechanics



Mk=[n

i=1 Wiik]2

gni=1 Wi

2ik


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Thank You

Questions?!

Satish A Annigeri (BVBCET Hubli) Response Spectrum Method 10 May 2007 27 / 27
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