Seismic Analysis of Multi Storied RC Buildings- Part 4

7/22/2019 Seismic Analysis of Multi Storied RC Buildings- Part 4

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Seismic Analysis of

Multi-storied RC Building

Presented by .

Rahul Leslie

Part - IV


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Methods of mode combinations

IS:1893 and other sources


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Combination of modal responses:

1. Absolute Combination (ABS) The modal responses of all the individual modes aresummed up:

Eg. for level 7,ABS = 1.178+ -0.69+ 0.335+ -0.08+ 0.035 = 2.318

Seismic Analysis of Multi-storied RC Building Presented by Rahul Leslie


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Combination of modal responses (cont):

2. Square Root of Sum of Squares (SRSS) The modal responses are squared, summed, and the root ofthe sum taken:

Eg. for level 7,SRSS = [(1.178)2+ (-0.69)2+ (0.335)2+ (-0.08)2+ (0.035)2] = 1.409



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3. Combination of ABS and SRSS (ABS&SRSS) The weighted sum of ABS and SRSS is taken The method was prescribed in IS:1893-1984 (4.2.2.2,

IS:1893(Part 1)-1984), removed in IS:1893-2002

Values for gare given by table Intermediate values can be

obtained by interpolation Eg. for level 7,

ABS&SRSS = 0.6 x 2.318 + 0.4 x 1.408 = 1.954

H (m) 1 2

20 0.6 0.4

40 0.4 0.6

60 0.2 0.8

90 0.0 1.0



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4. SRSS with grouping The ABS value of modal responses of modes with closefrequencies (ie., their freq.s seperated by not more than10%) are taken and the modal responses replaced by theABS value

The SRSS value of the modes and the ABSsvalues taken The method is prescribed in IS:1893-2002 as an alternativeto CQC method (7.8.4.4(a)&(b), IS:1893(Part 1)-2002)

Eg., if freq. are 2.2, 3.2, 7, 7.1, 8.6, 12.3,then SRSS is taken for 2.2, 3.2, ABS(7, 7.1), 8.6, 12.3

jand iare considered closeif their difference does not

exceed 10% of the lowerfrequency (3.2, IS:1893(Part

1)-2002and all major codes)



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5. Out-of-phase response combination This is a general category of methods, which includes CQCand SRSS

The general equation is

where rijis the cross modal coefficient


a) SRSS method

SRSS can be represented asrij = 1for i=j

= 0for ij


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5. Out-of-phase response combination (cont..)b) Ten Percent Method (TPM)

TPM can be represented as:For well separated modes,

rij = 1for i=j= 0for ij

For modes separated by not more than 10%

rij = 1for Qiand Qjhaving same sign

= -1for Qiand Qjhaving opposite sign

The method is not supported by IS:1893



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5. Out-of-phase response combination (cont..)c) Complete Quadratic Combination (CQC)

The CQC equation prescribed by IS:1893-2002 is (7.8.4.4,IS:1893(Part 1)-2002)

The CQC equation prescribed by NRC is

where is the damping ratio ( 0.05 for RCC)and = j/i



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5. Out-of-phase response combination (cont..)d) Double Sum Combination (DSC)

The DSC equation is

where sis the duration of earthquake,

varying from 14 to 40 sec.

The requirement for the effective duration of earthquake makesthis equation not useful

The method is not supported by IS:1893



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5. Out-of-phase response combination (cont..)e) GupthasMethod

The equation is

where

This method removes the handicap that DSC has The method is not supported by IS:1893



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Results of mode combinations


14/32Presented by Rahul LeslieSeismic Analysis of Multi-storied RC Building


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Missing Mass Correction


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Missing Mass Correction :

Missing Mass = 0.077% of total mass Zero Period Acceleration (3.11, IS:1893(Part 1)-2002)= 1.6

I II III IV V VI VII VIII1.441 4.51 8.098 11.782 15.309 17.908 69.357 103.083 (Hz)

99.922 % 0.077 %

33 Hz

ZPA



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Zero Period Acceleration = 1.0

(3.11, IS:1893(Part 1)-Proposed Draft)


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Missing Mass = 0.077% of total mass Zero Period Acceleration, (Sa/g)ZPA= 1.6 Horizontal acceleration coefficient, Ah

I II III IV V VI VII VIII1.441 4.51 8.098 11.782 15.309 17.908 69.357 103.083 (Hz)

99.922 % 0.077 %

33 Hz

ZPA



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0

23.57

23.57

23.57

23.57

23.57

23.57

x0.077

100

0

0.0182

0.0182

0.0182

0.0182

0.0182

0.0182

=

X (1.6)0.16 x 1

2 x 3Ah = = 0.04266

, 0.04266 x

0

0.0182

0.0182

0.0182

0.0182

0.01820.0182

=

0

0.0008

0.0008

0.0008

0.0008

0.00080.0008

0

0.5755

0.9114

0.9741

1.0422

1.116

1.4002

QP=

SRSS Q

Presented by Rahul LeslieSeismic Analysis of Multi-storied RC Building


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Combination of

Periodic and Rigid Responses

(Not supported by IS:1893)

Skip


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Combination ofPeriodic and Rigid Responses :

1. Lindley-Yow Method Each modal response Q is separated into an in-phase

(Periodic) component QR and an out-of-phase (Rigid)component QPbased on

provided



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Combination ofPeriodic and Rigid Responses (cont):

1. Lindley-Yow Method (Cont..) The in-phase (Periodic) component QR and an out-of-

phase (Rigid) component QPare defined as



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1. Lindley-Yow Method (Cont..) The in-phase components are combined by algebraic sum

The out-of-phase components are combined by CQCmethod



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1. Lindley-Yow Method (Cont..) The combined in-phase component and the combined out-

of-phase component are combined by SRSS method



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2. Hadjian Method Each modal response Q is separated into an in-phase

(Periodic) component QR and an out-of-phase (Rigid)component QPbased on

provided

(Same as Lindley-Yow)


SkipHadjian


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2. Hadjian Method (Cont..) The in-phase (Periodic) component QR and an out-of-

phase (Rigid) component QP are defined as


(different from Lindley-Yow)



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2. Hadjian Method (Cont..) The in-phase components are combined by algebraic sum


The out-of-phase components are combined by CQCmethod




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2. Hadjian Method (Cont..) The combined in-phase component and the combined out-

of-phase component are combined by ABS method

(different from Lindley-Yow)



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QR

0

0.604

0.6668

0.5879

0.666

0.6042

0.636

QP

0

0.3033

0.488

0.4987

0.5084

0.5331

0.697

Q

0

0.67588

0.82633

0.77092

0.83788

0.80574

0.94354

Lindley-Yow

SRSS

Presented by Rahul LeslieSeismic Analysis of Multi-storied RC Building


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End of Part - IV

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Seismic Analysis of Multi Storied RC Buildings- Part 4