Indo-Norwegian Training ProgrammeIndo-Norwegian Training Programme

Seismic Design of MultiSeismic Design of Multi--Storey Buildings:Storey Buildings:Seismic Design of MultiSeismic Design of Multi--Storey Buildings:Storey Buildings:

New Delhi,

26–28 May 2014

New Delhi,

26–28 May 2014

Seismic Design of MultiSeismic Design of Multi--Storey Buildings: Storey Buildings:

IS 1893 vs. IS 1893 vs. EurocodeEurocode 88

Seismic Design of MultiSeismic Design of Multi--Storey Buildings: Storey Buildings:

IS 1893 vs. IS 1893 vs. EurocodeEurocode 88

Presentation II:Presentation II:Presentation II:Presentation II:Basic Concepts of Structural Basic Concepts of Structural DynamicsDynamicsyy

D.K. Paul, FNAEEmeritus Fellow, Department of Earthquake EngineeringIndian Institute of Technology Roorkeewww iitr ac inwww.iitr.ac.in

TIME PERIOD OF VIBRATIONTIME PERIOD OF VIBRATION

Ti k b l l

TIME PERIOD OF VIBRATIONTIME PERIOD OF VIBRATION

Time taken by a system to complete one cycle of vibration

l1

stringoflengthlglT

21

extreme position

gravitytodueonacceleratig l

Time

Am

plitu

dem

DEGREES OF FREEDOMDEGREES OF FREEDOM

C.G. mmHeavy mass

Mass of tank with water and

mm

part column mass

Stiffness of circular shape 3EI/L3EI/L33

Assumed fixed at foundationlevel

pile providing

gWcWcWm SWT 21

fmT

LEIk

1;1

33

endotheratfixedendoneatfixedbeamofstiffnesstheiskwhere

Tf

kT ;

2

systemvibratorytheofperiodtimetheisTscinsystemvibratorytheoffrequencytheisf

Tankofmasslumpedtheism/

ShaftofweighttheisWWaterofweighttheisWTankofweighttheisW

systemvibratorytheofperiodtimetheisT

W

T

h flffhmaterialshaftofelasticityofulustheisE

gravitytodueonacceleratitheisgShaftofweighttheisWS

mod

shafttheofheighttheisLshaftannularofinertiaofmomenttheisI

Slab dimensions (5.0 x 5.0 x 0.1) m0.3 m

Material Properties:

E 25000000 kN/m2

3.0 m

E 25000000 kN/m

0.2

23.56 kN/m3 Z

Y

X

0.4 m

0.3

mY

0

X

y

LI

h

LIhILI

hEI

kc

b

c

c

3

66

3

yg L

hI

hb

c

2

y

h 24122

EIEIk

I

cc

b

yg L

332hh

k

y

2donacceleratixmassForceInertia

h)(2

2

yydtdonacceleratiAbsolute g

d 22

yyg

yg

yg

yydt

yddt

yd g

2

2

2

2

k

m

yyg yyg

VelocitylativeForceDamping Re

myk

yc yym

tCoefficienDampingcyc

g kyycyym 0)(

gymkyycym

EIGEN VALUE PROBLEMEIGEN VALUE PROBLEMEIGEN VALUE PROBLEMEIGEN VALUE PROBLEM

k 0

kyymkyycym

00

tbtay cossin

taykyym

sin0 tbtay cossin

k

2Time

Res

pons

e

mFig. 2 Un-damped and damped g p p

response of a SDOFS

EIGEN VALUE PROBLEMEIGEN VALUE PROBLEMEIGEN VALUE PROBLEMEIGEN VALUE PROBLEMyMKyyCyM

KyyMyMKyyCyM

0

MKtay

sin

MK

6 DEGREE OF FREEDOM6 DEGREE OF FREEDOM

THE STIFFNESSTHE STIFFNESSTHE STIFFNESSTHE STIFFNESS

IEk

isdirectionsYandXtheincolumneachofstiffnesslateralThe

y12

LIEk

Lk

xy

x

123

3

ElasticityofModulustheisEwhere

Ly

columnofheighttheisL

directionsyandxininertiaofmomenttheareIIElasticityofModulustheisE

yx ,

columnofheighttheisL

AEk

22 JGbkdkk

Lkx

whereL

bkdkkcolumns

yyxx

stiffnesstorsionaltheiskstiffnessaxialtheiskx

ModulussheartheisGSectiontheofareatheisA

.

/,

consttorsionaltheisJ

columnstheofccslabrigidtheofsizethearebd yx

Mode 1

Mode 2

Mode 3

Mode 4

Mode 5

Mode 6

Di iDi i MassMass StiffnessStiffness Time Time i di d

Time period Time period ( )( )DirectionDirection MassMass

(kN.sec(kN.sec22/m)/m)StiffnessStiffness(kN/m)(kN/m) period period

(sec)(sec)(sec) (sec)

(ETABS)(ETABS)

Translation in X Translation in X direction direction

(horizontal) (horizontal) 6.006.00 71112.071112.0 0.06000.0600 0.06100.0610

Torsional motion Torsional motion about Zabout Z--axisaxis 58.00 58.00 597349.5 597349.5 0.06200.0620 0.00690.0069

Translation in Y Translation in Y direction direction

(horizontal)(horizontal)6.00 6.00 40000.0 40000.0 0.07700.0770 0.07900.0790

( )( )

Translation in Z Translation in Z direction direction (vertical)(vertical)

6.00 6.00 4000,000.0 4000,000.0 0.00770.0077 0.00770.0077(vertical)(vertical)

EARTHQUAKE GROUND MOTIONEARTHQUAKE GROUND MOTIONCh i i f h k d iCh i i f h k d i Characteristics of earthquake ground motion areCharacteristics of earthquake ground motion are

Peak ground accelerationPeak ground acceleration Frequency content of ground motionFrequency content of ground motion Duration of shakingDuration of shaking

Koyna Earthquake of December 11, 1967

RESONSE SPECTRUMRESONSE SPECTRUM

gymkyycym

xm

k

y

11T

fkmT 1;

21

Sa RESPONSE SPECTRARESPONSE SPECTRA

PGA

Period (sec)

PGA

m

Tf

kmT 1;

21

k

PGA

SELECTION AND DESIGN GROUND SELECTION AND DESIGN GROUND MOTIONSMOTIONS

MODIFYING EXISTING GROUND MOTIONMODIFYING EXISTING GROUND MOTION

1.1. Matching predominant ground periodMatching predominant ground period2.2. Ground parameter scaling (PGA, PGV .. )Ground parameter scaling (PGA, PGV .. )

SPECTRUM COMPATIBLE GROUND MOTIONSPECTRUM COMPATIBLE GROUND MOTION

1.1. WAVEGEN Code is used to generate spectra compatible WAVEGEN Code is used to generate spectra compatible d tid tiground motionground motion

SPECTRA COMPATIBLE GROUND MOTION

Northridge earthquake

tion

(g)

0 0

0.1

0.2

time (sec)0 5 10 15 20

acce

lera

t

-0.2

-0.1

0.0

time (sec)0 5 10 15 20

MDOFS MDOFS -- MULTI DEGREE OF MULTI DEGREE OF FREEDOM SYSTEMFREEDOM SYSTEM

MDOFS - Multi degree of Freedom systemMDOFS Multi degree of Freedom system

0 zKzM

MpK 2

21 1

pMK

p

A

)()( ttz )()( ttz

m rjj

n )(

yCy

mp r

rjj

m

j

jjj

rrr

2)(

1

12

dtpy

p

mr

t

on

rjj

m

ir

sin1

2)(

)(

1

pm orrjj

j

2)(

1

m rn

r )()()( ttz

dtpy

pm

mz r

t

orrjj

n

j

jjj

in

ri

sin1

2)(

1

1

1

rdr

rrvr

ri

r

ri SCSC

pz )(

1)(

max)( 1

r

rar

ri

ri SCx )(

max)(

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