Seismic Analysis and Design of Structures

8/17/2019 Seismic Analysis and Design of Structures

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analysis

and design ofstructures

Presented by:Pavan Patchigolla, MTech,

Jr. structural Engineer,Metey Engineering and consultancy pvt ltd.


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Lecturer’s profle• Name : Pavan Patchigolla• Quali cation : MTech in Co puter aided structural Enginee• Designation : !tructural engineer• Area of interest : Tall buildings, Precast prestressed concrete

structures, co posite structures and co positeaterials, earth"ua#e resistant designs, $E%.

• Publications : Codal provisions on connections in precastconstruction, &E'EC() *+ -, anglore.

•

Computer skills Profcient in / progra ing languages 0c, C11, P2T3(), M%TL% ,

45!6%L %!5C7 and 8 so9t ares 0!%P*+++, ET% !, !T%%'7• Experience

'esigned, revie ed and e;ecuted < structures hich includeshigh=rise, industrial, precast concrete, co posite, insulated all paneltype, boundary poles and alls

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P%T3 &E%A5)@ !6P&EMEC(6&T 4E&'5CT..

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E%&T3B6%AE &E45E :

•

hat are Earth"ua#es D• &easons behind occurrence D• hy seis ic onation is re"uired D• Earth"ua#es and buildings:

• !o e devastations o9 poorly engineered buildings during past earth"ua#es.• EFects o9 Earth"ua#es on buildings.• Codal provisions to sa9eguard buildings.• 3o to a#e buildings ft 9or better seis ic per9or ance D• hy buildings are to be designed 9or respective seis ic Gonation D• 3o to reduce eFects o9 Earth"ua#es on buildings 0Earth"ua#e proo9 structures7 D• Care to be ta#en hile construction.• Co parison o9 "uantities o9 steel and concrete 9or a building designed 9or ()E 55 and

()E 555.

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!o e devastations o9 )on=engineered andpoorly engineered buildingsH

• $loor and roo9 collapsepossibly due load bearing all9ailure in shear and out=o9=plane and high inertia loads9ro &C slabs, MuGaFarabad,2 ! "as#mir eart#$uake%

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!o e devastations o9 )on=engineered and poorly engineeredbuildingsH

&uge 'ater tank 'as present ont#e top of multi(storey building%

Presence of bottom soft story%

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Presence of irregularities%

Pan caking failure%

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Before

After


Presence of irregularities%

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NEPA)

EA*+&Q,A"E+-DA. 2!(Apr(

2 /!0 1 %3!o e devastations o9 )on=engineered and

poorly engineered buildingsH

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Some de4astations of Non(engineered andpoorly engineered buildings5

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)earning from pasteart#$uakes( Seismic

6onation map of 7ndia%

• ith period, the seis icGonation ap changes itsseis ic Gones are 9re"uentlyrevised based on sei icactivity observed.

• 59 a particular area is in()E 555, it ay get revised

to ()E 54 in ne;t revision.• Let your buildings in and

around &aKah undry getsdesigned to at least 9or Gone555.

METE2 Engineering and consultancy Pvt L

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5n9or ation on seis ic Gonation..

()E )%ME %&E%

()E 55 --

()E 555 *?

()E 54 <

()E 4 *

%s per statistics and current Gonation ap,?+ o9 land ass is prone to earth"ua#e and *> ? METE2 E)@5)EE&5)@ %)' C()!6LT%)C2


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%n overvie ..• hat are earth"ua#es D

• % sudden violent sha#ing o9 ground, typicallycausing great destruction, as a result o9

ove ents ith in the earth’s crust or volcanicaction.

• hy Earth"ua#es D• hen t o bloc#s o9 roc# or t o plates rub against

each other results in enor ous a ount o9 energyhich causes the ground sha#e.

• %s an e;a ple, the energy released during huK0*++ 7 earth"ua#e is about -++ ti es or orethan -/ ato bo b on 3iroshi a.

'5P !L5P %)' !T&5AE !L5P ($ PL%)E! C%6!E! E%&T3B6

3( E%&T3B6%AE &E@&(6)' D.

METE2 Engineering and consultancy Pvt Ltd

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%n overvie ..• 3o Earth"ua#es are easured D

• M%@)5T6'E 0a "uantitative ter 7 is easured on ost co oninstru ent N&ichter scaleO. 5t is a easure on the a ount o9 energyreleased during a "ua#e.

• 5)TE)!5T2 0a "ualitative ter 7 is ostly co only easured on scalecalled NMercalli scaleO. 5t is the easure o9 the actual sha#ing o9 earth.

8roup 1agnitude Annual a4erage number

@reat < and higher

MaKor I=I. <

!trong ?=?. *+

Moderate /=/. dayR M =*: Qday

)6M E& ($ E%&T3B6%AE (CC6&&5)@ PE& 2E%&.

METE2 Engineering and consultancy Pvt L

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5)TE)!5T2 &%T5)@ &EM%&A 5 )(T $ELT )ot 9elt e;cept by a very 9e under especially 9avorable conditions.

55 ea# $elt only by a 9e persons at rest, especially on upper Soors o9 building.

555 ea#$elt "uite noticeably by persons indoors, especially on upper Soors o9 buildings. Many peopledo not recogniGe it as an earth"ua#e. !tanding otor cars ay roc# slightly. 4ibrations si ilar

to the passing o9 a truc#. 'uration esti ated.

54 Light$elt indoors by any, outdoors by 9e during the day. %t night, so e a a#ened. 'ishesindo s, doors disturbedR alls a#e crac#ing sound. !ensation li#e heavy truc# stri#ing

building. !tanding otor cars roc#ed noticeably.

4 Moderate $elt by nearly everyone. Many a a#ened. !o e dishes, indo s bro#en. 6nstable obKectsoverturned. Pendulu cloc#s ay stop.

45 !trong $elt by all, any 9rightened. !o e heavy 9urniture oved. % 9e instances o9 9allen plaster.'a age slight.

455 4ery strong'a age negligible in buildings o9 good design and construction. !light to oderate in ell built

ordinary structures. Considerable da age in poorly built or badly designed structures. !o echi neys bro#en.

4555 !evere'a age slight in specially designed structures. Considerable da age in ordinary substantial

buildings ith partial collapse. 'a age g reat in poorly built structures. $all o9 chi neys, 9actorystac#s, colu ns, onu ents, alls. 3eavy 9 urniture over turned.

5 4iolent'a age considerable in specially designed s tructures. ell designed 9ra e structures thro nout o9 plu b. ' a age great in substantial buildings, ith partial collapse. uildings shi9ted oF

9oundations.

E;tre e !o e ell built ooden structures destroyed. Most asonry and 9ra ed structures destroyedith 9oundations. &ails bent

5 E;tre e$e , i9 any0 asonry7, structures re ain standing. ridges destroyed. road fssures in ground.

6nderground pipelines co pletely out o9 service. Earth slu ps and land slips in so9t ground.&ails bent greatly.

55 E;tre e 'a age total. aves seen on ground sur9aces. Line o9 sight and level distorted. (bKects thro nup ard into air.

M%@)5T6'E ME&C5)TE)

*.+ 5

*.+=*. 55=

8.+=8. 555

-.+=-. 54=4

/.+=/. 4=45

?.+=?. 45=4

I.+=I. 455=4

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B6E!T5()! DDD

• hat happens i9 a B6%AE reaches your areaDD• %re you living in a !%$E& 65L'5)@ DD• A)( 5T. 5t is your &5@3T.• 3o to !%$E @6%&' your building DD

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hat are 5ndian seis ic codes D

• !eis ic codes are uni"ue to a particular region or country.• Provides guidelines 9or sa9eguarding the buildings and

structures considering various engineering aspects.• Their intention:

N'o not ensure N- DA1A8E during earth"ua#es but to thee;tent possible, ENS,*E that the structures are able torespond to earth"ua#e sha#ings o9 moderate intensities

ithout S+*,C+,*A) DA1A8E and heavy intensitiesithout +-+A) C-))APSE . O• !o e standards:

• 5! < 8, *++* 0P%&T=57, 5ndian standard criteria 9or earth"ua#eresistant design o9 structures.

• 5! -8*?, 8, 5ndian standard code o9 practice 9or earth"ua#eresistant design and construction o9 buildings.

• 5! 8 *+, 8, 5ndian standard code o9 practice 9or ductile detailing

o9 rein9orced concrete structures subKected to seis ic 9orces./> *> ? METE2 E)@5)EE&5)@ %)' C()!6LT%)C2


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E$$ECT! ($ E%&T3B6%AE! () &C 65L'5)@!..• &ein9orced concrete0&C7 building syste s

co prises o9 &C colu ns and connectingbea s hich is called &C $ra e.

• This &C $ra e participates in resisting theearth"ua#e 9orces. y bending in plane orout=o9 plane.

• Earth"ua#e sha#ing induces inertia 9orcesin Soor levels o9 building.

• These 9orces travel do n ards 0load

path7 to 9oundations via slabs, bea s andcolu ns respectively.

• Masonry 05nfll7 alls tend to resists theove ent and stops hen their ability to

carry earth"ua#e sha#ing e;ceeded.

E99EC+ -9 7N97)) :A))S 7N *C 9*A1ES

1-;E1EN+S -9 *C 9*A1ES

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Care to be ta#en hile construction 0 ea s7..

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Care to be ta#en hile construction 0Colu ns7..

@E)E&%L %&&%)@EME)T ($&E5)$(&CEME)T 5) C-),1NS

L5)A %&&%)@EME)T 5) C-),1NS

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Care to be ta#en hile construction 0Colu ns7..

!T5&&6P %&&%)@EME)T 5) C-),1NS 3((A! 5) C-),1NS

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Care to be ta#en hile construction 0 ea =Colu n Koint7..


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(pen ground story eFects..

T2P5C%L -PEN 8*-,ND S+-*.65L'5)@

!($T !T(&E2 %$$ECT! 5) -PEN8*-,ND S+-*. 65L'5)@!

• Li#e a hu an body ith a heavy upper body and ea# legs.

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TEC3)5B6E! E%&T3B6%AE P&(($ 65L'5)@!..

$&5CT5() DA1PE*S 45!C(6! DA1PE*S

• Though a costly aFair, can be achieved by '%MPE&! and %!E 5!(L%T(&!.

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TEC3)5B6E! E%&T3B6%AE P&(($ 65L'5)@!..

25EL'5)@ DA1PE*S


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!u ary or points to be re e bered..

!.)( P(5)T 'E!C&5PT5() 5M%@E

E%&T3B6%AE &E!5!T%)T'E!5@) D

T3E 65L'5)@ 3%! T( E 'E!5@)E' %!PE& 5! < 8:*++*.

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!.)( P(5)T 'E!C&5PT5() 5M%@E

* C()!5'E&%T5() ($()%T5().

'E!5@) ($ T3E 65L'5)@ 3%! T(E '()E $(& ()E 555 %! PE& 5!< 8:*++*, $(& &%J%3M6)'&2

%&E%.

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!.)( P(5)T 'E!C&5PT5() 5M%@E

8 !T&()@ C(L6M) = E%AE%M!.E%M !5 E !3(6L' )(T E M(&E

T3%) C(L6M) !5 E.

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!.)( P(5)T 'E!C&5PT5() 5M%@E

- (PE) @&(6)'!T(&E2.

!T5LT $L((& C(L6M)! !3(6L' E'E!5@)E' $(& *./ T5ME! ($ $(&CE!( T%5)E' $&(M %)L%2!5! %! PE& 5!

< 8:*++*.

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!.)( P(5)T 'E!C&5PT5() 5M%@E

/ 3((A 'ET%5L!.

8/ 'E@&EE 3((A! T( EM%'E $(& !T5&&6P! 5)E%M! %)' C(L6M)! %!

PE& 5! 8 *+: 8. T35! 5!

1-S+ 71P-*+AN+ .

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!.)( P(5)T 'E!C&5PT5() 5M%@E

I C()C&ETE !T&E)@T30B6%L5T27 &EP(&T.

!T&E)@T3 ($ C()C&ETE T( EC3ECAE' 35LE C()!T&6CT5() %)'

&EP(&T! T( E !6 M5TTE' T('E4EL(PE&. %! PE& 5! -/?:*+++,

M5)5M6M @&%'E ($ C()C&ETE T( E6!E' 5! M*+0'E!5@) M5 7. C(L6M)!

T( E 'E!5@)E' $(& % M5)5M6M@&%'E ($ M*/.

C-NC*E+E 17= NEEDS +-


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!.)( P(5)T 'E!C&5PT5() 5M%@E

< PEE& &E45E '()E D'E!5@)! P&('6CE' 2 % C()!6LT%)T

%&E T( E C3ECAE' 2 %)(T3E&C()!6LT%)T.

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&e9erences to be ade:

• !eis ic design o9 &C and Masonry structures W Paulayand Preistly

• @eotechnical earth"ua#e engineering W !teven L Ara er•

Criteria 9or earth"ua#e resistant design o9 structures 5!< 8:*++*, part =

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. asics o9 earth"ua#es

Table o9 contents• 'efnition and causes o9 earth"ua#es• Continental dri9t theory and plate tectonics• $aults and types• @eo etric notation• Earth"ua#e aves• Characteristics o9 earth"ua#e and aFecting 9actors• Measure ents o9 earth"ua#es

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'efnition and causes o9 earth"ua#es:

• !udden rapid sha#ing o9 earth• 'ue to rupture in earth’s crust• 'isturbance o9 elastic e"uilibriu o9 roc# ass• MaKor and inor sources o9 earth"ua#es

• Tectonic activity 0 aKor7• 4olcanic activity 0 inor7• Landslides 0 inor7• ursting in ines 0 inor7• )uclear e;plosions 0 inor7

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Continental dri9t theory and plate


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Continental dri9t theory and platetectonics :

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• !i ilarity bet een the coast lines• Proposed by egener in +.• **/ billion years ago, earth had only one large continent 0land

ass7 called NPangaeaO• Plate tectonic theory began to evolve based on the continental

dri9t theory• Convective currents in the crust o9 earth led to the separation o9

the super continent• Plate tectonics e;plains the ove ent o9 plates hich egner

has 9ailed to e;plain ithout addressing the cause o9 ove ent


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C()4ECT54E C6&&E)T!


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$aults and types :

• $aults• )e or pre=e;isting oFsets in the geologic structure o9 the crust are 9aults

• $ault geo etry• The orientation o9 the 9ault plane is described by its stri#e and dip.

• $ault ove ent• 'ip slip ove ent

• Move ent occurs along dip vector 0reverse and nor al7• !tri#e slip ove ent

• Move ent occurs parallel to stri#e vector 0&ight and le9t7• (bli"ue slip

• Move ent ith both dip=slip and stri#e=slip co ponents

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!an%ndreas 9ault 0Trans9or 9ault7


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$ault ove ent

@ i i 9 h" #


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@eo etric notation o9 earth"ua#es :

• $ocus:•

Point at hich 9ault rupture happens• Epicenter:

• Point on earth’s sur9ace obtained by Koining center o9earth and 9ocus

• 3ypo=central distance:• 'istance bet een 9ocus and epicenter

• Epi=central distance:• 'istance bet een recording station and

• Types o9 earth"ua#es:• !hallo earth"ua#e W $ocal depth I+ #• Moderate earth"ua#e W $ocal depth I+ W 8++ #• 'eep earth"ua#e W $ocal depth U 8++ #

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-

Earth’ssur9ace

. Center o9 earth*. $ocus or hypocen8. Epicenter-. (bserver’s point or

station

E h" #


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Earth"ua#e aves:

• T o types o9 seis ic aves• ody aves and sur9ace aves• ody aves are 9urther classifed in to t o types.• P= aves 0longitudinal7, != aves 0transverse7.• !ur9ace aves W 5nteraction bet een body aves and

surfcial layers o9 earth.• !ur9ace aves are classifed in to t o types, Love aves

and &aleigh aves.

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ave echanis ave echanis


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ody aves !ur9ace aves

E th" #


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Earth"ua#e aves:• P = aves are analogous to sound

aves and hence cannot travel throughsolids and li"uids• ! W aves travels through the ediu

causing shear de9or ations.• hy P W aves reach the ground 9aster

than any other aves D•

ecause, geologic aterials are strong inco pression.

• They produce pea# a plitudes as theytravel along sur9ace o9 earth thatdecrease e;ponentially ith depth.

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%ccelerogra

Characteristics o9 earth"ua#es aves =


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aFecting 9actors :• @eneral characteristics o9

aves:• % plitude 0P@%, P@4, P@'7• 'uration• $re"uency content

• % plitude: The a;. distanceattained by a particle or obKect9ro ean position.

• 'uration : Ti e interval o9strong ground otion.

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% plitude o9 a

'uration

Characteristics o9 earth"ua#es aves =


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aFecting 9actors :• $re"uency content : Measure o9

predo inant 9re"uency.• Each o9 these aFect the response o9

structure.• P@% W eFects the a plitude o9 structural

vibration• 'uration W !everity o9 sha#ing•

$re"uency W response characteristics o9structure• $actors aFecting these aves are,

agnitude, distance, geology, localsoil conditions, source echanis .

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$re"uency o9 ave

Buantifcation o9 earth"ua#es :


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Buantifcation o9 earth ua#es :

• 5ntensity, Magnitude are t o odes o9 "uanti9ying the

earth"ua#e.• 5ntensity

• Measure o9 strength o9 sha#ing• Measured on scale called Modifed Mercalli intensity scale

• Magnitude• Measure o9 physical sha#ing or easure o9 a ount o9 energy released• Magnitude o9 earth"ua#e doesn’t change but intensity changes• Measured in various ter s called &ichter local agnitude, body ave

agnitude, sur9ace ave agnitude and o ent agnitude.• Mo ent agnitude represents the energy released during earth"ua#e.

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Buantifcation o9 earth"ua#es :


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Buantifcation o9 earth ua#es :

• &ichter local agnitude:• ood %nderson seis o eter.• E"uals to logarith ic value o9 a plitude ith a base value o9 +.• % plitude value shall be easured on ood %nderson

seis o eter at ++# 9ro epicenter o9 earth"ua#e.• )ot al ays appropriate

•

ody ave agnitude• !ur9ace ave agnitude• Mo ent agnitude

• Esti ates the total a ount o9 energy released

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&5C3TE&!C%LE

!eis o eter

Magnitude saturation


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Magnitude saturation• $or strong earth"ua#es, the easured characteristics

beco es less sensitive co pared to s allerearth"ua#es.

• This eFect is agnitude saturation.• ody ave and &ichter agnitude saturates at ? to I• !ur9ace ave agnitude saturates at a value o9 <• Mo ent agnitude scale is the only scale hich does

not saturate.

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here,

5)TE)!5T2 &%T5)@ &EM%&A 5 )(T $ELT ) 9 l b 9 d i ll 9 bl di i

M%@)5T6'E ME


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5 )(T $ELT )ot 9elt e;cept by a very 9e under especially 9avorable conditions.

55 ea# $elt only by a 9e persons at rest, especially on upper Soors o9 building.

555 ea#$elt "uite noticeably by persons indoors, especially on upper Soors o9 buildings. Many

people do not recogniGe it as an earth"ua#e. !tanding otor cars ay roc# slightly.4ibrations si ilar to the passing o9 a truc#. 'uration esti ated.

54 Light$elt indoors by any, outdoors by 9e during the day. %t night, so e a a#ened. 'ishes

indo s, doors disturbedR alls a#e crac#ing sound. !ensation li#e heavy truc#

stri#ing building. !tanding otor cars roc#ed noticeably.4 Moderate $elt by nearly everyone. Many a a#ened. !o e dishes, indo s bro#en. 6nstableobKects overturned. Pendulu cloc#s ay stop.

45 !trong $elt by all, any 9rightened. !o e heavy 9urniture oved. % 9e instances o9 9allenplaster. 'a age slight.

455 4ery strong'a age negligible in buildings o9 good design and construction. !light to oderate in

ell built ordinary structures. Considerable da age in poorly built or badly designedstructures. !o e chi neys bro#en.

4555 !evere'a age slight in specially designed structures. Considerable da age in ordinary

substantial buildings ith partial collapse. 'a age great in poorly built structures. $allo9 chi neys, 9actory stac#s, colu ns, onu ents, alls. 3eavy 9urniture over turned.

5 4iolent'a age considerable in specially designed structures. ell designed 9ra e structures

thro n out o9 plu b. 'a age great in substantial buildings, ith partial collapse.

uildings shi9ted oF 9oundations.E;tre e !o e ell built ooden structures destroyed. Most asonry and 9ra ed structuresdestroyed ith 9oundations. &ails bent

5 E;tre e$e , i9 any0 asonry7, structures re ain standing. ridges destroyed. road fssures inground. 6nderground pipelines co pletely out o9 service. Earth slu ps and land slips

in so9t ground. &ails bent greatly.

55 E;tre e 'a age total. aves seen on ground sur9aces. Line o9 sight and level distorted.(bKects thro n up ard into air.

*.+

*.+=*.

8.+=8.

-.+=-.

/.+=/.

?.+=?.

I.+=I.

U *> ? METE2 E)@5)EE&5)@ %)' C()!6LT%)C2

!eis ogra s and seis ograph


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!eis ogra s and seis ograph

/> *> ? METE2 E)@5)EE&5)@ %)' C()!6LT%)C2

• Earth"ua#e is rando sha#ing o9 ground• Measured in )=!, E= and 6=' directions 9or

convenience• )=! and E= are horiGontal aves here as 6=

' is a vertical ave• 6sually, the ground otion 0acceleration7 is

recorded and hence the data is also calledaccelerogra

• The recording data is called seis ogra• The instru ent used 9or recording the ground

otion is seis o eter

3oriGontal avrecording

4ertical averecording

* %nalysis 9or earth"ua#e 9orces


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. %nalysis 9or earth ua#e 9orces

Table o9 contents• E"uivalent static analysis• Modal analysis• &esponse history or ti e history analysis•

&esponse spectru analysis

/> *> ? METE2 E)@5)EE&5)@ %)' C()!6LT%)C2


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E"uivalent static analysis M


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E uivalent static analysis

• %pproach defnes earth"ua#e

9orces acting typically defned 9ora seis ic response spectru0linear elastic design7

• %pplicable to buildings respondingin 9unda ental translational ode

• !pecifcally applicable to lo =risebuildings

• $5 E' base support• )on=t isting o9 structures/> *> ? METE2 E)@5)EE&5)@ %)' C()!6LT%)C2

M9u

'esign spectr

'yna ic analysis


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yna ic analysis

• hat is dyna ic analysis D•

%nalysis o9 a structure or structural ele ent under the 9orce that changesith ti e.• hat are dyna ic 9orces D

• Earth"ua#e 9orces, ind 9orces, achinery and blast 9orces.• hy is dyna ic analysis D

• 6nder, constantly varying 9orces or dyna ic 9orces li#e earth"ua#e andind 9orces, dyna ic analysis is per9or ed to ensure sa9ety.

• 3o dyna ic analysis is done.D• 5dealiGation o9 the structure to lu ped ass syste and fnally by

establishing e"uilibriu under dyna ic 9orces.

/> *> ? METE2 E)@5)EE&5)@ %)' C()!6LT%)C2

'efnitions o9 dyna ic analysis


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efnitions o9 dyna ic analysis

• 'a ping•

The eFect o9 internal 9riction, i per9ect elasticity o9 aterial, slipping,sliding in reducing the a plitude o9 vibration.• !tiFness

• &esistance o9 an obKect under unit de9or ation.• % plitude o9 vibration

• The a;i u displace ent obtained 9ro the structure under 9ree or9orced vibration.

• )atural period• The natural period o9 a structure is its ti e period o9 un=da ped 9ree

vibration.

/> *> ? METE2 E)@5)EE&5)@ %)' C()!6LT%)C2



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efnitions o9 dyna ic analysis• Mode

•

%ll the asses o9 structure attain a;i u values o9 displace ents androtations and pass through e"uilibriu positions si ultaneously.• Mode shape

• The a plitude o9 ass o9 a structure in a particular ode.• Modal participation 9actor

• The a ount by hich a ode contributes to the overall vibration o9structure.

• Modal ass• 5t is a part o9 total seis ic ass o9 structure that is eFective in

corresponding ode.

/> *> ? METE2 E)@5)EE&5)@ %)' C()!6LT%)C2



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efnitions o9 dyna ic analysis• one 9actor 0 7:

•

The perceived a;i u seis ic ris# characteriGed by a;i uconsidered earth"ua#e 0MCE7 in the Gone o9 earth"ua#e in hich thestructure is standing.

• 5 portance 9actor 057:• % 9actor used to obtain design seis ic 9orces depending on the post

earth"ua#e 9unctional need, historic or econo ic i portance.•

&esponse reduction 9actor 0&7:• % 9actor to a#e the structure to re ain elastic during its response to

earth"ua#e shall be reduced to obtain design earth"ua#e 9orce.• !tructural response 9actor0!a>g7:

• % 9actor denoting the acceleration o9 the structure subKected to groundsha#ing./> *> ? METE2 E)@5)EE&5)@ %)' C()!6LT%)C2

Types o9 dyna ic analysis


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yp y y

• 4ibration analysis o9 structure is the base part 9or dyna ic analysis.•

$our types o9 analysis 9or vibration:• 6n=da ped 9ree vibration• 'a ped 9ree vibration• 6n=da ped 9orced vibration• 'a ped 9orced vibration

• Types o9 dyna ic analysis:• Linear dyna ic analysis

• &esponse spectru analysis• Linear ti e history analysis

• )on=linear dyna ic analysis• )on=linear ti e history analysis

/> *> ? METE2 E)@5)EE&5)@ %)' C()!6LT%)C2

5dealiGationM%!! W!P&5)@W

A


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M%!! W!P&5)@W'%MPE&

!5)@LE '($ L6MPE' M%!!!2!TEM

C

M

M

A C'a per and spring illoppose the disturbing 9orce

along ith inertial 9orcee;erted by the ass o9 the

obKect./> *> ? METE2 E)@5)EE&5)@ %)' C()!6LT%)C2

'yna ic e"uilibriu


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• 'e’%le bert’s Principle:• Moving ass generates inertia 9orces opposing the

otion.

F(t)

'yna ic e"uilibriu e"uation is,

5nertial 9orce

'a ping resisting9orce Elastic resisting 9orce

/> *> ? METE2 E)@5)EE&5)@ %)' C()!6LT%)C2

)(t F kuuC um =++

um kuuc

Types o9 vibrations


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• 6n=da ped 9ree vibration:

• 'a ped 9ree vibration:

• 6n=da ped 9orced vibration:

• 'a ped 9orced vibration:

/> *> ?

yp

METE2 E)@5)EE&5)@ %)' C()!6LT%)C2

0=+ kuum

0=++ kuucum

)(t F kuum =+

)(t F kuucum =++

!olution or &esponse


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p

• 'yna ic analysis is usually done 9or single degree 9reedo

syste s and 9or ulti degree 9reedo syste s as ell.• &esponse o9 the structure is 9ound out by solving the e"uilibriu

e"uation under the respective conditions.• The e"uilibriu e"uation is solved 9or response by t o ethods:

• %nalytical ethod 0Classical ethod7•

'uha el’s integration• Trans9or s ethod 0$ourier trans9or 7• )u erical ethod 0$'M, )e ar#’s7

/> *> ? METE2 E)@5)EE&5)@ %)' C()!6LT%)C2



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p

• The response o9 the structure is easured in ave 9or under specifed boundaryconditions.

• Every ave ill have its o n properties.• Ti e period, linear 9re"uency, ave length, a plitude are the i portant properties.• % plitude is a; displace ent occurred in structure.• $re"uency is the nu ber o9 cycles present in the ave• Ti e period is inverse o9 linear 9re"uency.

/> *> ? METE2 E)@5)EE&5)@ %)' C()!6LT%)C2

u

t

λ 3= f

a



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u

t

• The response o9 the structure is easured in ave 9or under specifedboundary conditions.

• Every ave ill have its o n properties.•

Ti e period, linear 9re"uency, ave length, a plitude are the i portantproperties.• % plitude is a; displace ent occurred in structure.• $re"uency is the nu ber o9 cycles present in the ave• Ti e period is inverse o9 linear 9re"uency.

/> *> ?


METE2 E)@5)EE&5)@ %)' C()!6LT%)C2

λ 3= f

a


83/106


84/106

Mass and stiFness atri;


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M%!! M%T&5

'%MP5)@ M%T&5

!T5$$)E!! M%T&5

/> *> ? METE2 E)@5)EE&5)@ %)' C()!6LT%)C2

+−−+−

−

+−−+−

−

122

2233

33

122

2233

33

1

2

3

0

0

0

0

00

00

00

k k k

k k k k

k k

ccc

cccc

cc

m

m

m


86/106

1 2


87/106

/> *> ? METE2 E)@5)EE&5)@ %)' C()!6LT%)C2

1ω 2ω 3ω

11φ

12φ

13φ

21φ

2

2φ

23φ

1φ 2φ 3φ

Procedure


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• 'ivide X)’ ulti degree o9 9reedo syste in to X)’ single degree9reedo syste s.

• Evaluate ass and stiFness atrices.• $ind the X)’ Eigen values and X)’ Eigen vectors and each vector

having X)’ 4alues.• Calculate odal ass.

• Calculate odal participation 9actor.

/> *> ? METE2 E)@5)EE&5)@ %)' C()!6LT%)C2

∑

∑

=

== N

iini

N

iini

n

W g

W M

1

2

1

φ

φ

[ ]φ φ

φ M M

P T T

n

1=


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'yna ic analysis 9orseis ic 9orces


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'yna ic analysis 9or seis ic 9orces


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• Ti e history ethod:• Ti e history ethod o9 analysis, hen used shall be based on appropriate

ground otion and shall be per9or ed using accepted principles o9dyna ics.

• &esponse spectru ethod:• &esponse spectru ethod o9 analysis shall be per9or ed using design

spectru specifed in 5! < 8:*++*•

$ree vibration analysis or odal analysis:• 6n=da ped 9ree vibration analysis o9 the entire building shall be per9or ed

o9 the structural syste to obtain natural periods and ode shapes.

/> *> ? METE2 E)@5)EE&5)@ %)' C()!6LT%)C2

Ti e history analysis


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• !tructure is subKected to ground otion hich is a ti e history.• @round otion loo#s li#e,

• The ground otion or ti e history is the plot bet een ti e step and theacceleration o9 the ground.

• The response o9 the structure is easured under the ground acceleration.

/> *> ? METE2 E)@5)EE&5)@ %)' C()!6LT%)C2

+ / + / *+ */ 8+ 8/

=+.-=+.8=+.*=+.

++.+.*+.8+.-



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• Procedure:• Prepare ass and stiFness atrices and rite e"uation o9 dyna ic

e"uilibriu and assu e uYZ".

• Per9or odal analysis and 9ind out Eigen values 0[7 and Eigen vectors0Z7.

• Pre ultiply e"uation ith transpose o9 ode shape coe\cient atri;.

/> *> ? METE2 E)@5)EE&5)@ %)' C()!6LT%)C2

g u M KuuC u M −=++

g T T T T u M q K qC q M φ φ φ φ φ φ φ φ −=++



94/106

•

Convert X)’ ulti degree 9reedo syste to X)’ single degree 9reedosyste .• !olve each e"uation independently to get ti e history o9 each ode.• (btain the value o9 displace ent o9 each degree o9 9reedo as uYZ".• The response in each ode is a ti e history o9 displace ents.• The over all displace ent o9 the X)’ M'($ syste is at respective nodes

are calculated as,

here, i Y Soor # Y ode

/> *> ? METE2 E)@5)EE&5)@ %)' C()!6LT%)C2

k

k

ii qu φ =

+ / ,+ ,/ *+ */ 8+ 8/

=+.-

=+.*

+

+.*

+.-

(verall&esponse

+ / ,+,/*+*/8+8/=+./

+

+./

+ / ,+,/*+*/8+8/=+./

+

+./

+ / ,+,/*+*/8+8/=+./

+

+./

1q 2q 3q


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+ / ,+ ,/ *+ */ 8+ 8/

=+.-

=+.*

+

+.*

+.-

@roundacceleration

/> *> ? METE2 E)@5)EE&5)@ %)' C()!6LT%)C2

111 qφ

112qφ

113 qφ

22

1 qφ

222 qφ

22

3 qφ

1u

2u

3u

&esponse spectru analysis


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• 5n this, the 9orces are generated 9ro the elastic designspectru provided by 5! < 8:*++*.

• $orces can also be generated 9ro site specifc responsespectra generated by nor aliGing ground otions.

• Procedure 9or calculation o9 design lateral 9orces is given

in 5! < 8:*++*, clause I. *> ? METE2 E)@5)EE&5)@ %)' C()!6LT%)C2

Procedure


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• Prepare ass and stiFness atrices and rite e"uation o9 dyna ice"uilibriu and assu e uYZ".

• Per9or odal analysis and 9ind out Eigen values 0[7 and Eigen vectors0Z7.

• Calculate odal participation 9actors o9 each ode.

• Calculate the seis ic eight o9 every Soor.• Calculate design horiGontal seis ic coe\cient 9or each ode.

/> *> ? METE2 E)@5)EE&5)@ %)' C()!6LT%)C2

Q KuuC u M =++

[ ]φ φ

φ M

M P T

T

n

1=

g S

R I Z

A ak 2=

(verall&

1q 2q 3q


98/106

&esponse

/> *> ? METE2 E)@5)EE&5)@ %)' C()!6LT%)C2

111 qφ

112qφ

113 qφ

22

1 qφ

222 qφ

22

3 qφ

1u

2u

3u

1 P 2 P 3 P

Procedure


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• Calculate the design lateral seis ic 9orce at storey N5O and ode N#O.

• Convert X)’ ulti degree 9reedo syste to X)’ single degree 9reedosyste .

• !olve each e"uation independently to get response o9 each ode.• The overall response o9 the structure can be co bined by the ethod

s"uare root o9 su o9 s"uares.

/> *> ? METE2 E)@5)EE&5)@ %)' C()!6LT%)C2

ik ik k ik W P AQ φ =

( )∑=

=i

k ik ik QV

1

( )∑=

=i

k k

1

2λ λ

%n e;a ple• % si ple t o storey one bay steel 9ra e8 t


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p y yhaving each bay o9 8 and each storeyheight being 8 .

•

5!M */+ sections being used 9or bea sand colu ns as ell.• Consider a live load on each bea as

/++Ag> .• %ssu e Gone 55 0 Y +. 7.• %ssu e i portance 9actor 05 Y .+7.• %ssu e response reduction 9actor 0& Y

-.+7.• Calculate odes, ode shapes, odal

ass, odal participation 9actor, seis ic9orces 9ro response spectru ethod.

8 ts

8 ts

8 ts

/> *> ? METE2 E)@5)EE&5)@ %)' C()!6LT%)C2

!olution• Mass o9 bea ( )410*55.47*3*7850 −=


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• Mass o9 colu n

• Mass o9 storey Y Mass o9 bea 1 0* Mass o9 colu n7

• !eis ic eight•

!tiFness o9 colu n

/> *> ? METE2 E)@5)EE&5)@ %)' C()!6LT%)C2

Kg 112=

))3*500%(50(94.335 +=

( )410*55.47*3*7850 −= Kg 112=

Kg 336=

3

12 L EI

=

m N /10*58.33000

10*27.40*10*200*12

6

3

63

=

=

• Mass atri;

3360

0336


102/106

• !tiFness atri;

• Characteristic e"uation

/> *> ? METE2 E)@5)EE&5)@ %)' C()!6LT%)C2

3360

−66

66

10*32.1410*16.710*16.710*16.7

0336*10*32.1410*16.7

10*16.7336*10*16.766

66

=−−

−−λ

λ

( )0=− M K λ

• Eigen value=

410*58.5λ


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• Mode value 0circular 9re"uency7

• Eigen vector

/> *> ? METE2 E)@5)EE&5)@ %)' C()!6LT%)C2

410*82.0λ

==2.236

22.90λ ω

−== 62.162.000.100.1

21

11

2

2

1

2φ φ φ φ

φ

• Modal ass

== 05.02 M M


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• Modal participation 9actor

/> *> ? METE2 E)@5)EE&5)@ %)' C()!6LT%)C2

−==

1708.1

1708.0

1

2

P

P P

n

95.01 M M n

8. !eis ic design concepts


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Table o9 contents•

!eis ic design philosophy• !eis ic per9or ance o9 structures• !eis ic design li it states• !tructural properties and defnition o9 design "uantities

/> *> ? METE2 E)@5)EE&5)@ %)' C()!6LT%)C2

-. 'iscussion on 5! < 8: *++*


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Table o9 contents•

Ter inology• @eneral principles and assu ptions• 'esign spectru , Gone 9actor, seis ic eight,

i portance and response reduction 9actor• 5rregular buildings and re=entrant corners• 'esign lateral 9orce and its distribution• !o9t storey, de9or ation and dri9ts

/> *> ? METE2 E)@5)EE&5)@ %)' C()!6LT%)C2

Seismic Analysis and Design of Structures

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