Note-Overview of Seismic Design of Structures

8/20/2019 Note-Overview of Seismic Design of Structures

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A Note on “Overview of Earthquake Design of

Structures”

1. Introduction to Earthquake Engineering

1.1 What is Earthquake

1. Da!ages due to Earthquake

1." Discussion

. Introduction to D#na!ics of Structures

.1 Introduction

. SDO$

." %DO$

". Earthquake Engineering & Ana'#sis and Design As(ects

".1 Introduction". Earthquake Waves and )ecord ti!e histor#

"." Design As(ects

".* Deve'o(!ent of Ana'#tica' %ode'

".+ Ana'#sis of Structures

"., Se'ection of Nu!-er of !odes

". %issing %ass /orrection

".0 /o!-ination of %oda' )es(onse

". Ducti'e Detai'ing As(ects

".12 Ste(s to /arr# out Earthquake Ana'#sis of Structures

*. )eferences

Note on “Overview of Earthquake Design of Structures” & 21


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Section 13 Introduction Earthquake Engineering

1.1 What is Earthquake4

An earthquake is an oscillatory, sometimes violet movement of the ground surface

that follows a release of energy in the Earth’s crust !his energy can "e generated "y a

sudden dislocation of segments of the crust, a volcanic eru#tion, or man$made

e%#losion &ost of the destructive earthquakes, however, are caused "y dislocation of

crust '1( !his earth motion is caused due to either sudden sli# or slow cree# of the

faults A fault is a fracture in the Earth crust along with two "locs sli# relative to each

other

A Note on “Overview of Earthquake Design of Structures” & 21

$igure 1.1 5ectonic 6'ate 7oundaries 89.


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1. Da!ages due to Earthquake

!he earth movement caused varia"le damages "ased on the "ehavior of the structural

characteristics

1..1 :round 7ehavior

!he effects of violent shaking on the ground are tem#orarily to increase lateral and

vertical forces, to distur" the inter$granular sta"ility of non$cohesive solid and to im#ose

strains directly on surface material locally if the fault #lane reaches the surface )hear

movements in the ground may "e at the surface or entirely "elow it *f the earthquake

fault reaches the surface, #ermanent movements of considera"le magnitude occur+ this

can amount to several meters in large earthquakes


$igure 1. 5#(es of $au'ts 819.


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1.. Structura' Da!ages

ue to violet motion of the earthquake there is a##recia"le dis#lacement of the to# earth,which led to damages to the structural elements


$igure 1." Da!age in the (ort of ;o-e< =a(an< 1+ 8"9

$igure 1.* >ndue Sett'e!ent and Da!age /aused to Structure due to

?iquefaction


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Page 8 of 3A Note on “Overview of Earthquake Design of Structures” & 21

$igure 1., Da!ages to the 7ui'ding Structure< ;o-e< =a(an< 1+.

$igure 1.+ Da!age to /ranes in the (ort of ;o-e< =a(an< 1+.


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$igure 1. Da!ages to the Storage Shed< 7hu@< India< 221.

$igure 1.0 Da!ages to 6etro' 6u!( Station< Wong< 7hu@< India< 221.


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1." Discussion

!he damages caused due to earthquake are varied Although this damages cannot "e

avoid, "ut it can "e reduce or lessen "y taking measures in the design and detailing of thestructures !he earthquake engineering deals with the earthquake resistant design of

structures, #assive or active devices to reduce the effect on the structures and retrofitting

measures for the structures


/onventiona' 7ui'dings Iso'ated 7ui'dings

$igure 1. >se of 6assive Energ# Devices to reduce Da!age to 7ui'dings 8"9


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!o understand the "ehavior of structure su"-ected to earthquake, one needs to know the "asics of )tructural ynamics *n the ne%t section ., the "asics a"out the structural

dynamics are #rescri"ed /hereas in the )ection 3, a thrust a made to give knowledge

a"out the earthquake or Earthquake analysis and design of structures

*n order to understand the structural "ehavior, there is enormous literature availa"le on

these to#ics )ome of the literatures for reference are0

1.".1 7ooks

12 Anil 4ho#ra .55.2, ynamic of structures7, #rentice hall of *ndia #rivate

limited, ew elhi

.2 &ario Pa9 1:8;2, )tructural dynamics7, 4ay /4lough = ?ose#h #en9ien 1:;@2, ynamic of structure7, &craw$hill

ogakusha Btd, !okyo, ?a#an

1.". We-sites

12 www nisee"erkeleyedu

.2 wwwe-seorg

32 wwwicivilengineercomCEarthquakeDEngineeringC)tructuralDynamicsC

2 wwwmceer"uffaloedu



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Section 3 Introduction to Structura' D#na!ics

.1 Introduction

!he term dynamic may "e defined sim#ly as time varying+ thus a dynamic load is any

load of which its magnitude, direction, andCor #osition varies with time )imilarly, thestructural res#onse to a dynamic load, ie, the resulting stresses and deflections, is also

time varying, or dynamic '6(


$igure .1 /haracteristics and Source of D#na!ic ?oads.8,9


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Almost any ty#e of structural system may "e su"-ected to one form or another of dynamic

loading during its lifetime From an analytical stand#oint, it is convenient to divide

#rescri"ed or deterministic loadings into two "asic categories, #eriodic and non#eriodic)ome ty#ical forms of #rescri"ed loadings and e%am#les of situations in which such

loadings might "e develo#ed are shown in Fig .1 As indicated in this Figure, a #eriodic

loading e%hi"its the same time variation successively for a large num"er of cycles !hesim#lest #eriodic loading has the sinusoidal variation shown in Fig 11a, which is termed

sim#le harmonic+ loadings of this ty#e are characteristic of un"alanced mass effects in

rotating machinery Gther forms of #eriodic loading, eg, those caused "y hydrodynamic #ressures generated "y a #ro#eller at the stern of a shi# or "y inertial effects in

reci#rocating machinery, frequently are more com#le% However, "y means of a Fourier

analysis any #eriodic loading can "e re#resented as the sum of a series of sim#le

harmonic com#onents+ thus, in #rinci#le, the analysis of res#onse to any #eriodic loadingfollows the same general #rocedure'1(

on#eriodic loadings may "e either short duration im#ulsive loadings or long durationgeneral forms of loads A "last or e%#losion is a ty#ical source of im#ulsive load+ for such

short duration loads, s#ecial sim#lified forms of analysis may "e em#loyed Gn the other

hand, a general, long duration loading such as might result from an earthquake can "etreated only "y com#letely general dynamic analysis #rocedures '1(

A structural dynamic #ro"lem differs from its static loading counter#art in two im#ortant

res#ects !he first difference to "e noted, "y definition, is the time varying nature of thedynamic #ro"lem


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..1 $ree Ci-ration Ana'#sis


$igure . SDO$ s#ste! and $ree 7od# Diagra!.

Ecer(t 5aken fro! )eference 7ookB


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.. $orced Ci-ration Ana'#sis


$igure ." SDO$ s#ste! under $orcing $unction and $ree 7od# Diagra!.Ecer(t 5aken fro! )eference 7ookB


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$igure .* $orced vi-ration res(onse.


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." %u'ti&Degree of $reedo! S#ste! %DO$B

&ost of the "uildings, we have degree of freedom more than one, hence in order to studythe dynamic "ehavior of the "uilding under earthquake e%citation, we need to study the

multi$degree of freedom system'@(


$igure .+ A!('itude res(onses for SDO$ S#ste!.

$igure ., Si!('e %ode' of %DO$ s#ste! $ra!ed StructureB 8+9.


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$igure . $ree 7od# Diagra! for %DO$ s#ste! 8+9.


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Ising the )u"$iteration !echnique, the Eigen Jalues Frequency2 and Eigen Jectors&ode )ha#es2 can "e evaluated


$igure .0 %ode Sha(e for the %DO$ s#ste! 8*9.


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!he forced vi"ration analysis for the structure su"-ected to dynamic loads can "e #erformed using any of the #rocedures0

1 !he time history method

. !he res#onse s#ectrum method

*n the ne%t section, we will talk a"out detail #rocedure to carry out the !ime history

Analysis and >es#onse )#ectrum Analysis, su"-ected to earthquake e%citation



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Section "3 Earthquake Engineering & Ana'#sis and

Design As(ects

".1 Introduction

*n 1:3@, 4harles F >ichter of the 4alifornia *nstitute of !echnology develo#ed the

>ichter magnitude scale to measure earthquake strength !he magnitude, &, of an

earthquake is determined from the logarithm to "ase ten of the am#litude recorded "y

seismometer

!he damage to the structures and environmental features due to the earthquake is

measured "y &odified &ercalli *ntensity )cale An *ntensity scale consists of a series of

res#onses, such as #eo#le awakening, furniture moving, and chimneys "eing damaged

!he modified &ercalli scale consists of 1. increasing levels of intensity e%#ressed as

>omans numerals following the initials &&2 that range from im#erce#ti"le shaking to

catastro#hic destruction !he lower num"ers of the intensity scale generally are "ased on

the manner in which the earthquake is felt "y #eo#le !he higher num"ers are "ased on

o"served structural damage !he numeral do not have mathematical "asis and therefore

are more meaningful to nontechnical #eo#le than those in technical fields


$igure ".1 5#(ica' Seis!o!eter A!('itude 5race 819.


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$igure ". %odified %erca''i Intensit# Sca'e819.


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". Earthquake Waves and )ecord ti!e histor#

Earthquake waves are of three ty#es0 com#ression, shear and surface waves

4om#ression and shear waves travel from the hy#ocenter through the earth interior todistant #oints on the surface )hear waves also known as transverse waves2 do no travel

as ra#idly 3555 mCs2 thought the earth crust and mantel as do com#ression waves

$waves for >ayleigh

waves72 or B$waves for Bove waves72, may or may not form !hey arrive after the

#rimary and secondary waves *n granite, >$waves move at a##ro%imately .;55 mCs


$igure "." 5#(es of Seis!ic Waves819.


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$igure ".* :round !otions recorded during severa' earthquakes 8*9.


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"." Design As(ects

!he structures are classified as regular or irregular


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$igure "., 6'an discontinuities in 7ui'ding 819.


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".* Deve'o(!ent of Ana'#tica' %ode'

An analytical model is develo#ed "y a##ro#riately ascertaining the degrees of freedom,

evaluating lum#ed masses and stiffness #ro#erties of the connecting structural elements

etc evelo#ment of analytical model is key to the efficiency of analysis #rocess and thesuccess of aEarthquake design

".*.1 %ode'ing of a Structures

!he Earthquake res#onse of a structure shall "e determined "y #re#aring a mathematical

model of a structure and calculating the Earthquake res#onse of the model to the

#rescri"ed Earthquake in#ut

!he model shall re#resent the actual locations of the centre of the masses and centre of

rigidity, thus accounting for the torsion effects caused "y the eccentricity

ifferent ty#es of model can "e develo#ed for the structures de#ending on the o"-ective

of the analysis ormally it can "e divided in two grou#s

12 )tick model

.2 3$imensional model

".*.1.1 %ode'ing of %ass

!he inertial mass #ro#erties of a structure may "e modeled "y assuming that the

structural mass and associated rotational inertia are discreti9e and lum#ed at node #oints

of the model Alternatively, the consistent mass formulation may "e used/hen a##ro#riate, three translational and rotational degrees of freedom shall "e

used at each node #oint )ome degrees of freedom such as rotation may "e neglected #rovided that their e%clusion does not affect res#onse significantly !he following

conditions shall "e met

1 structural mass shall "e lum#ed so that the total mass, as well as the center of gravity is #reserved

. !he num"er of dynamic degrees of freedom and hence the num"er of lum#ed

masses shall "e selected so that all significant vi"ration modes of the structure can "e

evaluated

".*.1. Da!(ing

am#ing is a common designation for all kinds of energy a"sor#tion of vi"ratory

system *n structural analysis the re#resentation of energy dissi#ation through equivalent

viscous dam#ing is very #o#ular "ecause it leads to linear differential equation of motionwhich are readily solva"le



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Jiscous dam#ing is re#resented "y following equations0

CV F =

/here 4 is coefficient of viscous dam#ing

!the dam#ing value of the material is e%#ressed in terms of dimensionless value called

dam#ing ratio given "y,

cr C C =ξ

where ξ is the dam#ing ratio of material

cr C is critical dam#ing

!he critical dam#ing of a material is a value for which the oscillatory motion gets sei9ed

am#ing ratios for structural materials are generally less than .5K and for

different materials dam#ing values are different *n order to o"tain modal res#onse, in

case the structure contains materials with different dam#ing !he #ercentage of criticaldam#ing in each mode has to "e evaluated using the weighted strain energy #rinci#le

Eva'uation of %oda' Da!(ing

( ) [ ] ( )

.

1

j

J

N

i

i

T

J

J

K

ω

φ ξ φ

ξ

=∑=

where

ξ L dam#ing ratio of the element su"system2

L stiffness matri% of the ith element su"system2

".+ Ana'#sis of Structures

For Earthquake res#onse analysis, any one of the following four analysis methods is

acce#ta"le !he methods are0

1 !he time history method

. !he res#onse s#ectrum method



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$igure ". )eco!!ended da!(ing ratios.


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".+.1 5i!e&istor# %ethod

!he time history analysis of a structure su"-ected to dynamic Earthquake load may "e #erformed "y linear or nonlinear methods ynamic analyses of "oth linear and nonlinear

system are "ased on solution of simultaneous differential equations su"-ect to a set of

initial conditions and forces

!he res#onse of multi degrees of freedom linear system su"-ected to Earthquake

e%citation is re#resented "y the following differential equations of motion

[ ] [ ] [ ]{ } [ ]{ } g b uu M X K X C X M

−=+

+

where,

[ ]C L dam#ing matri%[ ] K L stiffness matri%{ } X L column vector of relative dis#lacements

{ }bu L influence vector

g u

L ground acceleration

*n the modal su#er#osition method the equations of motion can "e decou#led using

transformation,

{ } [ ]{ }Y X φ =

[ ]φ L normali9ed mode sha#e matri%{ }Y L vector of normal or generali9ed coordinates m L num"er of modes considered

!he decou#led equation for each mode may "e written as

L generali9ed coordinate of the -th mode

L circular frequency of -th mode the system radCsec2

L modal #artici#ation factor for the -th mode

L M NO! '&( I "2

!hese single dof equations shall "e integrated for evaluating the res#onse


.

. g j j j j j j j U Y Y Y Γ =++ ω ω ξ

jY

jω

jΓ


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".+. )es(onse S(ectru! %ethod

/hen the res#onse s#ectrum method is used, the "asic equations of motionfor multi$dof system can "e written as,

[ ] [ ] [ ]{ } [ ]{ } g b uu M X K X C X M

−=+

+

where,

[ ]C L dam#ing matri%[ ] K L stiffness matri%{ } X L column vector of relative dis#lacements

{ }bu L influence vector

g u

L ground acceleration

*n the modal su#er#osition method the equations of motion can "e decou#led using

transformation,

{ } [ ]{ }Y X φ =

[ ]φ L normali9ed mode sha#e matri%{ }Y L vector of normal or generali9ed coordinates m L num"er of modes considered


L normali9ed mode sha#e matri%

L vector of normal or generali9ed coordinates

m L num"er of modes considered


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$igure ".0 )es(onse s(ectra dis('ace!ent co!(utation 8*9.


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!he decou#led equation for each mode may "e written as

L generali9ed coordinate of the -th mode

L circular frequency of -th mode the system radCsec2

L modal #artici#ation factor for the -th mode

L M NO! '&( I "2

the generali9ed res#onse of each mode shall "e determined from following equationusing res#onse s#ectrum

Γ =

.ma%2

j

aj

j j

S Y

ω

/here ajS is the s#ectral acceleration corres#onding to frequency jω

!he ma%imum dis#lacement of node i relative to the "ase due to node - is o"tained "y,

ma%2ma%2 jijij Y X Φ=

"., Se'ection of Nu!-er of !odes

!he following two criteria to "e ada#ted while choosing the minimum num"er of modes

to "e considered1 the num"er of modes e%tracted is such that highest mode corres#onding to a

frequency greater than or equal to 33 H9

. !he num"ers of modes e%tracted are such that the cumulated modal mass is morethan :5K in each of the three directions

Any one of the two methods can "e used to determine the no of modes to "e

considered in modal su#er#osition analysis

". %issing %ass /orrection0

um"er of modes included in the analysis shall "e sufficient to ensure that inclusion of all remaining modes does not result in more than 15K increase in total res#onses of

interest Alternatively, A)4E standard $:82 #ermits to include all the modes in the

analysis having frequencies less than the PA frequency or cut$off frequency #rovidedthat the residual rigid res#onse due to the missing mass calculated from the following

equation is added


.

. g j j j j j j j

U Y Y

Y Γ =++ ω ω ξ

jY

jω

jΓ


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[ ]{ } { } { } ma%1

ma%2 A

m

i

iibij S U M X K

ΦΓ −= ∑=

where, ma% AS L highest s#ectral acceleration at the cut$off frequency

for the modal com"ination #ur#oses the a"ove res#onse will "e considered as an

additional mode having frequency equal to the PA or cut$off frequency and will "ecom"ined using the )>)) rule

".0 /o!-ination of %oda' res(onse0

12 )>)) method.2 4Q4 method

32 15K method2 A


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". Ducti'e Detai'ing As(ects.


Figure 315 uctile detailing of )hear /all

Figure 3: uctile detailing of >einforced 4olumn


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Figure 311 uctile detailing of >einforced 4olumn section and at einforcement

Figure 31. uctile detailing requirements for )hear /all


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".12 Ste( for /arr#ing out Earthquake Ana'#sis of Structures

Ste( 13 Ascertain the Earthquake esign Parameter, )eismic one, !y#e of )oil,

*m#ortance factor, >es#onse >eduction factor "ased on the structure ty#e

Ste( 3 &odel the geometry, #rescri"ed the mass, dam#ing ratio

Ste( "3 4arry out the Free Ji"ration Analysis, evaluate Frequency and &ode )ha#es

Ste( *3 4arryout the Forced Ji"ration Analysis, Either !ime History &ethod or

>es#onse )#ectra &ethod

Ste( +3 4om"ine the res#onse as #er 4Q4 or )>))

Ste( ,3 4heck the rift limits of the structure

Ste( 3 esign the structural element "ased the force res#onse

Ste( 03 etail as #er the 4ode and )tandards to achieve the ductility assumed



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* )eferences

'1( &as-id < .5512 ,Earthquake esign of ay /4lough = ?ose#h #en9ien 1:;@2, ynamic of structure7, &craw$hill

ogakusha Btd, !okyo, ?a#an

Note-Overview of Seismic Design of Structures

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