Seismic Design of Structures

8/12/2019 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 Earths 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 7oundaries89.


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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'ts819.


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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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$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 are/

1.".1 7ooks

01 Anil 2. ho"ra 0-44-, 5+ynamic of structures, "rentice hall of )ndia "rivate

limited, 7ew +elhi.

0- %ario Pa8 019:;, 5(tructural dynamics,


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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, i.e., 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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..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 StructureB8+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 0Frequency and Eigen Jectors0%ode (ha"es 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 "rocedures/

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 193@, harles F. >ichter of the alifornia )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 0e$"ressed as

>omans numerals following the initials %% 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"es/ com"ression, shear and surface waves.

om"ression and shear waves travel from the hy"ocenter through the earth interior todistant "oints on the surface. (hear waves 0also known as transverse waves do no travel

as ra"idly 03444 mCs thought the earth crust and mantel as do com"ression waves.

#waves 0for >ayleigh

waves or B#waves 0for 5Bove waves, may or may not form. hey arrive after the

"rimary and secondary waves. )n granite, >#waves move at a""ro$imately -;44 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'ding819.


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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. 7ormally it can !e divided in two grou"s.

1 (tick model

- 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 discreti8e 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 ofgravity 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 equations/

CVF =

here is coefficient of viscous dam"ing

the dam"ing value of the material is e$"ressed in terms of dimensionless value calleddam"ing ratio given !y,

crCC=

where is the dam"ing ratio of material

crC is critical dam"ing

he critical dam"ing of a material is a value for which the oscillatory motion gets sei8ed.+am"ing ratios for structural materials are generally less than -4K 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

==

where

L dam"ing ratio of the element 0su!system

2 L stiffness matri$ of the ith element 0su!system

".+ Ana'#sis of Structures

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

acce"ta!le. he methods are/

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.

[ ] [ ] [ ]{ } [ ]{ } gb uuMXKXCXM.....

=+

+

where,

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

{ }bu L influence vector

gu..

L ground acceleration

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

transformation,

{ } [ ]{ }YX =

[ ] L normali8ed mode sha"e matri${ }Y L vector of normal or generali8ed coordinates m L num!er of modes considered

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

L generali8ed coordinate of the th mode

L circular frequency of th mode the system 0rad.Csec.

L modal "artici"ation factor for the th mode

L M NO&%' 0I!

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


.

..-

..

- gjjjjjjj UYYY =++

jY

j

j


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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,

[ ] [ ] [ ]{ } [ ]{ } gb uuMXKXCXM.....

=+

+

where,

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

bu

L influence vector

gu

..

L ground acceleration

)n the modal su"er"osition method the equations of motion can !e decou"led usingtransformation,

{ } [ ]{ }YX =

[ ] L normali8ed mode sha"e matri${ }Y L vector of normal or generali8ed coordinates m L num!er of modes considered


L normali8ed mode sha"e matri$

L vector of normal or generali8ed coordinates

m L num!er of modes considered


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$igure ".0 )es(onse s(ectra dis('ace!ent co!(utation8*9.


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

L generali8ed coordinate of the th mode

L circular frequency of th mode the system 0rad.Csec.

L modal "artici"ation factor for the th mode

L M NO&%' 0I!

the generali8ed res"onse of each mode shall !e determined from following equationusing res"onse s"ectrum.

=

-0ma$

j

aj

jj

SY

here ajS is the s"ectral acceleration corres"onding to frequency j

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

0ma$0ma$ jijij YX =

"., 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 considered.1. the num!er of modes e$tracted is such that highest mode corres"onding to a

frequency greater than or equal to 33 H8.

-. he num!ers of modes e$tracted are such that the cumulated modal mass is morethan 94K 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 /orrection/

7um!er of modes included in the analysis shall !e sufficient to ensure that inclusion ofall remaining modes does not result in more than 14K increase in total res"onses of

interest. Alternatively, A(E standard 0#9: "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


.

..-

..

-gjjjjjjj

UYY

Y =++

jY

j

j


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[ ]{ } { } { } ma$1

0ma$ A

m

i

iibij SUMXK

= =

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(onse/

1 (>(( method- Q method

3 14K method A


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/o!-ination of !oda' res(onses

With No /'ose'# S(aced %odes

)n a res"onse s"ectrum modal dynamic analysis if the modes are not

closely s"aced 0two consecutive modes are defined as closely s"aced if their

frequency differ from each other !y 14K or less of the lower frequency there"resentative ma$imum value of "articular res"onse of interest for design should !e

o!tained !y taking the square root of the sum of the squares 0(>((. %athematically

this can !e e$"ressed as follows.

here > is the re"resentative ma$ value of "articular res"onse of a givenelement to a given com"onent of an earthquake and >k is the "eak value of the

res"onse of the element due to the k th mode and 7 is the num!er of significant

modes considered in the modal res"onse com!ination.

R S(atia' /o!-ination

("atial com!ination of res"onse due to three com"onents of earthquake is carried out !y

(>(( method.


Njialso

i

ij

1

1.4

jiRRRR jik

+=

-C1

--


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


Figure 3.14 +uctile detailing of (hear all.

Figure 3.9 +uctile detailing of >einforced olumn.


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Figure 3.11 +uctile detailing of >einforced olumn section and at einforcement.

Figure 3.1- +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 arry out the Free Ji!ration Analysis, evaluate Frequency and %ode (ha"es.

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

>es"onse ("ectra %ethod.

Ste( +3 om!ine the res"onse as "er Q or (>((.

Ste( ,3 heck the +rift limits of the structure.

Ste( 3 +esign the structural element !ased the force res"onse.

Ste( 03 +etail as "er the ode and (tandards to achieve the ductility assumed.



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* )eferences

&1' %asid < 0-441 ,5Earthquake +esign of

Seismic Design of Structures

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