Post on 07-Aug-2018
8/20/2019 Note-Overview of Seismic Design of Structures
1/36
Page 1 of 3
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
8/20/2019 Note-Overview of Seismic Design of Structures
2/36
Page 8 of 3
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
$igure 1.1 5ectonic 6'ate 7oundaries 89.
8/20/2019 Note-Overview of Seismic Design of Structures
3/36
Page 8 of 3
1. Da!ages due to Earthquake
!he earth movement caused varia"le damages "ased on the "ehavior of the structural
characteristics
1..1 :round 7ehavior
!he effects of violent shaking on the ground are tem#orarily to increase lateral and
vertical forces, to distur" the inter$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
A Note on “Overview of Earthquake Design of Structures” & 21
$igure 1. 5#(es of $au'ts 819.
8/20/2019 Note-Overview of Seismic Design of Structures
4/36
Page 8 of 3
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
A Note on “Overview of Earthquake Design of Structures” & 21
$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
8/20/2019 Note-Overview of Seismic Design of Structures
5/36
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+.
8/20/2019 Note-Overview of Seismic Design of Structures
6/36
Page 8 of 3A Note on “Overview of Earthquake Design of Structures” & 21
$igure 1. Da!ages to the Storage Shed< 7hu@< India< 221.
$igure 1.0 Da!ages to 6etro' 6u!( Station< Wong< 7hu@< India< 221.
8/20/2019 Note-Overview of Seismic Design of Structures
7/36
Page 8 of 3
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
A Note on “Overview of Earthquake Design of Structures” & 21
/onventiona' 7ui'dings Iso'ated 7ui'dings
$igure 1. >se of 6assive Energ# Devices to reduce Da!age to 7ui'dings 8"9
8/20/2019 Note-Overview of Seismic Design of Structures
8/36
Page 8 of 3
!o understand the "ehavior of structure su"-ected to earthquake, one needs to know the "asics of )tructural ynamics *n the ne%t section ., the "asics a"out the structural
dynamics are #rescri"ed /hereas in the )ection 3, a thrust a made to give knowledge
a"out the earthquake or Earthquake analysis and design of structures
*n order to understand the structural "ehavior, there is enormous literature availa"le on
these to#ics )ome of the literatures for reference are0
1.".1 7ooks
12 Anil 4ho#ra .55.2, ynamic of structures7, #rentice hall of *ndia #rivate
limited, ew elhi
.2 &ario Pa9 1:8;2, )tructural dynamics7, 4ay /4lough = ?ose#h #en9ien 1:;@2, ynamic of structure7, &craw$hill
ogakusha Btd, !okyo, ?a#an
1.". We-sites
12 www nisee"erkeleyedu
.2 wwwe-seorg
32 wwwicivilengineercomCEarthquakeDEngineeringC)tructuralDynamicsC
2 wwwmceer"uffaloedu
A Note on “Overview of Earthquake Design of Structures” & 21
8/20/2019 Note-Overview of Seismic Design of Structures
9/36
Page 8 of 3
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(
A Note on “Overview of Earthquake Design of Structures” & 21
$igure .1 /haracteristics and Source of D#na!ic ?oads.8,9
8/20/2019 Note-Overview of Seismic Design of Structures
10/36
Page 8 of 3
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
8/20/2019 Note-Overview of Seismic Design of Structures
11/36
Page 8 of 3
..1 $ree Ci-ration Ana'#sis
A Note on “Overview of Earthquake Design of Structures” & 21
$igure . SDO$ s#ste! and $ree 7od# Diagra!.
Ecer(t 5aken fro! )eference 7ookB
8/20/2019 Note-Overview of Seismic Design of Structures
12/36
Page 8 of 3
.. $orced Ci-ration Ana'#sis
A Note on “Overview of Earthquake Design of Structures” & 21
$igure ." SDO$ s#ste! under $orcing $unction and $ree 7od# Diagra!.Ecer(t 5aken fro! )eference 7ookB
8/20/2019 Note-Overview of Seismic Design of Structures
13/36
Page 8 of 3A Note on “Overview of Earthquake Design of Structures” & 21
$igure .* $orced vi-ration res(onse.
8/20/2019 Note-Overview of Seismic Design of Structures
14/36
Page 8 of 3
." %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'@(
A Note on “Overview of Earthquake Design of Structures” & 21
$igure .+ A!('itude res(onses for SDO$ S#ste!.
$igure ., Si!('e %ode' of %DO$ s#ste! $ra!ed StructureB 8+9.
8/20/2019 Note-Overview of Seismic Design of Structures
15/36
Page 8 of 3A Note on “Overview of Earthquake Design of Structures” & 21
$igure . $ree 7od# Diagra! for %DO$ s#ste! 8+9.
8/20/2019 Note-Overview of Seismic Design of Structures
16/36
Page 8 of 3
Ising the )u"$iteration !echnique, the Eigen Jalues Frequency2 and Eigen Jectors&ode )ha#es2 can "e evaluated
A Note on “Overview of Earthquake Design of Structures” & 21
$igure .0 %ode Sha(e for the %DO$ s#ste! 8*9.
8/20/2019 Note-Overview of Seismic Design of Structures
17/36
Page 8 of 3
!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
A Note on “Overview of Earthquake Design of Structures” & 21
8/20/2019 Note-Overview of Seismic Design of Structures
18/36
Page 8 of 3
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
A Note on “Overview of Earthquake Design of Structures” & 21
$igure ".1 5#(ica' Seis!o!eter A!('itude 5race 819.
8/20/2019 Note-Overview of Seismic Design of Structures
19/36
Page 8 of 3A Note on “Overview of Earthquake Design of Structures” & 21
$igure ". %odified %erca''i Intensit# Sca'e819.
8/20/2019 Note-Overview of Seismic Design of Structures
20/36
Page 8 of 3
". 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
A Note on “Overview of Earthquake Design of Structures” & 21
$igure "." 5#(es of Seis!ic Waves819.
8/20/2019 Note-Overview of Seismic Design of Structures
21/36
Page 8 of 3A Note on “Overview of Earthquake Design of Structures” & 21
$igure ".* :round !otions recorded during severa' earthquakes 8*9.
8/20/2019 Note-Overview of Seismic Design of Structures
22/36
Page 8 of 3
"." Design As(ects
!he structures are classified as regular or irregular
8/20/2019 Note-Overview of Seismic Design of Structures
23/36
Page 8 of 3A Note on “Overview of Earthquake Design of Structures” & 21
$igure "., 6'an discontinuities in 7ui'ding 819.
8/20/2019 Note-Overview of Seismic Design of Structures
24/36
Page 8 of 3
".* Deve'o(!ent of Ana'#tica' %ode'
An analytical model is develo#ed "y a##ro#riately ascertaining the degrees of freedom,
evaluating lum#ed masses and stiffness #ro#erties of the connecting structural elements
etc evelo#ment of analytical model is key to the efficiency of analysis #rocess and thesuccess of aEarthquake design
".*.1 %ode'ing of a Structures
!he Earthquake res#onse of a structure shall "e determined "y #re#aring a mathematical
model of a structure and calculating the Earthquake res#onse of the model to the
#rescri"ed Earthquake in#ut
!he model shall re#resent the actual locations of the centre of the masses and centre of
rigidity, thus accounting for the torsion effects caused "y the eccentricity
ifferent ty#es of model can "e develo#ed for the structures de#ending on the o"-ective
of the analysis ormally it can "e divided in two grou#s
12 )tick model
.2 3$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
A Note on “Overview of Earthquake Design of Structures” & 21
8/20/2019 Note-Overview of Seismic Design of Structures
25/36
Page 8 of 3
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
A Note on “Overview of Earthquake Design of Structures” & 21
8/20/2019 Note-Overview of Seismic Design of Structures
26/36
Page 8 of 3A Note on “Overview of Earthquake Design of Structures” & 21
$igure ". )eco!!ended da!(ing ratios.
8/20/2019 Note-Overview of Seismic Design of Structures
27/36
Page 8 of 3
".+.1 5i!e&istor# %ethod
!he time history analysis of a structure su"-ected to dynamic Earthquake load may "e #erformed "y linear or nonlinear methods ynamic analyses of "oth linear and nonlinear
system are "ased on solution of simultaneous differential equations su"-ect to a set of
initial conditions and forces
!he res#onse of multi degrees of freedom linear system su"-ected to Earthquake
e%citation is re#resented "y the following differential equations of motion
[ ] [ ] [ ]{ } [ ]{ } g b uu M X K X C X M
−=+
+
where,
[ ]C L dam#ing matri%[ ] K L stiffness matri%{ } X L column vector of relative dis#lacements
{ }bu L influence vector
g u
L ground acceleration
*n the modal su#er#osition method the equations of motion can "e decou#led using
transformation,
{ } [ ]{ }Y X φ =
[ ]φ L normali9ed mode sha#e matri%{ }Y L vector of normal or generali9ed coordinates m L num"er of modes considered
!he decou#led equation for each mode may "e written as
L generali9ed coordinate of the -th mode
L circular frequency of -th mode the system radCsec2
L modal #artici#ation factor for the -th mode
L M NO! '&( I "2
!hese single dof equations shall "e integrated for evaluating the res#onse
A Note on “Overview of Earthquake Design of Structures” & 21
.
. g j j j j j j j U Y Y Y Γ =++ ω ω ξ
jY
jω
jΓ
8/20/2019 Note-Overview of Seismic Design of Structures
28/36
Page 8 of 3
".+. )es(onse S(ectru! %ethod
/hen the res#onse s#ectrum method is used, the "asic equations of motionfor multi$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
A Note on “Overview of Earthquake Design of Structures” & 21
L normali9ed mode sha#e matri%
L vector of normal or generali9ed coordinates
m L num"er of modes considered
8/20/2019 Note-Overview of Seismic Design of Structures
29/36
Page 8 of 3A Note on “Overview of Earthquake Design of Structures” & 21
$igure ".0 )es(onse s(ectra dis('ace!ent co!(utation 8*9.
8/20/2019 Note-Overview of Seismic Design of Structures
30/36
Page 8 of 3
!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
A Note on “Overview of Earthquake Design of Structures” & 21
.
. g j j j j j j j
U Y Y
Y Γ =++ ω ω ξ
jY
jω
jΓ
8/20/2019 Note-Overview of Seismic Design of Structures
31/36
Page 8 of 3
[ ]{ } { } { } 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
8/20/2019 Note-Overview of Seismic Design of Structures
32/36
8/20/2019 Note-Overview of Seismic Design of Structures
33/36
Page 8 of 3
". Ducti'e Detai'ing As(ects.
A Note on “Overview of Earthquake Design of Structures” & 21
Figure 315 uctile detailing of )hear /all
Figure 3: uctile detailing of >einforced 4olumn
8/20/2019 Note-Overview of Seismic Design of Structures
34/36
Page 8 of 3A Note on “Overview of Earthquake Design of Structures” & 21
Figure 311 uctile detailing of >einforced 4olumn section and at einforcement
Figure 31. uctile detailing requirements for )hear /all
8/20/2019 Note-Overview of Seismic Design of Structures
35/36
Page 8 of 3
".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 ðod or
>es#onse )#ectra ðod
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
A Note on “Overview of Earthquake Design of Structures” & 21
8/20/2019 Note-Overview of Seismic Design of Structures
36/36
* )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