ML20101G640
| ML20101G640 | |
| Person / Time | |
|---|---|
| Site: | 05200001 |
| Issue date: | 06/26/1992 |
| From: | Fox J GENERAL ELECTRIC CO. |
| To: | NRC |
| References | |
| NUDOCS 9206260207 | |
| Download: ML20101G640 (34) | |
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DR ADOCK 05200001 PDR GENuclearEnergy
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ABWR msme Sam!ard.limi ny n TAllLE 3.2 1 CIASSIFICATION
SUMMARY
(Canlinued)
Quality Group Quality Saftti Loca.
Clani.
Assurance Seismic Principal Componenta c;3fb kB bh pgig g ge Catecorvf Notes C
d N9 Turbine Gland Steam Sp!ern N
T D
E E
NIO Turbine Lubricating Oil Sptem N
T i
N11 51olsture Separator lleater N
T E
N12 Estraction Sptem N
T E
N13 Turbine flypass Spiem
-?'
I D
(:, d a
N14 Itcactor Feedwater Pump Driier N
T E
E N15 Turbine Ausillary Steam Sptem N
T
~~
N16 Generator b'
T E
N17 liydrogen Gas Cooling Spiem N
T E
N18 Generator Cooling Spttm N
T E
E N19 Generator Scaling Oil Sptem N
T N20 Exciter N
T E
N 1 Slain Condenser N
T E
(ce)
NO2 OITgas Splem N
T E
NO3 Circulating Wattr Splem N
T D
E N 4 Condenscr Cleanup Facility N
T E
Tu rbs e c 'op o t.J N
T B
6 I
pi pinj,mcl w d ej
~
su pports up
.O 4he hvh ne by pa ss vakVt
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Amendment 20 31214
eae.-
A-4__.
d_2Jd 4 44 4 4-444-6-4Ja-.me-_--AM+ 4 MMe h A N h.a * -*m
- WNd444*4d-~~4**AM+hhM'Ah 64E44"#***6NdN*""#'d'8WdM*W'M-##==*N*dEdN*Mam.Am.Sem-am.m+em m.se ME8 M h OVERSIZE DOCUMENT PAGE PULLED SEE APERTURE CARDS I
NUMBER OF OVERSIZE PAGES FILMED ON APERTURE CARDS 92.o 62.0 e.2.o7El APERTURE CARD /HARD COPY AVAILABLE FROM RECORDS AND REPORTS MANAGEMENT BRANCH l
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ABWR mam Etmidard Plant piv n 3
I TAllLE 3.2 1 CLASSIFICATION SUh151AIG' (Continued)
Quality Group Quality Safety Loca-Classi.
Assurance Seismic l
l'rincirial Comriones" h'
11onc Ocathind Mrrment' CtttgaD EE!.t1 l
I 112 Nuclear floller System (Continued) l 4.
Piping including supports 1
C,SC A
11 1
main steamline (MSL) and feed.
water (ITV) line up to and in.
cluding the outermost isolation valve 5.
Piping including supports-2 SC B
B I
MSL from outermost g
isolation valve to and including a
sei.smic interface restraint and 13Y from outermost isolation valve to the shutoff valve 6.
Piping including supports-MSL N
SC.T U
B (r)
$ 'E 5 from the seismic interface restraint to the turbine stop salve 7.
Piping from ITV shutoff valve 3
SC C
B 1
J, to seismic interface restraint 8.
Deleted 9.
Deleted
- 10. Pipe whip restraint MSL/ITV 3
SC.C B
(dd) if needed n
- 11. Pipine including supports-other
,E,,
within outermost isolation valves a.
RPV head vent 1
C A
B 1
(g) b.
Main steam drains 1
C,SC A
B 1
(g)
~@
11 Pipingincluding supports-other beyond outermost isolation or shutoff valves a.
RPV head sent beyond N C
C E
shutoff valves 5
b.
Main steam drains ht+
SC, T B/f B/E 1/~
td O
Amendment 20 339
~.._
e 4
Turbine lluilding Static Seismic Analysis justification
References:
- 1.
NUREG/CR 116), " Recommended Revisions to Nuclear Regulatory Conunission Seismic Design Criteria" j
2.
- Earthquake Resistant Design", by N.M. Newmark and W.J llall, as found in Section 3 of the " Structural Engineering llandbook, Second Edition", edited by Gaylord and Gaylord.
Reference I recommends thr following ductility factors to be used for seismic design of nuclear power plant buildings:
CLASS DESCRIPTION Ductility Factor IS Equipment, instruments, or components performing vital 1 to L3 functions that must remain operative during and aller earthquakes; Structures that must remain clastic or nearly clastic, Facilities performing a vital safety related function that must remair, functional without repair I
Items that must remain operative afler an earthquake but need no 1.3 to 2 operate during the event; Structures that can deform slightly in the inelastic range; Facilitics that are vital but whose services can be interupted until minor repairs are made.
11 Facilites, structures, equipment, instruments, or components that 2 to 3 can deform inelatistically to a moderate extent without unacceptable loss of function; Structures housing items of Class I or 1 S that must not be permitted to cause damage to such items by excessive deformation of the stre:ture.
C 111 All other items which are usually governed by ordinary seismic 3 to 8 design cades; Structures requiring seismic resistance in order be repairable after an earthquake Based upon reference 1, the spectral peak of Reg Guide 1.60 spectrum (using a ductility factor 4) would be reduced by 67% The Zero period acceleration would not change. If we assume that most of the structural loads come from the first mode, a dynamic analysis using the Newmark method (see reference 2) would show a reduction of upto 67% over a
- linear analysis, with inclusion of higher modes it would be closer to a 50% reduction. This reduction v ould bring a 0.3g SSE down to 0.15g The static approuch found in the uniform building code assumes a force distribution based upon the first mode of the structure Using Zone 2A with a 015g input assumes the building would go nonlinear
above a 0.15g earthquake, but would not colapse to somewhere above 0.3g. Margin is butit in through code allowables on story drif) and maximum stresses Attachment A is Newmark and llall section of Gaylord and Gaylord Structural Engineering llandbook.
Attachment B is table 23 j that provides site coemeients for various soil profiles It is GE's position to multiply lleg Guide 1.60 spectra anchored to 0 3g by 2.0 (maximum value oil table 23.j) to provide piping input spectsa for MSL dynamic analyses.
Any questions please call me at (408)925 4259 in order to clarify anything provided here.
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1 Earthquake-Resistant:
Design N. M. NEWMARK and W. J. HALL Professors of Civil Engineering, University of Illinois, Urbana
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- 1. Aosponse c Sirnple Structures to Earthquake Motions A series of structures of varying sim and complexity is shown in Fig.1, conesponding to a simple, relatively comiuct mach;ae anchored to a foundation in a, a simple bent or frame in h, a more complex fraine in c, multistory buildings of15 stories in d and of-10 stories in e, an elevated water tank in f, and a suspension bridte tesponding either latetally or vettically in g. A typical period of vibration T or fiequency of vibration f in the fundamental mode of vibration is indicated for each.
Each of the smietures shown in Fig. I can be icptesented by a simple oscillator consisting of a single mass supixnted by a spring and a da hpot (Fig. 2). The relation between the cittular fre<luency of vibration w = 2 f, the natural fretpiency f, and the E
period T is given by the following equation in terms of the spring constant k and the mass in:
k w=-
(1) m I
w I
((
4
, _ s i-(2)
./ = 1
_s..
\\m f
in general, the eficet of the dashpot is to pmdnee d uuping of flee vibrations or to rednee the amplitude of forced vibrations. The damping force is assumed to he equal to a dampingcuellicientij times the velocity $ of the mass relative to the ground.That value of
- 1) at which the motion loses its vibraton character in free vibration is called the critical dntnping coe,[licient, i.e., %a = 2mm. The amount of damping is most convenientiv considered in tenus of the Inoportion # of critical damping,
- =
(3)
=
run
_mw For most practical structures # is relatively small, in the range of 0.5 to 10 or 20 percent, and does not appreciably afTect the natural period or frequency of vibration.
31
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iD i u j 33 Earthquake. Resistant Design n!/
- 2. Entthquake Motions Stront5niotion catth pule.n e ele itisin HTonIs with lespet t to a
iin n.ims c in.c n obt.aoca fo, a n n,o her s e. n h.p ut m cronna o..nooan.n, oo-nn.
! Ji of tlisturb nice, sin h # quany b!mtina.unl nm le.o hietine.ne abo audahle. uni show l l nuny of the s,one c har.u teristics Ainon. the nuoc nin no shonmnmuon (.u tle p ul m tecnided so far is that nf the El Centro, ('aliL carti unal e of Nias 15.14 Ilt iIm o conh d
,'{};
au cleroenon, in the nonh. south e uncon"nt of he. ntal roouon i, shma n ni ne a on 3
l i the wune hLute,ue 'hnwu tuteeution of the Mtound an ch uhun a to en e the s anahon of f f Ctnutid \\ eIntity r w ith tinu, and the uitectatnin (d \\i<hn ity bi cis e !!u \\ all :tuin i>f nuit.]
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m=ou n om s Fig.1 En u.tures subje tesi to e.atin p ute. i on,-l m
a-
y Elastle Systems 33 i
seipiste base line conections of various l
displacement d with time. Thew intecrations h
soi-ts, atul the inagnitnue of the nia\\nnum <hspla< ement nuy vary depetuling on how t e il l
conettions are inade.The ma\\innun acceleration and velocity are relativelv insensitive to 1
the eOnc(tinus, however. For this e.ntluplate, with the intecrations shown in Fig. 3, the matinann tround acceleration is 0.32d, the nus; mum tround velocity 13 7 in.!see, and i
the maximutn ground displacement b.3 in. These tince inasimum values are of p.nticular interest hecause thev anons strub N[
help to define the tesponw inutions of the T
totes musidered in Fie. I most accurately if all thtet
%w
- rE ?
inasiina are taken into account.
a b
l a
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J'*"
L k
A Drw RESPONSE SPECTR A g
L*/
L**
i The resp.nise of the simple o cdla-g
- 3. Elastic Systems ut '/
tor shown in Fic. 2 to any type of urotind inotion can he Fig. 2 M,n ni owdeted leadily coinputed as a function of time. The masinnun h
values of the te ponse ate of p.niwular interert. The.
/), the f
masitutuns can he stated in tenn of the matiniuni defonnation in the sprine N,,,
=
i mnilmun spring force, the ma\\innun acceler.ition of the in. ass (which is related to the l
m e,innun spling fome directly when there is no dampine), or a iptantity, having the
,4 donensions of vehicity, which cites a measnie of the ma\\imatn energy absothed in the sprine. This ipiantity, desienated the p endos ch. city V, is dehned in sut h a way that the 0 3 r-i 02
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11 (:enho, Cali!, e uthquaia of \\l.o 15. Fun. nmtlrouth coup ment.
- k.
Fig. 3 Unetty ah otption in the spline is %mF The relations amone the inniinnin relative jli'placenu nt of the spline 1), the pseudovehicity V, and the pseudoa:eeleration A, which 4
is a measun of the force in the spone, are as follows:
T m
r = na) p a=~v=so m,
+[$
L w1
7 M.
p M
fl
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34 Earthquake Resistant Octlgn J' M, t
4, f
4
'M The pseudovelocity V is imadv etinal tu um nennouni niuw wh.nty for systenis with Il }( h
(' bi l' (II I N1 It*(flI('il( (*s Olf Illilv ( l l'{ ( l 7l 4 s ( l'Iin iV [(!ll! k It' j ll.l% IlInilill l!' alk s I" ehj f or ven lomfinpa in y s3 xtenn. The pseudmu < rh.. tion.\\ is cuetly npul to tho s eh cit 3 nusinnuni a((cleration foi systniu.ith no di opaw.dal n init. neatly ddh rent frotn t!w j
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ina\\iinunt ac t eleration i 3r systetus w ith nioderate ann enn% ( l r !.u u l, u e.' os ci ilm ulud-
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non:e of ficqncueies honi s et y lou to s cry hich value i
Ty pic.d plots of the in pun e of tim y stein
.e, a : nut tion vi pnn d ot bequenc y.ae j
c.dled w spon w s peella.11ot s f. o.n&let at:on.001 t ot uhtiw dnpha eumd. f or a sydeni w it h a mo !eiate arununt of danipaw sul p ted to an input winnbr to that of Fw 3.,ue i
situple, od c< nis onent to sh m n in Fw.1 This atitlan, tu ph >t < >t numnum n s pan" is t
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Fig. 4 Antim oc phis of ie sp.mc i
n 1
An equally useful plot, called the inn:ntste !c_ ant!nm plot, is show n in Fw 5. It
.j; indicates at one and the s.une time the response s.dnes D. V. and A,.nul has the addition,d y
i J
I snine that it.d so shows ne ae ele.u h tim estic;ne or huntine v. dues of the vanons t
lw.uneten dehning the tesluur* The bequency n plotted on a louaritlunie scale. Sun.e i
flu-IllpM'imyistileis'tijnocaltI!!ie j 't ilti;l. tlic It!Jalll} illite se.tle f(ir lM'll1 4! M iMlb! llas e g
eu tly the s.nne spxina of the points. or in edcet the plot wouhl be tuumd end foi cod TFe pwudos ehr its is plotted on a wrtwal -ale also lou.uithniieally. Then no duconal
- 'k j
1 weale s alone an asn tlut exti nds upuani hom nuht to lef t ;ne ph>tted v. dues of the
. 4l ', !
di pl.u t n.ent, and alone an.nis that estends opu.od fnon h it to iiu' t the pseudoacceleu-
] j1 tion, m suc h a w ay that an> one point defaws for a uis en in quency the duplacenient D.
i; the pseudos c:ocits U. and the p' endo.n eclerat:on A. Poir.s aic ituheated in Fiu. 5 fio the sq ws en sina tures of Fiu.1. plotted at thnr innlunent.d hequent ies.
M >!
A u n!e s anctv of inotions bas e been conudeied m Ref s. I tinough 3, raacme bom I
l f L !
suv!e pulses of displaccinent, s ch nty, m aueleratmn of the cround, thronch nune l j l l con plex nuitions such as those ansine from nucle.o blast detonations, and foi a variety of i ij e at : iuales as talen fnun available stmnu-un.uon rn onk. Response spec tra for the El Cemio c.uthquake are shovm in Fiu h I he -pettunn for smau.unounts of dampine i:.
l j 1 i
I, l, much unne heced than indicated by Fiu. 5, but for the hieher amounts of donpum the d
lt 's j h 4 t'e elllTe s ale lef at k s t'ly sliid n.!}l.11 a' sCa!t*w.11(' ('!if N'il ill tiiks illstalR e t(p r(' pit('ll!
jk i
the.unpliheations of the iespons irlatis e to the u,und motu,n values of displacement.
w wh.on, or.u < cie muon.
,k;3 The spn tra show n ni Fie 6,oc ts pm.d uf msponse s pn na for oe.u h aH ts pos of conuni i
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Design Rooponse Spectre 35 1
8 trmtion, it is noted that on the estreme left, conespooding to very-low ftequetwy systems, the tesponse for all degrees of datuping approaches an asymptote conespomling to the value of the maxiinum giotmd displaecment. A low-frequency.,ystem conesponds to one having a very heavy tuass atul a very light spring. WNn the grotmd moves relatively rapidly, the mass doe ( not have time to move,,uul tir 2 fore the masimum strain in the 300
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etent sediments of various kinds. For s $g w, ' d c cy,% a m t O1M, M I. "Q 34 Earthquake Retietent Design %{y,4 - relatively m snuments the wlootics.nni aispl menmnts n; chi wouim memases ahow the values shr..n. Ilowcwr. it is not hLely. hat nusimmn mnal wlot it. ' in cu e, of 4 d b to 5 fusm am obtainable under.nn cianmstann v 3 liepn sentative amphfic ation factors fo r ~.0 at ul N h l pe we n t d e
- 1m eh of horizont.d lj
} respum e.ue enen in Table 1. nim: these factors,.nal taliwa points H nul.\\ at about s i se .- i.l - iii a.e
- u. m o.'
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i y y o,% . ~+ y 7 y y,, __,,, N ; +-:- je -- g77 = y, r g y;-;- 4 t q 7 l
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- l ! I l ! ' - - - - + + -- - o - ', - - - - + - - - - + - 4 + o c, t +Y .1 @3 ,I _ T I ,I. l j 5, E., ,/_ - i ,s .I lll,I, ) l l 7 -V'.~ I E !o I/ l lI i -, C'. 6 +Y i j i i i ii. - - Li. I -v 1 + - -. -. - - t l l ,..q. ,.i --_. + i j s l1 l ! l l 'iit ' ) i 1 ._4 .+.! 4 -. y t 3.., l iI I [y I I { l .l l, l l - 3; i i i fl, 2 ; 1.-. ;. __ a l il 'O}_,A L 1 L. a_ o.1 lg_.y.._u4._,_.__._._.__._._-.._._._._--.._.a m.. .. ) 4... _ _ _. -. _n ,pp. gn _.__._- j .. _ '.- _T. _11..
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,7_. o_.7 J i ' i !Jt i_..t.T.*_ ___.L _7 r_ r__ ~._+. T.--+.-+. _.~ ~, 7 4 i J!. t 7 795 n 003 005 0.1 0.3 05 tD 3O SO 'D 3D l t : 1 0 Unmp. 3 cc* e:! t rem y 1, e s Y Fig. 6 Def,.. nation sec tra for elenc y stems -nbm ted to th" E l Centn> e.ai ule. i J, 1 3 a 1 and 33117 respectis ely, for all vahns <>f dauq>ine a lu>rizontal iesinore spectnnn can 1.e y { j drawn as shown in Fit' 7. i' The authors reco mnend tlut.nnpl fwatian factors for witiul nm,tnin he taken at tu o. d} 3 h thitds the vahics gn en in Table 1. J Fu:-ther information on consttuction of clastit,re poire spn tra is en en ni llef s. I to 7. i
- 5. Response Spectra for inelastic Systems
.\\ typiul inelastic-spune lou e-displacement ) jl{ o iclation is shown in Fic. S. Tlns can he approsimated by an clastoplastic wlation as indicated. with an clastic imtul wom, a plastic t eiline of con tant wsistance, and an q clastic unloadine. The approsunate miatM is drawn so as to have the same.nea betw een i the origin and u,, and between u, anl u.. as the at tual enn e The iatn. of the maunnnn pennis ihle or useful displacenmnt u., to the 3 wid <hsplacenmnt n, is c.dled tho Jm tdup 4 i factor, denoted by the symbol g. Unioadine is consuh wd to be eletic until y ieldine n j} wached in the opposite duettion. For equal yie d values in either dun tion. calculations of the wsponse of the system of l h ) { ol Fig. 2 for an clastoplastw re,ntance function can lie made. A s ariety of sm h calculations have been uude and am reported m liefs. 2 and A It is instructn e to plot the wsuhs of ] t such calculations on a clutt siniila. to the tripartite wsp4 Hre-s pet t rum ( hart, of Fies. 5 j and 6. Spectra for the c'.astic component of the wspanse of eletopletic systems to the El t! ;) f Centro earthquake, u tth a damping factor "f 2 pcK' t of entical in the claQie lance of [1 l wsponse, are shown in Fie. 9. The ductditt f actot g raates fnun 1 (clastic behavim) to 10. The displacement D/d.c from this fiente must be umhiplied by the eormspondine } 4 } j [ ductihty factor to obtain the total masinmm di4p!ateinent, but accelerations aie concet as trad dimetly ftom the plot. The cun es do not repmsent the vormet value of the nusinnun I pseudo velocity, which is why it is denoted by V f f i, l l 1 l u parcooleofsu n ~nstha M ino.e mr tv a o., m 1 a m,, n a o su.a m u-sa
- q 3 p.nm u b r.u n ph fm.a mn.
i a L
)
t 1
y
\\\\
iRh.
\\
1 I' l
--m et
, cA / l.
t n
Y
\\ /4
.i.
"s r
,' /
/ \\s /\\
,f,j% /\\
t if s
=
.j
\\l U (j \\,/ \\
j
' f,\\ / '
/ { [-
L, f
t f,/
,. o.
\\,,( v %m%,\\
j
._\\_v,.4 \\ /
_4 _\\
/
q.
.+-y Y; g j
g(
- f.._+ e.
a p q p_.
._y_
g 44,<./ N i.
s.sN t,
/q
/s
/N
c 4
4 8
1 1
3,
\\
{-
' )
7
,/
,/
j'
\\ /\\
/ \\ _
- 0, w.J)c. xJ=ws
'~'
/x l ;-(% f}ci.j, " l'n },'V i
.,[',
'v zt Nt
,n
', r N A 'e,.,._e h.,_/ l_\\_ _a N_ _.K,_.!_'s,,f_.f.f
,/ %, / N y N, h, ' N L / N y ' Q j ' N ( / y _
- N q
,{
J
! (
. N / K.
f A N, K.
,k.
<{' N_ /,.
Oi vg v !.
4 2
t u
ts
!a No I
r r.o.no, m Fig. 7 lbic honmnt hespm,e d"sien spn trum nonnalized to 1 Oc for i p rmnt dunpiin:. S l.1 percentile les el.
I i, a
TABLE 1 Spectrum Amplification Factors for Horizontal Elastic Re;ponso j
- Q i
ri One de'na (%lca Median DM )
4 o
Dampin e, h entical A
V D
A V
D 05 5 10 3.s l 3 31 3%
2 59 2 01 i
1
.l M 3%
2.73 3 01 2 31 1.82 c
3t6 2 92 2.12 2.74 2 03 1.63 i
^
3.24 2 64 2.24 2M 1A6 112 4 :
- ]
z.!)
23) 2.01 2.12 LM 1.39 I
3 2 36 2 08 1.b 5 1.h9 1.51 1.29
- h LW I SI 1.69 lb1 1.37 1.20
!I i
1.26 1.37 12 Ll7 1.0S 1 01 2
)
- i o,
,1 b
a
! ]
( k.h Ih hl O Ob[( *' d'h 3 C C "I h k
t w
~
b r
y
]
/ i
.j Ac tucI yW y
E, g,nt s
't L
\\
/,
'E f f eC1NO
/
j i
e w escsnt
.h
(
rE atcn [
/
/
i j'
?
/
I e
Y
~
5
}
I
-f
/
>/
J
't t
,/
,/
u
-U Um MUy
$l O
U US y
y 3
-e-i O'( f O C F
- U S.*
oi 1
Fig.8 llesistance-dup!.wenm nt relationship 4
1 y 3-7 t
1-
<3
.9] l 3
V il f(
38 Earthqurde Hosi:trint Dealgn Wn A responv. spechmn foi n,tal ichtive displm ment can L. ai.m n for the s.nm. comh.
I {
tines as Fie. 9 by multiplyine each con eN mditutes by the s alue of the con"spondine e a anodity raamr.,,mtea.ame. soch a imme sh_ d,at dm nonumoot.a aispucememi j
is viitually the sanm for all ductility fm toi s actually peihaps esen dn icasine shuhtly for the lareer diu tdity f.wtors in tin low-fn quency remon (helow about 2 Ild Eremer. it appeats hom Fie. 9 tlut the mauunun acce!crahon is im.olv the sune toi all dm tihtv I
fattor for freiluencies cicolet th.ni ;d wit 21) or.0 ll/. In l[tu een then is a transitud
'T hese ohserwtioth av ty pie.d of almt eattlo pule pectr.. (hmt m n m iah/e ahont in
-.l f..f
. -/.
f
. \\
e)
)
i l
4 p*
(.);^ii! i y i C '" ! ^
3 p
5[
/. ' %. ;
..i l I
i !
't i
i n.
l i
/
y.
\\g,/
i t
f (O - !.. 1 2 '.'
A.
,y'. 7.. f.,. -
w,..
s.
.c.
7, 1
%.. _y4.
.A
.L.
__-.~_.
-.-c.%,.
r
_ l Y-
-.N..
h..k..
..J.Y
. N.!'._
4, g..
..p :! '
l
[ $ Qt
.3 i
p J
y 1
c i
j s.
... r c.3 y..
s..
m S,
t
, ~ %.
g N.. A 3
5 T,,
W R[T l
l.Y.,_ J J
. l lp
, l i
i C
i 1
l'
\\
,s
.l g,,1 1
' l
).
i I
\\
II J
\\
..q..
.g M~. -
ig
.. ~ _...g.-,...._._
3 o _._ _.
~.,;,.
..., _ _ _. _. _. ~... _ _.. _........ _ - _ -. _,
y
_.....4.
4 o,....
__ w i -. _ -._._-.
_._._.____..-. ~.._.
'O.
p O g$
_. I *
.___.s_.
s O
1 I
(
I i
_, i -
v,
.._....a_.._.u__.__.,..~...~
...... _ ~ _ _,. -. _,. - -,.
f ie, *j
/,
l t
l D.C3
{
003 0 05 0.1 03 0.5 tv 30 50
'O 2D 4
t i t U r a1 raw N:s:,f f
Fig. 9 I h fonnahon sinto for clmtopletw a stenn u ch / p u t nt t utn J Janmm; suhy (ted to tiie 1:1 Cenno c.neinA c.
l
-t l
theln, foi single-decrt e-of-fleedoni sinu tures as hdlows for low.nnl internuuhate j 'l hequencies conespondme to sometinne of tlm order of about 2 ilz as.m uppei hunt, total
(
1 ielatis e displacenmnts.ne piesen ed.onLuc u r> ne.nly the s.nne for all ductinty fa< ton.
(
As a nutter of f.u t, inelastic srtems base perhaps cu n a smalle dnpl.u ement than ebstir ystems for hequencies belou about 0.311/ For hequencies hetu een about 2 and about S 11/. the he-t relationship app-an to be to equate the estemal applied encrev u it' a conespondine resistine encie). Timic n a transition remon h< tu een 5 and 30 to 3111/
dependnic on the dainpine ratio. u hile alu n e 3111/ the h uir 01.wer!cution is nearl) the s.nne for all dm tihty ratim. These oh'en atums enable one to deris e appmsonate inelas-tit-nnponse spectu fnnn an elm tic-responw spet inun as described m the nest paraeraph.
Tt) olitaill t!w ille}astje acet'}crat u m slH 4 tilln) b tult tim t'l<tstic-It'slh nim * '[3clt rll!!! 012 3 4 5 shown in Fic.10. values of D and V are dn ided by the din tility factor p to cet D' and U and s alnes of a.ne dnided h Gu 1 to cet.\\' Thus the s elocity cone pondine to 3
'E point _ l' is I n tones the s elocity for pomt 1. the acceleration conespondine to pomt I is IV2 1 times the accelet ation for point 3, and l)' U' and 3' are parallel to D, U, and
- 4 a, respectively. nte dut the hequeneit conespondine to conespondinay nund,cied points ate the same. The acc elciation spectrum is comph ted by connectine points 3' and l
- The amount of the shif t froin A to A' is soth as to eis e the wone enciey absorphon for j
the clastoplastie enn e as for an ebstic t un e for the s.une emiod of vihutio-The enn e o' H
l' 2' T 15 also represents the chstic component of displ u ement as disenssed e.nlier in
{
titis ;11ticle.
): E' Tic melastie-displacement spectnun in Fie 10 is obtained h3 leavine D and U L
nochanced, esteluline U L a p4 nnt 2 ' s eit mally ah< n e l', and duu ine 2" T, T T,.nnl M parallel to 2' T. T 4. md 1, resp.n tis ely, but at a s alue a tinms as meat.
m
j Multl Degroe of Freedom Systems 39 d
'.t 4 Inclastic-response spectra can be used only as an approsimation for nadti degree of-J' 5'
freedom systems but generally give reasonable results for systems with balanced resis.
If tances, i.e., Systems without maior diffelences in adjacent story stifTnesses.
i i
Additional mionnation on develoinnent of inelastie design resp (mse spettra inay be i
. found in llefs. I and 7 to 13.
'I
-t I
i 1
y 2
C.
N A" eotal inelastic displacement
( l1}
3"['P '"*
I Elastic A
D spectrum
,3\\
i 1
s v'
2'
\\4" l
,1 '
0
.\\
i} '
D /
g'
/
3 Inelastic occeleroiion
\\
j
/
spectrum and yield N
s Ao oy displacement
\\
\\.
y o
s
-u 4
s t,
~'
5 3
1 Fig.10 1nelastic destim spntra,
'/'
- 6. Multi Degree of Freedom Systems A multi degree-of freedom system has a number of f
difTeient niodes of vibration. For the shear heam a of Fig.11 are shown the fundamental mode oflateral oscillation h, the second mode c, and the third mode d. The number of modes equals the munbernidegrees of freedom, five in this case. In a system that has 1,
l independent (uncoupled) Inodes, which condition i.4 usually satisfied for buildings, each 3 ?
ais j,
e-j ;
j, 1
% @w,, e 9
~
)
(
/4.<_,
- L.
i j_
i M
t.-.
g
, JJ -l
-tI
' Y!} ;
- l. J
)
w 3 i J W '<
l
.}
s
~
a@
I %
l$'
(c)
.(b)
(c)
(d)
Fig,11 Edes of vibration of shear O'
3;%
Multi-degree-Fundamental Second Thir d I ""-
dQb' of -f reedom rnode mode mode r
- i&@ b system
\\,
3: y
, j y@
mode responds to the base motion as an independent, sinele degree-of freedom system.
}
.J Thus the modal responses are nearly independent fimetions of time, llowever, the i
]k ( +
maxima do not necessalily occur at the saine time.
, ;)
@W USc of Response Spectra. For multi-degree of-freedom systems, the concept of the fjN/jf:
JeS1ionse spectrum can he used for analysis in most cases, although the use of the
!j j - Q '
Ine,lastie-response spectrum is only approximately valid as i design procedme. For a
- j Sybteri tvith a number ofina3ses at nodes in a flexible framt work the equation of motion
~.p y@j7fR S, "; Can he written in anatrix fonn as follows; il t
' Q y fr.
ii
.y y p
~
$lcUl.. M, Mn + Ch + Ku = - M(0){l}
?\\
y p 7
g,:47'
<h l
<sh -
I
.hi$$3MN f!}
l h1' 3 10 EntthquakdRctlstant Design
- Lv1
+
where 6,0, iuul u are vectois, the epiantity in hnul e ts represents a nuit s ect< >r, atul u is a
[*l scalar quantity. The inass matus 31 is usually diaconal, hnt ni all cres both 31 aiul the
'g stilhmss matris K ale synnneltical. Wimn llm dalopine niatrix (? sitisfits c rit.lin ( of uli-
{
tions, the siniplt"t of u hit h is w hen it is a linear annlunation of SI.uul K the sy stem has p J 4
{
nonnal modes of nhration with nadd dispLmement s et toi< n,.
J When the nunles atul freipient ms of tlm eteni are obtaumd, the umd d asp ('ne ate t
detennined by usine mmlul puitic ipition intor s y, w hic h iu.i) lo (hlii < d in inattis notation for e.a h unide a folh >u '
[
rd3f { l) i
- ul31n, t
This is iestated in scalar funn in EV (lM for tinoe cases u lmie 31 is a diam >nal matin.
t The luiticular re ponse quantity desired-uy the sin at a particular point, tla relatn e displat ernent hetu een tu o referent e points, oi my other eihs t-n til tained by h
entubination of the nmdal values. 'l he pn.ced u t e is deu tilmed m Ad. 4.\\ det.uled discussion of t}m desitu a) proat hes emplos ed f> r hich rise Innhlines is ch en in Hets. 1, 9[
l 8, atul 11
(
l'w of Time lliston/. Alternatis ely one may male a calcolati<,n of re'ju ure liy consid-j l
ering the motions to he applied and computing the te3 pomes by a step-h)"tep nunwru al dynansic an.dysis. This implies a detenninistic appmat h, since a detenninistic tune historv is intoh ed. By use of sescial tune histones independently tonudewd, one can arrive at avetate or conservathe upper bounds of te';,onse, but at the esp'nse of a considerably ineteased amount of caleuktion. In echeral, hmees er, thete is no real advantage in usinc a time history as conip.ned with a response-spec tniin apptoac h for j
multi-decree-of-freedom s> t tems.
3fotions in Seccial Directiont Earthrpiate motions actually occur as random motions 1
in horizontal and vertical dimetions. In other n ords, a strut tme is subiet f( d to compo-l Dents of motion in the vertical duettion and in each of two perpendic ular hori/ontal directions. Three components of n,tational motmo, c onespondinu to a twis.t about a vertical axis and locking motioin about the tw o hiin?amtal axes aho inay esist, The hnear f
eround motions are appatently statntically independent. Consequently, if one us"s tune l
histories of mution, one must either use at tual carthquale wwids or u nthetic remids that maintain the s.une degree of statistical independent e as in at tual wmnis. Therchue.
g for time histories that invohe inelastic hehaunt it is.m os en unplineation to ( onsider f(
each of tht components ofInntion independently since, in conciah they ;dl occur at about q (
the saine time. flou cs er, these n only a small pmluhihty that the masuauni lesponses
- 1 will occur simultaneously, and methods h.n c heen derned for handling c ondoned lJ f!
motions in desiJn takita'. into account the abus e t on'ich rations ( Art. IR 1
l, COMPUTATION OF PERIOD Of iD R ATION' a
- 7. Fundamental Mode l' roc edme' ate availalde b,r the c omputatiim < >f the peniids id a i l vibration of undampedi nudti dt etee of in edom s y 3 t e m s ^' "' and appheatimo tii L
j actual buildines.ne descrih d in sm eral paper, " "
A Consider a sy stem with a mnnher of masses "hunped" at particulu points, le t t m e m.,
g i
l wpresent the nth mass of the sy stem, and assmne that the s3 stem is sihratine m the jth 1
mode, if the system is vibrating ma steady ntate without dampine, the con m.
displacement ny of the nth mass can lie wntten in the fonn o, sm %t W
c Ibe acceleTatioli es]mli('!)eed })y t}ie ill tu durille it s (N dlattiry lin 5 tit)n is divell lly t}W il second deris ative with wspet t to tine
~ Ut u i sill Ed I
( f n
9he [Udou ine artitles are }'ast d in pau tin ni.itt fla! 'It un Ih'f. I l IW j u nin ui-m i i t}ie } % 1tl.u nl
'f,L Ceinent Auomnon.
m unnum er less than to percent enn< a1 L ts the o meea pena by hm than 2 p-nent j
llence. nominal dunpum 4,es not aHect the penni appres uhk.
i9' i
im
.n
Fundamental Modo 3 11
$ $ * !!!' k, k
(' \\ $$ l$l' I Iks all l'(
- l' r d II!l, } nll l l'i I
l(* IlleIss b og, l s ( l.I]l sid('It 'l f I ', i d ' 6 k in ersed etiettive fou e or inenul fon e applied at the point n 'l1.c nmiti.d fun n W sm w,f are (onsidered to he applied to dm stmc tute at eat h mass pomt, wlmte the coelheient of tlm sine tenn in the inci"abfon e npmv mn has tlm form i
k 5,o m wf n.;
(M n
Sirme the ilmitial inn es tale acc ount of the inan etTrets, the dis plu euient s of tim stim tme due to the fon es ii, must le pmeiwly equal to the <puntities n.a. ( 'o n e qtn ' tly, in oldet to find tlm syn,ue of the eilenlar fn,pmimy for the Jth mode wi. it b tun 'ssuy luetels to hial a 'et of thsplameurnts n, i,f sut h inaenitudn that fon e'
( one t online to c.a h disphu 4 nmnt multiplo,1 by the local mass m.,. uni by the squ.ne of the cin nlar hequeno for the ;th mode 4 ene riw to th, (hspl.n ements n,g A ny pm edine that will e tahlish this tomhtion will un e both the modal hequem ies.uul the mo lal deflec t"m shapn. \\lnitiplyinc the nuenitudes of the inodal defhu tions hy a I
I com tant does not t h me-th" utuatmn, sinc e all the fonts, and conw<pmntly dl the deHet tion s consistent with thme foren. wdl I " nmitiphed hv the s,une mnstant.
lloumer, it is not possible without other knowledee of the situatmo to wnte dou n I
directly a conet i set of displa(etnents Ior the jth mode. Therefore, the calculations mu t l
a msult of a sy tematie method of j
make it possible to anive at thew deHettions as computatmn. The most uwtul pnicedures, at least for the detennination of the fundana n-tal mode, are IWleich's method, or modihcations themof. er inethods based on a pnni dme of suurssive appunimstmns des eloped miamally by 5todola. A dneription of the suu eun e-appnnimations pmtedme follows:
n t eac h nuss point of nuumtude n,n. Compute fm
- 1. Auume a wt of deflection a
thew dcHettioin an inettial forec (% riven by
.g. J k
,g. g ollknown tilt ulai flef jllelRy u bich may be tairied in tim W})cle t}ie glulltity W is ali oh n'anons as an unknown.
- 2. Apply these torces to th system and compute the conesp"mhne dellettmns, desicnated by the symbol n, n,a = new#
(10) i
- 3. Tin pmidein is to iiule oc and n.o as neady equal as possible. 'lo do this, o nus h varied. The s alue of u that cises the 1. st fit is a cood approximatmn to the cinulu fit,jilelWy bu' tlic linide l}lat (11G' spO!1ds to t} e deHettilyl og und) in i.'<'Imla} u 1111m an appnninution :n the fmatunent.d ioode in eencial, n,m a dl be a better appunimatum to the innd.unental mode shape than was n,m
- l. A lepetiti(ul (d ilW (id( u}aillH).s tblllJ ne aN llW startinf pollit Will It'.Ul ((1 a ID'W
{
doived deHection that will be an men h< tter appmsimation.
1 j
In most caws, even with a serv poor first assmopt;on for the fund.unental mode d"ihrtion, the pmeess will cons erge with nerheih!c errors to u in at most two or thtee h" and one can obtain a cood appnninution in only one c> ele. llon n er, the mode cy(
slope w ill not h, so.n enutely detennined unless the calenlation is mpeated sneul tinr1 lItlW ipt mtity sboWH in 1(q. iIll i.s nude a mininnUn (in ef fM t Winimi/ine ibe Squan o$
the errot 1.etu e rn the delive'l d 'Hection and the anu.ned deHection) the "best" value of consistent u ith tht assunmd delhx tion eun e can be determined:
m 5 m,(n, o,. i mininnun (111 Substitutine l{q. (10) into 14 (111 md (iputine to /cm the deris atis e with wspett to w gn es Y
~
_mun.n, u
s } 2 '1 f
to u --
_ m., n t.
W vJ}ile (d o givet })y l'q, (}]) esUt t'ds eclielally (411y s!iL'} lily, (fle trut' va}(It* I'irt!u fund.unental nmde.
d.
l
.c
]
t 3 12 Earthquako.Flesistant DosI n D
+,.
Rayleigh's tuethod is probably the tuost widely used engineering procedure for corn-y<I; puting the period of the fundamental mode. Without modification, however, it does not y*
Renendly give accurute values of the mrule shape, llayleich's method for calculating the y
lundamental frequency of a huilding frame can he related to the ptocedure described h
to neity thmughout the stnwtucc. In (lm case of a sertical or above by equating uim i
horizontal heamlike structure, the derived disphwements Ti,,3 u ill he pmportional to the deflections of the stmeture due to forces equal to the weicht of the structure. Since (y
- f. I Rayleit h's procedure using u,,, = 1 gives a quite accurate determination of the furnhunen-4 a
tal frequency, it is obvious that Eq. (12) will yiehl a highly acemate value if any nmre d
l l
teasonable deflection shape is anumed for the first mode.
(
The efTett of foutulation rotation, colmun shortening, or other contiihutions to dellee-tion can be readily taken into account in both the successive-approsiinations piotedure and the Rayleigh method.
The simp 1nt,,.#ph of the pmeedure for computine the perimi of va, %n of a Enample 1 stna tme is that of the sintle-degree of freedom systent Cmc ider the structme of Vic 2. u hk h ha a single inass m and a spnng constant L for a displ.urment u, the mertbl fmee n, from Dt On, m
fu h g
The derned dellection us is A
614) or-A A
1 It is obviom fmm Eq-(14) that u = u if d = Um, from uhir.h the npiessmn for the frequency n dM j
(13)
[
j f = 2n --r f
2n s m 1
and the penod is t
'N iIfd O'.
3*P ** 23 \\ L b
.f f
t and Consider the three-deper of freedom struetme whose rebtive spnng wastants Esample 2
[
maues are *,hown in Fig.12
/
For the purposes of this example it n aonmed that the stna ture ar.ts as a shear beam,i c. the relatne onuly tme only if dellettion of any ston is pmpodion.d only to the shear in that ston. This would be i
L l
the en.lers were mfuntch stdfer than the cohonns. but wah smtable
. t l "3'*
nuEhheations in whann'stdinen, as discuwed later, tla stnature i ;
can he analyzed quite.uturately as a she.u he.un.1 he m.e s m n
>>1 i!- i +,ii!
,,l [
gnen in tenns of weight dnided by the aneleration of cranty.
i l
g Com.equently, the umts used m the cakulation has e to be talen
(
with consktent valon. It n apparent fmm Eq. (100 that, for mau m k
(
tenus of weicht in pounds dhided t>y acceleratmn in inches per l-m2 second squawd and L in pounds per meh, the penod T will be in
- m units of seconds. Another set of consktent mnts im oh es displace-l
-.j ment in leet weicht in kips, acceleration ofgras 03 in feet per wennd
}'
squared, and spnne tomt-mt m kips per foot.
36 The assumed deflection n,, can base any umt3 u hat som er, and I -
I the dern ed deflectmn us uill be m the same units. Consequently,it is com enient to take n,n or ue, as dimensionless. This does not affect the results and makes it nmre dear that the nuidal dhplaer-ments ghe the defledmn pattern rather than the ahmlute e
9 i I
M maantudes.
j Cidcolations for the fundamental : node are chen in Table 2 for an
!R assumed shape of the mode unesponding to deflections at the first,
' f)
]N 4
semnd, and third stories of macuitudes 2,3, and 3, respectk ely. The inertial forms (A. are computed from Eq. (0) by multiplying the Fig. 12 Iloilding fnune for assumed deflectiom by the conesponding masses. The shears L are Etunples 2 and 4.
obtained by summine the inedial forces from the top down, since
[
there is no force at the top. These shears, divided by the spnng const.mts for the wrresponding floors, gn e the increments in story dbphurt ent bu.. From these, by st.uting with the known zero defk etion V
M n
i anheha.oneebumthev.auesatheacm aaaemon m a
The ratios u,,,% nise the vames of d at the cone spondme mass points for winch the dern ed curve I
D
[
and the assumed eun e aeree exactiv. If d has the smalk st of these values. 0 A00, the deris ed con e hes b
("
Y\\
l o
-i s
Modal Participation f actors 343
!1
-l.
f 0 Y o it h,. es t nula m non nie w s,,h v o{ v j
2 n e o u here un.de tl.c.m ona 1-une uhdeia w la tu een U Do and 0 W o t 1.n nub the tw o t mu s acn e m p ut ( on cqm nth, the ab.lw 1 m et and j
j upp r luiets to the s alue of d.nc n F M enl o W. um.n tn eh. (lls c ol.sf n a ne a; ph i nh in the l
r
( a c u here the a'mmi (un c.aul t} e denit d, nis e lm t n.
in d d j u oi.t s The lattern of dein ed de f!n t o e 2 i i 1 al 3 r 10. I N.aol 10 n lat n - to a umt delb t ti.n at tin f a t ma s..b.c the b.er. It t!o ut ulato ms m 'l a!Je ' ee n intc<l for. u m nl dr plxi m. nt s e t 1, 2.arul-1the denml dr p!x ement x.n e pn i m h th
.nne ~1he wnesp.ahnc ism n vure ot the fet.
no.de i m ular her pn nt s n m nMm 'I hu. the s due 0 517l m dt h nmned m 1 al.h 2 is 't en to l e a rJ that th denu I dehn n.n p m ni n n it or ik so sen s.!vpnamw m ihm eu n it u dl be o a mende Wer o t o 4 OL-o ch a n n w h. L r to the he.t n el"
.nem th.m n ela a~n a d p.ne m a t c l are n i ! m Se - oc u e, m 'l aM. 1 L rI i
I he i ah obtu e b.i in f rame b, he ii ch's n m t,ic ! nt n r. h t m M a h-r. '
g i t,n<
'! Le n m b n 2 p;i,w t of < qual :o mt f ih +1,.
a o
. n ; d.
. whnhnu:Lidm x.yli m..tth A % im.ro si op; et hn u+
.n e n 'T.
m r.
% n! 4,
u hn h h n o ! mt anl 1 M W uhnh.nc p e itha 6 ot T M ?.mJ ti n,
n.
4 i
aloc,i1,107 and 1n7.i,n tsen
.sl
- 8. Higher Modes $es etal nu t}e nh are,n.n l il t h h it t u u p t i n r>
the th oju m o n-id l
i n u o le - ImJlui th.nithe hunlana ilil u s ele i o a mnhm!, J:t e-.d-h s ra u n osnunlu' n; h pn t c< h ne s ar c < h. tilic.! :n lM 1 h ihm eser the lu ch-p ed hJital < ' m;,nto 4 t es en Inchh (inup!cx ' 4m in < nly a h '
deteinune all the no nlm. uni In, pie m ic i
nanntes i,y use of st.n ulani pu er.n n s..n ni A t.nied h.unl-ak ulat u m on tie,h.n c o, j
h uiJet ut uiten%t eu ert bn api'o nnuatin ' th. l'und.unental frequeiv", in j alo"!
d
- 9. Modal Participation f actors N os e t!" ovuh shapes determini d by tia-inellu u b i,t l
'. d 7 are.nluti.u3, in teims iJ a unihu m muhiphei. a omd.:/ ;#!n;: lti,m M f or in n t I, In's (l if i tlt t f'lllit n# ' ll n '.ictll.Il it s j u ni s s' i d 1 'Il t a t iir e
'\\ lU e la Tal t} a t uT ls Cls f'll 111 \\lt I'
Ili a liillh Hlegit c o il-liet i h n;1 s'. slt' :n t!Mt lias llu h lu in b lif i'l tin (i d:j 'h '(I n u " b' <dthhu eq. unl, to a lm In tum ithis onuhtuni is cenculh utidn d f or lunbhe>s. e m h n o. o l e i
en aation as an independent sin &deace4heedom tem. Tlg n s p. u n e of a st o n, tili!- as a Intit t o m t d tin n t ali I n. ss :itte n ill th t+ tin n:t) - Y s. o nit
]T t
lh I k, Y k f h k. k f
y k
I' i, !
il k i(
,k
,kl l(
l kf % !bl\\
i 4{
]kk'
$l k
..k sk j
s tory deflet tion. s tm > she.n..u t elerat n an en '
o., - (tule sir mding naulal < pnintity ha Jth unnle noidal pnth spation f.o tin khned in 1G. ;15 1
m t i - delln tion respon'c tin a me!c.deace-o!-tmet n u +m
.oh.u tnl to th, i
i
} )l f 's( l l 4'(
Lis(' ('s t ~li.it li)ll 1
af' Illi M d { l.li k il lj h't i l)
Ll!!1[ l' J is I'll is l
a b
l'.y N..
. 1s i
'n u ;.,
o i
r
){j\\{'
il N
,k lll j {
' ll \\ l)
]l({*
,[!t.
f ' { '.k I l s l
- fI Il ' ( tl }\\ I l*k} } { 's
)ll
('l l l l l )l}
})
li ll '
f m th" indn iduj no !c. d i to d m ce nnih ot em at il l-j lua anse tht mn n uum ir sp,in o 1 i n llill; il g"
i i. I!H t'li' l t l h 1113; ! (I;'
' l!I l
!!!!n' int.4' ls t 'lll a i s liit t *:
'!?
' 4 ' 1 ) l '. lIl s
8 h
L*
um m a i o! > >
d lo suu nnin J t,,.i p, hah!c ie mon'e An upi, hun > to th, ales ofthe mninnun no dal ic p u:
4 s
V op
. po o
il J, -b q 1:,h
- r i e n 1. d-Th-umt pud ul& ms; u + e u -pt ni t h,- (
r,
- LI s j!. !!)? )' n '
f ['l si t-1. i +i d t!a* st' in i)! tio
'j!
It' t iI !! u 4 pi 111 ;!
1: i Y
i/>
as, m
3
\\~
fle q- 'it-t}!
lut> ci j tils.ile11' I
,! ; n i t l 19 l. !, l ' i. : t - o m s, :t p nt !!
- in e ni ( 'It tilg ( as(s l
,1m-V, c u t!r
.n t : h
.t io n tiw t u n ne il tln-f em in trin id the spe, h al s eh its n l e -l = ec.\\, latIs i tha.i !b tlisii!a en n > sit lis;" e / ),
u-n ~
V, 02 u,Y) t Iy a
o-w, i
l L
huumerAN
L
,=-. ~ -- -K_
- l., _
- __ _ _. ? .:dL .:T2 MM:" :t'"&?E**jf{""f ^ & Sir & m , s. - _=. - 34g4_7 (sg ~ - - _g ,_g : w ,,. - g.g. -.I.1 "!.- -^ .-m <.sa e .,i TABLE 2 Fundamental Circular Frequency for F. cme of Fig.12 Derived Assumed "'" t displaceme nt displace ment Incrtial sig.ar in story M asses U *h Derived Assumed rO fC L, o*J ' kNP 3CP rilU n,w U d " ~, (!.!9plaPenlPnt ;' '"td ,'e. rit s [ and d.1S PISCP hip h t y w" t h p rif16' (/a, ~ " "9 g,'" g*" I u 5., n,. '"a"a' constants 7" v w4, I - 2 r w u,s i 4 >. }m j m "5; lm . ?5 j I s. i 3 "'1 3m/k k l 2 [] m 3 3m 4.5 if k 0.667k.im 13.5m ;'k 20.25 n*/k* i 6m 2m/k I i j 3g l i i 2.5m/k 5 0_S00k/m j 10 Om f k i 12.50m /k2 r 8 [] 2m 2 4 ". I l IOm 2.5m/k i aw l l l \\ n? I l' i i i I m, u,.d,s 46m '/k k f 4Gm /k N9m /2,k2 2 2 0.517 - I i w,2 =- = I n, G,$2 S9m /k2 72 3 s
Spring Constant for Equivalent Shear Beam 3 15 o E uA (22) s mn The equation that is most convenient to use is generally that one in which the spectnnn values are most hearly constant for the range of molal frequencies considered. Conse. quently, Eq. (19) might he used where the spectral displacenient is nearly constant, Eq. (21) where the spectral velocity is neady constant, and Eq. (22) where the spectral acceleration is nearly constant. For esample,if the period of the structure in Fig.12 is serv long in all three inodes, Eq. (19) micht be used, but if the structure is verv stiff, so that all three penods are very short, Eq. (22) would be appropriate. In all cases a better estimate of response would he obtained using a syn.ue mot of the sum of the squares appmach as in Eq. (20). j Example 3 The modal parthipation factors im the 6.une of I'ie 12 are nunputed in Table 1 l TADLE 3 Modal Participation Factors, Frame of Fig.12 g M ode Quantity 1 2* 3 w', 0.5k;m 2k m Gkim Deflec tion roof = us. 4 -1 1 ~ Deflection occond floor = u,. 2 1 -5 Deflection first floor - to. I 1 3 I m.u,0 S 2 2 Im.u 8 22 4 41 y 0.364 0.500 0.0154 w. !t
- Circular frequency aint deflechun liattern nir this mode are computed m llef.14,
- 10. Spring Constant for Equivalent Shear Beam $lany structures can he analyzed as shear heams by suitable Inodification of the stilhiess parameters. hlethods of perfonnine the l
analysis and of modifying the starnesses are described here. Ilowever, a more accurate analysis, which is perfectly general in applicability, merely requires the detennination of i the matris of cocilitients relatine either (1) the deflections at all mass points due to unit loads at individual mass points nr(2) the forces at all mass points requited to produce unit displacements at individual mass points. Most accurate analy ses must include consid"ra-tion of shear and flevue, foundation stiffness, and framing interaction elTeets. l In order to avoid confusing the principles of the earthquale analysis with the detaih of calculation of structural deflections, only the simple case of the shear beam is discussed l here. For a shear beam; the spring constant i for each story is the story stiffness, which is the lateral force reymred to pmdme a unit ielative lateral displacement of only the storv 1 considered. 9. Fra mes. The stoontillne:, of a moment.icsistine frame is the som of the stitruesses of j; the columns ie the storv. Thes. for a fraine with infinitely stiff girders gr = 1 12r'r ' i gy (2 31 ] s; j-The cifect of girder flexibility is shown in Fim 13, where the first-mode deflections of the i frame of Fig.12. with column bases assumed liwd, are shown for riuid eirders in a and for flexible ginle3s in b. Itotation of the joints reliews the column end moments, which y. reduces the shears and, theiefore, the story stifTnesses. The reduced stiffnesses could he detennined by computing the cohnnn moments for first-mode displacemer ts of the rigid-1
- i.
girder fmme and then distributing the moments tu account for uitder flexibility. The g resulting story shears divided by the corresponding relative stoo-deflections give the ,y story stitTnesses, Thhd mode deflections of the frune of Fig.12 are shown in Fig.13c and d. It is evident
- 74) g_
, that the story stitTnesses for this mode difTer fnun those for the first mode if giider u _u NS'
3 16 Earthquake Resistant Design
- { f h],
flexibility is taken into account lloweser,it is customary to use first mode stilfnesses, or I* !j appimimations to them, for all modes, sinec the first mode is genetally predominant. 1 The effect of girder flexibility can be detennined approximately for a single column by the equation L Re. Ncv -=1- --4 (24) h wt E Krr E Kn where Ker " stittness at top of cohuun Kc3 = stiffness at bottom of column SK r = sutn of all the stiffnesses at joint at top / 1Ka = sutn of all the stilInesses at joint at hottom j in derivmg Eq. (24)it is assume (I that alljomt rotations are the same, that the fixed-end i moments above and below eachjoint are equal.and that the fixed end nunnents at the top i / I i l l (c) (b) fc) (d) ,j + i: i s Fig.13 Mode sh.y ~s of building fr.une of Fn:.12 a and bottom of each column in a story are equal, in general, this assumption is sufficiently accurate throughout the greater poWan of a typical tall building, cuept in the hiwer q Q stories and, umler certain conditions, in the upper stories in these legions the story stiffness is sensithe to the relative stillnesses of coluums and girders and generally tequhes a more accurate determination, particulady if the girder stiffness is appreciably i less than that of the columns or the ammnement of beams and columns is inegmar. These N stifTnesses can be calculated, as outlined previously, by imposing unit displacements on U all stories simultaneously and distributing the resulting fised-end column moments in the [ . stories whose stiffnesses are to be detennined. The contribution of floor systems to stifTness shonhl be taken into account in evaluating i girder stiffness, Sheur Walls. Shearing defonnations must be considered in detennining the stifTness
- N li of a shear panel or wall. Since stiffness is the reciprocal of flexibdity, which is defined as the deflection due to a unit force, the stiffness of a wall totationally restrained at top and 1
bottom is tiven b.v 5 1 h' 1.2h 125) k 1CI'l GA [ If only the top (or bottom) is rotationally restrained ). T* yi' ca_ I h3 1.2h
- U These ei uations apply only to the unen & wall Structures with lateral resist.mee l
arising in major part from shear walls cammt be analyzed accurately by the use of the y N y shear-beam concept, but require more accurate treatment. I The above expiessions do not refleet the effects of foundation motion, which can be significant in estimating response. 3, j-Procedures for estimating the stifTnesses of uneracked shear walls of various shapes; Q with or without openings, ar 3 given in Ikis.19 to 21. ^i-Aucmblics. All vertical resisting elements in a story participate in the story shear hj provided the up ser floor has sullicient stifTuess and strength as a diaphragm to distribute 'k the shear among the elements. The elements inay be columns, bents, walls, diagonal f-) bracing, etc. The stiffness of such an assembly is the som of the stiffnesses of the _ elements. p
if Spring Constant f or Equhf alent Shear Dcam 3 17 y - J o 4 l Enompte 4 htoiy shears for the fr.une of l'4 12 are deterummd for an e.uthoo.d e wnespmdm.. o.rnlunse spettnan j appunmutely to the 19 to El Centro carthipule ( Fie 3' m this cumple. 'l he clas c l shown m rg 14 is obtamed using the pumlun s out!med in Ait.1. and the fiwletic auch ratmn and I dnphu ement sp (tra u me the prowdunw onthned m Ait 1 Tim elasta-teminse spettium (one-spouh to a maimmu emund.u c eleratmn of 0 h.uul d.unpme of 5 peu ent of entu al. The inelastw I I speanim is drawn for a duttihty f actor of 5 N. l w .\\ \\ ,N/ 's. / 'N i j'NN,.,p/ \\,N N,,/ \\,' Nli/ Nj/, / \\. .l / = s. / s i 4< 3 ) = <, s< t t / W-W-F*r ~ [c- ,--A- /a h.g, x.--- .s -4 M.-.' --t 4%;.---4,4--*-.*- +~ -*-.-*,-~# 4-+ ' f, p+ -4 r /;. i s.s i 1 - z l j gl_ \\ f /N l, N e' 's !,% % u i.e.. / \\l y< )&e c ,'l -'* \\ 1 . g 1 g / * / ,7_ 4p,.1 1 ~. / q' u n a / l'sL.'.,a ',g -y m_l,,., _. w kA y s N 4 N + x v ,- xg 7' \\Q
- s
', p N;/ I q9 j-y - x N}I j y v. x t' t3 ,1, Q f ..,--._'N_#_. A. i_/_', /\\ ,t. ,f . / ts \\ jf ./ i y --. y r y. %.- ~ .. #. m. ' N ? i c [i t w.c ! l - s > t s, !/', y,/..' l r t ? e q,,/.--'.m,', ' y! ,j/ j I 's ,f, s "N / s l i / s y/ 7 - -- a g/.. s. i w ;..n _. g '.. _.. s h.. w i.n j f,-,.. _ ~ _ r s K; f l e i >" i ,y+ ' i / i ,s,. 1, ,/- rew.camee s - e s s s<\\s'., f - m e.c e w' m i, . / au.,rea, w ee-e.o-.s- ..! \\ os.._. _ N,,,&T, ['.l \\,_A ' F. / r I. '}._'__f s._ p I .I. mm r ,', } / 3 / ',' \\l l / - s v '.i ./ p N s .' s's s N f, ~l.- v. * - ff. t 8 _ f ',, ' t w. _ __., ;3 s.. t % i, l l/, e r l i ~ s / s ]</ Ny, ,4,., N. m.,,~.-.-,.y,,- sg - ;- s -3
- y. w,
7-i s v / \\ ,L x l, N ; \\f, --i, ss .., T u -, - - -.. - ~ -... j - I,, . i -y-x,/ x i i s ,s ~, o i '\\ s- ,, ~ \\. t .4 \\. Y6 >' 3, cI -p s I 1 I N / J ' \\'=% / / %./ i s i / gs x.-.' -.\\ -.t -+.'- } ,c s N, l 's 1 / L ~ -. u ---.-..,: ' \\. I \\ \\ '\\ / \\.,' j n. / / 't s. rN / \\ ,A ). ,/ 4, s , a,. .4 j t ,/
- x s
s / N s i s <) o, r': m c os i 3
- i..
x m t.o so ac j frequency N! i 8 Fig.14 llesponse spet tr nm for E tunp!c I I l The upper-ston stiliness I h assmned to be 60 kips m. and the roof mes to be m = WW = 120 Lipc l 0.313 L ip-snA in. Thu s Um = 192 see-2, and suth uns s aine know n the three modd j l E I m..sec frnpa ncies can he deterunned fmm the alues of d in Tah!. 3 and the correspondme s wid i i displatement responses uml from the clastoplastic, pet tunu m Fe 11 't he resu!ts.ae s how n m l t l Tahic 4. TABLE 4 Displacement Response, Frame of Fig.12 /e o 2-b lt ,s(*(' Id, s('( [, h 5 o $. t ,r i ..I a % = At 19 6 3i OS 1 ( 3 6Um b l ~;2 MD 54 Om i ) I ) s 1.Isk s lY' t$\\ [!k sk! (I!I ( ' k 11 s'I I 1('. N s. $ (' ! } I', N l i9 'I i' (.' k k#.l!Is d e O!' N I ( (l'il $'\\ 6 hetu et a the om!.d dnpi.u en ents m 1 able 3 ~11.cs e are muluphe 1 b the ayupnate mod J ;.atici;v g ~ 3 tmn im ton from Table 3 to obwn the o n deficcnons in inthes p i inch of sin ti.J Aplate.m nt. whnch uhen muhiphed by the w aspondine saluc3 of L. gis e Se story shcan m Ltps per mch of l' mud.d displacement. These.ue then udtipbed hs ti;c appmpnic v.Jues of D, fann Tahh 1 to W m th" stm shears. l he inm te pmse of 9 stuns with a seuil nunder of deen es of fa ed im is smly slichdy len than tb sum of the al%hac values of the wdal maum t 1 hev smns are risen m Tahh> 5. For compson, l. thac.ne also (S en the syn ue root of the sum of th uptoes of th" s alum of the inodal shcan. It n
- 7 j
q 4. -
! if - l l l' !:1 t s 3 18 Earthquake Resistont Design ,,S ( 'j noted that the values mmputed,ue mnshtent u ith a a4ponse spn tium dra n i.i a do< tihty la, t r of 3 and an caith pi the inn nsity muespwime to the l'.I (N ntro e u11epuke for a dampmu of ab"ut ".
- [
l percent ( otical. j l DESIGN in tin desien of a luulding to resist earth ptake sontions the
- 11. Gercral Considerations j
designer works within eet1ain tonsttaints such as the,,ochitectinal t onfieuration of the buildinu. the foundation conditions, the nature,uul estent of the haard should f ailure or [ colhipse occur, the possibility of an c.uthquale, the pomble intensity of e.uth<piales in i TADLE 5 Story Shears, Frame of Fig.12 Story Quantity himle 2 1t 12 G-1 ___.__.._4..___ .j 60 1ho 210 ,e l Stiff ness, kips /in. n - u,,_i. I 2 1 1 llelative rnodal deflection u .ll. 2 -2 O 1 3 0 -5 3 Itclative rnodal deflection, in./in, of one-1 0 724 0.361 0.361 lf tral diopheetnent = h u, - u a) 2 -1 0 0.500 I f n 3 0.272 -0 361 0.136 p it ii O l 510'lal shear, kips /in. of spettral displate-1 11 60 57 9 rnent a kh(u, - t%-i) 2 -00 0 120 3 10 - 06 33 J. Slodal shear for values of D, in Table.1, 1 30 16 60 I lf kips = D,kw(u, - u,_i) 2 - 17 0 31 3 t -6 3 b e E 97 f j Slax possible story thear, kips. Square root of turn of squater, kips .l 31 M M t i i l the iegion, the cost or available capital for construt tion, and siinilar factors lie inust base sotne basis for the selection of the strength and the piopoltions of the huilding and of the j f various ineinhers in it.The icquin d strength depends on fattors such as the intee.in of c.uthquale motions to be espected, the flesihihty of the structme, and its duc tility m 3 iesen e stiength hefore d;unate occurs, liceauw of the intenclations,unone flexibihts and 'q strength of a structure, and the forces generated in it by esthquake motions the dy namic [i dedien pmeedure must take these various factors into account. The ideal to be achiesed is (( one involving flexibility and energy-absod> int capacity w hich will pennit the catthquake 'n h{ displacements to take plaec without umluly latte finees beine uenerated. To achim e this j end, control of the construction pmeedures and apinopriate inspection practices are il necessary. The attainment of the ductility tequired to iesist earthquake motions must he 1: emphasized. i
- 12. Effects of Design on Behavior A structure which is designed for very much laruer i
i[ (( horizontal forces than are ordinarily presenhed will have a shorter period of vibration 4;j g hecause ofits greater stitTuess. The shorter period results in hiuher 3pectr;d accelerations, il so tlrt the stiffer structure may attract more horizontal force. Thus, a structme desiened Jq Q for too I uge a force will not necenarily he safer than a similar strutture based on smaller j l' j a forces. On the other hand, a design based on too small a force makes the strnetme nwre l} *0 flexible..nd will increase the relative deflections of the floors. In eencral, yielding occurs first in the story that is weakest compared with the nuuni-ttules of the shearing forces to he transmitted. hi many cases this will be near the hee of 3 the structuie. If the system is e,sentially eletoplastic, the forces transmitted throuch the yielded story cannot exceed the yield shear for that story. Thus the shears, accelerations (
) lJ Design Lateral Forces 3 19 N s y atul relative deflections of the pottion of the structure above the yichled floor ate reduced i, compared with those foi un elastic structme subjected to the same base motion. Conw-f quetitly, if a structure is designed for a hase shear which is less than the maximtun value computed for an elastic sy stem, the lowest story wil} yield and the shears in the upper i stories will be reduced. This means that, with proper provisian for energy absorption in g the lower stories, a structure will,in general, have adequate strength provided the design l ? sheating fotees for the upper stories are consistent with the desien base shear. The l Unifonn Ihtilding Code (UllCP recommendathus are inteinled to ptovide sneh a consis- ) tent set of shears. A significant inelastie defonnation in a structure inhibits the higher modes of oscilla-f' tion. Therefore, the major deformation is in the mode in whuh the inelastic defonnation f predominates, which is usually the fundatnental mode. The period of vibration is efft e-( tisely inertased, and in inany tespects the structure resporuls ahnost as a single degree of-freedom systeto correspomline to its entile mass supported by the story which becomes f~ itmlastic. Therefore, the base shear e.m he computed for the modified structure with its futulunental period defining the nuuhhal spectrum on which the design shouhl be based. The fundamental per_iod of the modified structure cenrrally will not be materially ditTerent from that of the origiind cla tic structure in the case of framed stnictures. In the case of shear wall structures it will be lonter. It is partly beautse of these f.u ts that it is usually appropriate in design tecotumetula tions to use the frequency of the fund.unental mode, without taking ditett account of the higher modes. lloweeer, it is desirable to consider a shearing force distnlmtion which accounts for higher-mode escitations of the pmtion above the plastic region. This i-h_ imphed in the UllC and Structural Engineers Association of California (SEAOCP tecom-mendations by the provi.sion for laterabforce coellicients which vary with height. The distribution over the height corresponding to an acceleration vaning unifonuly imm zem at the base to a maximum at the top takes into account the fact that local accelerations at i higher levels in the structure ate greater th.m tho3e at lower lesels, because of the latter motions at the higher elevations, and accounts quite well for the moments and shears in the structure.
- 13. Design Lateral Forces Althoueh the comp!cte response of multi degree-of-freedom l
systems subjected to earthquake motions can he calculated, it should not he inferred that l' ~ it is genendly necessaT to make such c.deulations ar a routine matter in the design of multistory buildines. There are a great many uncertainties about the input mutions and about the structura; charactetistics that can affect the computations..\\loreon r, it is not 4 pencrally necessary or desirable to design tall structures to remain completely clastic [ under ses ete carthquake motions, and considerations of inelastic behavior lead to further discrepancies between the results of routine methods of calculation and the actual response of structures. i l The UllC and SEAOC reconnuendations for earthquake lateral forces are, in general, consistent with the forces and displacements determined by more elaborate procedures. A 7 2; structure designed according to these recommendations will remain clastic, or nearly so. }! under moderate earthquakes of frequent occurrence but must he able to yield locally f without serious consequences ifit is to resist an El Centro-type earthquake.Thus, desien { for the required ductility is an important consideration. Duetility factors (br various types of construction are difheult to characterize briefly. The ductility of the material itselfis not a direct indication of the ductility of the stmetme. - Lahomtory atul fiehl tests and data inun operational use of nuclear weapons indicate that L r structures of pmetical configurations having frames of ductile materials, or a combination of ductile materials. eNhibit ductility factors y rancine from a minimmo of 3 to a maximum i of S. } The dnctility factor to he used fhr daign depends on the, of the building, the hazatd j involved in its failure, the fnuning or layout of the structua. nd ahme all on the method of construction and the details of fabrication of joints and connectors. Duetility factors ] l7 columonly used are 3 to 4 Ihr reinfhreed-concrete structures and 3 to 6 for steel structmes, . ;y with lower values in both cases if nunprepion behaeior toutrols. A ductility factor of about.1 to 6 is implicitly assumed for ordinarv structures desiuned to UllC carthquake , g requirements. fR -The Applied Technoloey Coimeil has des eloped comprehensis e seismic design provi-L M sions for buildings, which are intended to pmvide a basis for building codes in the United -? j;$ ' i pf g y
E*. i-43 3 20 Earthquake-Resistant Design ~ j: a fA ( States." Provisions of the 1976 UHC Code.ue given in hec.19, Art.11. The 1975 SEAOC i j formula for the seismic hase shear is the s:une as the UBC fommla. In ge neral, seismic id [, coellicients have been increased in camparison with catlier values, and more fators ate l considered in arriving at the lov shear The rmwei vahies ate sometimt; 1.5 to 2 times 21 i the values in the older codes. i Other parameters and methods of ituportance in seismic design sie eisen in Refs.1,5, g igl l1 10 to 12,25, 26, and 29.
- 14. Seismic Forces for Overturning Mornent and Shear Distribution When modabanalysis
^ o 7 5g i j te< lmiym s ate not used in a complex stmeture, or in one havine ses cral degrees of ,,j freedam,it is cenendly necessary to define the seismic design fottes at each mass poim of T ! the situcture in order to he able to compute the shears and tuoments to be used for dei.ign. 1 The method desenhed in the SEAOC Code is meoimnended fm this purpose. It is .g g. ? ~ essentially the folhming:
- l. Compute the total h tse sheat corresponding to il scistme coelheient for the
] ll ,tructme m'dtiplied by the ;,tal w 'iuht. q-
- 2. Assign a force F = 0.07W, but not more than 0.25V, to the top oithe stiact"re.
] ~. h, .s i
- 3. Assume a lim ar varial:oa of accelenuion in the stnnfure from /eto at the base to a a
f: j i mas.mtun at the top. [ -l.\\lultiply t'.e acceleration asstuned in a by the mes at eaca - wtion to find an i ' l1 inertial force actin at each level. ]'
- 5. Adjust the assumed value of acecleration at the top of the strmttne in 3 so that the total distriheted later.d foices add up to the total hase shear comprted in 1.
P
- 6. Use the resulting seismic forces, assicned to the various mssses at each elevation, to compute shears and molnents throughout the stnnetme.
- 7. The resulting ovetturnine moments at e.nh elevation ar I at the base may cause r[
tension and compression in the columns and walls of the structure. Provision must ht. i h made for these forces. H S. The oserturning moment at the hase should be considered as causing a tilting of i 'j the base consistent with the foundation compliance, and also may cause a p.utial uplift at j j one edge of the hase.The increased foundation compression due to such tilting should he C 'onsidered in the foundation desirn. 15.' . 11ru Energy absoq) tion in the linear rante of tesponse of struttures to } dynatt.
- 1s due primanly to dampine. For com enience in analysis the damping is
! l- [j generally a_sumed to he viscous m n ure. D unpmg iesels have been determi ' from {j obseITation and men 3nremeat, but show a fairly wide spicad. Damping value s. ' use in +' design e generally taken at lower len I 'han the me.m or a"erage estimated values. O [ Damping is us' tally taken as a percemate of tht critical damping value, i.evels of j a dampine suunnarized from a variety of sources are given in Refs I,25, anc: E Recom-mended damping values for particulat :tructural types and materials are given in Table 6. The lower levels of the s alues are considered to he neade lower bounds and are therefore i V c! ll highly conservatise, the upper levels aie considered 'to he averate or slichtly above ] averate values, and prohahly are the values tha hidd he used in desien when moder-ately conservative estimates are made of the other par.uneters entenne into the dmien j eritt iia. t }
- 16. Gravity Loads When stnat ares defonn '.ateraJly hv i considerable aniount, the 4
effect of gravity loads can he ofimportance. In accordar with the retommendations of (' most codes, the efIects of gravity loads on memhet moments Wd eEett) as the 'tructure j defonus are to he 1.ddt A tiirectF to the primary and e.n-thquake effects. In eenend, in coinputing this elitet, cue must use the actual dedeetion of the struettue, not that fI corresponding to reduced sei> ;ic coefficients. d,
- 17. Vertical and Horizontal L 'ation Usually th > stresses or 3Sains at a point are
[ kI affected primarily by earthquake motions in only one direction. Ilowever, this is not { always toe case, and certainly not for a simple square buildinu supported on four columns } wl.cre, in general, a corner colmon is afTeeted equally by earthquakes in the hvo i t horizonta' arections and may he afTeeted also by s ertical earthquake forces. Since the [ cround moves in all three directions, and even tilts and rotates, consideration of the combined efTects of all th-se motions must he included in the desien. When the response ] in the various directions may he considered to he uncoupled. " various components of l hate mwon can he con iden d wparately, and edMdual mouse wtra can he dete miacd for each component of direction or of transien* ha m di< placement. Calcula-f I r I .i
T I, Curtain Wall Dulldings 3-21 }' . t e
- 1 tions have been made for the elastie-response spectra in all directions for a nuinher of 4
earthquakes, f tudies by the authors imheate that the vertical response spectnnu is not l ft more than about two-thiids the hori70nLd lesponse spectrum for all frequencies, and it is Ii recommended that this nttio he used in desitn. For those paits of struettues or components which are affected by motions in various directions, the response inay cern mHy he coniputed by either of two methods. The first l involves computing the response for each of tir bret tions independently and then taking the square root of the sunn of the squares et resulting stresses (fcrees, etc.) at a particular point as t}m combined response. Alternatively, one can coinhine the seismic forces corresponding to 100 percent of the motion in one direction with 40 percent of each of the motions in the other two orthoconal directions, and add the absolute values of these effects to uhtain the inasimtun resultant forces, strains, etc. This must he done, in some I for each of the three principal dilettions. la teneral, this method is slichtly
- cases, con se tratis e.
E TABLE 6 Recommended Damping Values
- s
'l c(I.. k.3 ' f iit :; so Stres, bs el Type atal analition of stnitture d.o:.pm; Vital piping 1-0 Worknu stress n. (na tuote than
- b. Welded steel, plestressed concrete, well-2-3 7
about % yichl remforced wncrete tonly sheht crackmd llemforced connete uith considerable 3-5 c. point! ennkiag
- d. Ikhed and or rneted stech wood struc-5-7 tures with nailed or bolted jomts Vital pipmg
%3 At orjust hel,w a, yield point k Welded s?cel, prestressed concrete twith-5-7 out complete loss in prestressi
- c. prestre' A concrete with no prestress left 7-10 i
- d. lleinfore i cencretr 7-10 e, llohed anda in eted steel, wood senic-10-15 tures wab bolted Mmts
- f. Wood structures with nailed jomts 15-2n
- Adapted from Ref> 4 and i l
l .\\ related matter that merits attention is the plovision for relatise motion of parts or elements having multiple supportt
- 18. Unsymmetrical Structures in Torsion Consideration shouhl be gisen to the elfects of torsion on unsynnneirical structures and even on symmetrical structures where torsions may arise accidenia.!y for various reasons. including lack of homogeneitv of the structure f
or because of the wave motions des eloped in earthquakes..\\ lost code. innvide s alues oi l" torsion. If analyses l accidental ececutricity to account for " calculated" and 'ateident indicate gteater values, the analy tind values sho ni he used. t 1k Curtain Wall Buildings
- The stwneth and rigidity of buildines with noncalculated j
hller walls, partitions and stain are many times those of the fraines u hich were intended to prmide tlw entire ;ructural reshtance. Thi3 generally accounts for the relatively gmd seismic and windstann historv of multistorv fnuned buihlines of this type. Ilowes er, the l l f rames (annot function effectivelv in lateral resistance under ses ere shocks until the l surrounding ricid materials have ihih.1, nerhaps u ith considerable ceimomie loss. l Buildinus u ithout any appreciable lat al resistance except in the fr.une proper ma> le I l subject to larce storv distortious even in moderate earthquakes in spite of meetine present-day :cismic codes. Eneineers and architects should not inject ricid but britt!c l elements into otherwise flesible structures without p:ovision for sto:y distoition, since the f nonstruef und damace mar constitute not only a seven' financial loss but also a phy sical dancer to persons in and about such buildines. A!! brittle elements either 3hould he W' g f lc 'This discussion is largely fron 11ef. 27. j e Q;4 r
F .l, +$h{ gi 4 3-22 Earthquaho-Resistant Design p =<' p })ellliit'ed to ulov(* Ireely Wit lli!! t}m hillK ttin' tir s}Udlld !b' esiMTtM !(I ai i III M M l l dkf' thev should im sn designed and detailed as to pm% t huddine oc cup.ma aml people on T@n theltwets. It shouhl he noted that waHs or p utition elements thutim hee of ti. f rame or 5 N which faH ont umler minoi distortions do not e mtiihnte hmmfit ial d.unpme edu"s j m h l enciey alnorption. memnetint mensamm mumt unca mudt+o huihume amos a 1 strutture.uuinst mild cartb pukes.uul u im! but.J-o ms ite amatei u i nue she.u s. Unlew h desiened for mow shear than code,alues cencraut pn wnhe un h ticid cleumnts shonhl L y f he amsidered esperulahle,uul other ; mvnions nude tu ws em emmecm ws. u hem a 1 l am a mmme. m +umeirom. mumm w 1 _ nvato m e ndma m n a u r _. f j the desien c.m he.wunnidished by (1) pms idina tient c!cumnts to..u ry tk shear for maroe u of qmae twomo -mrmm e. anuo m,+ d-~r. o la n, p i pres ent escessis e dn!t due to ruinn ti w ilnl f,irc e; a m l 12) im n icline a dt h'l!c iranm 1:i y er mtrol de sibility, ahu o h cimt 1), a' I pion ut lmihtin ' iu bp+ m a 93 e'te !mt P milde W i 'h cartivinate (oh s ay,30-ye.u fwipwney ) in w hic h the i "h o c ra s n uy fa d.
- 20. Core Walls Core walls entlosine " levators stairu dort shaft, etc. a; & intn
} iior of a buildme which is mit too tall or 3}mulet w dl he stif fet th.m the framewoi Whih-it nuy he penuissible by mde to design the wre walls fmr the lateral forem uul tk framewoik for the s ertical loml if sy nonctiy imht ates no torsion, them is,m inter.u tmn p 3, between tk elements even witigmt torsion. Tim p dar nummnt of inertia of buildine4 in u }iiL}i efire Walls (dit'r file (al}v siendie.dtt latt'ra!-It sistallt (dellielit s !luy !m ttio sllLdl Iti resist accidentally induced inmon. uul.my stnn tum of wusiderable heteht or s!cudm-ness wquires lateral stwneth ami neidity whme it wiH du the most coud, w hich is eenemHy at or twar the perimeter. For hmbhnes over 13 ' tones or M0 ft in heicht, th 19 73 SEAUC Code w< puws a comph te quee fiam, caiuhle of wsistme at least J3 }; percent of the se;.mic lo.ul. Thr e linnts shonhl eeneralh he followed as a mininonn j mquhement with the reabration th a fr.une inter.u tmn ihmuchout senmic wsponse must 4 lie e,uefuMy evaluated. q! difiewnt types of com tructmn must he considewd. The ditierent e m pattern of dispha e-6 k g k 6 4 4 4 g is ment of a frame and a shear waH n shown in Fw 13. The p.utaion of shear hets.cen t6m 1 l* must he such as to produce equal deH tmns of the tu n. Becauw of the biference m l j shape of the curves. it app"ars that the shear n all w ill take nn ac than the total shear nt.a I' the base hut wiH he restrained relatisely in the oppoute dnectmn, h3 the frame in the i j upper p;ut of the stno ture. Prmision for the mterm ton must he mmle if the structme n to liclus e pnip('l}y. hit:reos er, if t}i" slica! E all I.llls (!llli'.le t}m (lei!ct t h n t tlIt}W stn Ktnic the ch,mee in ei fieuratioi. and enerey -absorbine cap &ity must !v musiJen d m asse-Q' tQ{ ine the overaH hehasior of the unnposite sum tme not wnudere 1 in Possihle sohamns are n unc.ued varie 1. Sen m tin es ;he u. dis me f( p! detennining ik resntance. Sometunes th. coun t tions betw een u ali and fr.une are o l es kul!L'( Is i }II-nllkI rt' a!ksl Ill 'tkilll, ()r a O Illj) t 'I t' kil!('li' 'Ils fl b ll t.t s ie })n ts'll f*C 3r bs modih ine the shem stithmo ot ech stom t J ine nao at < ount hath tunn and waH. L a 'f Ij eeneral rule,it n succested that taH slcod, u !h mefemhh he loat' <ll.etu een colunms that can serve as dana of a s ertical cinim. impo. tant in the desan Jattached elements ot l
- 21. Parts of Buildmgs Three factors.u t i
,l Innhlines: I I L The eh ment is !t usuauy has a shmt per al of s detmn wina nuy tune in to tiw J hi.;h spet tral p'ak m ce!" rations }l
- 2. The dampine is often suun an 1 tk lo; al strm tural u stem um co npletely lack j l the desimble pulity ot beine staican> indeternon.*
s 1
- 3. Niany elements, such as p.a apet u aHs,,ne subie<ted in a hiah-level buildine l
l j f motion of increa-ed accelerations. rather than to the cround mutmn. Tlie d<wien id attache d ilernents m odses a ocid ;! cal if <lif nenits iii analy sis Imt j alcolational techniques are availa! ' %me of timw a: demihed in Ref. 7 u hem a ] j/ desien simphfication is invoked ia u hit h th" n sp,mw of tb attac hment is wLted to the i modal w pom e of the structure. This resmn" is ads ted hs the nuss of the at'achumnt f [' mlatis e to that er the structure. Whem th'- n e t e nus is intnutesnnal, the wspmc.c is le affected primacdy by the d.unpme of th-ru 'me ao l 'h e impnomt. lmt Isrr a fmite q] 5 l even thoueh unalh mLtwe nu's an cE( tis c relatit e danpine i, no vh ed u hn h i i i t -s t n it IllW ("f f t '( ik s l' lli l s ' raIki). u 't'. l! el t() t le s([uart' rt H N f 1 at-14 [l t i [Til t e ll e l
4, A r s e Effects of Soll Conditions 3 23 I The studies reported in Ref. 7 atal other iesearch imlicate that,in general, the maximum response of a light-equipment mass attashed to a stmc;ure, even when the equipment Inass is tuned to the saine frequency as the structure, will not exceed the basic tesponse spectnnn to which the primary stnietute responds multiplied by an amphfication futor AF defined by 1 AF= (27)
- < + #, + s/_7 whete #,.
proportion of critical damping for equipment prop < ution of critical damping for s* ueture
- 4
= y = ratio of generalized mass of equipm, nt to tenerlized mass of structure with the tuode displaecment vector taken to have a unit participation fattor The generalized n ass for the nth mode Ti,, is defined for either the equipment or the stnicture as A = u[.\\llG i.' Y in which.\\f is the mass matris and u the mod.d displaecment ' eetor (for either the n equipment or the structute) nonnahnd in a unit participation factoi. Esamim. tion of the results of Eq. (2D will show that a mass ratio for equipment to structure of 0.0001 corresponds to an equivalent added damping factor of 1 penent and a mas. ratio ef 0.001 to an added factor of about 3.2 percent. . v. - m.. =u v., 4 j u-f r0me u-4211 . mv.. "q ~ n l s' r -._J bdi+? i tM i wh'. T, l t;g;. m tm . h s l %'/ 4' A Jd l i t I y m, ( ! tw i .m& ~ l j l th I I l-; . l'yl g.; ' Es4 } &; q.h L'~ l ! I tD.L Li ! l H l l lj q l I 1 w: KO] l s Fig.15 Tah building with inoment-7~t-L/ i j IM n sist..at fr.une and shear walls in ren-d / T/ / L.. {/// tiq ter interim bay. (c) Buerg in it) Frame cire (c ) w:4 a!cr.e ncamot d.t;tated ct;.ccea pasmen Codes usually specify much larcer design coeflicients for pirts and appendaces than for the structure as a whole. These puts must hejoined and connected so thai there will he strength and inh ( rent ductility whatever the direction of motion. Thoroughness of plan-j. ninu and detailing and the manner in which the parts are joined, or intentionall) 1 Separated, can do a great deal towanl improving seismic re3!st.mee.
- 22. Effects of Soit Conditions The response of a <ructure to earthquak e moJons depends on the manner m which it is supporte_l on or in the soih Interaction hetu een the stnicture and the soil mar allow energv to be abserhed or in result in a motion of the base which differs somewhat from that of the surmundine ground.Thus there is some loss
,4 of energy between the umund and the structure, so that the structme cenerally is not a subje,'ted to accelerations as large as those in the earth. .Q[duyu s
- .gy +y 1
- - ~ ~. - _. _. - - - _ _. _ _ 7 idb' 3 24 Earthquake Resistant Design '} n!* ?p ! V It is shown in Ref. 2S that loncer-period motions (say I see or longer) are primarily due i i to surface waves such as Rayleigh waves or Lose waves, it is quits likely, howes er, that h for moderate distances, beyond those corresponding to the depth of focus, surface waves N have an important effect even for moderately short-period structures, and more complex l }g motions than those due only to horizontal shears propagated vertically ulnvard must be - h" > f] considered, Moreover, vertical motions cannot be accounted for by a simple horizontal-I shear-wave model. ~ Considemtions of variation in intensity of motion with depth beneath the surface are ~ very complex. There are few data that directly relate surface motions to motions beneath the surface; observational data include two or three small earthquakes in Japan. These .md other limited data indicate some reduction of surface-motion intensity with depth,but [ for large motions or high intensiti s they do not suppoit the contention that variations in h.V intensities of motion with depth can be computed accurately by methods involving only [ f the vertical propagation of a horizontal shear wave. - f in regions where unusual types of ground motion can he expected because of oscilla-i [ tions of the soil over deeply buried rock, mod. ' cations to the response spectrum must he J considered. This is particularly essential in places like Mesieo City, where amplification 'h of ground motions in the range of periods from about 2 to 2.5 see occurs because of the natural frequency of the bowl of soft soil on which most of the city is founded. The Latino s Ameneana Tower in Mexico City was designed for a base shear of the order of 500 metric tons, corresponding to an earthquake of modified Mercalli intensity VIII hut taking into account the amplificatmn of motions conesponding to the natural period of vibration of l rJ j the soil on which the building rests." Shortly after construction was completed, a major llfT earthquake occurred, corresponding to the utensity for which the building was designed. Records were obtained on instruments which had been installed in the building, The l!! ) values recorded were almost precisely those which had been considered m the design as I. being consistent with the probanle values predicted by a modal analysis, The forces tnmsmitted to a structure and the feedback ta the foundation are complex in (y nature, and modify the free-field motions. A nmnher of methods for dealing with soil-h structure interaction have been proposed. They involve (1) procedures similar to those applicable to a rigid block on an clastic half space; and @ linite-ekment or finite- -j' diiTerence procedrres corresponding to various forcing functions acting on the combined structure-soil complex. Ilowever one makes the calculation, one nonnally detennines the fundamental fre quency and higher frequencies of the sod system which interacts with the structure, and the effective dampine parameters for the soil system taking into account radiation and materitl damping. Both these quantitie.s are necessary to obtain rational results, and l procecinres that emphasize one but not the other cannot gise a proper type ofinteraction. j! i In general, considemtion must he given to the influence of local soil and geologie j,W conditions us they affect the site ground motins,in tenns of botn intensity and frequency 'i content. Soft soil conditions, for example, ndy prech:de the des elopment of high ace dera- - tions or velocities within the foundation materials, Consideration must also be gisen to j possible development of unstable conditions such as soil liquefaction, slope instability, or excessive settlements. Further, because of the nature of fonnation of soil deposits and I l 'q 'l '[ their lack of uniformity, attention must he eisen to the determination of the in situ j j properties and the methcJs of sampling and testim; used to infer these properties. 1 f ! Because of variations in properties and the diiliculty of detennining them accurately, I b some variation in the basic panuneters used in the calculations must he taken into 0 account. The method of mleulation used should asoid as much as possible the introduction of 3 spurious results arising from the calculational technique.1 or example, it is often neces- -jl sary to avoid " reflecting" or "hml" boundaries where these do not actually exist. It is not entirely rational to depend only on calculational methods to modify earthquake .j motions from some deep 19yer or bedrock to the surface. It would be desirable to base d inferences about site intensity modification on actual observations of surfae: motions as r 2f well as on emeulations until measurements of motion become available from actual earthquakes at vanous depths hencath the surface for a number of diiTerent foundation j conditions. -1
- 23. Detalling and Quality Control Ductility, involving defonnations into the inelastic range, is a necessity if stnictures designed by accepted seismic desitu procedures are to y
4 gQ
f kl I Detailing and Quality Control 3 25 ..l e he capable of resistin g e.uthquakes of the intensity corresponding to those which have i been recorded a the United States aiul elsewhere. Theiefore, particular attention must be given to stress concentrations, the choice of types of fnuning and cormeetion details, and similar matters, in order to ensure that the required du(tility can be achieved. The only altennitive is to desien the structure for greater forces. Additional ductility or consideration of other energy-absorption capacity may be indi-cated for special stinctures, for more severe earthquake risks, or m the upper sto-ies of slender buildings. These (htetility ratios can be achieved in most structural materi ds, but ir order to ensure that they will be achieved, attention must be eisen to appropnate -otrol aml inspection procedmes durine construction, as well as to the factors cited. The items to which particular cate must be given in the desien and detaihne ut I cinfou edsoncrete structures are desenbed in Ref. M. The followine mattets need f particohtr attention:
- l. In order to amid compressisc failure or crushine of concrete m flexoral compw-sion, either a limit must be plaet d on the.unnunt of tensile reinforcement or comprewise icinfoicement must be used to cise ad<htion.J strencth and ductility on the comineune side. In essence, the chffewnee betw een the percentaces of tensile.uul compwuive steel m a flexural member shouhl not exceed 2 percent of the net settion. When compteoise steel is used it should be tied into the beam to avoid bm kling failures. Such ties are furnished by adequately.ur. meed shear remforcement.
- 2. In eeneml. faihue of conewm in shear or diocon,d tensiim aho involves low doetihty, so that appropriate winthement must be provided in beams. by either stirrups i
or inchned bart Ilowes er. owmu to the fact tlut flexures in cadhquakes cencialiy res erse l themselves in direction as the buihline oscilhues, bent-up bars are not usually acceptable ualess thes are bent up aml bent dow n so as to tive winfmeement in the two di ections.
- 3. Fuither attention is reiptired for concrete columns where the flexure is relatisely small compared with the compression. Restraint of the concrete provided by contaitunent, such as that gis en by spiral reinf orcement or closely spaced ties, adds to the compressn e
. strength as well as to the ductdity in comprenion and can eenerally be used ta proside for .:reater resistance.
- 4. Appropriate bond and am horace of winfincement must be prosided in all cases hy sutlicient lapping of splice 3, or mechanical connectior.s, welded connections, etc., to avmd faihire by loss of anchorace.
- 5. Tensile forces in minfoiecd-concrete columns can cause erious difheultms. Such i
tensions can arise fmm ovendl llexure of the buildine caused bs overturmne moments. i Specialicinforcement to resist osedumine flexnre may be needed in the outer cohunns of j narrow buildings. Reconunendations in this recard are eisen in ACI 31S-77, Appendn .\\? In steck pmbhm similar in principle but different in detail mu3t be considered. Connections shoukt be designed to avoid tearine or fracture. :d to ensure an adequate path for stwss to tnnel aeruss the connection. Because of the possibility ofinstabihty by buckling, particularly when steel deforms into the inela3 tic rance, adequate stiffness and restraint of outstandme lees of members must be provided. and the thickness of unre-l' strained liances or other ch ments must be appropriately determined in accordance with applicable plastic-desien inovisions of building codes such as Part 2 of the AISC Specifi-cation and stwneth-desien approache, eenendb. In eeneral, tohanns in the hm ei stories of either steel or winforced-concrete buildines shouhl have a resen e of compressis e stwneth for dead load to provide for the additional fle xural ud m erturning compression in the cohunns under lateral loadine in order to ensure apropriate ductihty. Items w hich do nos lend thennelves readily to analy tical consideration may hase an important e ffect on the wsponse of struttmes and f acilities to earthquake motions and must he considered in the desien. Amone these are such matteis as details and material properties of the elements and components and inspection and quality control in the con >truction procedme. The detads of tonnection of the sti ot tu re to its suppmt or toundations, as well as of the various elements or items within the 'trutture or component, are of major importance. Faihire-often occur at toenections and joints because of inadequacy of these to cauy the force 3 to which the are subjected under dyn.unic conditions. Inadequacies in properties of material are often encountereo and may lead to brittle fracture esen thouch eneruy absorption may have been counted on in the desien &v
n Njd ,[+,L Tpf- { g {. 3 25 Earthquake Resistant Design u y I. N and may he wailahle under std.ie loadinc conditions. Some of the aspeW of thew topics Q l are considered in detail for icinfinced concrete in Refs 11 and 29,unl for steel in Reis. 30 and 31. Both the desiener and the constnutor inint take into account the rc<piirenients for y ,I attaining strength atul duttility in huildmus dmiened to resist e.uthquales. y SinYeys ni carthquakedunaged huihlines tianuclnutt the wotld clhuly show that h careful auention to the yn.dity of materials,uid construction significanth en uwes the 3 II proluhility tlut a structure will withst,ual eartlo pukes. l 1 24, Cost The cost of providine eartinpiate wsntante is not a dunt innenon of eone g'l ) ratine or of the wisnne cuellicient. Eartlulnake-icsist uit design, po ved) done, of ten [ ] luovides for wind requirements at little or no.ulditio" ' cost. V ( h ij REFERENCES n 4 9 ). i
- 1. Newnmk, N. 51., and E Ron nblueth: Tim J.u n e nt al s M Earth puk e IMu.eenne.' he:m p
t hdl, Inc, Entlew ood Chtis, N.J.,177 L p y;
- 2. NewomL, N. 51...uid A. S. Veletsot Dmen Procedures for Slak l'olatmo Sy stenn of Under-
? cround Pmtective Mructures, s ol. III, Rmponst Spectrum of 5mele-Dettee-of-Freedom Elastic d j nul loclasne Systems, Report for Air Fone Weap .s 1.ahoratory, by Newnu i, Hansen. and Auoct ites under Suhontmet to NtilD Diviuon, General American Tram;urtation Corporatmn, ff, J ' BTD TDR 63 W6, JM 3 Vele' sos. A. S., N. St. Neu nurk, an.1 C. V Chela;uti. Defaunat on Spectra for Ekstic.md Elacto l Plas^ic Systt ms Sulvetted to Ground Slmi.an! Eanhquake Nto ions, Troc 3d h!d Conf 1 Ear luivalc Engmcenne, New Ze d.md, s ol.119% k
- 4. Ne vmark, N. N1, J. A. Blume, and K. K. Kapur. Smume Desien Spectra f,a Nndear Pon er Plantt v
i 4 J. 'ouer Dw. ASCE, November 1971 ?
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'ari, N. 51.. and W. J. Italb Pn.cedures and Cntena far F uth pule Beust.mt Ik uen, f ' budding Practiws for Disaster Nhticat:on.' Natwn.d Bureau of 5tanJards Bmldmg Suence denes 46, sol 1 Februarv 1973 i I h Newmaik, N. 51., and W. J. Itall Seismic Deuen Criter a for Nudear Reac tor Facdines, Proc 4tli World Conf. Eanhconic Enancenne, Santu m. Chde, s ol IL 1%9. h' i 1 7, Newmark, N. '
- anhquake Response Analvsts of Reactor Structures. Nucl Enc. Dcs, W 20, no. 2. July 1971
[ S. Newmark. N. 51.: Current Trends m the Senmic Analyss and Desien of thch line Struct' es, chap.16 m R. L. Wiecel tedJ "EanhquA e Enemeenng,' Prentice Hall, Inc Enclewood Cids, p p j l NJ.,1970. 9 Veletsos, A. S., and N. Nl. Newmark: EiTects of inelastic Beharmt on the Response of Sunp!e Sy stems to Earthquake.Ntonons Troc Cd World Conf Eartiuinale Emr.ccrina Tokw, wl.11. j 19 4 j i
- 10. Proc. ld World Conf. Eartlujuule Erigmcenoc. New Zealand National Commutee on Earthquake i
j l Encmeenng, New Zealand Inintunon of Entmeers, Welimcton. New Ze.dand 19E
- 11. froc. 4th World Conf. Earriniualc Encincenne, Chde.m Association on Senmolny and Earth-b( i quake Entun ennc Cassdlan 2~l7, Santum, Chde,198 h
J N
- 12. Troc. 5th World Conf Eanleinale Enewonne s EDIGRAF-Fditnt e Lbran n 00137 Rume,
.1p Itah-Vu Giuseppe Chunm, R 1973 11
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!l Tre Symp Eanla;ualc Enmwenne Unn ers;ts of Bntnh Columbia, Vancouver, September )jq 1965 y if
- 14. Blume, J. A., N. NL Newmark, and L IL Conunc: Dmien of N!ulti-Storv RemforecJ Conciete
- p Bmldincs for Eanh
- puke Ntotions," Portland Cement Assocution, Clocaco, llL,1961 1 j j !
- 15. Jacobsen. L S., and R. S. Ayre. "Enemeenne Vihmnons/ chaps. 5, 9. NicGraw Hill Book jj Company, New York,19%
j1 l lh Timoshenko. S., D. H. Young, and W. Weaver, Jra "Vibratmn Problems in Enemeering, 4th ed.. John Wiley A Sons, Inc., New York,1974. !j ii l
- 17. Bhune, J. A.: Penod Detemiinatmns anl Other Earthcpuke Studies of a Fifteenatorv Buddu :
! 1 C ' Proc. World Conf. Eartiniaake Enam enna, Berkeley, Cahf.,1936 jj 1% Zeevaert, L, and N. 51. Newmark: Aseismit Design of Latum Amencana Tow er in Nieuco City, y "j l Proc. World Conf. Eartluionle Encinrenng, EERI, Berkeley, Calif.,19% 3.f
- 19. Derecho A. T., D. 51. Schultz, and NL Fmteh Analysis and Desien of Sm.dl Reinforced Concrete jf Buildings for Earthqtuke Forces, Ern.. Bull. Fortland Ccment Anoc., Skokie, 11!., 1974.
iK
- 20. Paulay, T. Some Aspects of Shear Wa!! Denen. Indl. N. Z. Soc. Eartlopunte Enc.. vol 5 no 3,
. ji Septemlx r 1972. Nj^ 21 Building Code Requirernents for Remfmced Concrete ( ACI 31477h Amencan Concrete Insutute Detrol. Ntich. 5 21 Umform Boihhne Code, International Confer"nt - of Bail; ion: Oiheials, Wlutnei. Cahi.,1976 ) 23 Recommended Lueral Force Requrement3 am! Commencu,,, Senmohmy Cmn mitee,5tnctural 'w-Engineers Associanon of Cahfornia,1973 n, 4A
Re ferenc es 3 27
- 24. licconunemled Compreheinise Seisnue Ibien Provisions for Buddmes, Apphed Technoloa
~ - - Council, San Fr.uiciso. Cahf.,1977. 21 Newm.uk, N. M.: Desien Critena for Nudear ficactors Subjected to Earthquake lla7,uds, Iroc. ~ IAEA ranci on Aschmic Desi::n arul Testir:a ofNuclear Funistics, Ja;un Eanhquake Encincenn; Promotion Society, Tok vo,1969.
- 26. Newmark, N. M., and W. J, lialb S weial Topics for Consideranon in De,ign of Nucleu Power i
Plants Subjected to Seismic Wtmn, Proc. IAEA Fanel on Ascismic Desian and Testine of Nuclear Fanlitics, Japan Earthquake Enanet ring Promotion Society, Tol> o,1969. 27.13lume, J. A.: Stnu tural Dynaraies in Earthouake Besistant Desien, Trans. ASCE, vol. 125,1960.
- 28. Ilanks, T. C.: Strone Ground mtwn of the San Fernando, Cahf,, Earthquake: Ground Displace-ments, Bull. Scional Soc. Am, vol 65, no 1,1975.
29 Newmark, N. M., and W. J f f all: "D> namic Behasior of Reinforced and Prestressed Cont a te thukhnes under linnrontal I orces and tJie Desien of Jomts (inclndme mud, Earthquake, B!ast Effec tp," Prelinnnary Publications 5tn Coceres<. Internation.d Association Bridee and Structural Eneineenne, New York,19th.
- 30. Popos. E. P., and V. V. Bertero. C3 the lauding of Steel Beam s and Conn,xtions, j rn: t. Du.
ASCE, June 1973, (See also Errata. J. Struct. Dn A5CE December 19731
- 31. Krawir Ller, II., V. V. Bertero, and E. I'. Form. shear Behavwr of Steel Frame Joints, J. Stna +
l Dit ASCE, Nos ember 19.a. 1 4 5 4 s 5 l i r-i
y _ J 23 1, 23-J 1991 UtJ1 FORM BUILDit4G CODE ,ye , a: W 5.u. .+w 3 7 TABLE t10. 231 SEISMIC ZOtJE FACTOR Z ,u, + ZOriE 1 2A 20 3 4 . J-Z 0.075 0.15 0.20 0 30 0.40 a. 5b The zone shall he determined f rom the seismic zone map in Figure No. 23-2. a MnCN1 err e n( Q TAOLE tJO. 23-J SITE COEFFICIEt4TSI l t TYPE OESCRIPTIOtt S FACTOR I j S A voil protile with either: 1.0 i ( o A rock like material characterized by a shear-wase velocity greater than 2,500 f eet per second or by other 3 suitable means of classification, or (b) Stiff or dense soil condition where the soil depth is less than 200 f eet. S2 A. soil profile with dense or stif f soil conditions, w here 1.2 the soil depth exceeds 200 feet. S3 A soil profile 70 f eet or more in depth and containing 1.5 'i more than 20 feet of solt to medium stif f clay but not more than 40 feet of solt clay. j Sa A soil profile containing more than 40 feet of soft clay 2.0 d characterized by a shear wave velocity less than 500 f eet j per second. 1 .J 'The site factor shall be established from properly substantiated geotechnical data. In loca-4 tions w here the soil properties are not known in sufficient detail to detennine the scil pio- ] file type, soil profile S shall be used. Soil profile Sa need not be assumed unless the 3 j building official detennines that soil profile S4 may be present at the site, or in the es ent that soil profile S4 is established by geotechnical data. . )l 3 1 .1 s q ~A a j 184 . -] a}}