Text

Rept on Investigation of Structural Strength of Concrete Block Walls Supporting Seismic Category 1 Pipes,Arkansas Nuclear One,Unit 2
	ML20214Q777
Person / Time
Site:	Arkansas Nuclear
Issue date:	04/30/1980
From:	; BECHTEL GROUP, INC.
To:	;
Shared Package
ML20214Q757	List: 0CAN098604, Forwards Listed Info to Resolve Open Items in IE Bulletins 79-02 & 79-14,per 860623 Insp Exit Meeting.Bechtel Repts on Investigation of Structural Strength of Concrete Block Walls Supporting Seismic Category 1 Pipes Encl; ML20214Q772; ML20214Q777;
References
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	Download: ML20214Q777 (27)
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' INTRODUCTION _ '
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.res,ultadof.da?de'. tailed evaluation of the d
1.cThis) report. dogc. ibes jthp...
til,ockf. walls, supporting Scienic gatructural?:capabilityoffconorCategory"1 pipess t Arkan'sa,sjNuc,,eara,Qnej } U
,q g'
a (Cosmissioni(NRCprogu'eitiithatda.Mtiailhd evaluation of the w
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t6? meet th'eZdesign41o'Adlsybefperfpqseffa'slpart pf. an. evaluation-P 3
(systems. ?TheSNRC request-S{ ofipipe ! suppor't's >in 'Se. smiW Catego,ryisdntainedlin Secti'drs55Flof.N i
11e'tii'nE No.b79--0 2, Revi '
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.Oj y1 22.1 METHOD OP. EVALUATION
@[W 2.
~~SUMMARY~~
~~MP F~~
j fj q,f A field survey was conducted to identify concrete block walls Y
Gj which. support Seismic Category'l piping.
% '. Altotal 'of 8 walls ~ were,identifiedtJas5follows :
Vd 9.5 A '.
y 7
~
co.
~
wpp -
p;d
-h e
O t
4 walls supporting largee pipes)I(g$1/2"Ediameter. and. larger) yy af' a ";:L..s%:%
~
l 8-a g.
Walls ~ supporting smallipipes '(2*? diameter or smaller) i S. f
".%?',
None of the block walls,is' designed [as a load-bearing wall that Yb]
o t
supports the building structure iiWthe vertical direction or acta N
l p.
~
The walls are pri-y as a shear wall in" the horizontal'idirection.
~
fire partition walls.
In genesc.1, PU
'rf marily used as shielding.~ ori cd the walls are not used;to support,large piping and~other heavy r
q s
n h
O);.
Light objects andismallipipe' hangers are attached to 2),
objects.
m.
the walls somewhat more frequently. 73 F
,_3
. f.",
, i.
Pj J.
In the block wall analysis, cracked'"section properties are us fu b
M 1
saoment of inertia is used to account for the ef fecta duo to ' the d
p, w
partially cracked condition. Walls which span vertically between
.d<
r.
Walls whlch'are 7;" _
f;%
floors are analysed as simply supported beams.
d supported only by the floor slab'cbelow are analyzed-as a canti-d.4 I
Support at crosswalls,is generally ' neglected.
f cs fi levered beam.
In some. cases,;. cross' wall:. support':isiconsidered and'the walla g}]j are analysed?as' simply" supported l plates.
Although"crosa wall t.1 support and offects of: openings 3are not generally -include y(}
k.. '
T l
presence of the cross' walls and openings and using finito element f
analysis, shows that stresses can be expected to be lower than g@
~
lT r
L*
Ef;7 ?
generally calculated.
y" capability of the walls is evaluated by. comparing calculated y W.a otresses to allowable. stress: limits.
Stresses aro calculbted as c
c A'
the sum of stresses due to wal1< inertia forces and Boichic: Category
[i T
1 pipe support reactionstresulting from a combination stWortical
" N.
3-H earthquakemotionandgent.dir6ekten'of' horizontal'tarthqubko y yl h/R g.g' oy, W4.
'Ml
~.C. ;.
e.vt :
Q mg.
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fb.hh F
qq. a....
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b%2N 9%% Q:
,l
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Ah g?.%,5. ?.,',%' ' ',
I:
Y ' y$ a:%.,Q.. Wsj$W"=$. p.t,. y w q.y
.. 34 m -
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, re..
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~~<>n-L,3.y.,.r;-e,...,~~
~~TwoQigeqtfo..o t i~~
a r
3 r
P62g;q.o;;.r,..;%pUy.hoQpqt.a f,' esp!) quake. motion cre u
..+ c.. m g $ g m.w9 :::ation.
ns.
p pstimposed.on~.the walls by h i:. -
y& aM :
, cons ide red / s ignultanepps1p qop$'MQl6C an 4 :m p W GH/.E Category 1?pipp*paupports;arepob airy,edigron pip ^e support hhW
~
^ -
-h
'~ QYW.?Tiyjy!
the
".,12.
The out-of-planejinertia".fgrcp'genepat,ed(by the maso cf fpgg:7e M g r'in obtainedras,sthelproducttpf) f lliacceleration and th-n11 M{ M.wah : Win : the : computiatilon(3cQ'epa OMEM.'s teightj ~[Aii;;hllbsa M0W 8/allMweight is aN O i
~~iweldht,off all attachnan Nithf;F," Tbc ~ allow'ance'"i'sNebifiled%yMiisipariisbi14to 'actu'alN 9~~
M[
The' wall;a'cceleration ilinsii?as'6the average apectral
' accelerationi 'coriesp'o{isideterndinir toltilie%al1%frequ'oney,. using th 4(pdyWc M response J spo ct'ra ' ati thel,floorsj aboils?'andibeloti... Conce rva t.h RIXQ'S.
damping values of"31 and.15t2are:.used1foretho?OBE caco,and e r
~
D:OMj
- case, respectlivel'.
l' % M f M M P
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y e.
l.c a;;
%y c is4fe, -
2.2 RESULTS OF EkALUATION; i
l.1, gw z ycq,#xJ.W 3 Calculationaishow, that ' stress'es ' in'concre te bloche,
~~nortar, steel.' ties, and reinforcing { steel, resulting. fror et~~
~~%@ F;~~
~~grout, bined ef f ect's' of' wall inerti' ',forcesland ; pipe support rec t l,c r a~~
d.@,V-
~
W during the OBEland DBE2.are within" allowable /limita.
A cua m 3P E
. of maximun calc. u. lated. stres'seiPa. ndF..al.l. o.w.able,limitc 'is : cc:
~
g%@C%
qgi
? h6' d 4
followS*
,o gi: > T. < - e b..gr j:
OBE' DSn ~~
~~r w Maxinum M O b.x~~
's. Max.imum
.e Calculated Allowable Calculated A11c-e:g'QQf
.-ggf Stress
'!x t.
Masonry wall tiexurab 500 530 NQ:Q}4
.cospressive stress.(psi),,'410.'l s.'a q,Roinforcing aL.el w.M.19,600?.er.20,000 29,700 3 0, C M y.f.gEO, e
e
(-
tenaile stress-(psi)-
'c ffyW 7
McQM,.
It~.4r stress sin.verti- :
e.
2' 11.0 35MC cal cortar joints'.beOT. ;,
'8.3
- ;12
Mi;s.W WM tween block vythes'"(psi)"' ' '
s -
v.s.
r;.7,.4 Shear stress.in verti-11.0
' cal joint betweeni' grout..
8.3
,43 h}p.;/.7 and block wythe-(psil-S hasonry wall flexural 3
-7 g.
l tension and-shear 8.3 43 11.0
$!l p' Td strcases (psi)
~
P Lp m.m sile force (kips)..
-.-3.5 4
3.8 3.!.EM Concreto an.chor-te.n-u,.. -
,.,; ;.e,;.
g.w :
[ ;'
o.3.y._ w.~ ;;p :
j
@@,b.
2.3 OXiCLUSIONS s
y w...
All concrete block walla.in ANO - Unit 2 that support SeP d e l
n..
N',
Category 1 piping are capable of withstanding the combined CCc:
M 3
ig$U).
of wall inertia, forces.and pipe support' reactions during * M e
. W '.
M.*';_
and D3B without exceeding.the allowable etrono li.mits
...s o4, e, W; a T:
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52:U3.
' DESCRIPTION ' OF CONCR5T51514Cgommq
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' WALL IDENTIFICATION E S.7 g yki;Q:
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=u:} f -f~'i'.
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n A field survey.was conducted in" January'and February 1900 to p
W.i identify and_ determine? actualfcon'ditilons at walls supporting g %g*T;., with Referencei.7.; WW.G,WNM[gocedures twe Mb)p.{.2 iSeismic CateigoYy(1" piping 6ySui%y T
p 3 3 :.g y... y. ~ +..vf ;g...,. g..,
g
~~s..c..~~
p$7ch%g,M Survey Report'.
j:
Recults of the ; field (survey. a're"desc' ribe'd 'in dotiail Jin the P.bld The survey-shows ' th'at? 8 walls 1 directly suppcrt
}ljl n
Ti93
- Scismic Category.1 piping.T. A listiof,: the. wallt,, shovi ng wall 1
i MTMir..
thickness, helight, ' function, typef o'fp support', land. types of attach-
[
. P- :Jg.
ments on the wall,' is' given in.sTap'le 51.' '. Location'and errangmnmt i
t Md
~
Calls of the walls are shown in' plan jiew{insFigures 'lito' A.
~
Whjjk.:r shown as shaded are" walls,'that</ support. Seismic Category 1 pipes.
}'
8,Mf'.
Halls shown asi cross-h'atched 'dojno,t? support Sciemic. Category 1
[i s
7 S; '
pipes but may be;:.requiredy:lduringla$ seismic' event,::to asciet in l
d'jy(ik s uppo r t ing : th e ' w alls!. s h..own.m. asi?s had.e,;g,. m.I..T '
'3*
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jgtsp? Mall tagi num5ers JslioEn ';.irg Figursaf>lNto'.4 'dosignate 'wal1~' facan i
Catchcry fG 'S i that have beenlaurvey'ed'F At' one$ailg:aupporting Seicmictthetw id t f>.;K N 1 pipos,sible when the field ! survey'wa's' Coo'nddctied.:,, ' - ' p <* %m., OhE s. - yv.e:? f L. .n g' s n.F.,.. ' Wall attachments ' generally aroslimited to-small.pipinplaticacupportn, r E y SR A d$r electrical conduitsiand boxes,' instrument lines, venti I F cts. duct supports, and similar:ligh.t o.b e.4,.:. ' F,2 f 4W'- ..c .3 .. - 3
~~v. 4:.t d~~
~~'9 mr -~~
~~. te.. c. .., y Classification of ths:8 walls sup @ porting Soismic Categorysl;~~
~~w i r ;-fe-C ~~~
~~e. p o e pipes is as followns. - 7'.~~
~~.A a.~~
.2 0 y g@wpsg Walls support,ing' large pipes l~.(2al/2" diamator or'-lartjer): .. c =:. 4 ~ Oc-Wallssupportingsmallpipeal(2"*or-lessdiametor) G p None of the walls identified is. a. load bearing wall that supportn Mh ut the building structure in the vertical' diraction or acts..ca a chtar d 4%Kg wall in the horizontal direction.l :In general, the valla fulfill W Q' 7. h, o.wk a shielding or fire' protection \\f.u.nction. ~ i av. W,; ,W W';. 3.2 EL CONSTRUCTION DETAIL 8 - {.1 $:s si Host of the block walls are shielding walla constructed of heavy-h M,% ;;:- k ia weight hollow concrete blocks 'in which all celle aro filled uith N hM and in which continuous reinforcemont in embodded in evorf P
d,, %,

grout, tW..
other cell. ?-h g1 f :a.% e Halls are constructed of a single wythe or of core than cua rlthc. j.j r.;9 -r - g$f; yf2 Walle conatructed of more than one wythe could at( the cptite. 02 the contractor be made of two wythee with contor space filid Mth y) e. T @ @j;i l grout, or of two or more. contiguous.wython uith vortical $o;.r2 l p, b.c }v i .cm. - r %p hc , 's [, [ s .;c py <r t - .. \\, $ ?) d fNN
~~., QQf&. }$h"V '.* :&%.l.yn - [~~
l( ~ VW
WN M T-9 " ~..... I j,9llQ wn ~ ./ y&qgff% A, W X@H,bf kh ,] n j ~ C h,M@@. 5%Y w. t mm n, u @.r.:.W:.d. g,(Q.y;g.e. " 5 7..,, $E e .s
~~, y Q~~
gf.d 5',t e ~ . -: q ' ( l. @ $., > W.j $ 2,c(7. 5 ; g., j '.'. v c. s,- r g ci,. c y.A ' ' h -w.s [ $, v. (gpa'cked with'mos;tarA,.ig,u..... i7?andi8f$owf cons truction of' valtv F r.gs S of,more thanl ongs;_wythe4.g'ti'[ W. dd,. v '. i 1 .bg ,,.n .y
~~c..~~
..m ,n w w-y.p.~ a. v ' d%g[d(Vortical reinforcing 'atie'ef/h.as~i.',shoinMn. Figures 7 and 8, concicts 5 bar,at-16Einchtspecing".in' center.of single vythe valla, pll ~ g' h .of one No.]iand-oneNo. 5.. barf at'.16?inchZ apacing?cpear(each '.f ace of multivythe qpm? r? Horizontal 4l'reliifdrcidg.isteelgas fshown - in Pigurc. N y%3^%@ walls. 62$d l I ]k%f consists ofa? bon'd befasifjtit@,f6ugNo.d4.Jbarsi at.48.~ inch' cpacing in single wythe 'wallspande.an.fidentpicaltbond' beanL at cach f aco. .i
2. M O M,'iof multivythe? walls. ' Addition'slVreinforcingils'provided around E k h @ doorways and openings *as'shown}161Fi,guren10. jAtJall block m il' Ry/Opy,yk intersections. with;-the;1ower..concreteifloors,. every vertical.
% M @ g Jreinforeing bsr.is'anchoredTtojtheyconcrete withia deformed.bar s WMMrig. - dowel threaded int 6 ai3/441nch-diameter 4concreto7 anchor. - At i i M "DP ' block wall intersections S ith:the'jbFperleoncrete? floors,'a pair
~~,1}~~
k : of continuous' 5 by 3" f angles' with?3/46$? anchors 'at"12": spacing, - L ATC.. attached to floors, ' are"used. At;. block ' wall ~ interse ctions '.with - [l! ~ Y,4 concrete walls, every pair.. of-h'or'ipointa13 bars is ' anchored ' to 9M R f.the concrete lwith a defoiped bar.[doweRthreaded 'into a 5/8--inch-I< .--9Wdiame te r concre to ianchor.'l - ConcEet4(an'chOrs '. are Phillip'n ' Fod jj @3h.W. Head self-drilling %oncNt.eTexpans' ion %nchots. li Ei p".W .6: 'MQ;,, T,.tgj$g ';p.'.q, pqQ'.~ In addition to the.above> reinforcing 3s. teel,- joint' reinforcing ',i if,M - aconsisting of~ extra heavyIDur-O-Ma114 truss steel bars.is plac:S ?y in alternate '. horizontal 3 joints :(l'6"dspacing ). of ' shielding; ualls ,t ~ h3.,$Cr5gM@P shieIding walls No. 3 steel tioiba'rsChooked around-vertical :ain- ,4,Mp and in every'horizontalijoint~(857 spacing) of otherJwallni' 'At j j [y %gd: forcing bars are placediat 32"' spacing. horizontally and'lG"' j( Mp. spacing vertically. Figure ll'shows'i'the. arrangement of joint !j h reinforcement and ties. 3. ~- ti 9 % e $' fl t 9 33 WALL MATERIALS 'l
~~g. g -~~
~~(d , M5 tiaterials used for the wall construction are as follows~~
i
~~, %.n,:$,. 1 p,fg.l Concrete blocks: ASTN C90, Grade PI. Heavyweight units cured ll 3.g!( and oven dryed density 135 pounda por cubic 1 m,., foot.~~
~~J 1~~
~~e lt "J~ $l b -).41 Mortar: AS'1% C476, Type PL, 2000 pai compressiv'.:~~
[
{warf{ strength at'24 days. 2/ Grout: ASTM C476, 2000 'pei. compressive utronsth @,%p S F' r heavywoight unita, groet at 28' days. o dry density 147 pounds per cubic teot. 1' 4 l Qt ' % noinforcing bars: ASTM A615 grade 60.- l ! f%.,... # " i j e') I!orisontal joint ASTM A82 Dur-O-Wall extra hoevy truct ty p. 1 l h,,(I } reinforcccent: r.- q l e f.l.e s ly;..Cr., i. e: w '+, It/[ k,, b. i.U l ?
~~.., '( * % h,~~
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$%@MTITT4 ]f.2n.f.? n g v .s ~ I $. P f $ $ $hf N & ? ry?b,. W S.'^ } w :5 g ap;ov%%.g. 3 &.3.:. .. e< ...c, w^ y.4 4.:, re m.,% l
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~ w %. S q i.+l w. m. c l 4 7.V f y m . ;k y i&W/M Um y:.' ? ?~ l $ $ h hg n;Qhf hl? W' g hlQQ.%&uld'$c%'$.'?n.'Q!$ Y.f[ -. kh h. T3.9l7%.~ $cy.E t 1 ' Nk$.,: 1,2 hk h:h$. ~ hh A. d ,Y? N "s. n"atesr N.SF/l b*..; g b D.m.m...- . n? o/g.m;<vm.,.T. c:Wp::n.e 4p. --..W EVALUATIONuC ..g. g v T m ~ ub. Mv. M - pp; g. y;d d m.: W, %.w:. mng% . 4 1 e, ~., -.,,.p y.r.,.,g ggg. . MAT E{tI. ATT PROPN"-. m.4 v4.s5., 3 , p' w.,, V - < Glw., ' f ., d.hed ' 'i. ~- 1.M'terialpr,cportio($..,d1 , i;; .-. !),cM O '? ffi b ) a us9 t pn' arMacif611c-m : , ;;@ M; dQQ " "p; M,. 'R.Qk0.pc2 n ' M.*c*h. ~.. %. w...w..,mf k@,....,;y,M 2..m.%Q a 6:W;s., N.b $ m . hfN, l ...v x m.wg ?;EN;( _,-Grout;qompros.sive?*t 'y'3 w %c& &( 6 ) M., 500 rmi- , 4.y.. ' 9{ g,, ; Masonry 1 ultimate.l.on g s c .;9 MM.g s's - .:.., :~.-id ~9 0 0 0 P c < m:v m 3..si .m.p e:v g.,. m . gf g3,2 <cws'd rdg g,cpr:4'h,J.2000pri ,.a /.,;-Q;-s h., ' MortaricompreaQvej y pg W .y.s ~ - ,, l&;.a;.7 >wer@{,:.w:.%. ; g ~jf"fe'M " ^"] ' .j,' .' h0100 3.r.s!. .u. - ;m
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t n M h. w .?f. W. .Pr cen u@w..w...... 3 2.; Nk I he W E., .c 9 c w i M/fC *th.!h4.2cLOADlCOMBINATI.OWS tmy., On:n.. 1 pl m; pp^ 'a;,p,.i3f@, y A g -t 3.y g u g - W p m ; m.tLoad, W in.Lat. 'o'nslusad p m .M w , gins 1y$5HQu$wq. k. ic v.s. m! 3'.e?J-: G:hff@h.ff $0$kh ~ J
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4- -. % c,_ ~ ".p i.b e g M. v.: w(:', ~< D 3 +i L',+p u-wi.. - s,y; E W, gn2 u y. c. mn .Q. nf ?n,;p':.g. .a. r g y. 4 q... .a .b. D,.+ &,)+f.:s.,.m & .,7-i'M '.,..fL. g :'f.c,.,.,L, ~, v + 2 f d',T r : 3.C; vQ' '.:;. ?- y l c j.R, w g '., t,s w/..g ,. i ',. ~? ~ 4*. '.@,, -nye,* [s DML$Pg8ph, $,... e..t,R@5.df4:p.Q-,g&.I M w.r .i E,E. ;@;; : ),. '.Dhyd J g. p5.W;c,/ 9.1 ic. PFe@M, l S$$' '.OM,$ .W,Q. .M. c? "' '.'W. M f:: U%/,4 In which' gpt//. 'y s. y.' . / e ;.n q,m ^Q> O MI . %g.: c ~, ^~ m. w;.,. 2antiplu:ifanv fy:;; D =. Dead iloadl,ogh . To.406,9equiplbuting streiin.i-lf4. otherperuneny, gettg% nM; , h. WQY(..". ;OBE)Floadingy J =. Operating.,X W ke. i. ' :4 a, u y...
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~~a %p;M > E' n Desig..,.$!T3 @@ )'g@88)?. loading.. -E: .IV ~ .d.. Eo = ForceNonj % Q ~ 'pD ^ n Basis %&g@: Q Qgl'. gg.. ' f f(? l a,trU.S, k0.thernalhexpan,ien ja' v.;...~~
~~of.pipen. W Q?~~
~~ditions<. fdur Et.,J,.hr Q.&, ' 1.1:N .. W'E@V@2fgJ ~ ALLG*ABLE: STliESSRS t k'i 4 7 hiint[ combination IY ' 4.3 ?; 'l'. l' " K : f L. f(yy; h s m'cim ' Allowablo stresaflimital ~~~
~~;Q.~~
~~An Doction 4.2'atnYasifo11 4. wy ,:9i.' g f:s.f..y. .\\.,-;gsg: y. + Vt 1 g. . > +.. Q;.. 4/ - w r b ls"~~
~~Y 'j'.. %..,,~~
~~.,,k.... f,w,F, .. ' '.J y,.- . '.,,, ' m lW :M'.T ?g y A,., i' f w M t s,'~~
~~r... -~~
% '. : n. ;t $hh$2s_b[M k1,. ~,I ,K.,... I k.Y
r r m w ~~ v?*--m z L,v:.h r%R, a '< sJ '. - ou nk %;y m 3,.,0i , hhqNM .,. > > gy T
~~f q~~
~~Wy ' - . Y u.~~
~~M~,. ',,. @;> 1. %~~

$. 4{ w. k b ?, [ j'%d $ : f '.' n y t..~,D/4:){y 3^ Y ,i,WM .= e s. l e es x y~,h.c,. &g. - c, a. ' q, y .c c,hk ,eg l4 ;. W, h W..' ":::Qy'O. [ W; M h F'Ly;* L,y&.M.- wN n!. mm v f ?ableLStrosa^P. w 3 n g W y;p,~,. Load!Combinatio., c:.v f l:ns.p,fi g ^ s:s&MnW3Wl ~ ' ~~- LG ? - E
~~1. h Q,8 M a. K.,, K' $. W.4 ' bQ f f,,py~1~~
$0 :W'- TW tSglp M: h>l = G Lm n L h,g@h..* h.1 q p;) r I'$$pt:(y.t;g.h.,'.;pg$,Q<M O ' ,y. flMS *:Ti 7 Y .l 3 M,. h.(c b[ 1 3.. cq . w,.. 3 .n q. a... p(..,f ~. ar... Nfljf C. -q'k 5}.6*.0 M ~.l 5 W. y-,Ij$ ;
~~s? CW' ? y. %~~
~~,g. .s 4 h,, ~Jl[&.{Q,Q,~..M .%,V~$.\\ '; & ;:l.k,.w'g h.Q G f .e \\$fW$ ' k. ~~~
~~'.* Allowable stresaflfoIWah4 '~~
~~cQDCrestu3 anchors13' l.0 S. L c3} W.'~g@,- q:%..,. '/ d i ~ p ' pap >.@e l::.Mw o p ble..n m..R. e s. _y~~
~~1... '.id, C., f,. ~te~~
'?g'- .1 ptorking:'s tress : Ni r, r rInntho' abov'estable,!S -denotes g E.W 5 !' i i d force.aterials as.apecified.'ing,.. 110 wing 111s @t:; 9e ! a] ) FN. et. ' - 2c. 7.: i; W m. ' %c.M.. < c M.n...M..gy f c .e c w h,7 ' Roinforcingw teelitensile,w.. ssM ..M ",' d. 2h00'Olpsi 31l rs oc Masonry wall' flexuralicompress'Q>Y treas' .a.# Mb' WW W :. W@W W@f TM$%(:. Masonry; wall flexural.%q, ',o.n iva O.'33 f'n.a 500 pci s1 ' ':?Wh * &Q $l:h !. ?% IY> Labea Q c.1.1 Qt.*n f 43 pni t q' E ) 7.%j:.y., -g #.E, ' ia - &.7 . r, g.a u j..:. w.,. : +- 2 ,m
p,,. y.s.<2 4.m..

o......
~~t :i Sheart. stress: in,..k r morta be ese e;-!O12 p;siJ.' +~~
~~F g,5. 9. xs.~~
~~o a b,s~-a, w-:,r. o.m . n, ..i u m~~
~~.. y;1 ;<., -~~
~~... m.8 -~~
~~m.. #n.~~
~~p,. . w,. e ce. e ..-2/ M L; r s .w e. n?:.~~
~~..' Shear' stress. ins.vertica,1-w M @n.Jr d',7501 2000'* 43 L y,p.~~
cvP l 4 d.@3: 6;%.P./ i> h "Y'groutfand block {with @@,k. V A M n 'i " 4?.$ Q "ofl.the M@4;p 4M2KNT^ i l ) J ?' hy% r 1 JoFAM,W,.ModulunTof. elast,.ic,ity 7.y r5gg. gall'gg3;p.Vc,, s1000 %J gg j s s ~
~~c., g, -;~~
~~Egg~~
~~.. ~~~
~~concret'ed,d'N, ' 4 M V;16. 0 d.Q l - 3/4"-diame ter a self-dril'lin @@&a.y.~~
~~anchor tensile".or.!shearyf "gs~~~
~~i.* 'I y E i TMN Er Msi ~ a< .g p' r~~
~~o. % :rgg~ r:j.~~
~~M;h. :', -..; cn-~~
~~i 5.?.:2Q,w;. '~~
~~?M .%#M ll~~
~~.QG;p?!~~
~~%%k.< NWW,. 4.4 DAMPING VALUES~~
D.
' F:, . a ).. &q %'.. f ' 4: m w c: ,. ~., n' ' ' + 4 ph[&s2} p, @ Wall, analysis is perf ormed_.,using',.dp)ap@in.f',p.g3 values o im s= g gi? T 'fp{A t i. c5% for DBE. 'The damping ~v,aluesy,useaCare lesu7than.thoso spac H iw t[.] M,WS@;G ifor reinforced concrete structuteIs*i(]NRC? Regulatory Gu 1.'l-j My,3? Therefore, the dLaping"valuesyused ~ considered'conceryative for [ l bg{ys$i d' the concrete masonry;walley M/g,;;.$.L,%r. q ,7
~~.. (~~
~~.m w.., Jy4pq - ANALYSIS TECHNIQUE,;, J.~. 1D.v..,p$,: %.>.' .u [ ;4 EDNM, uG : 5 a p .s pp. k I 'h 5.11 GEN 'D r mmm.% ' i by g$: s evaluat edibyjocuparing'calculcted atr = m l3 t lls i.~~
~~Capability of wa to allowable stress limitaWContiined 'strosaan aro calculated n~~
@hy&~-. the sum of stresses :resulting; fromT. wall? inertia. forces and Ca1.nic M MI: i i y t'f'E 'Catogory 1 pipe support'reactionsWeStre'coes are 'calculed a h 1 lih'Y sum of stresses resulting fece7vettlical;.carthquaho notion und 3 U ' ,iM& ' _one direction of"horisontalVeerthqimekefactione Two directio9of ' horiz s/ , W'D' K Ia [ ):P Pipe support reactions.are".obtained:.frem p' calculated cm tho<ipo support ins p!.3
~~.J K~~
atreso analyses 6 Wall.; inertia /foreta'are % ' J..0.,~ product of wall acceleratioWand ' Al %eigh'ttincludin@ Hot:me h@y:3.n. i for attachments..,Malifstite. b.rulated cubihad. M@.y [1 w m'\\.n. 2, A r;,, p4 m. m n. . n..M di \\t. h Ml.'...., c' - -,M,'A ,.6 I. h.g g EM p,M) j.M.wh. 8 q h p.4w.. ~.. ~pi - m.- w 7 hg 3/y 3b;[M y ir.? h$.. N 4-* i 1 3 m4.p,,.~su m.'s r ; r.77.M:W[1, 6E' E.f ..n yw y,@ gm :,;. y,,. - - /. c 3 a t. tJ . ag,p N 5g g_ m A S p. p4 p. , e vy up$g m& g .a r. c
Y ? D.ri?hTV M
~~W W M~~
~~.;f~~
~~3 h y .~~
~~a. e, h t. '.c .. A ; b db. ((. 9 [. Ib f, 7;;s.i~~
~~) ;.; ' Y~~
~~.' g.L t.a jc ,.,,,, p;,,p{. ' 'N i,?~~
~~w. g+..,.~~
4 p '5; y3.~[.,q;g.g. '5: .. w -g:w n^ g t i g,$the f 011owing (e f f acts /ar; mods)/.. 'lQ: eyplp< ate the: vall c m' )sup. ported beam,or.. plate e,Tevaluated: h. C D' Fj w iV t' ~ ~2 9 ~ #9 7 "'D "~MEE ' - f a) Flexural" tensile" stress'Iihtall reinforcing bc.ra [d e E' a y' r i Y. b) Plexural:tensilelforce'in;' anchors. anchoring cantilever d t [g. p' wall rei.nforcing'barsJ7p...' Plexural"cbkpressive stressiin'the wall 4 c) Nyik,,.M d) Transverse { shear 'stresslin ither, wall,' !j b e) Shear ' stress"at'.verticali joint ^between wythes or be tween a wythe 'and grout. fill ines' pace between wythes f)3 Q)W*, W[P,. [ Local shear.and compressive atress tint mortar joints pro-b f) ! b ;M.' duced by concrete blockfact'ionfin trahsferring pipe y support reaction to reinforcini;i bar Lties'. [Q[#%3 dQ: Capacity of reinforcing lfies2 to transfer pipe support ,j r g) C37 reaction from one wythe-to'another. [ [ /4 v >, ;.f. - t, r.c. M y-e 1-WALL MODEL J. h 5 2 f[J y Walls are generally modeled as simply. supported beams spanning '[ ~ 2 fro:a floor to ceiling are.nodeledMTwoiwalls which 'donot extend
i
~~.from floor below to floor above'9~~
~~g..~~
icantilever beams supported I A-y Support at: cr6siif walls';is generally ~ neglected. ud't? y floor below. b.In some case _s,.wben the.stressesiby'.ibeanlanalpaislare high,feross h} Sih.; wall support tis considered?'anditheswalls are,modeled as aireply supported plates. Existing opeiiing'arin the. walla daled. b ,,AJQ3.h As discussed in Sections 5.6 andi6515',..'.it is'shown' are -notlr.O E -Y t4 that.a trec ces calculated using the simplified;models~canEbe expected tr e::cced l! J _i. E k stresses calculated using more'. exact models in which openingc cre hlT ,3 y ](.f q -included. ~ ', " " ~ (?r 9. J.k }l Walls consisting of moYe "than.one.wythe' to make.up the required R thickness are modeled'both with1and.without grout. filled canter ly1 . %T'. ' 7~and 8-representing optional construction shown in rigure J,' d.'
~~space, r7j s~~
s. All walls are generally considered to have a density of 150_pounan p %g..e'. I 4 per cubic foot. The wall weight is; increased, generally by lot. 4j %y to represent the weight of all attachments such as piping, piping b]l j. supports, electrical conduits and boxes, instrunentation,.and ~ I ) g p., p In order to verify 1the allowance, the actual ventilation ducts. Fj L i %5-Y
~~weight of all attachments was calculated 'at four walla having~~
! relatively thinner sections and numerous attachments. Holght of f igt/h 3, ! attachments was calculated 'using data from the field _ curvey, pip:- d} P l (lfl, isupportdrawings,andotherdesip" documents.
~~s 6 $;b~~
, Actual weights were found to"be not more than 6% of tho' vall j i jweightinmostcasesanddidnotexceedtheallowanceinany .]1 p, case examined. fi 3 g ~ S. 5.3 WALL INERTIA FORCE tg s n y Out of plane inertia force generated by tho mass of the vallo is calculated as 'the product of wall accelerationa and unli N W@. weights including allowance fos attac,hmenta. f,., iw;_. 9 yi s >, TR -[ ' '. ]4 * ' f'. .s t' 7, -
~~f. ')~~
~~[,,[-M %,p[,,~~
w'", -[ 3 kkR3;$hhh,a - Y h h pg 3 y&
yy. .pg 3 dW s i fWh., DQ: -p.) L.
~~%M*Motw,,~~
~~aAfQ' } w..j,ry y g~~
~~i yo y~~
4.; .M., - Vi \\ i m %. ' a. fE*,SU. c p,,1 tedi.sf.ng th Ecisckd n 4 A%d y rgq9en.pice are she. = g 1, 'ag 1ptedcpg the c m <<. g 5u ik poc pale oge grapio. %gp,uaing,Qheyrgs,ponse )s, aty,{es ,, e% dil"Trequsney, 4 .s'ag th'l top end 2-e $ h T' Qcgthep@3Iffag,eggya,h og coctic: ns. acS thy 3.. - pic:crgefs aygva g5 e' . all,3the act w ---qubncy3161;iMly.yy4ito?. a balculated usirq a w 'g%fullyjerackedt sec. tion';+pi
~~e., fore w._.~~
Ok' th There rj e wal15with Icne j$NffequoneyhthicQ1s ionitthe' Ka ?si . the opc'ctral puk on d. lthotfloorlap40trumTeu ;~ "'ga'nalysia, using 2c /&FI M'effeetivo mu;misent%f Nirierti'd;igi's; 'd ? to decount fa n tho 5 NC:th. deff ects ' due~ toD the - pa rtiallyicra ~ "dition 3 3 fpG, y C e.g4 j'c id The effective moment ofinertiaUcagbe(computed-by"thefolio %*fgMt equations .h ,e ; g f -q y-?;(,3 Q . y(. -s ]k y. l^y h l: M. y s [ e" fN.I9 1 ) }r Q N.in g ichy:.y 3 4,y j %gj',hlW X,&.k.. 4.)4 7 ?. ~ C: ?~ !y a.;. .,4.:.e:. w m t y; z n;g Y:.1. k m:7 l'f.l = effectivejmonie,n,tgfrw g. ? ,i 'y e y> y ; n..-@W m r MV I*'^= monentCofOirserti'" ffcr cke n$f'. L "l % l b '5 seetion. Y a ?
~~I bY~~
% OgglhM 'Qf ( = : a.b.nedt7.of. f crac. ke.d s. n u';'on%{l'M I rt eeti g ~ x n3;.w, m: w. .c s ' n E = a d =.y s p. u:.y.. m.,,. +. n #o w., n= calculat:ed mom.ent:ac2tna - x- h : u R >~ tapsume f r,eq' u~en-cy 1 W. "O m
~~C 0~~
~~~ 'l 0%Q{'[lQML9h.]r,; e'., O s. r, lil i 0:.~~
?
~~" i s~~
~~W' ~g';~~
n
~~cracking momentp~~
1% e .c 9,. er f%.! = modulus, of rupture 'of.;)mmeon.. 'W RW W, fr .flyp ry = 43'pai'". 4- - Mr'% y. j,1 3;il-Yt = distance from centroida axis of grosa.section e .h. neglecting'.reint gextremefAber.'in v 'f^
~~1 v~~
f b. E g 9 {,, l' f '~~ g g- .;j ' d Itoration p.ec.,edures' are: used"to;$_ 6tainnthe actualj fecqctm.cy , y J.1 ' of the wall'a'tYthe^stabilised:staieQfAs(indicated?in-Tabla ', { two walls are selected forathiaTiave.atigation. Tho hetual frequencies and the corres are abown in1 Table 61.;Ttie)ponding? stresses' for.'thoso n1hprinsses 1 fle ut r .*y)l then the allowable'valuesCphii,, ) .i.W '.> J' ,y .d' e: 7.':w s,4 asIsxIc c4Tsoomr. kntai.m "LoAos N m ye 4 .n s QN: soiamic category L pipe'c, p~ 'lona are obtained Ecca n. ;.a e Ja 1 07/W c parate pipe *supp'6rg and nalynonv W ob21 w s ^ Rih, -QV. ' '. T'i..qN W W% T y....- s,,,, y.- [ h- ~^~ ^ d J.,' 5 ) h- ,..[ Mk l %ge
... i?hyry @My.A.W4:y@.. ~,.A ,- er --r-,, f w gm, % 4 l$ l$la'l@. 7 ' 3: k .q@.%:M%, "y* N; ,m "-'] hj ,,g y
~~,.UTC~~
~~'~j q*@ND, ~:& N~~
V
~~.n .> ? ? ' ^ ' o~~
~~.t"y%%'y[ch:~: -~~
~~??:f'h.f ,. }.if ': ' ~' Y W ?.p$$ 1 ! 2 uppor$;p.bg,'qadgaroj.calculatody, conoid'ncdh1 O.Mg M~~
4 in the,wallidu.../r N (fO. #'

s.
c. i' y to pipe y. f fe,ctiveltridth equalf ts g..theforcesfto, f.gis tri.bu 'j y n t.,.. <..o s: "...c~ ,b = 6 t:.Kc, M w/.w in which: . (. e, y ,L,.1 r r. g-t. Ib, r U-b = the effective width: e., :i L f W 6c; g. M ,n c i 4,. " JJ t'= the wa'll thickness' fo. %y, 8 O" l Aic Ok..n c = the width of ~ tho. load contact area. 'h 7. M ~ the effective. width comiputed bycthe above equation , 6:' is limited uin ' the evaluation to lthe value obtained f rom ( Howeve r, ) -E b = 1.4e + c,'in which e'is'the' distance from the concentrated j T 'T load to the nearest support. c .~. 7. ,' \\.,, -d]s ) 55 STRESSES , d.W. ; r. N 1 Stresses due.to ef fects of 'out-offp.lAn'e). wall inertia ' forb[d'and f e3 T. R Mpipe sopport loada are calculated;;us'ing"elaatic' theory and.S L i W;&ff assuming thatiterisile7forcesJare+ resisted;only by the '.tentiile; 3 ! reinforcement. '; Presence 70f 0dhead!jloadkaxial, stresses,'.which':l reduce gj m../ 'in the. reinforcement', -is. conservativolfyhegldeted ,-y $ ' tensile stresser: d
M Lin

most cases'/ except.for?.(thos'eTwallYwhich were highly.L.cticaded.
~~p. a;.;;.w., 'q ~ ,a, Shear stresses must be" transferred':.acitoss horizontal join,tdF' -e~~
~~'N.,, t'botween blocks ' to transfer out-of-plane '. loads to supportingh.'.~~
~~Shear stressesimust' be transferred acrosa vertii::41yQ .d i floors. [:l l~~
~~i. ~ joints between wythes, or between'wythem and grout fill.ito@~~
~~[g; e achieve composite ' action of ' adjacent wythes. These strescoc,';r 1 1 [j. resulting from out-of-plane-loads.are calculated as ' '~~~
~~}.y~~
~~~ g. e y -w Y*@ M,b[EN' where J d b f = shear stress [" y i', V = total shear force at the section M m@-~~
~~~, e.~~
~~M b = width of the wall strip being conaldered Ka 'l m z. g } $y yg;wc; jd = distance from centroid of compressive area to~~
~~3 Mu r~~
~~,g reinforcing bars. y1 - n:r~.' r.-~~
~~r7' N/fhe !!ffects of building story interstory displaceconta resulting trca.~~
[' seismic loads are calculated for the in-plane direction only, A pffG ao out-of-plane stresses due to interstory displaccconta arn va .W Q + %rg,, j$' s. 4, ,z. y, 'L "b 9s. ), 'Ih \\ ' n.n [. f/2,,[ _.t,, a. e e L n% R ie I
~~C 4~~
.fak U fgjj;gh
M . g p .n - -7 Nfl3,9.;o y%-U.%+%, s. ./ .] . m%>;M8) J %y:. ~ ypm.w i.Qc ;Ly.Q. " is hMhd.D@%. : ' 9g [$ h f~; 4 @$ : $h [J..,$.phsw. '. ion, sh. k f. $by.W Y WMCa.WW# .c L 2 lgyM iJect oar.; o treac gic r 9 nottaigniticantr.5For.the
~~? ica M.~ul.a,t.'e.d.3bgy..sv,.W.m W,y g % n e g. h)y ;M.u.~~
~~..,e G~~
~~M.. w. gM 4. ~v n ff, u ; h..: grQ. p ;'[;; mx n.y ,.y, ~ n X.. V i.Q. " * %m.p.. .s- ~ MMW~ i .z A.%..wheres L -e.. v. w : u.?: ipchi.wij%. ~s.n, %'2 k.):i~~
~~..m q~~
~~t qq f -, y =. w'h ;.. y, >-ear; atresslg<. :,y..).... U. M. E &: _. c T$.b. 'f~~
~~sh.,~~
~~I .~ .s s ,o g ..v* 4 vr. w.w '~' .7 a,q. A *j.i ' lmodulus" of;lri'gidity'.,= 40y /f f a ; ' s s h,' G 5' O ph = U = interstory idisp,lacementK',g;;.'Q. H.3 . XD.., :c.~~
~~f E~~~
21 i;. PE s -M,. A .s. 'aq..,..q....,... ..M h = inters tory heigh t.s.'.' "i 7c s.N. 1., [] g. A ,v .i. n.w:,,. ~ m t<... el h Where pipe supports or ot[Urf.attachmNnts are anchored to tbo 5%),1% wall and through bolts arelnotiused}forgload' transfer,11t tin 3 U Mf important that'the applied,'. loa'dsiddinot pull the blockc.'out. 5. M;$.MF.' ~. locally, nor' pull the.'wyth5s!cf.%focksTapart? ~ InXt heco O dMM ".. regions,' shear.a^Gd compresaIiversGQsgs'iin ' joints fbetseen?'E t t' k 1,#%. ' eval.uate. thel. wall capa. l.i.sM_. h'IM.O.h@ .in$ielbars', U 5 N&.' blocks, and.,tensileiforcesy# %t.f 9,', '/ e' d.E.j....Q F, zj -d / 'WL. - .b [-D - 4 J W. p g.3:P~:@~f. itiy*-- c a $J~gleM;c..... -,w. EFFECTS 0F.C LARGB ; OPENING 3y# s yd,W,. QY., . m ; Q; p. M - ,q : E-i 5.6 s
~~m. ::;~~
.. g~ :y.p.-ip y. S p 2.. y-u y My~ .e--. (GM6In' general', whe'.n.a.walle hastlar..ge: cpenings, walllfrequaiiciba* uc p...:.e :. r. $3fk.Wcan be expected 4tollieBlowe@while[s,tiidessoc#aayYbe?high'6rNhan. i] ..r.a 3 h tj WOg%f ip 'or.not calculated stressesyssi'apso'de'1'sCw'ithoutkope M,, n.the same wall"withoutf openings.91ni. order to-deterninc d:/dro': h ~Qh. WM i representative, ?two'selectedi' walls}[ad,an'alyzed by?firitthF " d Y element methods. using' the'. computer.3 program STARDYNE.; ;Uodelar j} y ;g,g E ! Y@si$p Hf used.are as shown in Figuresj52.Jand16.Y, Contiguration h fi.
L
/ P ; The, walla Carimodeled s Sj %g[.yFi. Supporting cross. walls are considered. ,a ' as free to rotate at support's%nithe7out-of-plane'direcl tion.'; 1 h, Medal analysis is performed >toidetermine' fundamental' frequency i] Wall acceleration',4cor' responding to"the'fundc ~ f" irh.g.. 'of the walls. nontal f requency, and inertila force"are determined ~ by ttiotena O M.'dM.j;:5 t h cathod discribed in Section.5.3. Wall: inertia force and pipe-9Ypr. oupport loads are applied;lusing',stiatic; option of STAnonMo. ' bl ' f.Q%=p [li obtain element forces 3,and'aoneataf from which'maconryland te- - b;M l i. 2,FdgM ic#orcing.ateelnstresses3re';. calculated. m .. 1 p,, ; y y 7,p.u s. g%.;.- m , j. MG 6, RESULTS ' OF ' EVALUATION V.,t- -5;jM.p.;.a 'n..,.;
~~d s-z i~~
4 M,qq,e. 6,1 FLEXURAL STRESSES' W fi ; OS^b# Tablo 2 shows maximum wall compressive stresses and naxinu2 .!j -Mhd. - '9 ) reinforcing steel tensile stresses resulting, from conbihod' s .j yf p; @s.,iM@d@hF of focts of wall inertia forcea7and,' pipe ~ support loada cddrinWN.: pI r /, Strosses shown:are basedion.concorvativo:danping MC t P., and DDL 'i hrP of 36 for OBE and ~ 56 for DSB,3 thuaikhovstreason chcun 'can to e W(,.M...:d@. '.~'... hgulatory Guide 1.61,, is juseds@'..W, ping valuo,'.cn tohh&in %./k. duced to a lower level'ifl4 highht dam
~~m. ~. ~..#. ~,.,. _ '~~
~~~[b, N ?.. c '.. '.:?.h? k" ..l .. o.. a a n,m..... 3 h., bh,~~
~~m. g. G Y M [h' f,Y. .~~
~~. l, 0,.qr ;* k g.. m.. a.g... ' :. x, p. Mhs dd.... > f n -. 4 y,y,, n 1 lp~~
~~4.,~~
.-} y ~n.m.s.aw g"~.y a-y. cnw
.: 1 q w~:7m.m 3 ~ mumgy-- o ,yjQU y, t.. N, M ^ 7 ?.WW h.;'. ~, +, Y,;, !} ~ y,D %m m. A M... M.v,:n. ca.u.s 3, M#.. i n.n. +.wmw.am.y hhhh,$ ~ Maximum ccl-m m , & wk,Y,,y. y yYib f gtp Y pl. ~ 9)& NUN $~' (.NJ @f%ille compressivoi stiresg;epare,,jggny, ally: low.: ^ f w.13o.ul.a to d i s tre s s 'e is > S 6 Wothe@,pg gAless7than'75%':of ellownble, '/q py,fo.rc.ono wall.MJor ;all i: i W.'.." f . vefgM.y:qWp^Q. JgWf ~' p therWalls?c419ulaK6dfstrgese kJ
~~M y~~
~~M'j[Roinforcinglsteelit'ehaJ.1EI.stesEesYare(within.allowablelimits. i< g g fEMaximum calculatedTat:ress)jia,59, o [ allowable,forlone wall'.. H RAll;except'twowalls$j&g" ' d(stressesIcssthan~602-~~
i

yp M.;, m :
~~av Ey,. , g.{1. O, [j iMQf { allowable [' ' b{.yg j WALL ANCHORAGE jMQfffl?'?gjiQf;p:' -:.;W ' il~~
~~@ y [r ~*t~~
~ .'. 0. ' - 4h rl ' ':P %.vq 6.2 y.- ~ Q f '%,, All walls are. anchored s to?.s'upNr;h.:t:iing, floors 'b'y dovels threcdcd p} c WOM. s - ; l into concrete expdns'io'n a:EchorsMfdfor walls', extending contin ' tj ONb'i l uously frouCfloorito ? floor %th[ehncho'rs.do' not' have a aignifi- !} %f W SW@.' e 'i cant f unction' as. lateral? support 7.tissprovided by shear trans cr MCTM ' across the mortar joint?tietsweenibl6ck.7 units iand the floor. !? $?T.Q: For walls not extending toith'eUfl'oor7above, 'i.e., ' cantilever ,{ dhfe walls, stability-of.the: walls"isi,directly related to capability i: @dS;x.Wf-%' 4 ' of the anchdrsito trarisaititens'ile:[foicces to the aupportinT ii v I ctwo walls which are tcantill.b.bws.c'*"n'chbr..a.t..e. n.sile : forces At concreto' floor.. Ta..b..,le. V. 5's a w ever ,3.F,o, rces.. calculated arc ~ i G(;f"J/ % < MID' I within allosable' limitaTan'd41EEs'ithan%20%.of anchdr. ult'incti NW.. l '. ;'.'$WTNF%$s.{2 - @&Wf ' ' * '" capacity? l'F Shear forces of, anchors qlik $ h@'.ethe; upper concrete"ficara, ..gW. ~ as shown in. Pigures974and{8',7a'9d?.tord;;c'a$culated.to boivithin cllo w
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4;:@?g $W able limits and' less"than :154t of 7 anchor ultimate ;ccpccity.: ~ m_.;.., =,m; > '. w%.o ,.?;Wl y,:M $,,^. f. W, a ' d.y u. ? ...k 9,;,&,,. 7 6.3 SHEAR STRESSES y, - .. y 4 shows maximum calculated h -of-plane flexural'cb a .k. Table {g W ^ stresces in ' selected'~ walls. J/The 'atrosses apply both to hori- % d ;.. '
~~ontal joints 'between blocks arid),to/ vertical joints botut.ca MINP vythes of multiwythetwalls. ' Walls"adlected representc ono i~~
oJ wall for each' wall thicknhs's. ;' Stresses' shown are baced ca. $;N';' conservative damping. values'. of]34'{for. OBE and 51t for DD:',; T%. Calculated stresses rangel.fron'244to:.73% of allowablen ' cc. W Maximum calculated, shear. stress'is.8.7 psi during DBE.' i z s ms.,. i, i. [Ng d @;i q.$ For the in-plane. direction, maxisu;s ' inters tory dicplactr.cnt j is 0.0006 inches per ifoot' of'he'ight,' resulting in a ma. irr. EDMlr shear stress'of.30'psip which7fis.,less than the allocablo' i Y
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~~p.O - 6.4 LOCAL STRESSES ' AT ATTACEMDtTS i my ca r.a t m.g. n:s k Q.. ', As shown in Table 2, through bolta are used for all pipo~~
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supports. However, the loads are not of large magnituc. i, ?< Thorofore, local stresses 'at attactutenta are not a concarm p@;.,.. i 'k f&l> b i. %.GC ll 5.jO,Y."' v. S. i 's is (1 g.h... r. .o .v. ,. 3 ' ?* % si.w Nk > j".1' 4 Y ',g h ' y fr ~l... .(s' t ,.e l ,.k)ll .{
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j -M + N fifG.1 MM.R'"Ta'ble 3 shods!Y;;c'cipaifs8n.{30.cliidu'la(t,edinaximiun fic.wral Y,n M8b.% w2 1 N H VWPTE ob tained ' by h'andicallpulatilo'n' sum friliifstpl'if ied jwall 'godels ; uitho u t cal'.c.u ation7using'. kall 'codels ~ulth ' g by). hdIGW. ' openings and finite:. ele'mentvCalculatedM requenciesgarefalso compared. T The data .,O t h W @ b W'oponings. ! ' $jQg@g; f,shown are giVenffoYjoastandtDBEiUp,6d.' include ef q.c M inertia'forcescandjpipaisuppor@tfl'oadar J.N-.q;q!.arQ ffo:5.j,7( -Q QRn.y - . J@M Prequencies calculatedfusi'ng? thef.fi' nite: elomont method are very O.F'$s.'J.close.tothosecalculated]using}shand'calculatlonandsimplifi^d dMa modols. This ' demons trateanthat. i h in Figprce S. 5y$p;Z.' and 6 do not changeth'e2:fregiiedc,open ngs.as b ijf! ~ ieMaignificantly.* y;. : Q,$g'g.g ~ ' ,3, 3 Stresses calculated us'ing c the"finit'e' el'ement method are. lower bf.i c k than those calculated 'using hand" calculation and simplified b $iW[jMJ This.is because.the finite ' element method providec. a $%:D: rodels. L h.hf more accurate '.resultin'gl{atress dued(toythe concentrated : pipe 1p%hf&,. support loa'ds. ~ ^' i'. 'M b '.',s.fMl.j. pfi,.. (,.y T' f - d; {L m:,Qrt'. i.s.e..s c.al..c.ulated, using didnl.ifid 3, L.. OTh.e. compari' son showad ha..t..N..,tres.'[dd{pected' t y ~p:fy& ; '4 g%.,J..?. zodels withouti. 4 Q:Q s '.?can be ex to bo concervdtive.. s- .o opaning.s 33-
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