Tn Pal-t izZ P~1PiE l rcen$ 0," tle 8eqs irarrent s Pas 52-

Cal ',Forr-,% a IE"&$:%U% e 3f %ach~:okagy Pasadena, C d f SCo~,.nl a

3.955

& e ~ i ~ ~ a ~ * y

Iw%roa%e blon

Gsne~aL Sok~tios by Dllie~enLfaL

7 &quationso

$L-pplfzaLie~ 02 ?iPPsrsn$ial PquaQions

to t h e Tkee Stiffe-ler P m e l ,

Approx%fi~a%@ S s l u t Psn by E-,ergy Fde$hsd,

P:~xiler l o al Txmq31 e ,

'kge-.i~%en$a2. T ~ s e s t $gation,

Diacnss3 sn eQ F ~ r 2 s r 5 ~ n o z t ~ 1 Ros~l:s.

CoaeLx&ion,

9sf erenc s j

In t h e p~esent devslo~x:~an$, the ~ O P I ~ B L e l a s t i c i t y

eg.aa.lioaa fop the stress d i ~ t r i b i : ~ - t ; i ~ n fn sheet $eafi

aTrolded by ca-sa,siderin; the shest as merely a m5df Tor &pans-

%t27?leing %he l ~ t i d fi?am O M 8 ~ t k f f w a e y a1,0'kh8r~ k? p O y k i ~ 2 of

th9 sheet %pee 89 includ.ed i!&th %hail, of %$a s t f f f e n a ~ t o aceourkt

%o?? -$.he Load % ; J = t t h e sheet way be s;i;lae@$ed pasi,s$; &aes 9 ~ -

~ a n s l , is r e ~ l a o s d by a s e ~ i s s s-f so luan~s having a:ci";l di Psi~ted

loads app l i ed by the sheet, It is f i ~ t h e r assimttd Lku~$; th9

sheet has SILT f i c i e n t l a t e ~ a l res tpa in t so ordy asji.2

dsfo.~x.i,tion n.izsd b e @susbderea,

Be$a-.s iz;ll;;:oi&le:f? as to bow the load

2s dj.s";yibzm$,e(i &~orzg fbe 3 y s . t ~ ~ ~ 3.P %01?,1~m3, i , t e o ~ ~ e n b e a t to

dsvelag ths diPf e~?,sn-i; is?. ;l.q."~3,%i 011 emre= ;3 l.rg tile de loz~aa t i 39 0%

t h e 3,ndivi d9L1aF, o o l ~ c ~ n rai?eeocs tan?, c~osa -ssc tf onaP areas, A , si3k, =-

j c c t e a .&o a y b f t - . a ~ y d i s t r i b i l t @ d t._ir19?, IoaAing T$( x], Ref9rring

t o Pig, 1 t he stress 6, at a dia-

f i 2 ~ ~ - + Y/

YO +[q2bZ--3-a - - - - - - - - - - -

Yn-, +[a; 0% 2 ]y , + Yw /

_ - - _ _ - - - - -

Pi-; D~ - qy,': YK Y,, 4 (a;+p2-yy,

n h s syataa of l i n 8 ) t second order &ifTsj:eati%a a a ~ j a + % o n s %a

simila? to that ~ b t a i g e a fop thb claes%@ag pro$lea of $he loaded

s$r:ng (rsfs~>i,a.~~es 2 & 31, th3 &ffesszcs bein: F i n %he present ease is real $na$ssd of j ,magi~isy , h e 3 ~ 3 t h e

is zaso,>iehYza it w f l l be y o s s l b l ~ to f i n d t h e particuS.ar

-aaqs aj:l"d S~ZS:..~; .:xce?t A a. n l ~ i e h j . ~ rs&l but double, d

The ge:ae~al. a ~ X ? ~ % i s a 38y nCJw be :v~i t tea i n th,@ fo~mri~:

yi, = A!n $13 h x + LTv s/* h J, x + *I, x ( 1 3 ) +Bq, cruh Jx r 4, c o ~ h J2u c 8'

D i f f eran%iaf tng aad a~lt iflaytag tg E, %be 3-xy2e3~i3ns ~ Q I * ,?hs

st x-e s Y k: ae aras

Eydatians (11) and (1%) ha-~2 been devalsped fop

---. 2 These s q ~ a t t a a a r~.411 50 appl%i& $a the ex>srfxe:iLal A1 pm2el tested a?&$hough an estima%s OF s is i n %:%s oxader of %,S,

Prom Fige the atYe8d a$ the p~S3t of apglieation

of fhe loeb i s r 0 :: .5(11x10 f r o i n ~ ~ h t e i i t he vn11is of

8, fox* .$ zF 4,000# becorn~s

IIp Plq '7 43 - eathYt,, - -. ------- - - e b l B s q e In, P

As can 5s seen f r o m %3@ p e c a d i w Chaiete~

wl%h many resnbo~ce::~e~~ts. Tle-..ePoi-.s, a solution has been pro-

posed usins the ?QZne-.:.-;f lLLet'lsd", eeas@2.it%al msa-.;fag of' v ~ $ k h .J*?

af the def lec t ions , Than

t z ~ d %he solati02 s"-%h%s squatloz~ w i l l g tve us t41e -$u-dcnom~

%::;is w i I J not be alloncible, Eere %he eneygy dwa to fbs S ~ ~ ~ P U E *

at-?@sa&s i.:~ :ragisn 09 t& asa",ea - A. $ ~ a a pep~esa.;kts an in-

-& dc 9 -Q.J- && . r = - it it-

D .=- = Q,53 3; 104 ; 43

pts2 p 2 2300 # 200 0 9

A ar 191

ka,~ - e Cc%35 In, C,95 x 104

:"is-;;; j" CT.2 6 7J Z C . ? ~ , ~ t,t\'ib '"" !,., Q P., 1 ""'I! :"" L;.;Jhl; 2- ?2sc::? Si.y~p?'~I..C!*?~ I -- -.Al* +

yl-otted in , Pig, % s ~ @ o a p ~ % s o ~ ~ w f $ h ealelzlated % h s o ~ ~ ~ ~ t i e a l

~i zl.isbe data as(.& p?,&.$.ea lu Figs, ~ Q L Z ab. iTalils cc?. stressas

far loads cP 2F 1. 200(?,;1, 40pb;;i a& ~ Q O S # olere eorp~-5ed. %o ds-

TABLE II

S h Stif fener Pael -