The Stress Distribution in Reinforced Plates Under Concentrated Edge Loads

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7 &quationso

$ L - p p l f z a L i e ~ 0 2

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PquaQions

to

t h e Tkee Stiffe-ler P m e l , Approx%fi~a%@ S s l u t

Psn

b y 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 ~ e s e n t

devslo~x:~an$, t h e ~ O P I ~ B L e l a s t i c i t y eg.aa.lioaa fop t h e 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?? -$.he Load %;J=t t h e sheet way b e s;i;lae@$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 s o l u a n ~ s having a:ci";l d i _Psi~ted loads a p p l i e d 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 r e s t p a i n t s o ordy asji.2 dsfo.~x.i,tion n.izsd b e @susbderea,

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

to

bow t h e l o a d 2 s 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 d i P f e~?,sn-i; is?. ;l.q."~3,%i 011 emre= ^;3 l.rg tile d e l o z ~ a a t i 39 0 %

t h e 3,ndivi d9L1aF, o o l ~ c ~ n rai?eeocs tan?, c ~ o s a - s s c t f 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 h e stress

6 ,

a t a d i a -

f i 2 ~ ~ -

⁺

^Y/

YO +[q2bZ--3-a

- - - - - - - - - - -

Yn-, +[a; ^0%

^{2 ] y , +} Yw ^/

_ - - _ _ - - - - -

Pi-; ^D~ - qy,':

^YK

Y,,

⁴

( a ; + p 2 - y y ,

n h s s y a t a a 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 ( r s f s ~ > i , a . ~ ~ e s 2 & 31, th3 &ffesszcs bein:

F

i n %he present ease is

real

$na$ssd

of

j , m a g i ~ i s y , 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

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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 t e a 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 J 2 u}

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D i f f eran%iaf tng aad a ~ l t 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 5 0 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 ~ S 3 t of apglieation

of

fhe

loeb

i s r 0 :: .5(11x10 f r o i n ~ ~ h t e i i t h e vn11is of 8 , fox* ^.$ zF 4,000# becorn~s

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-

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e b l B s q e In,

As

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

wl%h

many r e s n b o ~ c e : : ~ e ~ ~ t s . 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 d e f l e c t i o n s , Than

t z ~ d %he s o l a t i 0 2 s"-%h%s s q u a t l o z ~ w i l l g t v e

us

t41e -$u-dcnom~

%::;is w i I J

not

be alloncible, Eere %he eneygy dwa

to

fbs S ~ ~ ~ P U E *

a t - ? @ s a & s i.:~ :ragisn 09

t&

asa",ea

-

^A. $ ~ a a p e p ~ e s a . ; k t s

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in-

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^{9 -Q.J-} &&

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r = -

it it-

.=- D

=

^{Q,53 3; 1 0 4} ;

43

^{pts2 p 2 2300}

#

200 0 ⁹

A ar 191

k a , ~

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_x

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

I +

--

^-.Al*

y l - o t t e d in, P i g , % 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?. s t r e s s a s

far

loads cP 2F 1.200(?,;1, 40pb;;i a& ~ Q O S # olere eorp~-5ed. % o ds-

TABLE

II

S h S t i f f e n e r Pael

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