M"-f .5o Ar"**f{i"+ ( -l-- trn'$tfo,ofi',ro ...-rx*io)

- t\xh'

2xt

x)= 3* 2x3

h,

x'\ -- - .,(1

toJ

x\= C

xl- 4

-ax(lL

!:11'

6xe

h3

l2xhz h3

/c^t -\53*

142

h'h

h

h'h"

h

\4

n''

5<raco8 -GrY

Iiltl r

I V.(n\

..! o.So

2-ET 8TT -QEL qEE.

\4 hz h5 hz

ET 4ET - 6 EI__ LErl,( h qz

-\2rr -6er lLur -6F -t( h3 v?

6 EI TEr - ( ET- lEt[z- t" hz h

h

g8_Civ-Bg pecember, 200g)

For the plane stain element shown in Figure 2, determine the etement stresses oxt oxt and t,corresponding to the followiqg aodal riilpiacesresfs.

ur = 5.0 mrn \ =2.A rnrn

'*z =tt,frrrm .,:. =fi,* fXm

w.=5.*mm \=fi.0 rnmUse "E =TAGPaand y = C.3 .

Figure 3 {aii dimmsic,ns are in rnillim.eh.es).

Lt1= 5,0 .^^.,'. V, = I, O .a.'*a

U^ - O. O t^^r^

- 5. O ^.,t

o,o15-o,ol -o,O 15 O o,Ol5 orol O

l. ( ror ro

) r.la

t*

98-Civ-89 - May ?*1 1 Page 4 cf4

Problem 3

Llsing two beam ei*ments, calc.ulate the reaetians and draw the shear and moment diagrams

&r f&e &"{rur:f[ire s&r:wn SsJow'{Frg. ij. AIi me]-fiber"s ftave dle sarne ngrJrey. f = 3OG rfPs',

I = 40 x 106 nlmn,

The stifftress ffiakix of the beam element is shown below.

U*\=!!LI L

I{

J,

2

EU-z

4

12612,2;-;

lJ 1- l-

664

LL12612;-72tr!

LLL

AAu^u z-*LL

?5 klil c:;

v ru' 2[vrr

??

OZ\l eL) e

- lzgr 2Er - nErp3Ll el 2.? -(

6 Tr <LFI

Q,' {r ?LLT

(r

l2_Er err - ITEL GEIt? ttr ?"? t;

k A f s't 9ET_\z) ) T t- T 8"

L /- 1-

-lzEr - 6Er ILET -Grrt; ?i {.; %,

Crr 9n -611 AvrOLL1

(, tF {..

3tru ,b

ET CET

n,VL e? er

Crr(.\

(E)T ry

03\e tt

Tr=

lerfT (fI -lzEr BEr <c o I

T

{,' ,t) (irrF-r -G€r trrrl ,-r]cEr[-r ,r\-rtrt err

(,3 (,t

c1r 1-E1, Grrt' ,r\"trl",,,\-ct.4Em \K'ff) \("rtl 3n c) _ lZgt - 6Er lzrr -(rr

(-r <r ( Er 2Er ^6* Art/2_L, <, g("

d_.

G\ t-) C+)

_e

MC^) oJx ( 6

M(x) - to

X)= Loo - !

_zx3 ro

XA x--6 = 5oIV\= lo =-5oPw

6:6 i= - 3g- s- Loo 16. 6e

=lol= -37

t2

6oY*t*'r

M:S" Ir-l