Embed Size (px)
Citation preview
7&
nME2 t
NATIONIT, U}TIVERSITY OFSINGAFORE
ME2II4 _ MECH.ANICS OF MATERIALS tr
(S€me$er II: AY2005-2006)
TitDc Allos€d: 2 Hours
INSTRUCTIONS Tt) CANDIDATES:
l. This €xamination papcr contairs FOIrR (,1) questids atd cllnpris€s SX (6) priniadp6ges-
2. Answrr all FOI,R (4) qu6tids.
3. All quGtions cary cqld |rla*s.
4. This is a CLOSEDE(X)X EXAMINATION.
Prgc 2 ME2l 14
ForEulre
Th€ follo*ing formula€ witten using slandard rDtations may be us€d.
Yield Crirerir:
(l) Tr€sca Yield Critorion
l _' * =tG* -".")=?
@ Von Miscs Criterion
-
/jk", -",f * (", - o3f * (o3 - o,f ]=o"
Strrir GDcrgr eq!.tiorri
Axial loading:
Bending:
Torsion:
u=tI1o*6 2EA
u =t!4a,62Er
L12U= l-:-d('o2CJ
CoDstitotiv. rchtioD! for itoiropic cb.tic m.ted.b3
"-=+G-",=iG,
-!o, - * - )
-u"-)
-.,--)
I' t n = E r n ,
' .= j (o . -no,
e=--!-2Q+v)
l lf o = e r , , r - = 6 r .
Page 3 ME2l 14
Ouestion I
A cylindrical prcssure vessel 250 mm irmer diameter and 5 mm wall thickness is subjected toan internal pressue of2.5 MPa. The cylinder, which is cquipped with two rigid end plates, isbutt-welded circumferEntially and the welded seams are inclin€d at 125" to rhe longitudinalaxis as shown in Figurc l. Ifan axial comprcssivc load of50 kN is applied to ih€ end plates,usins the Mohr's circle determine
(a) the str€sses at the weld. Indicate yoor results on a sketch showing both direction alldmagnitude ofthe slesses, and
(15 nark)
tbe maximum in-plarc shea.ing sf€ss in rhe cylind€r.(1 nmrks)
(b)
Ifthe axial compressiv€ load is increased, would you expect the maximumstress in the cylinder to incr€rse or decrease? Explain rfiy.
in-plane sherring
(6 narks)
Rigid end plates
Figrre I
Wddlines
Pagc 4 ME2l t4
Ou€stiotr 2
Figure 2 shows a pin-connect€d steel fame made up of circular cross-section members whichhave a feld stress in compression of200 MPa. Memben AC and BD ar€ of30 mm diameterand members AB and CD are of25 mm diameter. When ihe tumbuckles are tightened, thediagonals AD and BC are in tension.
(a) If member BD is loaded by a vertical force of500 N, and assuming a factor ofsaf€tyof 1.5, determine the maximum allowable tension that can b€ applied to diagonal BC.AssumeE=200GPa-
(c)
(15 narks.l
Ifa large horizontal force F (indicared by the dotted line) is also applied on memberAB in the direcrion shown, would it resuh in rhe buckling of memb€r AB? Explainwhy.
6 narks)
Stale lhe assumptiors made in the derivation ofthe Euler formula (you do not need toderive the Euler formula used).
(5 narks)
500 N
o)
JE <....--..-. F
c
Tumbuckle
D
4.5
#,77
3.05 |n
Figure 2
Pg.FACULTY OF ENGINEERING
Solution to Question No. .....{....
/a./,",^,r of cjl",te" = >-P = 12f ^.^'
q=+. e+z! = (z'Y n/a'
e, L^ = t#? > 3t.Lr n/^
Y + t = B r + r = l 3 o m f f \
a (v]'r.;') = a (r.1u'- t..r')
Course & Year: .....1?.8*?.(!.*.....-..
s,*iect: ...*!- fu .(..................
= 4 o o ( " - ̂ '
n Fa-
I t.'7 f r'th.
r - -k= *
= -12' r ( t (a
fldrlr clrae
R = D9 =hJ:ft!
= z t.88 r1(a
FACULTY OF ENGINEERING
Solution to Question No. ..........
^)
rg. _
zr?Flk$'
t - ,9) 7he
(.p*- t. n"tr's cir.te )
\ .-"r$*" 1jr\::'
/'Y\ .trr\\.,".<
\ry9
\ te! o
raa l l ,aua ia - p lane s h<ar,'^! S/P.JJ
te .X );"&. is z L n ?a,
FACULTY OF ENGINEERING
Solution to Question No. ..........
P o J
7r' 6r-<as; J
-fhe c1"oI co-,4 frcss:,le
lo",A
ho;rt ted',.,z -ihe lor5;r^a,-^a( s?rer r ,;
-*e cSlia/er a n "1 4eace v<s^tti' j '""t
a/\ in cfeqCe th tAe ,"'' ali,nn- r|'t-plen€
94ett'r.i3 5f,'€! J ( t." . a- iq z ><at< ia +he
t'ad; as 6f ++e Maf,rl "irck).
'4t nPo"
gircle
f f i ' =
T,=Q'J '=
'or"1 +|rf fi,Ar's'3z t4(a,
ilNo,,
FACULTY OF ENGINEERING
C 0 9
ry.9course & Yea!: ...... .'.?SX/1.(......
Subject .........1?F.2!r.k..................
Solution to Question No. ..?.....
le^yr. (ac = Cf.s't 3.0('){ = &(4
I
r J ' ' 5_--_*,fr1r".t-
)L
?:8. - o.tgt.(7
yr .1"
3+.f
4l ' 1 L Y t O
' " 1 " Y
-rfr*>ax,ix t tz#( s . o r t r o r ) z
4.o' l l<xt
&
&
Tur = o'r t Ts. o ' t3
f i9, c)t t d f - ' t - r 9 -J-AB= -<4-a+-" '
L ^ U = 3 . o f 4 l-1 ,L ET l^
f A a ( c " ) ) L<-Aa
Gu= fu. casp = o.16 fo..
o'f f frc 6s 'L : Ftt>
1 rZ-TV ='O
frl-e n kr
Set by:
FACULTY OF ENGINEERING
a . 1 l
-kN
-f<N
Checked by:
Solution io Question No. ..........F z - n
A t h J J ^ b e f ^ a = ' - 1 - 4 o 1 -{ 's
- I ! :
-
" 1 - t- * ' . " = T = 4 k rr r r L a . r ( r . e J
$r y;eld",^r,
A t l o w q 6 6
f/lenhrC _' f i < l -
= i 3 6 =O Y
htx +1 |t . f
+ .3 . 1 t X t o ' ' q n +
t l c J-
h( lo"qbQ Tr*
Tsz k"t Lrso
G ' tx ,o t ) '- 3 . S 3 - k N
+F = r.r1 &N
z \ -1 -o ' t = 2 . f L
v6pl44 | ,f - s .
6r -1 4 " )
A, . A g
\
?
A c , 1 3 p
J-B' -
lLI\?
- , 2I t 4 - i _ , - u' + = 4 ' L t
=
>a r1(a-
( 1 | , . n '
x d-T+
= 4 \ ' n
€4
.3I'g'FACULTY OF ENGINEERING
Course & Year: ....,..:,
Subject:
Solution to Question No.
]n yt"A,"1
urt"iA
A K'ioint
.M
a-! jof"t C
v"t'L| 'not
i" i l ' ' "11"1
act-c
si?a\941
+L>',.g{ -td'-L
3Oso'= 7o'7
> €tso t'l t2a-
4r lo" labQ
ts? A-6b l7o 7 = Q4. l &nl
) . ( '
Htn.. v"r.qa. <tlo*q L(" {u a = > .r o- -f<N
&) -dr
$'.e f unL -r1't >?sutt ln-rL b"^a< "4 d/
i> 6- f tn^<2\
| 61"-^ i - r
>) A*{a\ 4,"d
C< ̂ -freid-Pl
|Qtist b1^J|j vwov-ent ' He'ce #'<
ay|)fu-ta- + a\ 1"'7 '{-"'- 4 '7.+L* di*"tin S/to'ln hiir ( t?J'''tt "'-
4a gtee( (ro,'< >o6+';i abo't
por"r't C '
/ \ s sa4
"t- 4< Cn/q -,n
