ME2114 Solution 0506-1

7

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n NATIONIT, U}TIVERSITYOFSINGAFORE

ME2II4 _ MECH.ANICSOF MATERIALS tr

(S€me$erII: AY2005-2006) TitDcAllos€d: 2 Hours

INSTRUCTIONSTt) CANDIDATES: l.

This €xaminationpapcrcontairsFOIrR (,1)questids atd cllnpris€sSX (6) priniad p6ges-

2.

Answrr all FOI,R (4) qu6tids.

3.

All quGtionscary cqld |rla*s.

4.

This is a CLOSEDE(X)X EXAMINATION.

Prgc 2

ME2l 14

ForEulre Th€follo*ing formula€witten usingslandardrDtationsmaybeus€d. Yield Crirerir: (l)

Tr€scaYield Critorion

'* =tG*-".")=? l _

@

Von MiscsCriterion -

/jk",

-",f * (", - o3f* (o3- o,f ]=o"

Strrir GDcrgreq!.tiorri Axial loading:

u=tI1o* 2EA 6

Bending:

u=t!4a, 62Er

Torsion:

L12 U= 'o2CJ l-:-d(

CoDstitotiv. rchtioD! for itoiropic cb.tic m.ted.b3

"-=+G-!o,

-*-)

",=iG, -u"-) ' . = j ( o . - n o , -.,--) ' t n = IE r n , f o = le r , ,

e=--!-

2Q+v)

l

r-=6r.

Page3

ME2l14

OuestionI A cylindricalprcssurevessel250mm irmerdiameterand5 mm wall thicknessis subjectedto an internalpressueof2.5 MPa.Thecylinder,which is cquippedwith two rigid endplates,is andthe weldedseamsare inclin€dat 125"to rhe longitudinal butt-weldedcircumferEntially axis asshownin Figurc l. Ifan axial comprcssivcloadof50 kN is appliedto ih€ endplates, usinstheMohr's circledetermine (a)

the str€sses at the weld.Indicateyoor resultson a sketchshowingbothdirectionalld magnitudeofthe slesses,and (15nark)

(b)

tbemaximumin-plarcshea.ingsf€ssin rhecylind€r.

(1 nmrks)

wouldyou expectthe maximumin-planesherring loadis increased, Ifthe axial compressiv€ or decrease? Explainrfiy. stressin the cylinderto incr€rse (6 narks)

Rigid endplates

Wddlines Figrre I

ME2lt4

Pagc4

Ou€stiotr2 Figure2 showsa pin-connect€d steelfame madeup of circularcross-section memberswhich havea feld stressin compression of200 MPa.MembenAC andBD ar€of30 mm diameter andmembersAB andCD areof25 mm diameter.Whenihe tumbucklesare tightened,the diagonalsAD andBC arein tension. (a)

If memberBD is loadedby a verticalforceof500 N, andassuminga factorofsaf€ty of 1.5,determinethe maximumallowabletensionthatcanb€appliedto diagonalBC. AssumeE=200GPa(15narks.l

o)

Ifa largehorizontalforceF (indicaredby the dottedline) is alsoappliedon member AB in the direcrionshown,would it resuhin rhe bucklingof memb€rAB? Explain why. 6 narks)

(c)

Stalelhe assumptiorsmadein the derivationofthe Eulerformula(you do not needto derivethe Eulerformulaused). (5 narks)

500N

J E



fi9, c)

J-AB= L^U =

' t - -"r' 9 t d4 f -- a + -t <

3.of 4l

fAa

(c")

l' 1L YtO

4'

"1"Y

- 1 , LE T l ^ )

L

ax,ix t tz# (s.ortror)z 4.o'l l

d/

b1^J|j

|Qtist

ay|)fu-ta- + di*"tin

+L*

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gtee(

4a por"r't

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