advanced strength of materials paper model

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Regulation : R13 Code No: ME503/1

I M. Tech. I Semester Examination, February 2014

ADVANCED MECHANICS OF SOLIDS

Time: 3 hours (MD Max. Mar!s: 0 In!t"u#tion!: 1$ An!%e" ONE &ue!tion '"o( ea#) unit

*$ All +ue!tion! #a"", e&ual (a"-!

3$ A!!u(e (i!!ing data. i' an,

NI I1 a "hat are #rinci#a$ axes an% #rinci#a$ moments o& inertia' 23M b n extru%e% bar o& a$uminum a$$oy has the cross section sho)n in &i*ure. 2.1 m $en*th

o& this bar is use% as a sim#$e beam on a s#an o& 2 m. a concentrate% $oa% o& + - isa##$ie% at mi% $en*th o& the s#an an% ma!es an an*$e o& φ 1.4 ra% )ith the x axis.Determine maximum tensi$e an% com#ressi/e stresses in beam.

24MOR62 a "hat is the conce#t o& shear center' Ex#$ain. 4M

b ocate the shear center &or the beam cross section as sho)n in &i*ure. 3oth &$n*es an% )ebthic!ness is mm. 5M

NI II a "hat is Membrane na$o*y &or torsion' Ex#$ain )ith exam#$e. 4M

b ho$$o) rectan*u$ar thin )a$$ stee$ torsion member has the cross section sho)n in &i*ure.

The stee$ has a yie$% stress is 60 M7a an% shear mo%u$us o& e$asticity o& 88.+ M7a.Determine the maximum tor9ue that may be a##$ie% to the torsion member, base% on a&actor o& sa&ety 2 &or the octahe%ra$ shear stress criterion o& &ai$ure. "hat is the unit an*$eo& t)ist )hen the maximum tor9ue is a##$ie%' 5M

OR6

1 o&




4 a Deri/e an ex#ression &or thic!ness o& a %isc o& uni&orm stren*th. +M

b thin %isc o& uni&orm thic!ness is o& 500 mm outer %iameter an% +0 mm inner %iameter.

It rotates at 000 r#m. Determine the ra%ia$ an% hoo# stresses at ra%ii o& 0, 2+ mm, +0

mm, 100 mm, 1+0 mm, 200 mm, 00 mm an% 400 mm. %ensity o& the materia$ is 8500

!*m an% ν0.2+. 8M

NI III

+ a Ex#$ain the in&inite beam on e$astic &oun%ation. +M

b $on* +0 mm %iameter stee$ bar is su##orte% by a number o& #airs o& 2 mm %iameter hi*h stren*th stee$ )ires. n en% /ie) o& the beam an% )ires is sho)n in &i*ure. The

#airs o& )ires e9ua$$y s#ace% at l ;00 mm. $oa% 7 is a##$ie% to the center o& the $on*

beam at the same $ocation as one #air o& )ires. Ta!e EsE) 200 <7a, σs 00 M7a an%

σ) 1200 M7a.

8M

OR6

6 a Ex#$ain the short beams on e$astic &oun%ation. +M

b $on* rectan*u$ar section brass beam has %e#th o& 20 mm an% a )i%th o& 1+ mm an%

rests on a har% rubber &oun%ation as sho)n in &i*ure. The /a$ue o& the s#rin* constant &or

the har% rubber &oun%ation is 0.2 -mm. I& the beam is sub=ecte% to a concentrate% $oa%

7 is 800 - at the $ocation sho)n, %etermine the maximum %e&$ection o& the beam an%maximum &$exura$ stress in the beam. Ta!e E b 52.8 <7a.

8M

NI IV

8 a Deri/e an ex#ression maximum stress &or a co$umn sub=ecte% to eccentric $oa%. 6M

b >om#are the cri##$in* $oa% *i/en by ?an!ine@s an% Eu$er@s &ormu$ae &or tubu$ar strut 2.2+

m $on* ha/in* outer an% inner %iameters o& 8.+ mm an% +.+ mm res#ecti/e$y, $oa%e%throu*h #in =oint at both en%s. Ta!e yie$% stress as 1+ M-mm 2, a18+00an% E200

<7a. I& e$astic e$astic materia$ &or the materia$ is ta!en as 200 M7a, then &or )hat $en*th

o& the strut %oes the Eu$er@s &ormu$a ceases to a##$y. 6M

OR6

5 a Deri/e an ex#ression &or Eu$er@s cri##$in* $oa% &or i 3oth en%s are &ixe% ii Ane en%

&ixe% an% other en% is hin*e%. +M

b ho$$o) mi$% stee$ co$umn hin*e% at both en%s is o& circu$ar cross section )ith an

outsi%e %iameter o& 100 mm an% an insi%e %iameter o& 50 mm. the $en*th o& the co$umn is

2.+ m. Determine the maximum #ermissib$e $oa% )ith an eccentricity o& 1+ mm, i& themaximum com#ressi/e stress is $imite% to 8+ M7a. Ta!e E 20+ <7a. 8M

NI V

; a Deri/e an ex#ression o& a constant o& area o& cross section (#2 &or trian*u$ar cross

sections. +M

2 o&




b Fi*ure sho)s a cast iron &rame B sha#e% cross section. The u$timate tensi$e stren*th o& thecast iron is 20 M7a. 8M

OR6

10 crane hoo! ha/in* a tra#eCoi%a$ horiConta$ cross section is +0 mm )i%e insi%e an% 0

mm )i%e outsi%e. The thic!ness o& the section is 60 mm. The crane hoo! carries a

/ertica$ $oa% o& 20 - )hose $ine o& action is +0 mm &rom the insi%e e%*e o& the section.

The center o& cur/ature is 60 mm &rom the insi%e e%*e. Determine the maximum tensi$e

an% com#ressi/e stresses in the section. 12M

o&

advanced strength of materials paper model

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