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PSNA COLLEGE OF ENGINEERING AND TECHNOLOGY, DINDIGUL – 624

622

DEPARTMENT OF MECHANICAL ENGINEERING

IMPORTANT QUESTIONS FOR SERIAL TEST II (UNIT II)

PART A:

1. What is Global co-ordinates?2. What is natural co-ordinates?3. Defne shape unction.4. What are the characteristics o shape unction?5. Write down the expression o stiness !atrix or one di!ensional bar

ele!ent.". #tate the properties o a stiness !atrix.$. Write down the expression o stiness !atrix or a truss ele!ent.%. Write down the expression o shape unction & and displace!ent ' or

one di!ensional bar ele!ent.(. #tate the principal o !ini!u! potential ener)*.1+. #tate the principles o ,irtual wor.11. Distin)uish between essential boundar* conditions and natural

boundar* conditions.12. What ate the dierences between ,alue proble! and initial

proble!?13. Defne heat transer.14. Write down the expression o shape unction & and te!perature

unction or one di!ensional heat conduction ele!ent.15. Write down the expression o lon)itudinal ,ibration o bar

ele!ent.

Part –

1. Deri,e the shape unction or one di!ensional linear bar ele!ent

based on )lobal co-ordinate approach.2. Deri,e the stiness !atrix or one di!ensional linear bar ele!ent.

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!" /or a stepped bar loaded as shown in /i).10 deter!ine a nodaldisplace!ents b support reactions and c ele!ent stresses.

F#$"%ssu!e 6 2+ x 1+" & 7 c!2

4. he tapered bar o unior! thicness t 6 1+ !! as shown in /i)-2 has

 8oun)9s !odulus 6 2 x 1+5:&7!2 and !ass densit* $%(+ )7!3. ;n

addition to its sel-wei)ht0 the bar is sub&

at its !idpoint.

i. :odel the plate with two fnite ele!ents.

ii. Write the ele!ent stiness !atrices and ele!ent orce ,ectors.

iii. 'sin) the eli!ination approach0 sol,e or the )lobal displace!ent

,ectors

/i). 2

5. /or the two bar truss shown in f).

3 deter!ine the displace!ents o 

node 1 and the stress in ele!ent

1-3.

/i). 3

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". onsider a our bar truss as shown in f). 4. ;t is )i,en that 6 2 x 1+5

&7!!2 and e 6 "25 !!2 or all ele!ents.

/i). 4

$. he structure shown in f).5 is sub

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(. wall o +." ! thicness ha,in) ther!al conducti,it* o 1.2 W7!>. he

wall is to be insulated with a !aterial o thicness +.+" ! ha,in) an

a,era)e ther!al conducti,it* o +.3 W7!>. he inner surace

te!perature is 1+++o and outside o the insulation is exposed to

at!ospheric air at 3+o with heat transer coeAcient o 35 W7!2>.

alculate the nodal te!perature.1+.onsider a unior! cross-section bar with one end fxed. he len)th B@9

!ade up o a !aterial whose 8oun)9s :odulus and densit* are )i,en

b* B9 and BC9. sti!ate the natural reuencies o axial ,ibration o the

bar usin) both lu!ped and consistent !ass !atrix.