Jadavpur University 2007 B.E Mechanical Engineering STOF MATARIALS-A - Question Paper

EX/PM 12C/8/2006
First B. E. (Mech.) Examination, 2006
(2nt Semester)
Subject: Strength of Materials - A
Time : 3 hours Full Marks : 100
ans any 5 ques..
1. a) A prismatic steel bar having c/s area 3sq.cm. is subjected to axial loading
(Fig.1).
Fig.1
presume E = two x 106 kg/cm2, obtain out net change in length of the bar.
b) A bar of uniform thickness ‘t’ tapers uniformly from width b1 at 1 end and b2
at the other end (b1 > b2) over a length L. If an axial tension P is applied, obtain out
net change in length (Refer Fig.2)
Fig. 2
2 a) Prove that a hollow shaft is stronger and stiffer than the solid shaft of identical
material, length and weight.
b) A hollow steel shaft is to have outside diameter ‘d’ and inside diameter d/2.
compute the proper value of d for the shaft if it is to transmit 200 hp at 100 rpm
with a working stress in shear of 420 kg/cm2.
3. a) obtain out the change in radial dimension of a spherical container having radius
‘r’ subjected to uniform internal pressure ‘p’.
b) At atmospheric pressure, a thin spherical shell has internal diameter 700 mm
and thickness 10 mm. obtain out the stress induced and change in quantity if the fluid
pressure is increased to 2.5 N/mm2. Take E = two × 105 N/mm2 µ, = 0.25.
4. a) In case of a biaxial stress on an element as shown (FIG.3), 10
Fig. 3
obtain out normal stress (sn), shear stress (tn) on an arbitrary plane as shown.
½
10
10
10
10
10
EX/PM12C/8/2006
b) In the previous issue [4(a)], consider sx = 100 kg/cm2, sy = - 50 kg/cm2 and
? = 25°. Draw Mohr’s circle and from that obtain out sn and tn. 10
5. a) For the simply supported beam as shown (FIG.4), draw the shear force and
bending moment diagram.
Fig. 4
b) For the beam mentioned above obtain out maximum bending stress if the cross
part of the beam is as shown (FIG.5). 10
Fig. 5
6. a) For a simply supported beam with distributed load as shown (FIG.6) obtain out
deflection at midpoint of the beam.
Fig. 6
b) For the identical beam (FIG.6) obtain out maximum shear stress if the beam is of
rectangular cross part with width ‘b’ and depth ‘2b’?
7. Write short notes on any four: 4×5
a) Pure bending and ordinary bending
b) Young’s modulus and bulk modulus
c) Principal stress and complementary stress
d) Bucking - a issue of elastic instability
e) Torsional rigidity and flexural Rigidity.
8. a) Deduce the express ? =
GJ
? = TL for torsion of a shaft stating all necessary
assumptions.
b) Deduce the expression for bending stress,
I
s = My where the symbols have
usual meanings mentioning the assumptions.
2
2
10
10
10
10
10

Earning:   Approval pending.