B.Tech. III (Third) Semester Examination 2014-15
Course Code: EME301
Paper ID: 0963216
Strength of Materials
Time: 3 Hours
Max. Marks: 70
Note: Attempt six questions in all. Q. No. 1 is compulsory.
1.
a)
b)
c)
d)
e)
f)
g)
Answer any five of the following (limit your answer in 50
words).
(4x5=20)
A bar 4m long and 60mm diameter (E=205GPa) hangs
vertically and has a collar securely attached at the lower end.
Find the stress induced when a weight of 300kg falls from
100cm height on the collar.
At a point in an elastic material, two normal stresses of 50
N/mm2 (Tensile) and 30 N/mm2 (Compressive) acts right
angle to each other with shear stress of -25 N/mm2. Find
graphically the normal stress on a plane inclined at 30° to
vertical.
Derive an expression to find out the shear stress at any layer
in rectangular section. Prove that the maximum shear stress
in rectangular section is 1.5 times the average shear stress.
A cantilever beam of length L carrying a point load W at its
free end. By area moment method prove that the deflection at
free end will be WL3/3EI, where EI is the flexural rigidity of
section.
A weight of 200N is dropped on a closed coiled helical spring
made of 15mm diameter wire with 150mm mean coil
diameter and 24 coils. If the instantaneous compression is
100mm, calculate the height of drop. Take modulus of
rigidity 90GPa.
Determine the diameter of cast iron cylindrical column 5m
long with ends firmly built in, if it carries an axial load of
300N. Take rankine constant =1/1600 and σc = 600MPa.
A cylindrical shell is 3m long 1m internal diameter and
15mm thickness. Calculate the maximum shear stress
induced and change in diameter considering the internal
pressure of 1.5MPa. . Take E=204X103 N/mm2 and Poisson’s
Ratio = 0.3.
h) Explain four assumptions made for Winkler-Bach formula for
curved beam.
2.
and minimum stress. Also draw stress distribution across the
section.
(10)
6.
A thick cylindrical shell is of 200mm internal diameter and
has to withstand an internal pressure of 25N/mm2. Calculate
the thickness of metal necessary for the cylinder on the basis
of maximum shear stress theory of Failure. Also plot the
variation of stresses across the thickness. Take τy = 250 MPa
of the shell and 1/m=0.3 and factor of safety is taken 2. (10)
7.
A curved beam, trapezoidal in cross section with dimension
as shown in Fig 3 is subjected to pure bending with couple of
+400kN-m. The beam is curved in a plane parallel to the
depth. The mean radius of curvature is 50mm. Find the
position of the neutral axis, and the ratio of the maximum and
minimum stress. Also, plot the variation of bending stress
across the section.
(10)
8.
A cantilever of length 1.2 m and of the cross section shown in
Fig. 4 carries a vertical load of 10kN at its outer end, the line
of action being parallel with longer leg and arranged to pass
through the shear center of the section. Find the stress at
point A. Determine also angle of inclination of N.A. and
maximum deflection. Take Ixx = 4 X 10-6 m4, Iyy = 1.08 X10-6
m4, E = 210GPa.
(10)
Define principal plane and principal stresses.
A metallic bar is loaded as shown Fig.1. Find change in
volume. Take E=200GPa, Poisson’s Ratio = 0.25.
(10)
2MN
4MN
400kN
25mm
100mm
250mm
3.
A simply supported beam is loaded as shown in Fig. 2. Find:
i)
Deflection under the point loads C and D
ii)
Location and magnitude of maximum deflection
Fig. 2
4.
5.
Fig. 1
(10)
A circular shaft is supported in bearings 3meter apart and
transmits 75kW power at 150rpm. At 1 meter from one
bearing, it carries a pulley exerting a transverse load of 30kN
on the shaft. Determine the suitable diameter of the shaft
according to maximum shear stress theory of failure, if
maximum normal stress not to exceed 100N/mm2.
(10)
Write short note on middle third rule and middle quarter rule.
A column of rectangular section 250mm wide and 200mm
thick carries a load of 15kN at an eccentricity of 60mm in a
plane bisecting the thickness. Make calculation for maximum