Hall Ticket No Question Paper Code: AME004
INSTITUTE OF AERONAUTICAL ENGINEERING
(Autonomous)
Four Year B.Tech III Semester End Examinations (Regular) November, 2018
Regulation: IARE R16
MECHANICS OF SOLIDS
Time: 3 Hours Max Marks: 70
Answer ONE Question from each Unit
All Questions Carry Equal Marks
All parts of the question must be answered in one place only
UNIT I
1. Discuss about the relationship between stress and strain.
A rod 150 cm long and a diameter 2 cm is subjected to an axial pull of 20 kN. If the modulus of
elasticity of the material of the rod is 2 X 105 N/mm2; determine the stress, strain and elongation
of rod.
2. Derive an expression for calculating the stress in a bar when it is subjected to a sudden load P
from a height having length cross sectional area A and young's modulus E.
A 2.2cm diameter copper rod passes centrally through a steel tube of 5cm internal diameter and
7cm external diameter. While at 500C the ends are rigidly fastened together. Find the intensity
of stress in each metal if heated to 1500C.Take Es 2 X 105 N/mm2 12 X C Ec
1.2 X 105 N/mm2 18 X C.
UNIT II
3. Derive the equation for shear force and bending moment diagram for a cantilever beam of length
when it is is subjected to a point load of W at a distance of l from the fixed end.
A simply supported beam of length 8m is subjected to a point loads of 2 KN, 5 KN and 2 KN
at the distances of 2m 4m and 6m from left end. Draw the shear force and bending moment
diagram for the beam.
4. Draw the shear force and bending moment diagrams of a simply supported beam of length 7 m
and carrying uniformly distributed loads as shown in Figure 1.
Figure 1
Page 1 of 3
Draw the shear force and bending moment diagrams of a overhanging beam carrying UDL of 2
kN/m over the entire length and a point load of 2 kN as shown in Figure 2.
Figure 2
UNIT III
5. Briefly discuss about the theory of simple bending.
Calculate the maximum stress induced in a cast iron pipe of external diameter 40 mm, of internal
diameter 20 mm and of length 4 m when the pipe is supported at its ends and carries a point
load of 80 N at its centre.
6. Calculate the ratio of Maximum shear stress and average shear stress for a circle of radius r. The
beam is considered as cantilever beam with downward load.
A beam of I shape, having the dimensions of flange width b =100 mm and thickness of flange
10 mm, web height 250 mm and thickness 15 mm. The loads on the beam produce a shear force
of 35 kN at the cross section under consideration. Draw the shear stress distribution across the
section.
UNIT IV
7. Derive the expression for maximum principal stress theory.
The tensile stresses at a point across two mutually perpendicular planes are 120 N/mm2 and
60 N/mm2. Determine the normal, tangential and resultant stresses an a plane inclined at 30
degree to the axis of the minor stress.
8. Explain the construction of Mohr's circle for two like stresses and on two mutually perpendicular
planes with a shear stress
At a point in a strained material on plane BC there are normal and shear stresses of 200N/mm2
and 340N/mm2 respectively . On plane AB perpendicular to plane BC, there are normal and
shear stresses of 180N/mm2 and 340N/mm2 respectively as shown in Figure 3. Determine the
following
Principal stresses and location of the planes on which they act.
ii) Maximum shear stress and the plane on which they act.
Figure 3
Page 2 of 3
UNIT V
9. Derive the torsion equation of a circular shaft which is fixed at one end and free at another end.

A composite shaft consists of a steel rod 60 mm diameter surrounded by a closely fitting tube
of brass. Find the outside diameter of the tube so that when a torque of 1000 Nm is applied to
the composite shaft, it will be shared equally by the two materials. Take C for steel 8.4 X 104
N/mm2 and C for brass 4.2 X 104 N/mm2.
10. Derive the expression for polar section modulus of a circular shaft.
A thin cylindrical of internal diameter 1.25 m contains a fluid at an internal pressure of 15
N/mm2. Determine the maximum thickness of the cylinder if:
The longitudinal stress is not to exceed 30 N/mm2.
The circumferential stress is not to exceed 45 N/mm2.