Hall Ticket No Question Paper Code: BST001
INSTITUTE OF AERONAUTICAL ENGINEERING
(Autonomous)
M.Tech I Semester End Examinations (Regular) February, 2017
Regulation: IARE-R16
Theory of Elasticity and Plasticity
(STRUCTURAL ENGINEERING)
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. The state of stress at a point with respect to the xyz system is
Determine the stress tensor relative to the coordinate system obtained by a rotation through
30 about the z axis.
The state of stress at a particular point relative to the xyz coordinate system is given by the
stress matrix 2
Determine the normal stress and the magnitude and direction of the shear stress on a surface
intersecting the point and parallel to the plane given by the equation 2x-y+3z 9
2. For the stress tensor given below, determine the principal stresses and the direction cosines
associated with the normal to the surface of each principal stress.
2
6664
3000 1000 1000
1000 0 2000
1000 2000 0
3
7775
N/m2
Page 1 of 3
The state of stress components at a point are given by the following array;
2
6664
10 5 6
5 8 10
6 10 6
3
7775
MPa
Calculate the principal stresses and principal planes.
UNIT II
3. Prove that the following are Airy's Stress functions and examine the stress distribution represented
by them;
i. Ax2 By2
ii. Bx3
iii. A(x4 3x2y2)
Show that the Airy's stress function

xy3 3
4xyh2

represents stress distribution in a cantilever
beam loaded at the free end with load P. Find the value of A if xy 0 at y h
2 where
b and h are width and depth respectively of the cantilever.
4. A load P 70 kN is applied to the circular steel frame shown in fig below. The rectangular cross
section is 0.1 m wide and 0.05m thick. Determine the Tangential stress at points A and B.

A Steel ring of 0.35 m mean diameter and of uniform rectangular section 0.06m wide and 0.012m
thick is shown in fig below. A rigid bar is fitted across diameter AB, and a tensile force P applied
to the ring as shown. Assuming an allowable stress of 140 MPa, determine the maximum tensile
force that can be carried by the ring.
Page 2 of 3
UNIT III
5. Derive the conditions of compatibility in three dimensional stress strain system.
Explain Principle of superposition in three dimensional stress strain system.
6. Show that if the rotation is zero throughout the body then the displacement vector is the gradient
of a scalar potential function. Give an example for each irrotational deformation.
Explain reciprocal theorem for three dimensional stress strain system.
UNIT IV
7. A Square shaft rotating at 250 rpm, transmits torque to a crane which is designed to lift maximum
load of 150 kN at a speed of 10 m min. If the efficiency of crane gearing is 65 estimate the
size of the shaft for the maximum permissible shear stress of 35 MPa. Also calculate the angle
of twist of the shaft for a length of 3m. Take G 100 GPa.
A 300 mm steel I-beam shown in fig below flanges and web 12.5 mm thick is subjected to a torque
of 4 kN.M find the maximum shear stress and angle of twist per unit length G 100 GPa.
8. An elliptical shaft of semi axes a 0.05 m b 0.0025 and G 80 GPa is subjected to a
twisting moment of 1200 N.m. Determine the maximum shearing stress and the angle of twist
per unit length.
A hollow aluminium section is designed as shown in fig below for a maximum shear stress of 35
MPa. Find maximum permissible twisting moment for this section and the angle of twist under
this moment per meter length G 28 GPa.
UNIT V
9. Explain the mechanism of plastic deformation.
Explain the yield criteria and flow rules for perfectly plastic and strain hardening materials.

10. Explain St. Venant's Theory of plastic flow.
Discuss the mathematical formulation of plastic potential.
Page 3 of 3