Hall Ticket No Question Paper Code: BSTB02
INSTITUTE OF AERONAUTICAL ENGINEERING
(Autonomous)
M.Tech I Semester End Examinations (Regular) January, 2019
Regulation: IARE-R18
ADVANCED SOLID MECHANICS
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. Generalize the constitutive relations in theory of elasticity problems.
The displacement field in a body is specified as
u x3+3y2
v 3y2+4x
w 0
Determine the stress and strain component at a point whose coordinates are take E 2 x
105 N/mm2, Poisson's ratio 0.3.
2. Explain the concept of stress with neat sketch.
At a point the rectangular stress components are xy yz
xz 1 all in units of kPa. Find the principal stresses and check for invariance.
UNIT II
3. Show that ey B Cy ey Dy sin xsinx is a stress function in two dimensional
stress field.
With respect to the frame of reference Oxyz, the following state of stress exists.
Determine the principal stresses and their directions.
The stress acting on an element of a loaded body is shown in Fig.1. Apply Mohr's circle
to determine the normal and shear stresses acting on a plane defined by 300.
UNIT III
5. Explain how Fourier series can be applied for two dimensional problems under gravity loading.

The displacement field for a body is given by
deformed position of a point originally at
6. Develop differential equation of equilibrium for two dimensional problems.
Consider the displacement field U What are the rectangular
strain components at the point P Use only linear terms.
UNIT IV
7. Give the torsion equation for circular cross-section and explain its terms.
Given the following stress equation P
rcos. Determine the stress components and

8. Write the simple bending equation for symmetrical cross-sections of a beam and discuss the
assumptions followed in the bending equation.
Explain plane stress and plane strain problems with examples and neat sketches.
UNIT V
9. Derive the torque equation of rectangular bar.
The following Figure 2 below shows a two-cell tubular section whose wall thicknesses are as
shown. If the member is subjected to a torque determine the shear flows and the angle of
twist of the member per unit length.
Figure 2
10. Write about membrane analogy theory.
Explain in detail about Strain hardening and Isotropic hardening .