15ME552
Model Question Paper (CBCS) with effect from 2015-16
Fifth Semester B.E. Degree (CBCS) Examination
Theory of Elasticity
Time: 3 hrs. Max. Marks: 80
Note: Answer any FIVE full questions, choosing one full question from each module.
MODULE I
1 a Derive the equations of equilibrium for a 2-D stress state. (08 Marks)
b State of stress at a point is given by σ ⌈
12 6 9
6 10 3
9 3 14
⌉ MPa. Find principal
stresses and directions.
(08 Marks)
OR
2 a A point under three dimensional stress system is on xyz coordinate system. Derive
the Cauchy's stress equations for the component of the stresses on an arbitrary
plane.
(08 Marks)
b A rectangular component of stress at a point are given as follows:
x 100 MPa, y 75 MPa z 50 MPa
xy 70 MPa, yz 50 MPa, xz 30 MPa
Find stresses on octahedral plane
Stress on plane whose outward normal has direction cosines
2
1

2
1
(08 Marks)
MODULE II
3 a Derive the first and second set of compatibility equations. 1 0 M a r k s
b The displacement field is given by u v w (4z2).
What are the strain components at and express them in matrix form.
(06 Marks)
OR
4 a Discuss the significance of compatibility conditions. Also, define plane state of
strain.
(06 Marks)
b If strain at a point is given as follows:
x 4x10-3 y 3x10-3,
z 2x10-3
xy 2x10-3, yz 1x10-3, xz -3x10-3
Find the principal strains and determine the direction cosines of maximum principal
strain.
(10 Marks)
MODULE III
5 a Determine the bending stress component in case of bending of cantilever bean by
an end load.
(09 Marks)
b A thick cylinder of internal diameter 150 mm and external diameter 200 mm is
simultaneously subjected to internal pressure of 10 MPa and external pressure of
4 MPa. Given, E 2x105MPa and 0.25. Determine:
Circumferential stresses at ri and ro.
Plot variation of radial and hoop stress across the thickness.
Change in internal and external radii.
(07 Marks)
USN
Important Note: 1. On completing your answers, compulsorily draw diagonal cross lines on the remaining blank pages.
2. Any revealing of identification, appeal to evaluator and /or equations written e.g, 38+2 40, will be treated as malpractice.
as malpractice.
15ME552
OR
6 a
b
Derive the equations of equilibrium in polar coordinates.
The state of stress at a point is given by:
200 x MPa, y MPa, 50 z MPa
40 xy MPa, 50 yz MPa, 60 zx MPa.
If E 2x105 N/mm2 and G 0.8x105 N/mm2, find the corresponding strain
components from Hooke's law. Take ν=0.2.
(10 Marks)
(06 Marks)
MODULE IV
7 a Determine the maximum shear stress under torsion of a circular bar. (16 Marks)
OR
8 a Derive expressions for shearing stresses induced in a bar of elliptical cross section
that is subjected to a twisting moment. Also, show that maximum stress occurs at
the ends of the minor axis of ellipse.
(08 Marks)
b A hollow disc of internal radius 100 mm and external radius 150 mm rotates at
200 rpm. Determine the circumferential stress at ri and ro . Also, find the change in
internal and external radius. Assume: 7.2 x 10-6 kg/mm3, E 2 x 105 MPa and
ν=0.3.
(08 Marks)
MODULE V
9 a Determine the radial and tangential stress distribution in a solid long cylinder
subjected to a radial temperature distribution.
(09 Marks)
b Derive Euler's expression for buckling load for column with one end fixed and
other end free.
(07 Marks)
OR
10 a Derive the expressions for stress components in a thin circular disc subjected to
temperature.
(10 Marks)
b Explain the significance of thermo-elastic stresses. Also, write the thermo-elastic
stress strain relations.
(06 Marks)