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 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.
(10 Marks)
b Explain stress invariants and plane state of stress. (06 Marks)
OR
2 a Derive expressions for Octahedral normal and Octahedral shear stresses in terms of
stress invariants.
(08 Marks)
b
Rectangular component of stress at a point is given by σ ⌈
50 30 10
30 30 20
10 20 15
⌉ MPa.
Determine the stresses on a plane whose outward normal
Has direction cosines
1
√2

1
√2
0
Has direction ratio
(08 Marks)
MODULE II
3 a Discuss the significance of compatibility conditions.
Given the following strain field:
2 2 4 4 5 x y x y x
2 2 4 4 6 3x 3y x y y
x y y x xy xy 10 4 4 8 3 3
0 z 0 yz 0 xz
Determine whether the above strain field is possible.
(10 Marks)
b Displacement field at a point on a body is given as follows
u v w (xyz2+x2). Determine the strain components at
and express them in matrix form.
(06 Marks)
OR
4 a Derive the first and second set of compatibility equations. (10 Marks)
b Define strain invariants and plane state of strain.
(06 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.
15ME552
MODULE III
5 a Derive the biharmonic equation considering the plane strain condition in the
Cartesian coordinate system.
(10 Marks)
b The state of stress at a point is given by:
MPa, 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.
(06 Marks)
OR
6 a Derive the expressions for stresses in a thick cylinder under the uniform internal
and external pressures.
(16 Marks)
MODULE IV
7 a Derive the expressions for stresses r and in a solid rotating disc of uniform thickness. (09 Marks)
b A solid disc of 150 mm radius rotates at 500 rpm. Given: mass density 7.2 x 10-6
kg/mm3, E 2x105 MPa and ν=0.3. Find the value of circumferential stress at the
center of the disc and at the outer periphery. Also, find the change in radius.
(07 Marks)
OR
8 a A disc of uniform thickness with inner and outer diameter 100 mm and 400 mm,
respectively, is rotating at 5000 rev/min. The density of the material is 7800 kg/m3
and ν=0.28. Determine the radial and circumferential stress at a radius of 0.05m.
(08 Marks)
b A thin walled box section having dimensions 2a x a x t is to be compared with a
solid circular section of diameter as shown in Fig. Q8(b). Determine the thickness t
so that the two sections have
The same maximum shear stress for the same torque and
The same stiffness
Fig.
(08 Marks)
MODULE V
9 a Explain the significance of thermo-elastic stresses. Also, write the thermo-elastic
stress strain relations.
(06 Marks)
b Obtain the expressions for radial and tangential stresses in a solid circular cylinder
subjected to uniform temperature. Also, obtain similar expressions for hollow
cylinder.
(10 Marks)
OR
10 a Derive Euler's expression for buckling load for column with both ends hinged. (08 Marks)
b Derive the expressions for stress components in a thin circular disc subjected to
temperature.
(08 Marks)
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.