## Mechanics of Materials Question Paper of 3rd Semester AE Download Previous Years Question Paper 5

• Tuesday, August 30, 2016
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Roll No. ......................
Total No. of Questions : 09]
B. Tech. (Sem. – 3rd)
MECHANICS OF MATERIALS
SUBJECT CODE : AE – 201
Paper ID : [A0701]
Time : 03 Hours
Instruction to Candidates:
1. SECTION-A is COMPULSORY consisting of TEN questions carrying
TWO marks each.
2. SECTION-B contains FIVE questions carrying FIVE marks each and
students has to attempt any FOUR questions.
3. SECTION-C contains THREE questions carrying TEN marks each and
students has to attempt any TWO questions.

SECTION-A
1. (a) Define Poisson’s ratio.
(b) List the assumptions taken in the development of theory of simple
bending.
(c) What is the difference between a closed and an open helical
spring ?
(d) Define Buckling factor.
(e) Why are spherical pressure vessels preferred over cylindrical shapes?
(f) What is ‘Wahl factor” used in analysis of springs ?
(g) State Castiglione’s theorem.
(h) Draw the variation of shear stress in a circular shaft under torsion.
(i) What is the difference between a strut and a column?
(j) Write the expression of strain energy in a beam due to torsion.

SECTION-B

2. Derive the expression of critical load for a column of length L, with
both ends fixed.
3. Plot the shear stress distribution along the cross section of the beam
shown below, which is subjected to a shear force of 20 kN.

4. Derive the expression for slope and deflection for a simply supported
beam of length l. The beam is subjected to a pure couple at a
distance ‘a’ from the left end support. Any method can be used for
the derivation.
5. A bar made of steel has the dimensions shown in the figure. If an
axial force P = 80kN is applied to the bar, determine the change in
its length and the change in the dimensions of its cross-section after
applying the load. The material behaves elastically. E for steel = 200
GPa and Poisson’s ratio = 0.32

6.  Derive the expression for-stresses in a thin cylindrical vessel of mean
radius R and wall thickness h subjected to internal pressure p

SECTION-C

7. A solid alloy shaft 50mm in diameter is to be coupled in series with a
hollow steel shaft of the same external diameter. Find the internal
diameter of the steel shaft if the angle of twist per unit length of steel
shaft is to be 75% of that of the alloy shaft. Also determine the
speed at which the shafts are to be driven to transmit 200kW, if the
limits of the shearing stresses are to be 55MPa and 75MPa for alloy
and steel, respectively. GSteel = 2.2 GAlloy.

8. Two parallel but out-of-plumb walls 6m apart are stayed together by
a steel rod of 25mm diameter at a temperature of 78°C passing
through steel plates, washers and nuts on outer side of the wall at
each end . Determine the pull exerted by the rod when it is cooled to
24°C, for
(a) if the walls do not yield, and
(b) if the walls yield at two ends by 2mm. Young’s Modulus for
steel = 200GPa and coefficient of thermal expansion for
steel = 11x 10–6/°C.

9. Draw the shear force and bending moment diagrams for the beam
shown below. Write down the equations for shear force and bending
moments as a function of x, where (1.2m  x  3m). Also show
salient points on the diagrams along with their values.