**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. G

_{Steel}= 2.2 G_{Alloy}.
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.

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