**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.

2) Attempt any
Four questions from Section - B.

3) Attempt any
Two questions from Section - C.

**Section - A**

1.

a.
Giving the mathematical
formula, define the modulus of elasticity.

b.
Why is a spherical shaped
pressure vessel preferable over cylindrical shapes?

c.
Define ‘Pure Bending’ of a
beam.

d.
Draw (only draw) the variation
of shear stress in a circular shaft under torsion.

e.
Defining all the variables,
give the mathematical form of Rankine formula used in columns.

f.
What is the difference between
the closed coiled and open coiled helical springs?

g.
What is the difference between
a strain energy and proof resilience?

h.
Define column.

i.
Write the expression for
Castiglione’s theorem.

j.

**Section –B**

2.
Draw and explain the
stress-strain curve for ductile materials.

3.
An cylinder is 4m long 0.9 in
diameter and 14 mm thick at atmospheric pressure. Calculate the dimensions when
subjected to an internal pressure of 2 MPa. What is then the maximum shear
stress in the shell?

4.
Derive an expression of
buckling load for column with one end fixed and the other end hinged.

5.
A hollow shaft of diameter
ratio 3/5 is required to transmit 800Kw at 120rpm, the maximum torque being 25%
greater than the mean. The shear stress in not to exceed 65 MPa and the twist
in a length of 3m is not to exceed 1.4 degrees. Calculate the minimum external
diameter satisfying these conditions.

6.
Assuming all the parameter,
derive an expression for strain energy due to bending for a beam of length, l.

**Section-C**

7.
A vertical tie rod rigidly
fixed at the top end consists of a steel rod 3 m long and 21 mm diameter is
encased throughout in a brass tube 21 mm internal diameter and 30mm external
diameter. The rod and the casing are fixed together t both ends. The compound
bar is suddenly loaded in tension by a weight of 10 kN falling through 3 mm
before being arrested by the tie. Calculate the maximum stresses in steel and
brass. Take the young modulus for steel and brass as 200 GPa respectively.

8.
Calculate the spring constant
and total elongation of two springs which are connected in series. One spring
having 16 turns of 1 mm wire radius and 22 mm mean diameter is connected to
other spring having 12 turns of 2 mm wire diameter and 13 mm mean diameter.
Also calculate the safe axial load, if the maximum stress in both springs in
less than 400 N/mm

^{2 }. take G=8 x 10^{5 }N/mm^{2 }
9.
A beam 8.5 m long rests on
supports 5 m apart. The right hand end overhanging its support by 2m end left
hand end by 1.5m. the beam carries a uniformly distributed load 20 kN/ m run
between the supports only. The beam also carries a point load of 60 kN the
extreme right hand end, and a point load of 40Kn at the left hand end.
Construct the shear force and bending moment diagrams stating there on all the important values of shear force
and bending moment. State the position of the points of inflexion on the
beam.

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