**Roll No. ......................**

**Total No. of Questions : 09]**

**B. Tech. (Sem. – 3rd)**

**MECHANICS OF MATERIALS**

**SUBJECT CODE : BTAE-301**

**Paper ID : [A1112]**

**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. Write briefly :

a. Explain the
difference between stress and strength.

b. Name four
ductile materials.

c. What is the
difference between Yield Strength and Ultimate Strength?

d. Define S.F. and
B.M.

e. What is the
expected nature of S.F. and B.M. at point of contra flexure?

f. What are the
assumptions of Simple Bending Theory?

g. What is the
difference between section modulus and moment of inertia?

h. What are
assumptions of Rankin-Gordon formula?

i. What is meant by
Modulus of Rupture?

j. What is meant by
Hoop Stress?

**SECTION-B**

2. Derive the formula for stress, strain
and deflection in a bar of varying

cross-section and
uniform strength.

3. Explain the method of construction of
B.M. and S.F. diagrams by use of

cantilever moments.

4. Show the application of bending formula
to a composite beam made up

of two different
materials.

5. Explain the
concept of complimentary shearing stresses in shafts under

pure tension.

6. Apply following
theories of failure to thin cylinders :

Principle stress
theory, Principle strain theory, maximum shear stress

theory, strain
energy theory and distortion energy theory.

**SECTION-C**

7. Following figure shows the stress
condition at a point. Find the normal,

shear and resultant
stresses and the direction of resultant stress for the

plane inclined at
30° as shown in figure.

8. A hollow steel
shaft 8 cm outside diameter is coupled to a solid phosphor bronze shaft of 8 cm
diameter. Neglecting the effect of coupling, find the suitable internal
diameter of the steel shaft, if a torque is to be applied to the compound shaft
to develop a maximum shear stress of 40 MaPa in the bronze shaft and a maximum
shear stress of 72 MPa in the steel shaft. Angle of twist in the steel shaft is
not to exceed 1°. Length of steel shaft is 1 m and of bronze shaft is 1.2 m.
Also find the total angle of twist for whole of the shaft. Take G

_{steel}= 80 GPa and G_{bronze }= 40 GPa.
9. Find the
critical load for a standard rolled steel angle 50 × 50 × 6

(ISA
5050) column 2m long having area of angle as 5.68 cm 2 , minimum

radius
of gyration as 0.96 cm, E = 210 GPa and proportional limit stress

in
simple compression = 210 MPa for following conditions :

(i) the column has rounded ends

(ii) both ends are fixed

(iii) one end is fixed and the other hinged

(iv) one end is fixed and the other is free

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