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

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.