MFM 5

Second Semester M.TECH Mechanical Engineering

Examination Jan/Feb 2014

APPLIED ELASTICITY

Time:-3Hours Max. Marks: - 80

SECTION-A

Answer any six questions. (5*6)

1. Briefly describe the Airy’s stress function method.

2. Give the general solution of Biharmonic equations.

3. What are conformal transformations?

4. Give brief introduction to the elementary theory of torsion of prismatic bars.

5. A hollow circular torsion member has an outside diameter of 22 mm and inside

diameter of 18mm, with mean diameter D=20 mm and t/D = 0.10. Calculate the

torque and angle of twist per unit length if shearing stress at mean diameter is 70

MPa. Calculate these values if a cut is made through the wall thickness along the

entire length. G = 77.5 GPa.

6. Give the solution of bending problems with the help of soap-film method.

7. Describe the Betti’s method in short.

8. Give a Statement about the membrane theory of shells in brief.

SECTION-B (10*2)

Answer any two questions.

9. A steel gun barrel is subjected to an internal pressure of 70 MPa. The internal

diameter of the barrel is 75 mm and external diameter of 225 mm. a steel band 25 mm

thick and internal diameter 0.075 mm smaller than the external diameter of the gun

barrel is shrunk on to the gun barrel. Calculate (a) the shrinkage pressure on the gun

barrel, (b) maximum stress in the steel band, and (c) minimum temperature to which

the band must be heated to make the assembly.

For steel E = 200 GPa, v= 0.3 and coefficient of thermal expansion = 10*10-6/o C.

10. An 150 mm*100 mm*12mm unequal angle bar is placed with the long leg vertical

and used as a beam supported at each end, the span being 3 m. if a load of 6500 N is

placed at the mid length of the bar, determine the maximum stress due to bending.

11. Discuss the bending of a long circular pipe by a load uniformly distributed along a

circular section.

SECTION-C (15*2)

Answer any two questions.

12. Explain various Cartesian co-ordinates related to basic equations of elasticity.

13. Discuss various applications of conformal mapping in detail.

14. Describe the effect of transverse shear deformation on the bending of thin plates.