Deemed University 2009 M.Tech Mechanical Engineering University: Lingayas University Term: I Title of the : Advanced Mechanics of Solids - Question Paper

Roll No. ..

 

Lingayas University, Faridabad

M.Tech (Mechanical Engineering) (Term I)

Examination October, 2009

Advanced Mechanics of Solids

Paper: ME -505

[Time: 3 Hours] [Max. Marks: 100]

 

Before answering the question, candidate should ensure that they have been supplied the correct and complete question paper. No complaint in this regard, will be entertained after examination.

 

Note: Question No. 1 Part A is compulsory. Attempt any two questions from Part B and any two questions from Part C.
In all attempt five questions.

 

PART A

Q-1.

(a) State the expressions for the Saint Venant's equations of Compatibility. (3)

(b) Distinguish between hydrostatic and deviatoric state of stress. (3)

(c) State the Maxwell-Betti-Rayleigh Reciprocal theorem. (3)

(d) How is membrane analogy helpful in analysis of complicated
cross- sectional shapes? (3)

(e) Differentiate between Centre of Twist and Flexural Centre. (2)

(f) What do you understand by rotating disk of uniform strength? (3)

(g) State the theorem of Stationary Potential Energy. (3)

 

PART- B

Q-2. Verify whether the following field satisfies the equations of compatibility.

p is a constant:

= py, = (x+y), = p (x+y), =2pz, = 2pz (20)

 

Q-3. State the various theories of failure. Discuss their significance and applications. (20)

 

4. (a) Derive an expression for change in length of a linear element.

(b) The displacement field for.a body is given by :

u=[i + j + k] x 10^-4

What is the deformed position of a point originally at (1,2, 3)? (20)

PART- C

 

Q-5. An external pressure of 12 MN/m² is applied to a thick cylinder of internal

diameter 150 mm and external diameter 300 mm. If maximum hoop stress permitted on the inside of the wall is 30 MN/m², calculate the maximum internal pressure that can be applied. If the cylinder has closed ends, calculate

change in the outside diameter. Take E = 2I0 GN/m² and v=0.3. Derive the expressions used. (20)

 

Q-6. With respect to the frame of reference O (x y z) ,lhe following state of stress exists. Determine the principal stresses and their associated directions. Also, check on the invariance of I₁. I₂, and I₃:

 

= (20)

Q-7. A 10 cm x 12 cm rectangular flat plate of 5 mm thickness is simply supported at edges and subjected to a uniform lateral pressure of 400 kPa. Determine the central deflection and the maximum stress. Take E = 210 GN/m² and v = 0.3. (20)

 

Q-8. Discuss the Prandtls membrane analogy for torsion of complicated cross

sectional shapes. (20)