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APJ ABDUL KALAM TECHNOLOGICAL UNIVERSITY
FIRST SEMESTER M.IECH DEGREE EXAMINATION, DECEMBER 2017

Mechanical Engineering

Machine Design
01 ME6105 CONTINUUM MECHANICS

Answer any two full questions from each part
Limit answers to the required points.

Max. Marks: 60 Duration: 3 hours

PART A

1. a. Write down the equation for Mohr's circle of two-dimensional problems.
Write down the equation for the radius of the 2D Mohr's circle? (3 marks)

b. What are spherical and deviatoric parts of a tensor? ( | marks)
€. ௨2 ,oxz=l,0 andou ‏مح‎ be the known components of

stress at a point. Find the value such that at least one plane
passing through the point is stress free. Also determine the direction
cosines of normal of the stress free plane. (5 marks)

2 , 2. Derive an equation for octahedral shear stress in terms the stress
invariants, (4 marks)

b. The principal stresses of stress at a point are 01 02 and %with 9792793
. Now, derive equations of the direction cosines of a

plane passing through this point, which is subjected to normal stress
and shear stress on and respectively. (5 marks)

3 ,9. With the help of mathematical derivations obtain the relation between
circulation of a vector field per unit area around a point in a plane and curl
of the vector, (4 marks)

b. Differentiate between vector space and space of inner product.
(3 marks)

c. Whatis ? Find the value of (2 marks)

PART B