B B4818 Pages: 3

Reg No.: Name:

APJ ABDUL KALAM TECHNOLOGICAL UNIVERSITY
FOURTH SEMESTER B.TECH DEGREE EXAMINATION, APRIL 2018

Course Code: ME202
Course Name: ADVANCED MECHANICS OF SOLIDS (ME)
Max. Marks: 100 Duration: 3 Hours
(Data handbooks not permitted)

PART A
Answer any three questions, each carries 10 marks. Marks

1 2) Define the term “State of stress” at a point. (3) b) Derive the Cauchy’s equation for
components of traction along the x,y and z (7) direction. Also derive the characteristic equation
for the principle stresses and principle plane from Cauchy’s equation.

2 The state of stress at a point is given by the Cartesian stress tensor

2 -1 1
-1 3 -1 kPa 1 -1 2
Find the following:
a) Thethree stress invariants (3)
b) Characteristic equation (2)
c) Principal stresses (2)
d) Any one unit normals of the principal planes. (3) 3 ೩) State and explain

Generalized Hook’s law (5) b) Derive the relationship between stress and strain for an
isotropic material in terms of (5) Lame’s coefficient.

4 Derive the expression for stress function and components of stress for the bending (10) of a
cantilever with an end load.

PART B
Answer any three questions, each carries 10 marks

5 a) Derive the equation for radial & hoop stress developed in a thick cylinder subjected (6)
to both internal and external pressure for a plain stress case.
b) Plot the variation of radial and hoop stress developed inside the cylinder subjected (4) to
only internal pressure
6 A disc with a hole has an inner radius of 10 cm and outer radius of 35 cm. If the disc
is running at 3500 rpm, determine the following:
a) The distributions of radial stress and tangential stress. (4)
b) Plot the variation of radial and tangential stress across the radius of the disc. (3)

c) Find the maximum values of radial and tangential stress. (3)
Take Poisson’s ratio is equal to 0.3 and density of steel equal to 8050 kg/m3.
7 A crane hook of rectangular cross section 25 mm wide and 55 mm deep has an inner (10)
radius of curvature 80 mm. The load line is at 70 mm from the inside of the section.
Determine the maximum fiber stress induced, if it carries a load of 30kN.

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