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D192024 Pages:3

tensor for this case assuming a state of plane strain with Poisson ratiov = 0.25.

PART छ
Answer any three questions, each carries 10 marks
Derive the compatibility equation in terms of stress function णि polar co-

ordinate system
Write the equilibrium equation in polar coordinate system

In a very thick cylinder with outer radius much larger than the inner radius a,
subjected to an external pressure P,and zero internal pressure, prove that the

⋅ ⋅ ⋅⋅ a?
radial and tangential stress variations are മ. = 10 (1 — 72೫0 = Po(1 +

a2

2
Obtain the strain energy in terms of material properties for a shaft subjected to a
torque T.
For a given stress tensor at a point on a steel object with E= 207 x 10° kPa and
G=80x10° kPa, determine the value of strain energy density.

9 0 3
[०] 5 10 -10 1 |x10°kPa

3 1 112

Explain about unsymmetrical bending of beams.
A beam symmetrical about y-z axis is subjected to a bending moment M, about
an arbitrary axis in the y-z plane. Obtain the equation for flexural stress.

PART C
Answer any four questions, each carries 10 marks
Verify that function w(x, 9) = Axy is a Saint Venant’s warping function, where

A is aconstant. Find the general expression for slope of tangent at a point on the
boundary curve of the bar with this warping function. Find out shape of the cross
section and J integral.

Explain about centre of twist.

Derive the governing equation and boundary condition for torsion of non circular
cross section in terms of Prandtl stress function.

What is torsional rigidity?

The aluminium (G=27GPa) hollow thin walled torsion member hasdimensions as
shown below. Its length is 3m. If the member is subjected torque of 11KN-m,

determine the maximum shear stress and angle of twist.

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