Kerala University 2009 M.Tech Civil Engineering Structural Engineering and Construction Management - Theory of Elasticity - Question Paper

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First Semester M.Tech. Degree Examination, June 2009 Branch : Civil (2008 Scheme)

Structural Engineering and Construction Management (Common)

CSC 1005 : THEORY OF ELASTICITY

Time : 3 Hours Max. Marks : 100

Instructions : 1) Answer any five questions.

2) All questions carry equal marks.

1. a) What is generalized Hookes law ? Esatblish the stress-strain relationship for isotropic materials and hence the relationship between the elastic constants.

b) The state of stress at a point with respect to the xyz system is

^f 300 200 -200 200 0 -100 200 -100 - 200

MPa

V /

Determine the stress tensor relative to the x y'z' coordinate system obtained by a rotation through 30 about the z-axis.

2. a) Derive the compatibility conditions for 3D in terms of stress.

b) Show that j^{x2( - 3c2y} + ^2c3)^{-)y3( - 2c2})jisan acceptable stress function and hence find the stress field it represents.

3. a) What is stress-function in the solution of two dimensional problems in elasticity ?

Obtain the biharmonic equation in polar co-ordinates from the Cartesian Co-ordinate system.

b) Derive the equilibrium equations in polar Co-ordinate system.

Derive the stress components of a rotating circular disc of uniform thickness with central hole of radius a.

4. a) b)

5. a) b)

Determine the stress distribution in a curved bar with constant narrow rectangular cross-section in pure bending.

Analyse the torsion of an equilateral triangular bar.

Find the shear stresses and the angle of twist in the multi-cellular structure, as shown in figure, subjected to a torque of400 kNm. Wall thickness of the structure is uniform and is equal to 15 mm. Take G= 31.1 GPa.

Discuss St. Venants semi-inverse method for torsion of general prismatic bars. Also obtain the relation between torsion, angle of twist and torsional rigidity.

6. a) b)

Derive the expression for 'T_max'and 0 for thin rectangular section subjected to a torque T.