Kerala University 2009 M.Tech Civil Engineering Structural Engineering and Construction Management - Theory of Elasticity - Question Paper
(Pages : 2) 3599
Reg. No. :....................................
Name :.........................................
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 jx2( - 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 'Tmax'and 0 for thin rectangular section subjected to a torque T.
Attachment: |
Earning: Approval pending. |