# [AMOS] ME 202 ADVANCED MECHANICS OF SOLIDS S4 KTU MODEL QUESTION PAPERS FOR KTU STUDENTS [SECOND YEAR] Part - ||

__APJ ABDUL KALAM TECHNOLOGICAL UNIVERSITY__**ADVANCED MECHANICS OF SOLIDS S4 KTU QUESTION PAPERS**

**ME 202 : Advanced Mechanics of Solids**

Max Marks: 100 Duration: 3 hrs

(Assume missing data if any ; Contains 3 Pages)

__PART A__

__(Answer any three questions)__b. The state of stress at a point is given by the following components.

Determine the magnitudes of all principal stresses? (8 marks)

2. Components of displacement field in a body, in cartesian coordinates, are given by Find the strain tensor at point (1, 0, 2) ? (10 marks)

3 a. State generalized Hooke’s law? (3 marks)

b. State St. Venants principle for end effects with an example? (4 marks)

c. Write down boundary condition equations for stress analysis problem? (3 marks)

4 a. Derive compatibility equation in terms of stress for the case of plane stress without

body force? (10 marks)

(3 x 10 = 30 marks)

__PART B__

__(Answer any three questions)__5. For a stress function in polar coordinates, Î¦ = r2 cosÎ˜ , determine the stress components? (10 marks)

6 a. Write down the general expressions for stress distribution in a thick cylinder ? (2 marks)

b. Applying boundary conditions in the above equations, determine the stresses at inside and outside surfaces of the cylinder, when it is subjected to a internal pressure of 10

MPa.

Take internal and external diameters of the cylinder, respectively as 100 mm and 200 mm. (8 marks)

7. A cantilever of length 2 m, having rectangular cross-section 40 x 80 mm2 , is kept with its longer edge vertical. It carries an inclined load W at the free end.

The angle of inclination of the load to the vertical axis is 25o. What is the maximum vlaue of load W that can be applied if the maximum tensile stress is not to exceep 200 MPa?

(10 marks)

8 a. What is strain energy of deformation? (2 marks)

b. A cantilever of length L carries a uniformly distributed load of intensity w / unit length.

Determine the total strain energy due to bending moment? (8 marks)

(3 x 10 = 30 marks)

__PART C__

__(Answer any four questions)__10. Using principle of minimum potential energy theorem, determine the displacements u1 and u2 of the spring system shown? (10 marks)

11. Using St. Venant’s theory of torsion, show that simple torsion theory for circular cross-sections is exact? (10 marks)

12. Apply Prandtl torsion theory to thin rectangular sections and derive the expressions for approximate formula for shear stress distribution? (10 marks)

13. Determine the torsional shear stresses for the section shown, when it is subjected to a twisting moment T? Assume uniform thickness, t. (10 marks)

14. An angle section shown below is subjected to a torque

T= 50 kN-m.

Find the maximum shear stress? If another angle section is welded to the previous one as shown, find the reduction in maximum shear stress? (10 marks)

(4 x 10 = 40 marks)

(Total : 100 marks)

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