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Reg. No. : .................................... Name : .........................................
Third Semester B.Tech. Degree Examination, November 2009 (2008 Scheme) Branch : Industrial Engineering 08.304 : MECHANICS OF STRUCTURES Time : 3 Hours
Max. Marks : 100
Instruction: Answer all questions in Part – A and any one question from each Module in Part – B PART – A 1. Explain Saint-Venant’s Principle. 2. Obtain an expression for the volumetric strain of a rectangular bar subjected to an axial force. 3. Explain the construction of Mohr’s circle and its use. 4. Obtain an expression for the strain energy stored in a body when load is applied suddenly. 5. Obtain a relationship between Bulk modulus and Young’s modulus. 6. What are the assumptions made in theory of simple bending ? 7. Prove that the maximum shear stress in a rectangular section is 1.5 times the average stress. 8. For a shaft subjected to torsion prove that T J = N θ l , with usual rotations. 9. Distinguish between direct stress and bending stress. 10. Discuss the failure of a thick spherical shell subjected to internal pressure. (10×4=40 Marks) P.T.O .
PART – B MODULE – I 11. A steel rod of 25 mm diameter passes centrally through a tight fitting copper tube of external diameter 45 mm. The tube is closed with the help of rigid washers of negligible thickness and nuts threaded on the rod. The nuts are tightened, till the compressive load on the tube is 50 kN. Determine the stresses in the rod and tube, when the temperature falls by 60°C. Take E = 200 GN/m 2 for steel and 100 GN/m2 for copper. Take α = 12×10–6 per °C for steel and α = 18×10–6 per °C for copper.
12. A point in a material is subjected to a tensile stress of 100 N/mm 2 and a compressive stress of 60 N/mm2, acting on two mutually perpendicular planes. There is also a shear stress of 15 N/mm2 on these planes. Determine the maximum and minimum principal stresses. Also determine the value of maximum shear stress. 20 MODULE – II 13. Draw the shear force and bending moment diagram for the simply supported beam loaded as shown in Fig. 1. Also determine the maximum bending moment. 20
Figure-1 14. A simply supported beam is loaded as shown in Fig. 2. Calculate the slope and deflection at C. Take EI = 40 MNm2.
MODULE – III 15. A solid shaft 120 cm long and 2.5 cm in diameter transmits power. In order to save weight , it is replaced by a hollow shaft of the same outside diameter of 25 cm. What should be the inside diameter of the hollow shaft which will transmit same power as that transmitted by solid shaft ? The angle of twist over the length is also to be same in both cases. Modulus of rigidity of the shaft may be taken as 20 0.85×105 Pa. 16. A masonry pier of 3 m×4 m is subjected to an off centre vertical load of 50 kN. The location of the load is given by the co-ordinates (1, 0.5) taking the centre of the pier as the origin of the co-ordinates. i) Find the stresses developed at each corner of the pier. ii) What additional load should be placed at the centre of the pier, so that there is no tension anywhere in the pier section ? iii) What are the stresses at the corners, with the additional load in the centre ? _____________