Anna univ CE 251 — STRENGTH OF MATERIALS

PART A — (10 ? 2 = 20 marks)
1. What is a rigid body and a deformable body?
2. The Youngs modulus of steel is 200 kN/mm2 and concrete is 20 kN/mm2. What is the modular ratio?
3. A cantilever beam is subjected to a moment M at free end. The length of the beam is L. What is the bending moment at fixed end?
4. What is point of contraflexure? Whether point of contraflexure will occur in a cantilever beam?
5. Sketch the shear stress variation across the I–beam cross section due to bending.
6. What is flitched beam?
7. A simply supported circular beam of span 4 m carries a 10 kN load at midspan. The cross section is 100 mm diameter. What is the maximum bending stress?
8. What is close coiled helical spring?
9. What is the diameter of Mohr’s circle if the principal stresses are 40 N/mm2 and 80 N/mm2.
10. Give two examples of conjugate beam with the corresponding real beam.
PART B — (5 ? 16 = 80 marks)
11. A simply supported beam of length 4 m carries two point loads 3 kN each at a distance of 1 m from each end. E = 2 ? 105 N/mm2. I = 108 mm4. Using conjugate beam method determine slope at each end and deflection under each load.
12. (a) Two vertical rods are loaded as shown in Fig. Q 12 (a). N/mm2 N/mm2. Find the stresses in steel and copper rods.

Fig. Q 12 (a)
Or
(b) A steel tube of 30 mm external diameter and 20 mm internal diameter encloses a copper rod of 15 mm diameter. The ends are rigidly joined. The temperature of whole assembly is raised by 190?C. N/mm2 = N/mm2 per ?C, per ?C. Calculate stress in the rod and the tube.
13. (a) Draw the shear force and bending moment diagrams for the beam shown in Fig. Q 13 (a)

Fig. Q 13 (a)
Or
(b) A beam of size 150 mm wide, 250 mm deep carries a uniformly distributed load of w kN/m over entire span of 4 m. A concentrated load
1 kN is acting at a distance of 1.2 m from the left support. If the bending stress at a section 1.8 m from the left support is not to exceed 3.25 N/mm2 find the load w.
14. (a) The stiffness of close coiled helical spring is 1.5 N/mm of compression under a maximum load of 60 N. The maximum shear stress in the wire of the spring is 125 N/mm2. The solid length of the spring (when the coils are touching) is 50 mm. Find the diameter of coil, diameter of wire and number of coils. C = 4.5 ? 104 N/mm2.
Or
(b) The stresses at a point in a strained member are shown in Fig. Q 14 (b). The greatest principle stress is 150 N/mm2. Find the value of q. Also find maximum shear stress at that point.

Fig. Q 14 (b)
15. (a) A cantilever beam 4m span carries a point load of 10 kN at free end. Find the deflection and rotation at mid–span using principle of virtual work. EI = 25,000 kNm2.
Or
(b) A simply supported beam of 10 m span carries a uniformly distributed load of 1 kN/m over the entire span. Using Castigliano’s theorem, find the slope at the ends. EI = 30,000 kNm2.