# Sathyabama University Question Papers BE

# Mechanics of Solids – II Sem IV 2008

Answer All the Questions

1. Differentiate between determinate and indeterminate beams?

2. Draw the conjugate beam of a cantilever beam subjected to point

load at the free end.

3. What are the assumptions made in the Euler’s theory for long

columns.

4. What is meant by effective length of columns?

5. What are the stresses set up in a thin cylinder subjected to

internal fluid pressure?

6. What is meant by shrink fit in thick cylinders?

7. What are the significant of failure theories?

8. State distortion energy theory of failure.

9. Define shear centre.

10. What are the causes for unsymmetrical bending?

PART – B (5 x 12 = 60)

Answer All the Questions

11. A beam of length 5m and of uniform rectangular cross section is

supported at its ends and carries uniformly distributed load over

the entire span. Calculate the depth of the section if the maximum

permissible bending stress is 8N/mm2 and central deflection is

not to exceed 10mm.

(or)

12. Determine the slope at supports, deflection under the load and

maximum deflection of a simply supported beam of length 10m,

which carries a point load of 10kN at a distance of 6m from the

left end. Take E = 2 x 105N/mm2 and I = 1 x 108mm4.

13. Derive the expression for Euler’s crippling load when both ends

of the column are fixed.

(or)

14. A hollow steel column whose outside diameter is 200mm has a

thickness of 20mm. It is 4.5m long and is hinged at both ends.

Calculate the safe load by Rankine’s formula using a factor of

safety of 4. Calculate the slenderness ratio and the ratio of Euler’s

and Rankine’s critical loads. Take fc = 550N/mm2 a = 1/1600 in

Rankine’s formula and E = 9.4 x 105N/mm2.

15. A boiler is subjected to an internal steam pressure of 3N/mm2.

The thickness of the boiler plate is 2.5cm and the permissible

tensile stress is 125N/mm2. Find out the maximum diameter

when the efficiency of longitudinal joint is 90% and that of

circumferential joint is 35%.

(or)

16. A steel cylinder of 200mm external diameter is to be shrunk to

another steel cylinder of 100mm internal diameter. After

shrinking, the diameter at the junction is 150mm and the radial

pressure at the junction is 12.5N/mm2. Find the original

difference in radii at the junction. Take E = 2 x 105N/mm2.

17. A bolt is under an axial thrust of 7.2kN together with a transverse

shear force of 3.6kN. Calculate the diameter of the bolt according

to

(a) Maximum principal stress theory

(b) Maximum shear stress theory

(c) Maximum strain energy theory

Take elastic limit in simple tension = 200N/mm2, factor of

safety = 3 and Poisson’s ratio = 0.3.

(or)

18. State and explain and five theories of failure.

19. Locate the shear centre for a channel section.

(or)

20. A cantilever beam of span 4m has a rectangular cross section

40mm wide and 60mm deep. The beam is subjected to a

concentrated load of 3kN which is inclined at an angle of 30° to

the vertical plane and located at the free end of the cantilever.

Calculate the bending stress developed at points A, B and C near

the fixed end.