Sathyabama University Question Papers BE
Mechanics of Solids – II Sem IV 2009
Answer All the Questions
1. Write the expressions for determining the slope and deflection of
a simply supported beam, carrying a uniformly distributed load of
w/unit length over the entire span.
2. What is a cantilever?
3. Define the terms: column and strut.
4. Enumerate the limitations of Euler’s formula.
5. Name the stresses set up in a thin cylinder subjected to internal
6. Differentiate between a thin cylinder and a thick cylinder.
7. Briefly explain principal planes and principal stresses.
8. State St. Venant’s theory.
9. Define the terms: neutral axis and section modulus.
10. What do you mean by unsymmetrical bending?
PART – B (5 x 12 = 60)
Answer All the Questions
11. What is Maraculay’s method? Where is it used? Find an
expression for deflection at any section of a simply supported
beam with an eccentric point load, using Macaulay’s method.
12. (a) A cantilever of length 3m is carrying a point load of 25 kN at
the free end. If the moment of inertia of the beam = 108 mm4 and
value of E = 2 x 105 N/mm2, find the slope and defection of the
cantilever at the free end. (4)
(b) A cantilever of length 2m carries a uniformly distributed load
2 kN/m over a length of 1m from the free end, and a point load of
1 kN at the free end. Find the slope and deflection at the free end
if E = 2 x 105 N/mm2, and I = 6.667 x 107 mm4. (8)
13. Using Euler’s formula, calculate the critical stresses for a series
of struts having slenderness ratio of 40, 80, 120, 160 and 200
under the following conditions.
(a) both ends hinged and
(b) both ends fixed. Take E = 2.05 x 105 N/mm2
14. A hollow cylindrical cast iron column is 4m long with both ends
fixed. Determine the minimum diameter of the column if it has
to carry a safe load of 250 kN with a factor of safety of 5. Take
the internal diameter as 0.8 times the external diameter. Take
fc = 550 N/mm2 and a =1/1600 in Rankine’s formula.
15. A boiler shell is to be made of 15mm thick plate having a
limiting tensile stress of 120 N/mm2. If the efficiencies of the
longitudinal and circumferential joints are 70% and 30%
(a) the maximum permissible diameter of the shell for an internal
pressure of 2 N/mm2, and
(b) permissible intensity of internal pressure when the shell
diameter is 1.5m.
16. A steel tube of 200mm external diameter is to be shrunk on to
another steel tube of 60mm internal diameter. The diameter of
the junction after shrinking is 120mm. Before shrinking on the
difference of diameters at the junction is 0.08mm. Calculate the
radial pressure at the junction and the hoop stresses developed in
the two tubes after shrinking on. Take E = 2 x 105 N/mm2.
17. Derive an expression for the major and minor principal stresses
of an oblique plane, when the body is subjected to direct stresses
in two mutually perpendicular directions accompanied by a shear
18. A bending moment M applied to a solid shaft carries a maximum
direct stress s at elastic failure. Determine the numerical
relationships between M and a twisting moment T which, acting
alone on the shaft , will produce elastic failure, according to each
of the following theories of failure.
(a) Maximum principal stress (b) Maximum principal strain
(c) Maximum strain energy (d) Maximum shear stress
(e) Shear strain energy. [Poisson’s Ratio = 0.30]
19. A beam of angle section 150 mm x 100 mm x 10 mm is simply
supported beam over a span of 1.6 m with 150 mm leg vertical. A
uniformly distributed vertical load of 10 kN/m is applied through
out the span. Determine the following. Take E = 210 GN/m2.
(a) Maximum bending stress (b) Direction of neutral axis
and c. Deflection at the centre.
20. Locate the shear centre of the section shown in Fig.1 and 2.