# Sathyabama University Question Papers BE

# Mechanics of Solids – II Sem IV 2008

Answer All the Questions

1. Draw the conjugate beam for a simply supported beam of span (I)

subjected to a point load (P) at the mid-span.

2. Give the slope and deflection boundary conditions in a cantilever

beam.

3. Define the radius of gyration.

4. Differentiate long column from short column.

5. Write the stress components in a thin cylindrical shell subjected

to internal pressure.

6. Give the Lame’s equations to solve thick cylinder problems.

7. Write the expression for maximum shear stress for a state of

stress having sXsY and TXY.

8. List any four theories of failure.

9. Define shear centre.

10. Determine the moments of inertia of a rectangle of size 10mm x

6mm.

PART – B (5 x 12 = 60)

Answer All the Questions

11. A simply supported beam of span 6m is subjected to two

concentrated loads of 10kN and 20kN at 2m and 4m respectively

from left support. Determine the maximum deflection by

Macaulay’s method. Assume flexural rigidity is constant.

(or)

12. A cantilever beam of span 5m is subjected to a udl of 2kN/m over

a length of 3m from the fixed end. Calculate the slope and

deflection at the free end by Conjugate beam method. Assume

flexural rigidity is constant.

13. A column of height 8m is fixed at both ends. The cross section of

the column is 300 x 200mm. Calculate the slenderness ratio that

will govern the buckling. Also find the buckling load. Take E =

210 GPa.

(or)

14. A steel bar of solid circular cross section is 50mm diameter. The

bar is pinned at each end and subject to axial compression. If the

proportional limit of the material is 210MPa and E = 210GPa,

determine the minimum length for which Euler’s formula is

valid. Also determine the value of the buckling load if the column

has this minimum length.

15. A thin cylinder of 80mm outer diameter and 72mm inner

diameter is subjected to an internal pressure of 0.1 MPa.

Determine the longitudinal and hoop stresses. If the maximum

hoop stress is limited to 17.5MPa, find the thickness of the

cylinder.

(or)

16. A pipe of 150mm internal diameter and 200mm external diameter

fails under hoop tension for an internal pressure of 50MPa.

Determine, for a safety factor of 4, the safe internal pressure for a

second pipe of the same material and internal diameter but with

40mm thick wall.

17. An element in plane stress at the surface of a large machine is

subjected to stresses sX = 15MPa, sY = 5MPa and TXY = 4MPa

Mohr’s circle, determine the principal stress and maximum shear

stress.

(or)

18. Estimate the torque on a 10mm diameter steel shaft when

yielding begins using

(a) Tresca theory,

(b) von Mises theory.

The yield strength of the steel is 140 MPa.

19. An unequal angle section of uniform thickness 5mm has leg of

lengths 60mm and 40mm. Estimate the moment of inertia about

both the axes and also product of inertia.

(or)

20. Locate the shear centre for the section shown in figure.