1. Choose the correct answer from the given alternatives:

Modulus of rigidity is defined as the ratio of

longitudinal stress to longitudinal strain

shear stress to shear strain

stress to strain

stress to volumetric strain

If the principal stresses at a point in a
strained body are PI and P2 then the resultant stress on a plane carrying the maximum shear stress is equal to

sqrt(P1^2

sqrt(P1^2 p2^2

sqrt(P1^2 p2^2

sqrt(P1^2 2

The sum of normal stresses is

constant

variable

dependent on the planes

None of the above

A prismatic bar when subjected to pure bending assumes the shape of

catenary

Cl1bic parabola

quadratic parabola

arc of a circle

Buckling load for a given column depends upon

length of the column only

least lateral dimension only

both length and least lateral dimension

None of the above

Polar modulus for a solid shaft of diameter D is

n/16 D^3

n/32 D^3

n/16 D^4

n/32 D^4

If the length of a simply supported beam carrying a concentrated load at the centre is doubled, the deflection at the centre will become
two times

four times

eight times

sixteen times

2. A steel rod of 20 mm diameter passes centrally through a tight fitting copper tube of external diameter 40 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 the tube, when the temperature of the assembly falls by 50°C. Consider,

for steel, E =200 a =12 x

for copper, E =100 a =18 x

3. A simply supported beam of 6 m span is loaded with a uniformly distributed load of 1·5 kN/m over the entire span and concentrated load of 4 kN and 5 kN at distances of 2 m and 4 m from the left hand support respectively. Find the magnitude and position of the maximum RM. (Bending Moment).

4. A rectangular beam 240 x 400 mm is simply supported over a span of 4 m. Find the safe concentrated load at mid-span, if the allowable bending stress is 120 N/mm^2.

5. A cantilever has prop P at a distance l from the fixed end and on this length there is a uniformly distributed load of w per unit run. If the prop is rigid and holds its point of application on the horizontal, find what proportion of the total weight is taken by the prop.

6. Find the maximum torque which can be applied safely to a shaft of 300 mm diameter. The permissible angle of twist is 1·5° in a length of 7·5 m and shear stress is not to exceed 42 N/mm^2. Take C =84·4 kN/mm^2.

7. Calculate the safe compressive load on a hollow cast-iron column with one end hinged and the other rigidly fixed. The external and internal diameters are 120 mm and 90 mm respectively and length of the column is 9 m. Take factor of safety as 3 and E 95 GPa.

8. Write short notes on any four of the following:

Stress -Strain Relationship

Normal and Shear Stresses

Evaluation of Extreme Stresses

Torsion of Circular Shaft

Factor of Safety