What is Hooke's law and Bulk modulus of rigidity?

Derive the expression among Young's modulus of Elasticity Bulk modulus "K" and M (Poisson Ratio) as given below
E =3K M).

2. A round bar of steel tapers uniformly from a diameter of 2·5 cm to 3·5 cm in a length of 50 cm. If an axial force of 60 kN is applied at each end, determine the elongation of the bar. Take E =205 kN/mm^2. 10

3. A piece of metal is subjected to tensile stresses of 60 N/mm^2 and 30 N/mm^2 at right angles to each other. Find the normal and tangential stress on a plane, which makes an angle of 40° with the 60 N/mm^2 stress.

4. Draw the S.F. and B.M. diagram of abeam shown below:

<img src='./qimages/15439-4.jpg'>

Explain the assumptions made in simple theory of bending.

A steel plate 10 cm wide and 2 cm thick is bent into a circular arc of 50 meter radius. Find the maximum intensity of bending stress. Take E 2·05 x 10^5 N/mm^2.

6. Find the maximum and minimum intensities induced on the base of a masonry wall 6 m high, 4 m wide and 1·5 m thick subjected to horizontal wind pressure of 1,500 acting on 4 m side. The density of masonry may be taken as 22,400 N/m^3.

What is slenderness ratio Discuss the different conditions of column.

Explain the limitations of Euler's formula in detail.

8. A hollow C-I column whose outer diameter is 200 mm and has thickness of 20 mm, is 4·5 m long and is fixed at both ends. Calculate the safe load by Rankine formula using F.G.S. as 4. Take =550 a 1/1600.

9. Derive the relation between twisting moment, twist and shear stress of a solid circular shaft as given below:

0s/R N8/l q/r Tr/j

where cr maximum shear stress

R Radius

N Bulk modulus

e Twist angle

l length of shaft

J Polar M.O.I.

q shear stress at a distance

10. Write short notes on any two of the following:

Fatigue Testing

Principal Stresses

Different Properties of Steel