3.a. Rails of 20 m length were laid on the track when the temperature was $20^{0} \mathrm{C}$. A gap of 1.6 mm was kept between two consecutive rails. At what max temperature the rails will remain stress free? If the temperature is raised by $15^{0} \mathrm{C}$, what will be the magnitude and nature of stresses induced in the rails?

3.b. A composite bar of length 700 mm is made up of an aluminium of length 400 mm and steel bar of length 300 mm. The cross sectional areas of Aluminium and steel bars are of 100 mm x 100 mm and 50 mm x 50 mm respectively. Assuming that the bars are prevented from buckling sideways, calculate the compressive force P to be applied to the composite bar that will cause the total length of the bar decease by 0.25 mm. Take modulus of elasticit of Aluminium and steel as 70 Gpa and 200 Gpa respectively.

4.a. Derive the relation between rate of loading, Shear fore and Bending moment.

4.b. Draw S. F. D. and B. M. D. for the cantilever beam loaded shown in figure 1.

5 Draw S. F. D and B. M. D for the beam shown in figure 2.

6 Design the cross section for a beam acted upon by a bending moment of 80kN-m. If width of beam is 230 mm, calculate depth. Take stress f = 10 Mpa.

7 An I beam 300 mm deep and 100 mm wide has equal flanges of 10 mm thick top flange and 8 mm thick bottom flange is subjected to a shearing force of 200 kN. Draw the shear stress distribution across the depth. Obtain what percentage of shearing force is carried by the web?

8 An element in a plane is subjected to normal stresses p1 = 150 Mpa, p2 = 50 Mpa in two mutually perpendicular directions accompanied by a shear stress q = 40 Mpa. Determine the stresses acting on an element rotated through an angle by $40^{\circ}$ clockwise. Also determine the principal stresses and the planes on which they act.

9 Discuss in detail about various theories of failures.

10 A simply supported beam 8 m long carries concentrated loads of 40 kN each at a distance 2 m from the ends. Calculate: a) Maximum slope and deflection for the beam, and b) Slope and deflection under each load. Take: $\mathrm{EI}=1.2 \times 10^{4} \mathrm{kN.m}^{2}$

11 Determine the slopes at the ends and deflection at the mid span section of a beam loaded shown in figure 3 using Conjugate beam method. Take elastic modulus s 'E'.