1.a. Draw the shear force and bending moment diagram for a cantilever beam with uniformly distributed load and a concentrated load at the free end.

1.b. A cantilever 3 m long carries a UDL over the entire length. Find the deflection at the free end if the slope at the free end is 3 °

1.c. Derive the relation between E G K .

1.d. Obtain an expression for strain energy stored due to torsion in a shaft.

1.e. A bar of 12mm in diameter is acted upon by an axial load of 20KN. The change in diameter is measured as 0.003 mm.Determine (i) the poisson's ratio (ii) the modulus of elasticity and the bulk modulus .The value of modulus of rigidity is 80 GPa.

2.a. A steel of 35 mm outer diameter and 30 mm inner diameter encloses a gun metal rod of 25 mm diameter and is rigidly joined at each end. If at a temperature of 400C there is no longitudinal stress, determine the stress developed in the rod and the tube when the temperature of the assembly is raised to 240.° Take

Young's modulus for steel = 205 GPa,

Young's modulus for gun metal = 91.5 GPa

Coefficient of thermal expansion of steel = $11 \times 10^{-6/0} C$.

Also find increase in length if the original length of the assembly is 1 m.

2.b. Draw share force and bending moment diagran for a simply supported beam as shown in the figure

3.a. The tension flange of a girder of I-section is 240 mm X 40 mm, Whereas the compression flange 120 mm X 20 mm. The web is 300 mm deep and 20 mm thick. If the girder is used as simply supported beam of 8 m span, determine the load per m run if the allowable stress is 90 MPa in compression and 30 MPa in tension.

3.b. A hollow cast iron column whose outside diameter is 300 mm has a thickness of 30 mm.It is 5 m long and fixed at both ends.Calculate the safe load of Rankine formula using a factor of safety 4.Calculate the slenderness ratio of Euler's critical load to Rankine's critical load. Take N/mm^2 and in Rankine's formula. Also take $E=8 \times 10^4 N/mm^2$

4.a. A hollow shaft of diameter ratio 3/8 is to transmit 600 KW power at 110 rpm. The maximum torque being 20% greater than the mean. The shear stress is not to exceed than $63 N/mm^2$ and twist in a length of 3 m is not to exceed 1.4 degrees. Calculate its external and internal diameter which would satisfy above condition take $G = 8 \times 10^4 N/mm^2$

4.b. Figure below shows a rectangular plate with hole drilled in it.Determine the greatest and the least intensities of stress at the critical section of the plate when subjected to an axial pull of 90 kN.

5.a. A simply supported beam is subjected to the loads as shown in figure. Determine the maximum deflection induced in the beam .Take value of $EI = 1.2 \times 10^5 N-m^2$

5.b. Draw shear stress variation diagram for a beam section shown in figure Take SF = 100 KN.

6.a. A steel rod consist of two equal portions each 1 meter long is a as shown find the total strain energy of the rod when it is subjected to an axial pull of 150 KN.Take $E - 200 \times 10^3 N/mm^2$

6.b. An unknown weight falls bt 22 mm on to a collar rigidly connected to the lower end of the vertical bar 3 m long and $500 mm^2$ in section.If the maximum instantaneous extension is known to be 2.5 mm, find the corresponding stress and the magnitude of the falling weight.Take $E = 2 \times 10^5 N/mm^2$