1.a. Define the following : (i) Elasticity (ii) ductility (iii) Toughness (iv Hardness (v) Stiffness (v) Resilience

1.b the tensile test was conducted on a mild steel steel bar. The following data was obtained from the test. Diameter of the steel bar = 16 mm; Gauge length of the bar = 80 mm; load at proportionality limit = 72 kN; Extension at a load of 60 kN= 0.115 mm; Load at failure = 80 kN; Final Gauge length of bar 104 mm; Diameter of the rod at failure = 12 mm. Determine : (i) Young's modulus (ii) Proportionality limit. (iii) True breaking stress (iv) Percentage clongation.

2.a Derive a relation between modulus of elasticity and bulk modulus.

2.b At room temperature, the gap between bar A and bar B shown in Fig. is 0.25 mm. What are the stresses induced in the bars, if the temperature rise is 35°C . Given A_A = 10000 mm²; A_B = 800 mm²; E_A = 2 x 10⁵ N/mm²; E_B = 1 x 10 ₅ ; α_A = 12 x 10 ^-6 /°C ; α_B = 23 x 10^-6 /°C; L_A = 400 mm; L_B 300 mm.

3.a A point in a strained material is subjected to a tensile stress of 500 N/mm² and 300 N/mm² in two mutual perpendicular planes. Calculate the normal, tangential, resultant stresses and its obliguity on a plane making an angle of 30°C with the axis of second stress. Also find the maximum shear stress.

3.b A thick cylindrical shell of 160 mm internal diameter is subjected to an internal pressure of 8 N/mm². Find the thickness of shell if the permissible or hoop stress in the section is not to exceed 35 N/mm².

4.a An elemental cube is subjected to tensile stresses of 30 N/mm² and 10 N/mm² acting on two mutually perpendicular planes and a shear stress of 10 n/mm² on these planes. Draw the Mohr's circle of stresses and hence determine the magnitudes and directions of principal stresses and also the greatest shear stress.

4.b A thin cylinder shell with following dimensions is filled with a liquid at atmospheric pressure: Length = 1.2 m, External diameter = 200 mm , Thickness of metal - 8 mm. Find the value of the pressure exerted by the liquid is pimped into the cylinder and the hoop stress induced if an additional volume of 25000 mm³ of liquid is pumped into the cylinder. Take E = 2.1 x 10 ₅ N/mm² and μ = 0.33.

5 For the beam shown in Fig. Q5. Draw shear force and bending moment diagram. Locate the point of contraflexure if any.

6.a Derive a relationship between bending stress and radius of curvature.

6.b Derive the deflection equation ,$\mathrm{E} 1 \frac{\mathrm{d}^{2} \mathrm{y}}{\mathrm{d} \mathrm{x}^{2}}=\mathrm{M}$.

7.a State the assumptions made in pure torsion theory.

7.b A solid circular shaft has to transmit a power of 1000 kW at 120 rpm, Find the diameter of the shaft, if the shear stress of the material must not exceed 80 N/mm². The maximum torque 1.25 time of its mean. What percentage of saving in material would be obtained if the shaft is replaced by a hollow one whose internal diameter is 0.6 times its external diameter, the length, material and maximum and shear stress being same?

8.a Derive a Euler's crippling load for a column when both of its ends are hinged.

8.b A 1.5m long column and position and the other end is free. Taking the factor of safety as 3. calculate the safe load using Euler's formula. Taking E = 1.2 x 10 ₅ N/mm².

9.a Derive an expression for strain energy due to shear stresses.

9.b Write a note on: (i) Maximum principal stress theory. (ii) Maximum shear stress theory.

10.a A hollow circular shaft 2 m long is required t transmit 1000 kW power, when running at a speed of 300 mm. If the outer diameter of the shaft is 150 mm and inner diameter is 120 mm. Find the maximum shear stress and strain energy stored in the shaft.

10.b A solid circular shaft is subjected to a bending moment of 40 kN-m and a torque of 10 kN-m. Design the diameter of the shaft according to, (i) Maximum principal stress theory. (ii) Maximum shear stress theory.

Take μ = 0.25, stress at elastic limit = 200 N/mm² and factory of safety = 2.