Strength of Materials - Dec 2011

Mechanical Engineering (Semester 3)

TOTAL MARKS: 80
TOTAL TIME: 3 HOURS (1) Question 1 is compulsory.
(2) Attempt any three from the remaining questions.
(3) Assume data if required.
(4) Figures to the right indicate full marks. 1 (a) If a round of 37.5 mm diameter and 2.4 m length is stretched by 2.5 mm, find its bulk modulus and lateral contraction. Take, young's modulus = 110 GN/m² and shear modulus =42 GN/m² for the material of the bar.(5 marks) 1 (b) Derive the flexure formula, $$\dfrac {M}{I}=\dfrac {\sigma}{y}=\dfrac {E}{R}$$(5 marks) 1 (c) A fitched beam consist of steel and timber as shown in figure. Determine the moment of resistance of the beam. Take $$ \sigma_{s}=100 \ N/mm^{2} \ and \ \sigma_{w}=5 \ N/mm^{2}$$
(5 marks) 1 (d) Draw the S.F. and B.M. diagrams for the beam loaded shown in the figure.
(5 marks) 1 (e) Calculate the bursting pressure for a cold drawn seamless steel tubing of 60 mm inside diameter and 2 mm wall thickness. Ultimate strength of steel is 380 N/mm².(5 marks) 1 (f) Find the maximum power that can be transmitted through a 50 mm diameter shft at 150 rpm, if the maximum permissible shear stress in the shaft is 80 N/mm².(5 marks) 2 (a) A beam weighing 450 N is held horizontal by three verticle wires, one attached to the middle of the beam and the others to the ends of the beam. The outer wires are of brass with 1.25 mm diameter, and the central wire is of steel with 0.625 mm diameter. Estimate the stress induced in the wires, assuming that the beam is rigid and the wires are of same length and unstretched before attaching to the beam. take youngs's moduli of brass 8.6 × 10⁴ N/mm² and of steel as 2.1 × 10⁵ N/mm².(10 marks) 2 (b) At a point a material under stress, the intensity of the resultant stress on a certain plane is 50 N/mm² (tensile) inclined at 30° to the normal of that plane. The stress on an plane at right angles to this has a tensile component of 30 N/mm². Find,
(i) The resultant stress on the second plane
(ii) The principle planes and stresses
(iii) Plane of maximum shear and intensity
(10 marks) 3 (a) For the beam show below, draw A.F., S.F. and B.M. diagram and mark important points.
(10 marks) 3 (b) Two wooden planks of 150 mm × 50 mm cross section are connected together to form a Tsection of a beam. If a sagging moment of 4 kNm is applied to the beam about horizontal axis,
(i) Find the stresses at the extreme fibres.
(ii) Calculate total tensile and compressive forces developed in the section.(10 marks) 4 (a) Determine the slope deflection at the free end of the beam loaded as shown in the figure
(10 marks) 4 (b) A rectangular pier is subjected to a compressive load 450 kN as shown in the figure. Find the stress intensities at the four corner if the pier.
(10 marks) 5 (a) A cylindrical shell of 900 mm long, 200 mm internal diameter and 8 mm thickness is filled with an incompressible fluid at atmospheric pressure. If a additional 20 cm³ fluid is pumped into the cylinder, find
(i) The pressure exerted by the fluid on the cylinder and
(ii) Hoop stress induced(10 marks) 5 (b) Internal diameter of a hollow shaft is 0.6 of its external. It has to transit 300 kW power at 80 rmp. If the shear stress is not exceed 60 N/mm², find the internal and extermal diameter of the shaft, assuming that the maximum torque is 1.4 times the mean torque.(10 marks) 6 (a) A 200 kg weight is dropped on to a collar at the lower end of a vertical bar of 3 m long and 28 mm diameter. Calculate the height of drop, If the maximum instantaneous stress is not to exceed 120 N/mm² what is the corresponding instantaneous elongation? Take E=2×10⁵ N/mm²(10 marks) 6 (b) An 800 mm long piston rod of a steam engine is subjected to a maximum load of 60 kN. Determine the diameter of the rod using Rankine's formula. Take permissible compressible compressive stress as 100 N/mm² and Rankine's constant as 1/7500 for hinged ends. The rod is assumed to be partially fixed with length coefficient 0.6.(10 marks) 7 (a) A beam of channel section 120 mm × 60 mm has uniform thickness of 15 mm as shown in the figure. For a shear force of 50 kN, show the distribution of shear stresses for a vertical section. Find the ratio of maximum to mean shear stress.
(10 marks) 7 (b) A simply supported beam, with a span of 1.3 m and a rectangular cross section of 150 mm wide and 250 mm deep, carries a concentrated load of W at the centre. If the allowable stresses are 7 N/mm² for bending and 1 N/mm² for shear, what is the value of the safe load W?(10 marks)