Strength of Materials - May 2012

MU Mechanical Engineering (Semester 3)

Total marks: --
Total time: -- INSTRUCTIONS
(1) Assume appropriate data and state your reasons
(2) Marks are given to the right of every question
(3) Draw neat diagrams wherever necessary 1 (a) Find an expression for total elongation of a bar due to its own weight, when the bar is fixed at its upper end and is hangging freely at the lower end. 5 marks

1 (b) Establish the relationship between shear force, bending memont and rate of loading in beam. 5 marks

1 (c) A rectangular beam 200 mm deep and 300 mm wide is simply supported over a span of 8 m. what uniformly distribution load meter the beam can carry, if the bending stress lis not to exceed 120 N/mm² ? 5 marks

1 (d) For a rectangular section, show that the maximum shear is 1.5 times the average shear stress. 5 marks

1 (e) For acircular shaft, derive the torsional formula, $\dfrac {T}{J}=\dfrac {G\theta}{l}=\dfrac {\tau}{R}$ 5 marks

1 (f) Two elastic bars of same material and length, one of cicular section of diameter 200 mm and the other of square section of side 200 mm absorb the same amount of strain energy delivered by axial loads. Compare the stress in two cases. 5 marks

2 (a) A steel rod of 30 mm diameter and 5 m long is connected to two grips and the rod is maintained at a temperature of 95°C. Determine the stress and pull exerted when termperature falls to 30°C, if
(i) The ens do not yeild and
(ii) The ends yeild by 0.12 cm
Take E=2 × 10⁵ MN/m² and ? =12 × 10^-6/°C 5 marks

2 (b) The normal stresses in two mutually perpendicular directions are 60 N/mm² and 30 N/mm², both tensile. The complimentary shear stresses in these directions are of intensity 45 N/mm². Find graphically or otherwise, normal and tangential stresses on the two planes, which are equally inclined to the plane carrying the normal stresses mentioned above. also, find the principal stresses and maximum shear stress. 5 marks

3 (a) A Crane-chain with 6.25 cm² sectional area carriers a load of 10 kN. As it is being lowered at a uniform rate of 40 m/min, the chain gets jammed suddenly, at which time the length of the chain unwound is 10 m. Estimate the stress induced in the chain due to sudden stoppage. Neglete the weight of chain. take E=2.1 × 10⁵ N/mm² 5 marks

3 (b) (i) Find the maximum and minimum stress intensities at the bese of a uniform circular chimney, having external diameter 2 m, internal diameter 1.6m and height 25 m, when it is subjected to a wind pressure of 1.5 kN/m². The density of chimney material may be taken as 78.5 kN/m³ 5 marks

3 (b) (ii) Find the maximum height of the chimney in the (i) above to avoid development of tensile stresses at the bottom. Take same pressure, material density and diameters, same as mentioned in (i) 5 marks

4 (a) Draw the axial force, shear force and bending moment diagram for the beam loaded as below.
5 marks

4 (b) A closed cylindrical vessel made of steel plates 4 mm thick plane ends, carries fluid under a pressure of 3 N/mm². The diameter of cylinder is 250 mm and length is 750 mm calculate the logitudinal and hoop stresses in the cylinder wall and determine the change in diameter, length and volume of cylinder.
E=2.1 \times 10^5 N/mm^2, \ 1/m=0.286 5 marks

5 (a) Determine the diameter of solid shaft, which will transmit 300 kW at 250 rpm. The maximum shear stress should not exceed 30 N/mm² and the twist should not be more than 1° in a shaft 2m. Take modulus of rigidity =1× 10⁵ N/mm² 5 marks

5 (b) A hollow cylindrical cast iron column id 4 m long with both ends fixed. Determine the minimum diameter of the column, if it has to carry a safe load of 250 kN, with a factor of safety of 5. take internal diameter as 0.8 times the external diameter.
Take f_c=550 N/mm² snd ? =1/1600 in Rankine's formula 5 marks

6 (a) Determine the deflection at B and slope at D for a simply supported beam shown in the figure. Also, find the maximum deflection and its location. Take, E=2× 10⁵ N/mm², I=300×10⁸ mm⁴
5 marks

6 (b) Using the transformed sections, determine the maximum bending stresses in each of the two materials for the composite beam section shown in figure when subjected to sagging bending moment of 80 Knm. Take E_AI=70 Gpa, E_Steel=210 Gpa
5 marks

7 (a) Consider a simply supported beam of length 3 m and cross section of 100 mm × 200 mm, carrying a uniform load 4kN/m. neglecting the wieght of the beam, find
(i) The maximum bending stress in the beam
(ii) The maximum shear stress in the beam
(iii) The shear stress at a point 1 m to the right of the left support and 25 mm below the top surface of the beam. 5 marks

7 (b) An l-section beam 350 mm × 150 mm has a web thickness 10 mm and flange thickness 20 mm. if the shear force acting on the section is 40 kN, find -
(i) Maximum shear stress developing in the section.
(ii) Sketch the shear stress distribution diagram
(iii) The total shear force carried by web. 5 marks