B.Tech II Year I Semester (R18) Supplementary Examinations June/July-2023

STRENGTH OF MATERIALS-I

(Civil Engineering)

Date:

Time: 3 hours

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Max. Marks: 70

Answer ONE Question from each unit.

All Questions Carry Equal Marks

UNIT - I

1. a) Define: Elasticity, stress, strain, Hooke’s law, Poisson’s ratio, stress-strain diagram for mild steel.
   

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   (7M)
2. b) A steel rod of 3 cm 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 the temperature falls to 30°C, if (i) the ends do not yield and (ii) the ends yield by 0.12 cm. Take E = 2 x 10⁵ MN/m² and a = 12 x 10^-6 / °C. (7M)



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3. a) Define: Shear force, bending moment, point of contra flexure, types of beams and types of loads. (7M)
4. b) A simply supported beam of length 6 m carries a uniformly distributed load of 2 kN/m over the entire length and a point load of 4 kN at a distance of 2 m from the right support. Draw the shear force and bending moment diagrams for the beam. (7M)

UNIT - II

1. a) Derive an expression for bending stress. (7M)
2. b) A wooden beam 4 m long, simply supported at its ends, is carrying a uniformly distributed load of 6 kN/m over its entire length. If the section of the beam is 100 mm x 150 mm, determine the maximum bending stress in the beam. (7M)



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OR



3. a) Derive an expression for shear stress. (7M)
4. b) A rectangular beam 100 mm wide and 250 mm deep is subjected to a maximum shear force of 50 kN. Determine: (i) Average shear stress, (ii) Maximum shear stress, and (iii) Shear stress at a distance of 25 mm above the neutral axis. (7M)

UNIT - III

1. a) Derive an expression for the slope and deflection of a simply supported beam carrying a point load at the centre. (7M)

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2. b) A cantilever beam of length 3 m is carrying a uniformly distributed load of 2.5 kN/m over a length of 2 m from the fixed end. Determine the slope and deflection at the free end. Take E = 2 x 10⁵ N/mm² and I = 8 x 10⁷ mm⁴. (7M)



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3. a) Derive an expression for the slope and deflection of a cantilever beam carrying a point load at the free end. (7M)

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4. b) A simply supported beam of length 5 m carries a point load of 5 kN at a distance of 3 m from the left end. Determine the deflection under the load. Take E = 2 x 10⁵ N/mm² and I = 1 x 10⁸ mm⁴. (7M)

UNIT - IV

1. a) Derive the torsion formula. (7M)
2. b) A solid shaft of 200 mm diameter has the same cross-sectional area as that of a hollow shaft of the same material with inside diameter of 150 mm. Find the ratio of the power transmitted by the two shafts to the same speed. (7M)



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3. a) What are the assumptions made in the theory of torsion? (7M)
4. b) A solid steel shaft has to transmit 75 kW at 200 r.p.m. taking allowable shear stress as 70 N/mm², find suitable diameter for the shaft, if the maximum torque transmitted at each revolution exceeds the mean by 30%. (7M)

UNIT - V

1. a) Derive an expression for the crippling load when one end of the column is fixed and the other end is free. (7M)
2. b) A solid round bar 3 m long and 5 cm in diameter is used as a column with one end fixed and other hinged. Determine the crippling load. Take E = 2.0 x 10⁵ N/mm². (7M)

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3. a) What are the assumptions made in Euler’s column theory? (7M)
4. b) A column of timber section 15 cm x 20 cm is 6 m long both ends being fixed. If the Young’s modulus for timber is 17.5 kN/mm², determine: (i) Euler’s crippling load and (ii) Safe load for the column if the factor of safety is taken as 3. (7M)

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