JE – 670

*JE670*

II Semester B.E. (Civil) Degree Examination, June/July 2013 (Y2K6 Scheme) CE201 : STRENGTH OF MATERIALS Time : 3 Hours

Max. Marks : 100

Instructions : i) Answer five full questions selecting at least two questions from each Part A and Part B. ii) Assume any missing data suitably. iii) Write neat sketches wherever necessary. PART – A 1. a) Derive the relationship between bulk modulus and Young’s modulus of elasticity. 8 b) A tension bar of circular cross-section tapers uniformly from 28 mm to 22 mm diameter in a length of 300 mm. When an axial load of 70 kN is applied, the extension over its length is 0.5 mm. Find the modulus of elasticity of the material. If the Poisson’s ratio is 0.3, find the value of the rigidity modulus and bulk modulus. 12 2. a) How do you find temperature stresses in case of a compound bar subjected to temperature rise ?

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b) A reinforced concrete column is 300 mm × 300 mm in section. It is provided with 4 bars of 20 mm diameter. The column carries an axial load of 160 kN, find the stresses developed in concrete and steel rods. Also find the change in length of the column if the original length is 3 m. Take ES = 210 GPa and EC = 14 GPa. 12 3. a) Derive the relationship between load intensity, shear force and bending moment.

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b) Draw the BMD and SFD for the beam shown in Fig. 1. Determine the position and magnitude of maximum +ve and –ve BM and SF. Also locate the point of contraflexure if any. 12

Fig. 1 P.T.O.

JE – 670

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*JE670*

4. a) A circular pipe of external diameter 70 mm and thickness 8 mm is used on a simply supported beam over an effective span 2.5 m. Find the maximum concentrated load that can be applied at the centre of the span if permissible stress in pipe is 150 N/mm2.

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b) An I section beam of overall dimensions 150 mm by 350 mm has a web thickness of 10 mm and a flange thickness of 20 mm. If the shear force at the section is 50 kN, determine : i) The shear stress at the bottom of top flange. 12 ii) The maximum shear stress and its position. PART – B d 2y = M with usual notations. dx 2 b) Determine the deflection at the point B of the beam shown in Fig. 2. Take E = 200 kN/mm2 and I = 200 × 106 mm4.

5. a) Derive the equation EI

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Fig. 2 6. a) Define the terms :

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i) Polar modulus ii) Torsional rigidity. b) Determine the diameter of a solid circular shaft, which will transmit 400 KW at 300 r.p.m. The maximum shear stress should not exceed 35 N/mm2 1° in a 14 shaft length of 2 m. Assume modulus of rigidity as 90 KN/mm2.

*JE670*

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JE – 670

7. a) Explain :

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i) Short and long columns ii) Effective length of columns. b) Find the ratio of crippling loads given by Euler’s and Rankine’s formulae for an axially loaded tubular columns 3 m high with hinged ends. The inner diameter of the tube is 50 mm and the thickness of the metal is 6 mm. Take yield stress for the material as 316 N/mm2, modulus of elasticity 1 as 200 GPa and Rankine’s constant, a = 14 7500 8. a) Define the following :

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i) Principal stresses ii) Principal planes and iii) Maximum shear stress b) A thick cylinder of steel having an internal diameter of 100 mm and an external diameter of 200 mm is subjected to an internal pressure of 55 MPa and an external pressure of 7MPa. Find the maximum hoop stress. 14 ———————