Mechanics Of Solids Nov2003 Or 220352

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Code No. 220352 II B.Tech. II Semester Supplementary Examination November, 2003 MECHANICS OF SOLIDS (Common to Mechanical Engineering , Mechatronics and Production Engineering) Time: 3 hours Max. Marks: 70 Answer any Five questions All question carry equal marks --1.a) Define (i) Rigidity modulus (ii) Bulk modulus b)

A rigid bar AB is hinged at C and connected with a steel rod and copper rod at A and B respectively as shown in figure. Both the rods are rigidly fixed with the ceiling at the upper ends. A load of 40kN is applied at B. Find the magnitude of stresses in the steel rod and the copper rod. Area of cross section of steel and copper rods are 400 mm2 and 600 mm2 respectively. Take ES = 2 ×105 N/mm2 and EC = 1.1 × 105 N/mm2. 2.

Sketch the S.F.D and B.M.D for the beam loaded as shown in figure. Indicate the values at salient points. Locate the point of contra flexure if any

(Contd…2)

Code No:220352

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3.

A beam of span ‘L’ m simply supported at ends carries a central load ‘w’. The beam section has an overall depth of 290 mm with horizontal flanges each 150 mm × 20 mm and a vertical web 250 mm ×10 mm. If maximum shear stress is to be 45N/mm2 when the maximum bending stress is 150 N/mm2. Calculate the value of the centrally applied point load ‘w’ and the span ‘L’.

4.

Sketch the shear stress distribution across an I-section consisting of two flanges 200 ×10 mm and a web 10 mm ×180mm. Take F=20 kN.

5.a)

Find the prop reaction and draw the S.F.D. for the beam shown in figure.

b)

A uniform girder of length 8 m is subjected to total of 200 kN uniformly distributed over the entire length. The girder is freely supported at its ends. Calculate the B.M and deflection at the centre.

6.

A cast iron thin cylindrical pipe of internal diameter 200 mm and 15 mm thick is closely wounded by a single layer steel wire of 3 mm diameter under a tension of 50 N/mm2. Find the stresses set up in the pipe when the pipe is empty. Also find the stresses set up in the pipe and steel wire, when water is admitted in the pipe under a pressure of 5N/mm2. Take E for cast iron and steel as 1 × 105 N/mm2 and 2 × 105 N/mm2 respectively. µ=0.3.

7.

A rectangular block of material is subjected to a tensile stress of 100 N/mm 2 on one plane and tensile stress of 50 N/mm2 on a plane at right angle, together with shear stress of 60N/mm2 on the same plane. Find (i) Direction of the principle planes, (ii) The magnitude of the principle stresses and (iii) The magnitude of the greatest shear stress.

8.a)

Derive the expression

b)

T τ Nθ = = . J r  A hollow shaft 250 mm external diameter and 150 mm internal diameter is to be replaced by a solid shaft made of an alloy. Given that the polar modules of both the shafts is same, calculate the diameter of the solid shaft. &&&