8/14/2019 Mechanics of Solids March06 Nr210302

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Code No: NR210302 NR

II B.Tech I Semester Supplementary Examinations, March 2006MECHANICS OF SOLIDS

( Common to Mechanical Engineering, Mechatronics, Metallurgy & MaterialTechnology, Production Engineering and Aeronautical Engineering)

Time: 3 hours Max Marks: 80

Answer any FIVE QuestionsAll Questions carry equal marks

1. (a) Define and explain the terms: [6]

i. Modulus of Elasticity

ii. Modulus of Rigidity

iii. Poissons ratio

iv. Bulk Modulus.

(b) Two vertical rods one of steel and the other of copper are each rigidly fixedat the top and 600 mm apart. The diameter and length of each rod are 30mm and 375 mm respectively. A cross bar fixed to the rods at the lower endscarries a load of 5 kN such that the cross bar remains horizontal even afterloading. Find the stress in each rod and the position of the load on the bar.ES = 200 Gpa and EC = 100 Gpa. [10]

2. A steel rod 28 mm diameter is fixed concentrically in a brass tube of 42 mm outerdiameter and 30 mm inner diameter. Both the rod and tube are 450 mm long. Thecompound rod is held between two stops which are exactly 450 mm apart and thetemperature of the bar is raised by 700C. [16]

(a) Find the stresses in the rod and tube if the distance between the stops isincreased by 0.30 mm.

(b) Find the increase in the distance between the stops if the force exerted betweenthem is 90 kN

Take ES = 200kN/mm2 ; S = 11.2 10

6per0C

Eb = 90kN/mm2 ; b = 2.1 10

5per0C

3. (a) Classify the beams based on support conditions with the help of neat sketches.

[5]

(b) What are the different types of loads. Give neat sketches to represent varioustypes of loads. [3]

(c) A simply supported beam of span l is loaded with a triangular load with zerointensity at one end to w /unit length at the other end. Draw the shear forediagram and bending moment diagram showing the salient values. [8]

4. (a) State the assumptions involved in the theory of simple bending. [6]

(b) Derive the Bending equation from fist principle. [10]

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8/14/2019 Mechanics of Solids March06 Nr210302

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Code No: NR210302 NR

5. (a) What is moment area method? Explain the two Mohrs theorems, as applica-ble to the slope and deflection of a beam. [6]

(b) A cantilever of uniform cross-section of length l carries two point loads, W atthe free end and 2W at a distance a from the free end. Find the maximumdeflection due to this loading. [10]

6. (a) Explain horizontal and hoop stresses as applied to thin cylinders. [8]

(b) What thickness of metal would be required for cast-iron water pipe 90 cm indiameter under a head of 100m? Assume the permissible tensile stress for castiron as 20 MN/ m2. [8]

7. Derive an expression for the shear stress produced in a circular shaft which issubjected to torsion. What are the assumptions made in the above derivation ?

[16]

8. An open coiled helical spring is made out of 10 mm diameter steel rod, the coilshaving 10 complete turns, and a mean diameter 80 mm, the angle of helix 150.Calculate the deflection under an axial load of 250 N and the maximum intensitiesof direct and shear stresses induced in the section of the wire. If the axial load of250 N is replaced by an axial torque of 6 N.m, calculate the angle of rotation aboutaxis of the coil and actual deflection. N=0.85105N/mm2 and E=2.5105N/mm2.

[16]

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