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A solid circular shaft is subjected to pure torsion. The ratio of maximum shear stress to maximum normal stress at any point would be
  • a)
    1 : 1
  • b)
    1 : 2
  • c)
    2 : 1
  • d)
    2 : 3
Correct answer is option 'A'. Can you explain this answer?
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A solid circular shaft is subjected to pure torsion. The ratio of maxi...
Answer is b) 1:2
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Explanation:
When a solid circular shaft is subjected to pure torsion, the stress distribution at any point on the shaft can be represented by a stress element as shown in the figure below.

The stress element is subjected to a shear stress τ and a normal stress σ.

The maximum shear stress occurs on the surface of the shaft and is given by
τmax = T/(2πr)
where T is the applied torque and r is the radius of the shaft.

The maximum normal stress occurs at the center of the shaft and is given by
σmax = T/(2πr^2)

Ratio of maximum shear stress to maximum normal stress:
τmax/σmax = (T/(2πr))/(T/(2πr^2))
= r
Therefore, the ratio of maximum shear stress to maximum normal stress at any point on the shaft is equal to the radius of the shaft, which is a constant for a given shaft. Hence, the ratio is independent of the applied torque and the location on the shaft.

Therefore, the correct answer is option A, 1:1.
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A solid circular shaft is subjected to pure torsion. The ratio of maximum shear stress to maximum normal stress at any point would bea)1 : 1b)1 : 2c)2 : 1d)2 : 3Correct answer is option 'A'. Can you explain this answer?
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