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The maximum shear stress in a shaft, of diameter ‘d’ subjected to torsion ‘T,’ is given by:
- a)16T/πd3
- b)up>(B) 64T/πd3
- c)up>(C) 8T/πd3
- d)up>(D) 32T/πd3
Correct answer is option 'A'. Can you explain this answer?
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The maximum shear stress in a shaft, of diameter ‘d’ subjected to tor...
Torsion Equation:
Where T is torque applied on the shaft in N−m
is the polar moment of inertia m4T is shear stress in MPa, r is the radius of the shaft in m, G shear modulus or modulus of rigidity in MPa
θ is the angle of twist in radian, and 1 is the length of the shaft in m.Tmaxoccurs at rmax
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The maximum shear stress in a shaft, of diameter ‘d’ subjected to tor...
Torsion Equation:
Where T is torque applied on the shaft in N−m
is the polar moment of inertia m4T is shear stress in MPa, r is the radius of the shaft in m, G shear modulus or modulus of rigidity in MPa
θ is the angle of twist in radian, and 1 is the length of the shaft in m.Tmaxoccurs at rmax
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The maximum shear stress in a shaft, of diameter ‘d’ subjected to tor...
Maximum Shear Stress in a Shaft
The maximum shear stress in a shaft, of diameter ‘d’ subjected to torsion ‘T,’ is given by:
Formula: τmax = 16T/πd3
Where,
τmax = Maximum shear stress
T = Torsion
d = Diameter of the shaft
Explanation:
The maximum shear stress in a shaft can be calculated by using the formula τmax = Tr/J, where T is the applied torque, r is the radius of the shaft, and J is the polar moment of inertia of the shaft. For a solid circular shaft, J = πd4/32.
Substituting the value of J in the formula, we get:
τmax = Tr/(πd4/32)
τmax = 32T/πd4
Multiplying and dividing by d, we get:
τmax = 32T/(πd3) x d/d
τmax = 32Td/(πd4)
τmax = 16T/πd3 (as d cancels out)
Therefore, the maximum shear stress in a shaft, of diameter ‘d’ subjected to torsion ‘T,’ is given by 16T/πd3. Hence, option A is the correct answer.
The maximum shear stress in a shaft, of diameter ‘d’ subjected to torsion ‘T,’ is given by:
Formula: τmax = 16T/πd3
Where,
τmax = Maximum shear stress
T = Torsion
d = Diameter of the shaft
Explanation:
The maximum shear stress in a shaft can be calculated by using the formula τmax = Tr/J, where T is the applied torque, r is the radius of the shaft, and J is the polar moment of inertia of the shaft. For a solid circular shaft, J = πd4/32.
Substituting the value of J in the formula, we get:
τmax = Tr/(πd4/32)
τmax = 32T/πd4
Multiplying and dividing by d, we get:
τmax = 32T/(πd3) x d/d
τmax = 32Td/(πd4)
τmax = 16T/πd3 (as d cancels out)
Therefore, the maximum shear stress in a shaft, of diameter ‘d’ subjected to torsion ‘T,’ is given by 16T/πd3. Hence, option A is the correct answer.
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The maximum shear stress in a shaft, of diameter ‘d’ subjected to torsion ‘T,’ is given by:a)16T/πd3b)up>(B) 64T/πd3c)up>(C) 8T/πd3d)up>(D) 32T/πd3Correct answer is option 'A'. Can you explain this answer?
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