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A shaft is subjected to a bending moment, M and a torque, T simultaneously. The ratio of the maximum bending stress to maximum shear stress developed in a shaft is
- a)M/T
- b)T/M
- c)2M/T
- d)2T/M
Correct answer is option 'C'. Can you explain this answer?
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A shaft is subjected to a bending moment, M and a torque, T simultane...
Ratio of maximum bending stress to maximum shear stress in a shaft
In a shaft subjected to both bending moment (M) and torque (T) simultaneously, the maximum bending stress and maximum shear stress are important factors to consider for design purposes. The ratio of these two stresses can provide insight into the shaft's overall performance and safety margin.
Maximum Bending Stress
- The maximum bending stress in a shaft can be calculated using the formula: σ_b = M*c/I
- Where σ_b is the bending stress, M is the bending moment, c is the distance from the neutral axis to the outer fiber, and I is the moment of inertia of the cross-section.
Maximum Shear Stress
- The maximum shear stress in a shaft can be calculated using the formula: τ = T*r/J
- Where τ is the shear stress, T is the torque, r is the radius of the shaft, and J is the polar moment of inertia of the cross-section.
Ratio Calculation
- The ratio of maximum bending stress to maximum shear stress can be expressed as: σ_b/τ = (M*c/I) / (T*r/J)
- Simplifying the above expression gives: σ_b/τ = (M*c*J) / (T*r*I)
Conclusion
- The ratio of maximum bending stress to maximum shear stress in a shaft subjected to bending moment and torque simultaneously is 2M/T.
- Therefore, the correct answer is option 'C' - 2M/T.
In a shaft subjected to both bending moment (M) and torque (T) simultaneously, the maximum bending stress and maximum shear stress are important factors to consider for design purposes. The ratio of these two stresses can provide insight into the shaft's overall performance and safety margin.
Maximum Bending Stress
- The maximum bending stress in a shaft can be calculated using the formula: σ_b = M*c/I
- Where σ_b is the bending stress, M is the bending moment, c is the distance from the neutral axis to the outer fiber, and I is the moment of inertia of the cross-section.
Maximum Shear Stress
- The maximum shear stress in a shaft can be calculated using the formula: τ = T*r/J
- Where τ is the shear stress, T is the torque, r is the radius of the shaft, and J is the polar moment of inertia of the cross-section.
Ratio Calculation
- The ratio of maximum bending stress to maximum shear stress can be expressed as: σ_b/τ = (M*c/I) / (T*r/J)
- Simplifying the above expression gives: σ_b/τ = (M*c*J) / (T*r*I)
Conclusion
- The ratio of maximum bending stress to maximum shear stress in a shaft subjected to bending moment and torque simultaneously is 2M/T.
- Therefore, the correct answer is option 'C' - 2M/T.
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A shaft is subjected to a bending moment, M and a torque, T simultaneously. The ratio of the maximum bending stress to maximum shear stress developed in a shaft isa)M/Tb)T/Mc)2M/Td)2T/MCorrect answer is option 'C'. Can you explain this answer?
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