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A cold rolled steel shaft is designed on the basis of maximum shear stress theory. The principal stresses induced at its critical section are 60 MPa and -60 MPa respectively. If the yield stress for the shaft material is 360 MPa, the factor of safety of the design is:
  • a)
    2
  • b)
    3
  • c)
    4
  • d)
    6
Correct answer is option 'B'. Can you explain this answer?
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A cold rolled steel shaft is designed on the basis of maximum shear st...

According to maximum shear stress theory
Yield stress in shear


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A cold rolled steel shaft is designed on the basis of maximum shear st...
Understanding Principal Stresses
The principal stresses at the critical section of the cold rolled steel shaft are given as:
- σ1 (maximum principal stress) = 60 MPa
- σ2 (minimum principal stress) = -60 MPa
Calculating Shear Stress using Mohr's Circle
To determine the maximum shear stress, we can use the formula:
- τ_max = (σ1 - σ2) / 2
Substituting the values:
- τ_max = (60 MPa - (-60 MPa)) / 2
- τ_max = (60 MPa + 60 MPa) / 2
- τ_max = 120 MPa / 2
- τ_max = 60 MPa
Yield Stress of the Material
The yield stress of the steel shaft material is provided as:
- Yield Stress (σ_y) = 360 MPa
Factor of Safety Calculation
The factor of safety (n) is calculated using the maximum shear stress theory:
- n = σ_y / τ_max
- n = 360 MPa / 60 MPa
- n = 6
This means the factor of safety for the design is 6, indicating that the shaft can safely withstand six times the maximum shear stress induced.
Conclusion
Based on the calculations:
- The factor of safety of the design is 6.
However, the correct answer provided in the question is option 'B'. It seems there may be a discrepancy in the interpretation of the problem or details provided. Nonetheless, the calculations affirm that the factor of safety is indeed 6 based on the given data.
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A cold rolled steel shaft is designed on the basis of maximum shear stress theory. The principal stresses induced at its critical section are 60 MPa and -60 MPa respectively. If the yield stress for the shaft material is 360 MPa, the factor of safety of the design is:a)2b)3c)4d)6Correct answer is option 'B'. Can you explain this answer?
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