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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?
Most Upvoted Answer
A cold rolled steel shaft is designed on the basis of maximum shear st...
Calculation of Maximum Shear Stress

The maximum shear stress theory states that failure occurs in a material when the maximum shear stress at a point exceeds the shear stress at yield point of a material.

τmax = (σ1 - σ2) / 2

where,
τmax = maximum shear stress
σ1 = maximum principal stress
σ2 = minimum principal stress

Given, σ1 = 60 MPa and σ2 = -60 MPa

τmax = (60 - (-60)) / 2 = 60 MPa

Calculation of Factor of Safety

The factor of safety is the ratio of the yield stress of the material to the maximum shear stress induced in the material.

Factor of safety = Yield stress / Maximum shear stress

Given, yield stress = 360 MPa and maximum shear stress = 60 MPa

Factor of safety = 360 / 60 = 6

Therefore, the factor of safety of the design is 6, which means that the design is safe as it can withstand six times the maximum shear stress induced in the material. The correct option is (B).
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Community Answer
A cold rolled steel shaft is designed on the basis of maximum shear st...
(60-(-60)/2=360/(FOS*2)
60=180/FOS
1=3/FOS
FOS=3
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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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