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The principal stresses at a point in a critical section of a machine component are σ1= 60MPa, σ2= 5MPa and σ3  = -40 MPa. For the material of the component, the tensile yield strength is σy = 200 MPa. According to the maximum shear stress theory, the factor of safety is
  • a)
    1.67
  • b)
    2.00
  • c)
    3.60
  • d)
    4.00 
Correct answer is option 'B'. Can you explain this answer?
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According to the maximum shear stress theory (also known as Tresca's theory), failure in a material occurs when the maximum shear stress exceeds the shear yield strength of the material. The factor of safety is defined as the ratio of the yield strength to the maximum shear stress.

Given:
Principal stress 1 (σ1) = 60 MPa
Principal stress 2 (σ2) = 5 MPa
Principal stress 3 (σ3) = -40 MPa
Tensile yield strength (y) = 200 MPa

To determine the maximum shear stress, we can use the following formula:

τmax = (σ1 - σ3) / 2

Substituting the given values:

τmax = (60 MPa - (-40 MPa)) / 2 = 100 MPa

Now, we can calculate the factor of safety (FS) using the formula:

FS = y / τmax

Substituting the given values:

FS = 200 MPa / 100 MPa = 2

Therefore, the factor of safety is 2.

Explanation:
The maximum shear stress theory states that failure occurs when the maximum shear stress reaches the shear yield strength of the material. In this case, the maximum shear stress is calculated as 100 MPa, and the tensile yield strength of the material is 200 MPa. The factor of safety is calculated by dividing the yield strength by the maximum shear stress, which gives a value of 2.

This means that the component has a factor of safety of 2, indicating that it can withstand twice the maximum shear stress before failure. A higher factor of safety indicates a greater level of safety and reliability in the component.

Therefore, the correct answer is option B) 2.00.
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The principal stresses at a point in a critical section of a machine component are σ1= 60MPa, σ2= 5MPa and σ3 = -40 MPa. For the material of the component, the tensile yield strength is σy= 200 MPa. According to the maximum shear stress theory, the factor of safety isa)1.67b)2.00c)3.60d)4.00Correct answer is option 'B'. Can you explain this answer?
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