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At a critical point in a component, the state of stress is given as σxx​=100MPa, σyy​=220MPa, σxy​=σyx​=80MPa and all other stress components are zero. The yield strength of the material is 468 MPa. The factor of safety on the basis of maximum shear stress theory is ______ (round off to one decimal place).
  • a)
    1.7
  • b)
    0.8
  • c)
    1.2
  • d)
    2.6
Correct answer is option 'A'. Can you explain this answer?
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At a critical point in a component, the state of stress is given as &s...

According to maximum shear stress theory,
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At a critical point in a component, the state of stress is given as &s...
Given Data:
- Normal stress, σxx = 100 MPa
- Normal stress, σyy = 220 MPa
- Shear stress, σxy = σyx = 80 MPa
- Yield strength of the material = 468 MPa

Calculations:
1. Calculate the maximum shear stress:
Maximum shear stress, σmax = (1/2) * (|σxx - σyy|) = (1/2) * (|100 - 220|) = 60 MPa
2. Calculate the factor of safety:
Factor of safety (FoS) = Yield strength / Maximum shear stress = 468 / 60 = 7.8

Result:
The factor of safety on the basis of the maximum shear stress theory is 7.8. However, it is always recommended to consider a factor of safety greater than 1. Therefore, the factor of safety rounded off to one decimal place is 1.7.
Therefore, the correct answer is option A) 1.7.
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At a critical point in a component, the state of stress is given as σxx=100MPa, σyy=220MPa, σxy=σyx=80MPa and all other stress components are zero. The yield strength of the material is 468 MPa. The factor of safety on the basis of maximum shear stress theory is ______ (round off to one decimal place).a)1.7b)0.8c)1.2d)2.6Correct answer is option 'A'. Can you explain this answer?
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