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Principal stresses at a point in an elastic materia! are 100 MPa tensile 5 and 50 MPa tensile. Whal is the factor of safety against failure based on maximum shear strain energy theory? The elastic limit in simple tension is 173.2 MPa and Poisson’s ratio 0.3.
  • a)
    1.25    
  • b)
    1.78
  • c)
    2    
  • d)
    2.39
Correct answer is option 'C'. Can you explain this answer?
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Principal stresses at a point in an elastic materia! are 100 MPa tensi...

∴ 
Factor of safety,
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Principal stresses at a point in an elastic materia! are 100 MPa tensi...
The factor of safety against failure based on the maximum shear strain energy theory can be determined by comparing the maximum shear stress to the shear stress at the elastic limit in simple tension.

First, we need to calculate the maximum shear stress at the given point in the elastic material. The maximum shear stress can be determined using the formula:

Shear stress = (Principal stress 1 - Principal stress 2) / 2

Given:
Principal stress 1 = 100 MPa tensile
Principal stress 2 = 50 MPa tensile

Shear stress = (100 MPa - 50 MPa) / 2 = 50 MPa

Next, we need to calculate the shear stress at the elastic limit in simple tension. This can be determined using the formula:

Shear stress at elastic limit = Elastic limit in simple tension / (2 * (1 + Poisson's ratio))

Given:
Elastic limit in simple tension = 173.2 MPa
Poisson's ratio = Unknown

We need to know the value of Poisson's ratio in order to proceed with the calculation. Poisson's ratio is a material property and is required to determine the shear stress at the elastic limit.

Once we have the shear stress at the elastic limit, we can calculate the factor of safety against failure based on the maximum shear strain energy theory using the formula:

Factor of safety = Shear stress at elastic limit / Shear stress

However, since we do not have the value of Poisson's ratio, we cannot determine the factor of safety in this case.
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Principal stresses at a point in an elastic materia! are 100 MPa tensile 5 and 50 MPa tensile. Whal is the factor of safety against failure based on maximum shear strain energy theory? The elastic limit in simple tension is 173.2 MPa and Poisson’s ratio 0.3.a)1.25 b)1.78c)2 d)2.39Correct answer is option 'C'. Can you explain this answer?
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