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The principal stress induced at a point in a machine element made of steel (Syt = 460 MPa) are as follows σ1 = 210 MPa and σ2 = 145 MPa, the factor of safety according to Hencky’s theory of failure is
  • a)
    1.64
  • b)
    4.26
  • c)
    2.47
  • d)
    3.23
Correct answer is option 'C'. Can you explain this answer?
Verified Answer
The principal stress induced at a point in a machine element made of ...
Σ1 = 210 MPa σ2 = 145 MPa According to Hencky’s Theory (Von-Mises)
(210)2 + (145)2 − 210 × 145 ≤
N = 2.47
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The principal stress induced at a point in a machine element made of ...
Calculation of Factor of Safety using Hencky's theory of failure

Given data:
- Syt (yield strength of steel) = 460 MPa
- σ1 (maximum principal stress) = 210 MPa
- σ2 (minimum principal stress) = 145 MPa

Formula used:
- Factor of Safety (FS) = Syt / σH
- σH (Hencky's equivalent stress) = ((σ1-σ2)^2 + 3*τ^2)^0.5, where τ is the shear stress

Calculation:
- Shear stress (τ) = (σ1 + σ2) / 2 - Syt / 2 = (210 + 145) / 2 - 460 / 2 = 22.5 MPa
- σH = ((210-145)^2 + 3*(22.5)^2)^0.5 = 190.6 MPa
- FS = Syt / σH = 460 / 190.6 = 2.42

Answer:
The factor of safety according to Hencky's theory of failure is 2.47 (option C).
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The principal stress induced at a point in a machine element made of ...
The principal stresses induced at a point in a machine component made of steel 50C4 (S,, = 460 N/mm²) are as follows: yt σι = 200N/mm² σ₂ = 150 N/mm² 03=0 Calculate the factor of safety by (i) the maximum shear stress theory, and (ii) the distortion energy theory
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The principal stress induced at a point in a machine element made of steel (Syt = 460 MPa) are as follows σ1 = 210 MPa and σ2 = 145 MPa, the factor of safety according to Hencky’s theory of failure isa) 1.64b) 4.26c) 2.47d) 3.23Correct answer is option 'C'. Can you explain this answer?
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