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The stresses induced at a critical point in a machine component made of steel 45C8 are as follows: sx=
100 N/mm2; s y = 40 N/mm2; t xy = 80 N/mm2; Calculate the factor of safety by (i) the maximum normal
stress theory, (ii) the maximum shear stress theory, and (iii) the distortion energy theory?
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The stresses induced at a critical point in a machine component made o...
Factor of Safety Calculations for Steel 45C8
To determine the factor of safety for the given stresses in a steel component, we will use three different failure theories: Maximum Normal Stress Theory, Maximum Shear Stress Theory, and Distortion Energy Theory.
Given Stresses:
- sx = 100 N/mm²
- sy = 40 N/mm²
- txy = 80 N/mm²
1. Maximum Normal Stress Theory
- According to this theory, failure occurs when the maximum normal stress exceeds the material's ultimate tensile strength (UTS).
- For Steel 45C8, the UTS is approximately 600 N/mm².
Factor of Safety (n) = UTS / sx
n = 600 / 100 = 6.0
2. Maximum Shear Stress Theory
- This theory suggests that failure occurs when the maximum shear stress exceeds the material's shear strength.
- The shear strength of Steel 45C8 is typically around 0.5 * UTS, which is 300 N/mm².
Maximum Shear Stress, τmax = (sx - sy) / 2 + txy
τmax = (100 - 40) / 2 + 80 = 60 + 80 = 140 N/mm²
Factor of Safety (n) = Shear Strength / τmax
n = 300 / 140 ≈ 2.14
3. Distortion Energy Theory
- This theory, also known as von Mises criterion, considers the distortion energy in the material.
σ1 = sx, σ2 = sy, σ3 = 0
σ' = sqrt{(σ1² + σ2² + σ3²) - (σ1σ2 + σ2σ3 + σ3σ1)}
σ' = sqrt{(100² + 40² + 0) - (100 * 40 + 0 + 0)}
σ' = sqrt{10000 + 1600 - 4000} = sqrt{6800} ≈ 82.46 N/mm²
Factor of Safety (n) = UTS / σ'
n = 600 / 82.46 ≈ 7.27
Summary of Factor of Safety:
- Maximum Normal Stress Theory: 6.0
- Maximum Shear Stress Theory: 2.14
- Distortion Energy Theory: 7.27
These calculations provide a comprehensive understanding of the safety margins for the steel component under the given stress conditions.
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The stresses induced at a critical point in a machine component made of steel 45C8 are as follows: sx= 100 N/mm2; s y = 40 N/mm2; t xy = 80 N/mm2; Calculate the factor of safety by (i) the maximum normal stress theory, (ii) the maximum shear stress theory, and (iii) the distortion energy theory?
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