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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 stresses induced at a point in a machine component made ...
Introduction
To determine the factor of safety for the steel 50C4 component under the given principal stresses, we will apply two theories: maximum shear stress theory and distortion energy theory.

Given Data
- Ultimate tensile strength, σu = 460 N/mm²
- Principal stresses:
- σ1 = 200 N/mm²
- σ2 = 150 N/mm²
- σ3 = 0 N/mm²

1. Maximum Shear Stress Theory
- **Maximum shear stress (τmax):**
- τmax = (σ1 - σ3) / 2 = (200 - 0) / 2 = 100 N/mm²
- **Allowable shear stress (τallowable):**
- τallowable = σu / 2 = 460 / 2 = 230 N/mm²
- **Factor of Safety (n1):**
- n1 = τallowable / τmax = 230 / 100 = 2.3

2. Distortion Energy Theory
- **Equivalent stress (σeq):**
- σeq = √(σ12 + σ22 + σ32 - σ1σ2 - σ2σ3 - σ3σ1)
- σeq = √(200² + 150² + 0² - 200×150 - 0 - 0) = √(40000 + 22500 - 30000) = √(32500) ≈ 180.28 N/mm²
- **Factor of Safety (n2):**
- n2 = σu / σeq = 460 / 180.28 ≈ 2.55

Conclusion
- **Factor of Safety using Maximum Shear Stress Theory:** n1 = 2.3
- **Factor of Safety using Distortion Energy Theory:** n2 = 2.55
These calculations provide insight into the safety margins of the machine component under the applied stresses.
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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 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? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about 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? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for 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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