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PY 8: GATE ME 2017 Official Paper: Shift 2

CT 1: Ratio and Proportion

2672

10 Questions
16 Marks
30 Mins

**Concept:**

**\(\frac{1}{{FOS}} = \frac{{{\sigma _{mean}}}}{{{\sigma _{yield}}}} + \frac{{{\sigma _v}}}{{{\sigma _{endurance}}}}\)**

**Calculation:**

As the machine component made of a ductile material and subjected to completely reversed loading, hence all three fatigue loading theories will give same results

\({\sigma _{mean}} = 0;{\sigma _{variable}} = \frac{50-{\left( { - 50} \right)}}{2} = 50MPa\)

\(\frac{1}{{FOS}} = \frac{{{\sigma _{mean}}}}{{{\sigma _{yield}}}} + \frac{{{\sigma _v}}}{{{\sigma _{endurance}}}}\)

\(\frac{1}{{FOS}} = \frac{0}{{300}} + \frac{{50}}{{100}}\)

FOS = 2