GATE ME 2014 Set 4 — Question 40
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Machine Design → Static & Dynamic Loading → Theories of Failure
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Question
A shaft is subjected to pure torsional moment. The maximum shear stress developed in the shaft is MPa. The yield and ultimate strengths of the shaft material in tension are MPa and MPa, respectively. The factor of safety using maximum distortion energy (von-Mises) theory is _______
Correct answer
1.7 to 1.8
Solution
For a shaft under pure torsion, the state of stress is given by:Given the maximum shear stress MPa, we have:According to the maximum distortion energy (von-Mises) theory, the equivalent stress is calculated as:Substituting the values:The factor of safety (FOS) is defined as the ratio of the yield strength () to the von-Mises equivalent stress:Given MPa:The factor of safety is approximately , which lies within the range .
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