Solid circular shaft: torque–diameter relation at allowable shear stress For a solid circular shaft of diameter D, limited by maximum allowable shear stress τ, state the formula for the maximum torque transmitted.
Mechanical Engineering
Strength of Materials
Difficulty: Easy
Choose an option
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A(π/32)·τ·D³
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B(π/16)·τ·D³
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C(π/12)·τ·D³
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D(π/8)·τ·D³
Answer
Correct Answer: (π/16)·τ·D³
Explanation
Concept/FormulaFor a solid circular shaft: T = (τ/J)·(J·R) = τ·(J/R).Polar moment J = (π/32)·D⁴, outer radius R = D/2 ⇒ J/R = (π/16)·D³.Thus, T = (π/16)·τ·D³.
Final Answer(π/16)·τ·D³.