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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.

Q: 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.

Concept/Formula For 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.

Difficulty: Easy

(π/32)·τ·D³
(π/16)·τ·D³
(π/12)·τ·D³
(π/8)·τ·D³

Correct Answer: (π/16)·τ·D³

Explanation:

Concept/Formula
For 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.

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