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Minimum diameter of a shaft when bending moment is applied to the shaft

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When the allowable bending stress of a shaft with circular cross-section is ¥òa (MPa) and the bending moment acting on the shaft is M (Nm), find the minimum diameter Dmin (m) of the shaft.

¥òa*10^6 = M*y/I = 32*M/(¥ð*Dmin^3)

Dmin = (32*M/(¥ð*¥òa*10^6))^(1/3)

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Dmin = (32*M/(¥ð*¥òa*10^6))^(1/3)
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