According to the maximum normal stress theory, the diameter of circular shaft subjected to bending moment M and torque T is

(where σy is the yield stress in the uniaxial tensile test and N is the factor of safety)

1
\(\rm \left[\frac{N}{\pi\sigma_y}\left(16M+16\sqrt{M^2+T^2}\right)\right]^{\frac{1}{2}}\)
2
\(\rm \left[\frac{1}{\pi N\sigma_y}\left(16M+16\sqrt{M^2+T^2}\right)\right]^{\frac{1}{2}}\)
3
\(\rm \left[\frac{1}{\pi N\sigma_y}\left(16M+16\sqrt{M^2+T^2}\right)\right]^{\frac{1}{3}}\)
4
\(\rm \left[\frac{N}{\pi\sigma_y}\left(16M+16\sqrt{M^2+T^2}\right)\right]^{\frac{1}{3}}\)

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