If a shaft diameter d is subjected to bending moment M, the bending stress (σ_b) induced in the shaft is given by:

Explanation:

Bending Equation 

\(\frac{{{{\rm{\sigma }}_{\rm{b}}}}}{{\rm{y}}} = \frac{{\rm{M}}}{{\rm{I}}} = \frac{{\rm{E}}}{{\rm{R}}}\)

where

σ_b = Bending Stress, y = distance of fibre on a cross-section from its neutral axis

M = Bending moment, I = area moment of inertia, E = young’s modulus of elasticity of beam material,

R = radius of curvature to the neutral axis, Z = Section modulus

\({\sigma _b} = \frac{{My}}{I} = \frac{M}{Z}\)

\(I = \frac{{\pi \times {d^4}}}{{64}}\) , \(Y = \frac{d}{2}\)

\(Z = \frac{I}{Y}= \frac{{\pi \times {d^3}}}{{32}}\)

\({\sigma _b} = \frac{M}{Z}= \;\frac{M}{{\;\frac{\pi }{{32}} \times {d^3}}}\)

\({\sigma _b} = \frac{{32M}}{{\pi {d^3}}}\)