Circular Section:

Solid Circular Section

Assume the diameter of the solid circular section be d.

Moment of inertia about the neutral axis, I = πd ⁴ / 64

Distance of outermost layer from the neutral axis, y_max  = d/ 2

                       Beam Section                           Bending Stress Distribution

 Figure

Section modulus, Z = I / y_max

=          (πd ⁴/64)×(2/d)

=             πd ³ / 32

Consider σ be the maximum bending stress at the outermost layer.

∴  Moment of resistance, M = σ × Z

= σ(πd ³ /32)

The bending stress distribution is illustrated in Figure.