Section Modulus:

Assume M is the moment of resistance of a beam section & I be the moment of inertia of the beam section regarding the neutral axis.

The bending stress, σ at any layer in the beam section, distance y from the neutral axis is given by the expression σ = (M / I )× y layer. . The maximum bending stress takes place at the outermost

Let y_max is the distance of outermost layer from the neutral axis & the maximum bending stress at that layer be σ_max.

Therefore,        σ_max   = (M/L )× y_max

∴          M = (I / y_max) σ_max

= Z × σ_max

Where Z is known as the section modulus. Thus the section modulus is the ratio of the moment of inertia of the beam section regarding the neutral axis to the distance of the outermost layer of the beam from the neutral axis.

If σ_max is equivalent to the permissible bending stress, then M represents the greatest moment of resistance of the beam section.