The [[Stress|stress]] associated with bending [[Moment|moment]] can be written in terms of the beam section modulus, $S$. The section modulus is the ratio of the cross sectional area second moment to the maximum distance from the neutral axis. $S=\dfrac{I}{y_{max}}$ With this definition of section modulus, the maximum bending stress can be written: $\sigma_{max}=\dfrac{y_{max}}{I}∣M_{max}∣=\dfrac{∣M_{max}∣}{S}$ Considering that the maximum stress must be below the allowable stress, $\sigma_{max}\le \sigma_{all}$, we can determine an acceptable minimum section modulus for the beam. $S_{min}=\dfrac{∣M_{max}∣}{\sigma_{all}}$ All that remains to finalize the design of a beam is to account for stress caused by shear force.