The section modulus of a rectangle with breadth b and depth d will be:

Concept:

Section Modulus(z):

• Section modulus is defined as the ratio of moment of inertia of a beam about its C.G to the maximum distance of extreme section of the beam (Ymax).
• The section modulus (Z) of the cross-sectional shape is significant in designing beams.
• It is a direct measure of the strength of the beam. A beam that has a larger section modulus than another will be stronger and capable of supporting greater loads.

• The unit of the Section modulus is mm3

Section modulus, \(Z = \frac{I}{y_{max}}\)

For rectangular section:

Moment of inertia and the maximum distance of neutral axis from top fiber for a rectangular beam is given by,

I = \(\frac{bd^3}{12}\) and ymax = d/2

Hence, Z = \(\frac{\frac{bd^3}{12}}{\frac{d}{2}}\) = \(\frac{bd^2}{6}\)