Question

What is the unit of the Section modulus?
1. mm⁴
2. mm
3. mm²
4. mm³

Answer 1

Correct Answer - Option 4 : mm³

Explanation:

Sectional Modulus (Z):

It is the ratio of Moment of Inertia (I) of the beam cross-section about the neutral axis to the distance (ymax) of extreme fiber from the neutral axis. 

For a circular section, the section modulus:

\(Z = \frac{I}{y_{max}}\)

where \(I=\frac{\pi}{64} d^4\) = Moment of Inertia. 

y = distance from the centroid to top or bottom edge i.e. y = \(\frac{d}{2}\)

\(Z_{cirular\;section}=\frac{I}{y_{max}}\)

\(Z_{cirular\;section}=\frac{\frac{\pi{d^4}}{64}}{\frac{d}{2}}\)

\(Z_{cirular\;section}=\frac{\pi{d^3}}{32}\)

It can be seen that Z ∝ d³

∴ the unit of the section modulus is mm3.