Question

The first moment of area about the axis of bending for a beam cross-section is
1. Moment of inertia
2. Section modulus
3. Shape factor
4. Polar moment of inertia

Answer 1

Correct Answer - Option 2 : Section modulus

Section modulus:

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.

To calculate Z, the distance (y) to the extreme fibres from the centroid (or neutral axis) must be found as that is where the maximum stress could cause failure.

\(\begin{array}{*{20}{l}} {\frac{{\rm{M}}}{{\rm{I}}}{\rm{ = }}\frac{{\rm{\sigma }}}{{\rm{y}}}{\rm{ = }}\frac{{\rm{E}}}{{\rm{R}}}}\\ {{\rm{Z = }}\frac{{\rm{I}}}{{{{\rm{Y}}_{{\rm{max}}}}}}} \end{array}\)

where,

I = Second moment of inertia

Y_max = Distance of centroidal axis from the bottom

\({\rm{Z}} = \frac{{\rm{I}}}{{{{\rm{Y}}_{{\rm{max}}}}}} = \frac{{{\rm{AY}}_{{\rm{max}}}^2}}{{{{\rm{Y}}_{{\rm{max}}}}}}\)

Z = AY_max = First moment of inertia

Hence the first moment of area about the axis of bending for a beam cross-section is section modulus