= Solution
The <bending moment> $B(x)$ is the internal <torque> transmitted across a cut through an <elastic beam>, about the transverse bending axis. It balances the moments of the external <forces> on the isolated portion on one side of the cut. Its sign depends on the chosen convention, and its units are $\mathrm{N\,m}$.
The relevant “moment of area” is the <second moment of area> of the cross-section about its <neutral axis>:
$$
\boxed{I=\int_A z^2\,dA,}
$$
where $z$ is perpendicular distance from that axis within the section. It has units $\mathrm{m^4}$ and is a geometrical quantity, unlike a mass <moment of inertia>. For a homogeneous beam under pure bending, the <neutral axis> passes through the section's <centroid>, and its longitudinal <strain> is zero.
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