Before a section can be checked, the demand has to be known. For a simply supported beam — resting on two supports, free to rotate at both — the peak bending moment has a closed form, and which form depends entirely on how the load is arranged.

One load, dead centre: $M = \dfrac{PL}{4}$, read aloud M equals P L over four. $M$ is the maximum bending moment in kN·m, occurring directly under the load; $P$ is the point load in kN; $L$ is the span in metres — support to support, not the length of the member you ordered.

Load spread evenly along the whole span: $M = \dfrac{w L^{2}}{8}$, read aloud M equals w L squared over eight, with $w$ the uniformly distributed load in kN per metre and $L$ the same span in metres. The peak again sits at midspan. This is the most-used formula in beam design, and it is worth being able to write from memory at three in the morning.

Two habits keep them straight. First, the divisors are not arbitrary and they are not swappable: a concentrated load is harsher than the same total weight spread out, so the point-load case must give the bigger answer, and the smaller divisor (4) belongs to it. Second, watch the square. Spread load grows WITH the span — a longer beam collects more of it — and it also acts over a longer lever, so $L$ appears twice. A point load collects nothing extra from a longer span, so its $L$ appears once.

Run the units as a check. kN/m times m² is kN·m; kN times m is kN·m. Both land where a moment lives, and neither result is a joule — a newton-metre of moment and a joule of energy share their algebra and never their meaning.