For determining the greatest bending moment produced by a rolling load consisting of two concentrated loads at a fixed distance from one another passing over a span, the usual method involves somewhat intricate algebraic discussion. Even for two concentrated loads the discussion is complicated, and for three it would be still more so.

The method here explained, which applies directly to the case when the whole of the rolling load is on the span, uses the shearing force curve only, and gives a very simple geometrical construction for finding the position and magnitude of the greatest B.M.

We will begin by stating the construction, and then proceed to give a geometrical proof.