From the previous section, we see that the maximum moment occurs at a point of zero shears. For beams loaded with concentrated loads, the point of zero shears usually occurs under a concentrated load and so the maximum moment.

Beams and girders such as in a bridge or an overhead crane are subject to moving concentrated loads, which are at fixed distance with each other. The problem here is to determine the moment under each load when each load is in a position to cause a maximum moment. The largest value of these moments governs the design of the beam.

For a single moving load, the maximum moment occurs when the load is at the midspan and the maximum shear occurs when the load is very near the support (usually assumed to lie over the support).

$M_{max} = \dfrac{PL}{4}\,\,\text{and}\,\,V_{max} = P$

For two moving loads, the maximum shear occurs at the reaction when the larger load is over that support. The maximum moment is given by

$M_{max} = \dfrac{(PL - P_sd)^2}{4PL}$

where Ps is the smaller load, Pb is the bigger load, and P is the total load (P = Ps + Pb).