Distributed loads

The gravitational force acting on a body is distributed over the whole volume of the body. However, if the body is rigid, we can replace this system of distributed gravitational forces by a single resultant gravitational force (weight) acting through the centre of gravity of the body.

It is helpful sometimes to represent a system of distributed parallel forces by a so-called load diagram. Consider a horizontal beam AB with sand piled on it to a constant depth d, as illustrated in Figure 4.1. We can then represent the load due to the sand and the weight of the beam by a load diagram with constant intensity q, as shown in Figure 4.2. If the total weight of the sand over the beam is S, the weight of the beam is W and the length of the beam is a, then qa = S + W. Measuring distance in metres and force in newtons, the intensity q has units N/m.

If the sand is heaped with a varying depth d, as shown in Figure 4.3a, then the corresponding load diagram, shown in Figure 4.3b, reduces at the ends A and B to an intensity equal to the weight per unit length of the beam. As in the case of uniform loading, the magnitude of the resultant or total load Q = S + W must equal the area of the load diagram ABDC.