Distributed Load Diagram

Common Distributed Loads

To find reactions, a distributed force can be replaced with an equivalent point load.

For a general distributed load f(x) as shown, the equivalent point load F_r is found by integrating the distributed load over its length.

For the point load, F_T, to be equivalent, the moment generated about any point must also be equivalent. Thus,

This gives the distance x_r to the equivalent point load as,

Note that x_r is the distance to the centroid of the distributed load.