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Equipollent Force Systems (example continued)

The total distributed load acting on the beam combines a uniformly distributed load

of 10 kips/ft along with a linearly increasing distributed load with a maximum

value of 30 kips/ft. The equipollent load must have the same resultant force and the

same resultant moment about any specified point along the beam.

So the uniformly distributed load of 10 kips/ft can be replaced with (is equivalent to)

a total concentrated load of 12 x 10 or 120 kips acting at the center of the beam

(6 ft to the right of end A. Likewise the total concentrated load due to the linearly

varying distribution is 15 x 12 or 180 kips acting 8 ft to the right of end A

(centroid of a triangle). Note the location of the concentrated loads must provide the

same moment about a specified point (in this case, end A) as the original distributed

Note for more complicated distributed loads, integration may be required to get the

resultant force and resultant moment.