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 loading. Note for more complicated distributed loads, integration may be required to get the resultant force and resultant moment. Click here to view the “equipollent” force system acting on the beam. |
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