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Distributed loads appear in a great variety of problems, the most common being loadings on beams. This video shows how to replace the three most common distributed loads with a single force at a single location. These loadings include rectangular, triangular, and trapezoidal. Note that a trapezoidal loading can be treated as a combination of a rectangular and triangular load making it unnecessary to remember or find the equation for a trapezoid.
I also show how a loading that is a function of the distance from the left end of the beam can be replaced by a single force at a single location. However, determining the magnitude of this loading and its location involves integration.
Remember that once you have solved for the reactions on a beam with distributed loadings replaced by single forces at single locations, you must put back the distributed loads to determine any other quantity, such as the shear force or bending moment in the beam, or calculating the deflection at some point.
I hope this presentation has helped you understand how to deal with the classic fundamental distributed loads. -Tom
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