Distributed Loads: Problem Solving

Consider a tapered beam OB fixed at one end and subjected to a distributed load.

Determine the equivalent resultant force of the varying load and locate its position on the beam.

First, divide the distributed load into two triangular regions.

Next, the magnitude of the equivalent resultant load of the left and right triangular region is equal to the area of each triangle.

Each resultant load acts at centroids, located at one-third of the base length from the vertical side AD of the triangle.

The equivalent resultant load can be determined by adding the individual resultant load of each triangular region.

The moment about point O can be determined by adding the individual moment acting due to each resultant load.

Recall the moment principle, which states that the moment of the equivalent resultant load about point O equals the product of the equivalent resultant load and the distance from point O.

By substituting the values in the equation, the location of the equivalent resultant load can be determined.