# 4.2 Common Load Types for Beams and Frames

How can we deal with these types of uniform or other distributed loads when performing equilibrium calculations? The way to do this is to consider a equivalent total load caused by the distributed load, which acts at the centroid of the distribution. The location of this centroid is different depending on the type of load distribution as shown on the right side of Figure 4.1. For a uniform load, the total load is equal to the load per unit length multiplied by the total length (or $wL$). This is also equal to the area under the distributed load, in this case a rectangle. For the uniform load, the centroid is at the center of the distribution ($L/2$). For the triangular load, the total load is also equal to the area under the distribution in this case $wL/2$ ($\frac{1}{2}bh$) and this acts at the centroid of the triangle, which is located at one-third of the length from the high side. For the trapezoidally distributed load, the case is slightly more complex as shown in Figure 4.1.