[[Distributed Load|Distributed loads]] can be expressed as a singular equivalent point [[Force|load]] applied at the [[Center of Mass|center of mass]] for the distributed load. In 2D the center of mass (x‾x, y‾y) is defined by:
$\bar{x}=\dfrac{1}{A}\int xdA$
$\bar{y}=\dfrac{1}{A}\int ydA$
The magnitude of the equivalent point load for a given force distribution in the $x$ direction, $w(x)$ (N/m), is simply the sum of all infinitesimal forces.
$F=\int w(x)dx$