Example 1: Replace the force system shown by an equivalent resultant force, and specify its point of application along the beam.

Solution: With all the forces in the vertical direction, we know the resultant force will also be vertical. However, we may not know right away if it is pointing up or down. Also we do not know its magnitude. We assume the resultant force is acting in the upward direction and find its magnitude as

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Hence, the resultant force has a magnitude of 1,250 N and is directed vertically down. The negative sign indicates the direction of the force is opposite to that assumed.

The location of the resultant force is found through the equivalency of moments. That is

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Thus, the resultant force acting at 0.64 m to the right of point A has the same rigid-body effect as the four forces acting together.