## Lecture 5

Example Problem

Moments on a Beam

**Given:** a beam with the geometry and loading indicated (C = 3200 pounds and D = 1500 pounds)

**Determine:** the moment of the loads on this beam using the reaction at B as the center of moments**Solution:** Moments can be used to determine the reactions at the ends of simple beams. Either point A or point B could be chosen as the center of moments. Since the exercise indicated that B is the center of moments, the first step is to determine all of the loads that will tend to cause a counter-clockwise rotation about B. These loads are placed on the left side of an equation and all of the loads which will tend to cause a clockwise rotation will be placed on the right side. The 1500 pound and the 3200 pound loads cause counter-clockwise rotations. The reaction at A is the only load that causes a clockwise rotation to the beam. Notice that the reaction at B does not even come into consideration. Why is this?

(1500 pounds)(2 feet ) + (3200 pounds)(8 feet) = A x 10 feet

3000 pound-feet + 25600 pound-feet = A x 10 feet

This yields a reaction of 2860 pounds at point A.

Try this if point A had been chosen as the center of moments. What is the reaction at B?

Copyright © 1995, 1996 by Chris Luebkeman and Donald Peting

Copyright © 1997 by Chris H. Luebkeman