Reaction of weight on a beam

Question

A horizontal beam of negligible weight is 16.0 ft long and is supported by columns at either end. A vertical load of 13,000 lbs is applied to the beam at a distance x from the left end. Find x so that the reaction a the left column is 9600 lbs.

Answer 1

The upward reactions at both columns must add up to the downward force of 13,000 lb. So the reaction at the right column = 13,000 - 9,600 = 3,400 lb.

 

Since the beam is not moving, clockwise torques must balance counterclockwise torques. Consider torques about the left support

(the 9,600 does not rotate about left support, and can be omitted):

 

13,000 x = 3,400*16  

x = 4.18 ft