The document describes the forces and torques acting on a uniform beam supported by three men. It states that the upward force from each man is F, so the total upward force at the crosspiece is 2F. Equating the beam's weight W to the total upward force gives W=3F. Computing torques about the front end, using the beam's center of gravity being L/2 from the front, yields an equation that solves for the distance x from the crosspiece to the front end as x=3L/4. Therefore, the distance from the crosspiece to the rear end is L/4.

1. 63. Where the crosspiece comes into contact with the beam, there is an upward force of 2F (where F is the
upward force exerted by each man). By equilibrium of vertical forces, W = 3F where W is the weight
of the beam. If the beam is uniform, its center of gravity is a distance L/2 from the man in front, so
that computing torques about the front end leads to
L W
W = 2F x = 2 x
2 3
which yields x = 3L/4 for the distance from the crosspiece to the front end. It is therefore a distance
L/4 from the rear end (the “free” end).