The beam is in equilibrium, the sum of the
forces and the sum of the torques acting on it both vanish. As we see in the figure,
the beam makes an angle of 60 with the vertical and the wire makes an angle of
30 with the vertical.

We calculate the torques around the hinge. Their
sum is:

T L sin 30 - W (L/2) sin 60 = 0

Here W is the force of gravity acting at the
center of the beam, and T is the tension force of the wire. We solve for the
tension to get:

T = W sin 60 / (2 sin 30) = (222 N) sin 60 / (2 sin 30) = 192.3 N .