Let , , and be the horizontal reactions at the three joints, and let , , and be the corresponding vertical reactions, as shown in Fig. 94. In drawing this diagram, we have made use of the fact that the rods exert equal and opposite reactions on one another, in accordance with Newton's third law. Let be the tension in the cable.

Setting the horizontal and vertical forces acting on rod to zero, we obtain

(491) | |||

(492) |

respectively. Setting the horizontal and vertical forces acting on rod to zero, we obtain

(493) | |||

(494) |

respectively. Finally, setting the horizontal and vertical forces acting on rod to zero, we obtain

(495) | |||

(496) |

respectively. Incidentally, it is clear, from symmetry, that and . Thus, the above equations can be solved to give

(497) | |||

(498) | |||

(499) | |||

(500) |

There now remains only one unknown, .

Now, it is clear, from symmetry, that there is zero net torque acting on rod . Let us evaluate
the torque acting on rod about point . (By symmetry, this
is the same as the torque acting on rod about point ). The two forces which contribute to
this torque are the weight, , and the reaction . (Recall that the reaction
is zero). The lever arms associated with these two torques (which act in the same direction)
are
and , respectively. Thus, setting the net torque
to zero, we obtain

(501) |

(502) |