Why do extra moment equations not count toward a system of equations?

[Master1022]

I was just looking at indeterminate statics problems where you have a beam, three elastic wires (left, centre, and right that are holding it up), and some extra mass. (Just like example 5 in the notes below: http://fast10.vsb.cz/lausova/indeterm_all.pdf). I understand the method that was used to solve it. However, when we have the condition for the net torque = 0, why do we only use one moments equation. Couldn't we take moments about other positions and get more equations to add to the overall number of equations in our system of equations?

Thanks in advance.

 

[stockzahn]

I propose you just try and see what happens. Write down the net torque equilibrium conditions for the points of the beam, on which the forces $N_1$, $N_2$ and $N_3$ are acting on and try to solve the LES (or you write down the coefficient matrix and calculate the determinant).