Isn't the force calculated twice?

[arpon]

Isn't the force calculated twice here? For example, the force along AB is at first calculated for the resultant force along OB, then for the resultant force along AC.
I think the compression and tensile stress should be $\frac{F}{2a}$.

 

[haruspex]

Isn't the force calculated twice here? For example, the force along AB is at first calculated for the resultant force along OB, then for the resultant force along AC.

Forget that it is a solid block for the moment and think of it as a framework of rods. The vertex A is subject to tension F along AB and tension F along AD. The resultant is a force F√2 along AO.