FN:Andrew Kester, PE
Forgive me if this was answered already...
I am not sure I see any difference in a cable and a rod (other than some material differences) on how it will react under loading. I would think any structural member, if fully restrained (fixed) at its ends or pre-tensioned, will not go into bending, or more appropriately, the structural member (rod, cable) will not have any compressive bending stress as it will be taken up by the pre-applied tension. Sort of the opposite of pre/post tensioned concrete. This is the whole idea with cable guard rail systems, of course they cannot take any bending load, but once the load is applied the cable deflects and goes into tension (well, its already pre-tensioned). I see no difference with a rod or any structural member that is pre-tensioned. Once your rod deflects whatsoever, since it is restrained at the ends, it will go into tension. I would argue something like a large bridge cable is practically a rod anyway, the way they are fabricated with thousands of small wires tightly bound or braided together, but the same principles apply. The key with a rod would be to control deflection and prevent it from forming a hinge.
I think Harold has a lot of expertise in this area, perhaps he has a two-cents he can throw in (probably more like a couple bucks with Harold)...
I would be very irritated to have a civil engineer who admittingly does not understand the mechanics of this type of design questioning my design and wanting to see more calcs that he won't understand. I feel your pain.
I forgot your exact situation, but if the threaded rod is a handrail, make sure it meets the diameter requirements of code (for hands being able to grab onto).
Andrew Kester, P.E.