Okay. everybody is going on about the rat cage again......... Miss understanding and lack of knowledge aparently leads to gospil and arm chair experts or arm chair engineers . Look at the individual parts.
if your going to support your top plate with 16mm threaded rod, you can expect it to flex... but if your smart and put decent size aka M20-M24 you are loading these in compression and tension not so much bending. The reason why this occurs is due to the leaver arm, the bolts are resisting any moment induced by eccentric loading in a push pull, tension compression action.
if your going to put it 200mm away from the top of the pier you can expect it to flex but if your smart and keep it down around 80-100mm when you look at the bolts they have 2 bolts which make that M20-M24 bolt more like 30 or 40mm in diameter with the M20-M24 bolt spanning 40mm.
If you want an idea of the forces to start getting movement ill do a little sum for you
with M20 Grade 8.8 structural bolts
Phi Ntf = 163kN (Phi is 0.7* for the capacity its a statistical thing to assure that you will get 163kN)
assume your bolts are 300mm in seperation
two bolts resisting assuming there are 4 bolts in total
Moment = 163*2*.3
Moment = 97.8kN-m
what load does that relate to?
force* leaver arm = Moment
lets assume your mounts at maximum of say 500mm above
with simple rearrangement or algebra we get
97.8 = .5*2*x ----> 97.8/(2*.5)----> 97.8kN
97.8kN is required to reach the capacity of the bolts now to relate this force to something we are more intune to. 10kN=1ton=1000kg so you have 9.8ton approximately........... are you starting to feel what im saying here? 9800kg it will take to start making these bolts come to their statistical maximim loading! Do remember thats 9800kgs at perpendicular to the piers axis.
if you have a mount that is capable of 100kgs thats a big mount! if you have 300kgs of equipment on your pier that relates to 3.2% capacity.. but its in the wrong direction its concentric with the piers axis not at a perpendicular axis to the pier. Pier flexure is more often than not user error and the mis understanding of how to assemble and construct.
(dont get me started on concrete and reo.....)
Unless your running 20-30" type mirrors you will not get the amount of force that is required to start making the bolts i have just told you of to go into bending. Your equipment should be balanced. If it wasn't you wouldn't be able to make your adjustments as there would be significant weight on the actual adjustments. So the load is virutally concentric though the middle of your mount head. the bolts are in compression.
remember steel is strong far stronger than you think or generally can comprehend.
Peter I am with you that you shouldn't need to get a barcode staff and a total station to make sure that your tripod is level, thats just silly, but to say that levelling your mount head out doesn't matter
well you can sit there and spend ages getting your polar alignment done while ill be done in a matter of minutes with ease just because i spent a few minutes getting the level approximately right!
if your good with concreting and the like you can run your levelling at the bottom with your bolts and what not and then put in a high strength non shrink grout just like they do for every big building with steel columns. they put a little set down and have the bolts protruding. put the column down level it out, then grout. this will be the best possible way you could go about it..... It isn't hard and allows you fine adjustment before you finish up.
I may be wrong but from experience every time i spent that extra minute setting up the tripod it paid in spades after, with my POS eq6 i can meridian flip to the accuracy of 2-3 minutes of arc at 1200mm FL and a FOV of 38" by 54" that isn't bad. Also I have no T point or Maxpoint software for mount modelling and I am 99% doing photography.
Thats my thoughts on the situation and although I am not a engineer with 30+ years of experience I am a consulting structural engineer.
I hope that clears up some big miss information that is rolling around.