At what weight will loading a standard Olympic bar on a rack from one side move the centre of gravity outside the rack and cause a wreck?
I've never used enough weight to have this happen but I'm always a little worried.
This can be calculated by figuring out the location of the centre of gravity of the unevenly loaded bar. If the CoG is outside of the pegs, then the bar will flip off.
So, this means that the pegs are positioned 555mm from the centre of the bar, and the outer edge of the sleeve collar is positioned 685mm from the centre.
The CoG of the plates is in the middle of the plates. So the sleeve collar position plus half the total thickness of the plates. I.e.
685 + N*80/2, where N is the number of plates.
The CoG of the unloaded bar is in the middle of the bar, which is the position we are measuring from.
We can then find the combined CoG of the bar and plates by adding a fracting of the plates' CoG position, proportional to the weight of the plates divided by the total weight of the bar and plates.
So, calling combined CoG distance from the centre of the bar
D = (685 + N*80/2) * N*20/(20 + N*20)
D is greater than the distance from the centre to the peg (i.e. 555mm), then the bar will flip. Let's calculate some values:
Plates | D | Safe? -------+--------+-------- 0 | 0 | Yep 1 | 362.5 | Yep 2 | 510 | Yep 3 | 603.75 | Nope
So 2 plates on one side is a safe maximum. You might be able to push it out to 3 plates if you were using super-thin powerlifting competition plates, but a very sensible rule of thumb would be to never have more than a 2 plate difference in weight between the two sides of the bar. Also, make sure that the plates are pushed right up against the sleeve collars, as a single plate hanging on the very outer end of the sleeve could flip a bar all by itself.