What is the minimum amount of energy in any given caliber @ any given yardage you recommend to take an elk?

Just use a good bullet operating in its effective velocity range.

I know they say 1000 ft-lbs for deer.

For elk ideal in my book probably starts with a .30-06 and goes up from there.

I think the .300win.mag is probably one of the most ideal.

.338win.mag, .340wby.mag,
7mm Rem.mag

270win starting to get a lil light IMO. esp if I have a .300mag to use, etc...

I know you are looking for a number ...and I reload BUT I would have to say placement is way more important. But if I had to put a number on it 1200 lbs at impact. You left out velocity and this plays an important role. There is a point at which a lighter faster bullet will do more damage than a heavier slower bullet. so a .243 or 25-06 can do the job but its not the choice for most. That being said let the discussions begin.

All I can tell you is either what I've seen or what I've read. Based on those two things I go with the thought that is is not just energy. Consider that at some point a 50 gr. Vmax fired from a 22-250 has more energy than a 240 gr. bullet fired from a 44 Mag. Obviously one would be more appropriate to hunt elk with than the other.

And 1000 ft. lb. of energy applied in the correct place would be far more effective than 3000 ft. lb. poorly placed.

The common accepted thought being it should require 1500 ft. lb. to be suitable for elk. For what its worth.................