One of my favorites is the Black Gate at the Morannon. Two trolls, however strong, swing open the gate by pushing on a bar. By my guesstimates that would be like me opening a heavy door using a toothpick! Figure out the lengths on both sides of the pivot point, estimate the mass of the Gate and figure out the force that must be exerted by the Trolls and what substance on Earth, Middle or otherwise, would withstand such stress.
And does the bar which they push even bow/bend a bit?