2 ¾" shells are typically 2.25" long unfired, 2 ¾" fired. A 2 ¾" chamber shotgun has has a 2 ¾" chamber for the shell, directly followed by a forcing cone, which tapers down to the barrel diameter. As the shell fires, it unfolds filling the full length of the 2 ¾" chamber. (The length and taper of the forcing cone is exaggerated for clarity in these illustrations).
If you look below, you'll see an unfired 3" shell is only 2.56" long, so it will fit in the 2 ¾" chamber -- or at least appears to fit.
When you fire it it unfolds to 3", there is no room in the chamber for it to unfold into, so it unfolds into the tapered forcing cone which makes the exit diameter too small. This can make the chamber pressure rise to dangerous levels, You might bulge the barrel, might have it split open and rework your face.
And, last but not least, many autoloaders just can't handle 3" shells.
If it makes you feel any better, I was firing 3" shells in a 2 ¾" gun once upon a time until a friend made me read the barrel.
Oh yes -- best I know, you can always fire shells shorter than the chamber. Will hurt accuracy, and I wouldn't try it in a $2000 trap gun.
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