To avoid all PCs to walking around in heavy armor, 5e limits the three heaviest kinds of armor to PCs that have minimum strength of 13 or 15.
|Ring Mail||30 gp||14||—||Disadvantage||40 lb.|
|Chain Mail||75 gp||16||Str 13||Disadvantage||55 lb.|
|Splint||200 gp||17||Str 15||Disadvantage||60 lb.|
|Plate||1,500 gp||18||Str 15||Disadvantage||65 lb.|
There is no rhyme or reason to these numbers, apparently. A Str 12/13/14/15 would make a lot more sense and work perfectly well for gaming reasons.
But why not make Strength requirements for ALL kinds of armor? This is an idea I've got from Dragon Heresy. But I prefer formulas to tables. So:
The maximum number of slots you can fill with armor (including shields) is equal to half your Strength score (rounded up); otherwise, the armor reduces your speed by (at least) 10 feet.
This works quite well. For starters, to wear the equivalent of plate armor (AC 18), you'd need... Str 15!
This also bars anyone with Str less than 9 to have AC 15 armor, although light armor (and most kinds of medium armor) is still available for (almost) everybody that has proficiency in it.
You also require a bit extra Strength for using shields, which makes sense IMO, although you could always stick to the original rules and say shields have no Str requirements.
You don't have to apply this rule to monsters - maybe armor is lighter for them because of their dimensions - although it seems to work well enough as written.