Don Durito
Hero
Then give it some odds and make a random roll. I don't think using PCs skill roles to determine the personality of NPCs is a good use of the roll.a) Because you don't know if the person you are trying to intimidate is the kind of person who would be impressed by that sort of thing.
But, that's beside the point really. I don't see what rolling Strength is meant to contribute here. That the barbarian is a big strong hulking figure with a gigantic sword or axe is a visible fact in the game world. It can't fail to be a fact - so I don't see why you would roll it.
Well then make a Strength (Athletics) roll to open the door then, if the outcome is in doubt. And then take the outcome into consideration.b) Because in the process of ripping the door of it's hinges you might drop it on your toe, making yourself look like an idiot and ruining the effect.
But it's then a fact in the game world. If for some reason an intimidation check is still needed, then give the Barbarian advantage for their incredible display of strength.
But to my mind something's going wrong if we're letting the barbarian roll Strength(Intimidate) just so he can be equally as intimidating as a halfling rogue. Skills, and in particular social skills need to be adjudicated around the facts and context of the game world and not in a void.