The only problem with this is that, in general, tests of Strength make little sense with the wide variability of a d20 check. If the Str 18 character can't open the stuck door, the Str 8 guy shouldn't have a chance at all. I virtually never use Strength checks in my games as a roll. If you need to open the door, you need a Str 16.
I have been using a passive ability check (calculated the same as passive perception) for situations like that.