The trapdoor is a stronger action than it looks, but even old time rifle pressures are a lot higher than shotgun pressures. Any modern shotgun is more than adequately strong for all modern shotshells for which it is intended.
Pump and auto shotguns fall generally into two classes. The first locks by use of a locking lug that engages the top of the receiver. The second locks by using a rotating bolt head that locks into the barrel. The latter is at least theoretically stronger, but in practice there is little difference and the most popular guns have been of the first type.
Jim