Bismarck's armour and the eight-inch threat

Was Bismarck's armour designed to keep the ship operational after taking fire?

Broadly yes, though the scheme was heavily shaped around the eight-inch-gun threat.

Bismarck's armour scheme broadly aimed to preserve operation after the ship was hit. The protection was especially shaped around resisting eight-inch gunfire. That emphasis points toward a threat model involving cruiser-calibre weapons instead of an abstract contest between named armour philosophies. The answer encourages viewers to ask what incoming fire an armour scheme was designed to defeat.