My question is mostly in the title, but here's an example.
Jeff, a STR 19 Bear Totem Barbarian wants cover as he advances towards enemies. To do so, he rips a heavy wooden door off its hinges, and fashions it with straps to be held with two hands as a full-body shield.
Jeff can carry 285lb and push 570lb without encumbrance. Would he be able to benefit from full cover while standing behind his shield?
Best Answer
It's up to your DM
There are no rules about improvised shields and there are no shields that provide full cover in 5e.
It will be entirely up to the DM as to whether or not they allow the homebrew of a Tower Shield and how such an item would work mechanically.