What it says in the title.
Any effect that lists bonus Armor HP damage deals that bonus to Structure HP as well.
Against a 100 SHP Reactor block:
10 Cannon - 100 SHP damage
5 Cannon 5 Punch - 125 SHP damage
5 Cannon 5 Pierce - 150 SHP damage
ToddoftheYear on SMD Chat confirmed that Beams and Missiles also experience this odd behavior.