frame, building, structure
构 centers on the idea of a structural framework: a frame, a building, or any constructed structure. The meanings all relate to putting together a supporting skeleton.
构 is the simplified form of 構. The older form combines 木 (wood) with 冓, which likely contributed the sound and the idea of a wooden framework. The modern simplified right side 勾 is a replacement that does not reflect the original component history.
The left side is 木 (tree/wood), and the right side 勾 looks like a hook or bent frame. Picture wooden beams hooked together to form the frame of a building.
For コウ, imagine constructing a frame out of wooden beams that form the shape of a 口 (こう, mouth/opening): 口 -> コウ, and the frame creates the structure.