Mechanical engineers take the same structural design classes as civil engineers, which is the degree that people who call themselves structural engineers in the building industry have.
Now, who do you think does the structural design of aircraft, missiles, ships, satellites, trains, buses, cars, and machinery? I will give you the answer. It is mechanical engineers, and the science and math behind those structures is the same as that for buildings and at times more complicated because of the dynamics involved.
I am a mechanical engineer performing structural design with dynamics involved. It doesn't matter what you call it.