I owned a Trucking company for a few years and this was always a big concern.
This is from experience.
Most bridge's and over hangs on main roads and hwys are marked as you know. The posted Height is from the street to the lowest point which is most often the sides. I have driven under a bridge that was posted 12ft 8in in a truck that was 13ft 6in by going thru the middle. I did that at 2mph even though I had just watched another truck do it.
I also had a driver hit a bridge that was posted 14ft 2in in a 13ft 6in truck. The reason was they had just repaved the road and had not changed the height sign. I have also seen a truck hit a bridge because of snow and Ice build up. Most times there is a turn off just before you can use. Of course the best thing is to get out and look. I never trust the signs if it looks close. Remember if you do hit something no one is going to pay for it but you and they might even charge you depending on what you hit.
As for the Garage The wife get that so I don't even know what that would be like.