We had a covered drive in front of our church with the height clearly posted and a large sign posted, "No trucks". Each year we had at least one company paying to rebuild the covering. Everytime the driver commented, "It looked higher than that".
When we built an addition the drop off was redesigned so that there was no reason for any truck to drive under it. Hahahahah! It's only been rebuilt twice this year.
My brother-in-law drives a long-haul truck and has never done this once. I know it's possible.
My oldest Uncle used to be a trucker and he likes to tell the story of a twit who was given specific, very lengthy driving instructions for a particular city. I cannot recall which one - Chicago maybe? It has lots of underpasses they had to go around. Twit decided that he knew better than the other drivers, he could use a much shorter route! Yeah, he got very stuck in one of those underpasses and had to get help.
Dad had a driver he about wanted to strangle or at least slap upside the head with a clue by 4. It was near Christmas and for some reason this driver had to go up to Dallas/FW (there's a Miller Brewery there) to get a special order (normally things were shipped by rail - there was a siding that went right into the warehouse. Well he gets up there and a winter storm come barreling down. Dad tells him to park the truck at appropriate place, and get a hotel room. As soon as the airports reopen he will send boss's heliocopter or plane to get driver home for Christmas. Then they will send someone back for the truck after roads thaw.
Driver thinks that if he drives back to Houston, that will earn him brownie points with the boss for not having to send a for him. He jackknifed and lost the load, truck was totaled and driver injured. The press is never nice about a beer truck having an accident - especially when there are orders from the DPS to stay off the roads.
As far as underpasses and bridges. Dad's trucks had specific routes they were to take. Most of their trucks had no problem going under most standard underpasses. There are weight limits for bridges, and some residental streets also have weight limits. For an oversized loads I would assume they have to clear the route with the proper authorities. Often I see them having escorts in some areas.
I know there are also certain roads trucks with hazardous materials must stick to.