It sometimes makes me wonder if New York truckers really love the The Little Engine That Could story. They've seen the sign about the height clearance, they know the height of their truck and yet they're sitting there behind the wheel and saying "I think I can, I think I can, I think I can" until half the roof of the trailer has been torn off. There's one crucial point that they seem to always forget, it was the Little Engine, not the Big Truck.
When I used to live on J and E 12th, almost every week you'd have a trucker that either was smart enough to stop a foot in front of the train and was now needing help backing up, or one who was stupid and who managed to rip off the top of the cabin and a good part of the trailer. When DOT finally put the clearance warning sign all the way on Coney Island, it helped, a little.
If the clearance is one or two inches, maybe you shouldn't try it, especially when your truck isn't fully loaded and you just inflated your tires. If the height of your truck is half a foot more than the clearance, dude, go back to school and learn some basic math.
Stupid enough to risk it? At least do it slowly and not at full speed. And if you see you're not going to make it, it's probably better to get a ticket for blocking traffic than to get your pay docked and to get fired for damaging, really badly, the really expensive truck you're driving.
Trucks may be impervious to collisions with cars but they're not as immortal as they think. When it come to concrete and steel, you lose. Reminds of the joke about an American nuclear sub demanding that the British lighthouse move out of its way.