Without a near-certainty of damage, some drivers will just take a chance instead of detouring to a longer and safer route. I was in a long traffic jam just over a weeks ago because one such "I'll be able to get through" truck driver was stuck under a rail bridge. I know there are ample well placed signs there since I frequently travel that route.
I recall the tunnels between New Jersey and New York City had a rather good set up; may be it is there still. First are the warning signs, as one got close come the physical barriers. First is a structures with multiple heavy metal chains hanging down to the height limit. About 10 meter from entrance (if memory serves) is the second barrier has heavy metal chains now with bowling-ball size metal balls at the chain's end. The last barrier was a steel I-beam like structure about a meter from the actual tunnel.
Now if you hit those chains, you are going to hear it. If you push on, you know the metal ball is going to do a number on your roof but still easy to get out. If you hit the I-beams, well, you are hopeless as a driver. I would have no issue if for those stuck under the I-beam, they have their license suspended for a duration - they have shown they don't care about safety or road signs.
EDIT: adding this
Besides height, there is the weight limit.
A bridge that just completed another major repair was near my home. Before it were multiple well placed sign on weight limit. This bridge is historic dated back to the 1776 revolution. Trucks didn't care about that either. We (Township with State help) spend good bucks repairing the bridge since it is historic - preserving the original stones where possible during the repair. Huge expenditure which I supported (by voting).
This is not the first but the most recent repair already. Now added to the weight limit signs are "YOUR GPS IS WRONG: NO TRUCKS" and the added truck U-TURN space... There is no missing it. Hope this will stop them.