All the states highway departments (like the misnamed Caltrans.gov for California which really only does highways) have websites with pages listing any low clearance or narrow areas where a truck and trailer rig might have a problem. Most of the time in the west the problem is a bridge or underpass where the width of the trailer is a possible problem and not the height. In those ares there may be room if one uses both lanes and not the far right lane (like with the tunnel into Zion NP).
The state governments keep these up to date as the last thing they want is for a roadway to be shut down for hours or days as the result of a trailer getting stuck underneath a low clearance structure.
Of the states' listings I have looked at none had a maximum height of less than 14 feet and generally speaking the DOT regs for vehicle height of 13'6" has been tied to this. Go over 13'6" and you will need to be more careful as to where you go.