That depends on what the Gross Vehicle Weight Rating of the vehicle is, and what the vehicle weighs empty (tare weight).
26000 lbs of cargo? A tandem straight truck, such as a flatbed or a dump, could haul that amount of weight legally.
looking to be a certfied haul truck trainer
Depends on which size U-Haul truck you rent.
Depends on the vehicle. You can run line haul in a tractor-trailer or straight truck. If you're running a tractor-trailer, you need a Class A. If it's a straight truck, you need a Class B.
Parthenon
At U-Haul, the smallest truck that will hold 40 cubic yards (1,080 cubic feet) is a 24-foot truck. You will also need to check the weight capacity.
Long haul truck drivers transport goods over hundreds and sometimes thousands of miles. Short haul drivers usually work 8-10 hours a day such as cab drivers and delivery truck drivers.
Subtract the actual weight of the truck from 26,000 lbs (GVWR) to get the weight you can haul. This is assuming you are talking about a single straight truck with no trailer. It would be best to actually weigh the vehicle with full fuel tanks to get the most accurate measurement. You can get a weight at most places that sell gravel, stones, etc.
haul
The only information provided is that it's a 24' straight truck - that really tells us nothing in relation to the question you're asking. The payload it can haul is the tare weight (empty weight of the vehicle) subtracted from the Gross Vehicle Weight Rating. So, if it's a non-CDL Class 6 vehicle with a Gross Vehicle Weight Rating of 26,000 lbs. and a tare weight of 15,000 lbs., then it can haul 11,000 lbs. of payload. If it's a Class 7 truck (which does require a CDL) with a Gross Vehicle Weight Rating of 33,000 lbs., and a tare weight of 17,000 lbs., then it can haul 16,000 lbs. of payload. But without having the tare weight and Gross Vehicle Weight Rating of the vehicle you had in mind, it's impossible to tell you what you're looking for. Length doesn't determine how much weight it can haul.
Rent a truck to haul your belongings across the country.
I use my truck to tow my camper and haul junk to the dump.