The 2009 Silverado 3500HD dually we had was 12,000 GVWR. It had a steel landscape tilt bed on it with a 4ft headache rack and dump gate that was 2ft. Sides were 2ft tall using 2x12'. I added two more 2x12' and could toss in 1 cord. No one ever questioned it and I never had to report to scales but it was over. The TARE on the truck was 9,100. Leaving only 2,900 for cargo weight. Once we found that out, to be legal we bought a dump trailer that could hold/haul 2 cord (4ft x 8ft x 12ft).
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We've since gotten rid of that and went with a International CV515 with 12,000 hook lift. Even with a GVWR of 23,000lbs, the TARE comes in at about 12,500lb, and that is with an aluminum box. Leaving 10,500 lbs for cargo. The alum box being 4ft tall, 8ft wide and 12 ft long, just fits in 2 cord dumped in.
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Recently a customer came to pick up two cord with a 12ft dump trailer, to fit 2 cord it had to be stacked in because he only had 3ft sides.
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For a loose load (tossed in) in a 12ft trailer, every foot in height is 1/2 a cord.