Tracy, a "tridem" is a group of 3 axles that have an equalizing suspension. A tridem in Michigan will allow you 39,000 lbs/13,000 lbs per axle is the calculation on a grouping.
A tri-axle is where you have typically a tandem group of axles at the rear of the trailer and a lift axle in the middle of the trailer. The weight calculation gets tricky here. In Michigan once you go over 80,000 lbs gross only ONE tandem group of axlesis allowed the standard 34,000 lbs and all others get the 13,000 per axle allowance. So if you have a tandem drive tractor with a tri-axle trailer you get the allowable steering axle weight say 12,000 lbs and then you get EITHER 34,000 on the drives and 26,000 on the trailer tandems OR you get 26,000 lbs on the drives and 34,000 lbs on the trailer tandems. On the single axle on the trailer you would get 18,000 lbs IF it is 9' away from both the trailer and drive tandems.