Tractor trailers are among the most heavily regulated and controlled vehicles on the road, with axle weight and spread being the two most stringently monitored factors. Most DOT regulations deal with tire-load safety, but road width, construction and bridge height come into play as well. While federal standards set the baseline for weight-station requirements, what is and is not acceptable is ultimately determined by local and state jurisdictions.
Axle-weight restrictions are generally the most rigidly and regularly enforced, and don't vary much by state. A safe axle weight is 12,500 pounds on the front-steer axle and 33,000 on the drive- and tandem- (trailer) axles. Technically speaking, legal axle weight in most areas is 34,000 pounds, but a little work with your calculator will quickly reveal that 34,000 + 34,000 + 12,500 equals 80,500 pounds, which is 500 pounds over the maximum gross weight. Still, you can push either the drive or tandem axle to 34,000 if you're under 80,000 total and light on the other two.
Bridge length is defined as the distance between the center of the rear-most drive axle and the center of the front-most tandem axle. (Note that DOT measures bridge length from the center of the axle hub, not from the tire.) Bridge length is important because it determines how much of your truck's weight is present on small, local bridges, and because it plays a big role in determining how sharp a corner the truck can negotiate without hopping the curb. Many of these factors are extremely local; trucks operating in big cities like New York and Chicago are required to have much shorter bridge lengths than those in more rural areas. You'll need to know ahead of time what bridge lengths you're looking at in a given area. For a a handy bridge-length calculator, look in the Resources section.
Federal regulations state that your truck/trailer width cannot exceed 102 inches, but local jurisdictions can cut that down as far as 96 inches with or without notice. Changing trailer-width requirements without notice can be a profitable income generator for some local jurisdictions, so stay on assigned truck routes with established trailer widths.
Many northern, West Coast and Pacific Northwest states require that drivers carry tire chains and that those chains be displayed prominently. Generally speaking, such states only require that you display or use chains at all times in certain areas (like the high mountain passes in California), and others change chain requirements seasonally. Either way, the state will post signs in the areas where they're required. These states include (but are not limited to) California, Oregon, Washington, Idaho, North Dakota, South Dakota and Montana. Like trailer width, chain laws can be a good source of income for local jurisdictions, so always keep a set clean and on display where weigh-station employees can see them.