What the Bridge Formula does
Bridges are hurt less by weight spread out than by the same weight concentrated. The Federal Bridge Formula, set out in 23 CFR 658.17, limits the weight on any group of two or more consecutive axles on the Interstate System by the number of axles in the group and the distance between its outer axles. It applies to every group: the whole vehicle (the outer bridge) and each group inside it, such as the drive tandem plus the trailer tandem.
The formula
W = 500 × (L × N ÷ (N − 1) + 12 × N + 36)- W: the maximum weight in pounds on the group, rounded to the nearest 500 lb.
- L: the distance in feet between the centers of the outer axles of the group.
- N: the number of axles in the group.
The formula works together with three federal limits: 20,000 lb on a single axle, 34,000 lb on a tandem axle, and 80,000 lb gross vehicle weight.
Worked examples
A five-axle tractor-trailer with 51 feet between its first and last axles: W = 500 × (51 × 5 ÷ 4 + 60 + 36) = 500 × 159.75 = 79,875 lb, which rounds to 80,000 lb. That is why 51 feet is a common figure for a five-axle rig to reach the 80,000 lb gross limit.
Three axles over 20 feet: 500 × (20 × 3 ÷ 2 + 36 + 36) = 51,000 lb. Four axles over 36 feet: 500 × (36 × 4 ÷ 3 + 48 + 36) = 66,000 lb.
Two axles 8 feet apart are a tandem. The formula gives 38,000 lb, but the tandem limit of 34,000 lb is lower, so 34,000 lb applies. Two axles more than 8 feet apart are two single axles, so they can never carry more than 2 × 20,000 = 40,000 lb, whatever the formula gives.
Exceptions
The federal rules allow two consecutive sets of tandem axles to carry 34,000 lb each, 68,000 lb together, when the first and last axles of the two sets are 36 feet or more apart. At 36 feet the formula alone would give 66,000 lb. Beyond that, states set their own limits on roads off the Interstate System, some states kept older limits under grandfather rights, and permits cover oversize and overweight loads. This page does not cover state rules.
Questions
How do you calculate the bridge formula?
W = 500 × (L × N ÷ (N − 1) + 12 × N + 36), with L the distance in feet between the outer axles and N the number of axles. For 5 axles over 51 feet that gives 79,875 lb, rounded to 80,000 lb.
How long does a 5-axle truck need to be to carry 80,000 lb?
By the formula, 51 feet between the first and last axles: 500 × (51 × 5 ÷ 4 + 96) = 79,875 lb, which rounds to 80,000 lb.
What are the federal axle weight limits?
20,000 lb on a single axle, 34,000 lb on a tandem axle and 80,000 lb gross vehicle weight on the Interstate System, together with the Bridge Formula for axle groups. States can differ off the Interstate System.
Does the bridge formula apply to pickup trucks and RVs?
The federal formula is written for vehicles on the Interstate System, and a pickup with a trailer is usually far below its figures. The ratings that limit a pickup and trailer are its own GVWR, GCWR, GAWR and hitch ratings.