The bridge formula was predicated originally on 32,000-pound tandem axles with a minimum distance between the tractor tandem and trailer tandem.
For weights less than 32,000 pounds, the distance was shorter on a sliding scale basis. The formula protected a certain type of bridge then common on our main highways.
Today's Formula B is based on a maximum of 34,000 pounds on each tandem, 20,000 pounds on a single axle, and a gross combination weight of 80,000 pounds.
To protect bridges and highways, the formula spells out the distances required between axle groups for a given weight. And it says that any consecutive two or more axles may not exceed the weight as computed by the formula, even though all axle weights and overall gross combination weights are within the maximums spelled out above.
So someone spec'ing a new five-axle rig for the maximum 80,000 pounds has to consider a lot more than just putting 34,000 pounds on each tandem and 12,000 pounds on the steer axle. Without the required spacing, or "bridge," the rig is illegal. The same formula applies to all types of equipment, including heavy straight trucks.
The most popular 80,000-pound rig is the five-axle tractor-semi trailer combination, so we'll use it in our first example, and number the axles l through 5 (see sketch).
While the bridge formula law applies to each combination of two or more axles, the distance between axles 1 and 3, 1 and 5, and 2 and 5 are the critical combinations. If they're okay, the others will be, too.
Three "tests" of the bridge law must be met. They can be calculated with the 'actual formula, which is an algebraic equation. Or they can simply be looked up in the Formula B table, which was derived from the formula itself.
Test 1 is the "power unit bridge" because it calculates the maximum weight allowed with given distances between axles 1 and 3 of the tractor.
Test 2 checks the "external bridge," also called the "outer bridge," which is the distance from the front axle to the last axle, regardless of how many there are.
Test 3 is the "inner bridge," also called the "internal bridge," because it calculates the maximum gross weight allowed from axle 2 to the rearmost axle.
To reach 80,000 pounds requires loading both the tractor and trailer tandems to as close to 34,000 pounds each as possible, totaling 68,000 pounds. This leaves 12,000 pounds (or more if tandems are below 34,000 pounds) for the front axle.
To perform the three bridge tests, we also must know three pieces of dimensional data:
- Distance from front axle to tractor's third axle. Here it's 21 feet.
- Distance from axle 2 to axle 5 - the inner bridge. It's 34 feet.
- Distance from axle 1 to axle 5 - the outer bridge. This is 51 feet in our example.
There are two parts to each test. First we must calculate actual weight on axles 1 to 3: 12,000 + 17,000 + 17,000 = 46,000 pounds.
Then we use the bridge formula to calculate the legal gross. The maximum legal gross determined by the formula must exceed, or at least equal, the actual gross weights on the three axles. Using the formula
W = 500 [LN / N-I + 12N + 36]
where L is the distance in feet between the axles being tested and N is the number of axles (and LN is the distance multiplied by the number of axles), we calculate:
W = 500 x [63/2 + (12x3)] + 36
W = 500 x [63/2 + 36 + 36]
W = 500 x 103
W = 51,500 pounds
Conclusion: On axles l to 3. the formula says we're allowed a maximum of 51,500 pounds. Our actual weight is 46,000 pounds, so we're okay.
An easier way to get the same answer is to use the Formula B table, which is reprinted within this article. By reading down the left column to 21 feet, then counting across to the three-axle column, we see the answer is the same as we worked out with the formula.
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