Planning and Design


 
 
Clement News Item

 
Date: 01/22/2002

 
Item: Selecting The Right Trailer To Meet The Federal Bridge Law

 
 
LIVING WITH THE 'BRIDGE'

 A 1944 algebraic equation still governs truck
 weight and length. Here's how to use the "bridge formula."

 Living by the "bridge formula" is a way of life for truckers today. It's the law on the Interstates in every state with two exceptions: grandfather provisions that date back to 1956, or for states that stayed at the old federal maximum of 73,280 pounds gross after the national Interstate weight limit was raised to 80,000 pounds in 1974.

 Truck operators should understand the federal bridge formula - known as Formula B or Bridge Table B - because it is the basis for determining what a vehicle can legally weigh, and how long it must be.

 Formula B involves both axle weights and axle spacing. There's an "inner bridge" and "outer bridge" that must be met - bridge in this case meaning the distance between various axles.

 Original bridge formulas go back more than 50 years and started in the West. The idea was to protect marginal bridges by requiring a vehicle's weight be spread out over axles spaced far apart. That way the full weight of the vehicle isn't concentrated on a short section of a bridge.

 Many truckers in western states today use long wheel base trucks and tractors to get maximum "bridge." And where multiple unit, over-80,000-pound combinations are allowed, bridge laws determine how much can be carried, based on number of axles and distance between them.

 By comparison, many states in the East and New England have heavy axle limits and no restrictive axle spacing. An example is Pennsylvania, which on non-federal highways still will allow 73,280 pounds on a four-axle straight truck 40 feet long. This vehicle, with a normal 189-inch wheelbase, would be limited to 52,500 pounds when complying with the federal Formula B.

 It's an accepted engineering principle that concentrated weight is what breaks bridges and pavement if they aren't designed for heavy loads. So the U.S. Bureau of Public Roads (now the Federal Highway Administration) adopted the bridge formula concept for federal roads in 1944 and, except for modification in 1974, it's been with us ever since.
 

 How's It Figured?


 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.


Bridge Table B: Permissible gross loads for vehicles in regular operation
based on weight formula W = 500 (LN/N-1 + 12N + 36)

 Distance in feet between the
 extremes of any group of 2
 or more consecutive axles
 
2 axles
3 axles
4 axles
5 axles
6 axles
7 axles
8 axles
9 axles
4 ft
34,000
5
34,000
6
34,000
7
34,000
8
34,000
34,000
9
39,000
42,500
10
40,000
43,500
11
44,000
12
45,000
50,000
13
45,500
50,500
14
46,500
51,500
15
47,000
52,000
16
48,000
52,500
58,000
17
48,500
53,500
58,500
18
49,500
54,000
59,000
19
50,000
54,500
60,000
20
51,000
55,500
60,500
66,000
21
51,500
56,000
61,000
66,500
22
52,500
56,500
61,500
67,000
23
53,000
57,500
62,500
68,000
24
54,000
58,000
63,000
68,500
74,000
25
54,500
58,500
63,500
69,000
74,500
26
55,500
59,500
64,000
69,500
75,000
27
56,000
60,000
65,000
70,000
75,500
28
57,000
60,500
65,500
71,000
76,500
82,000
29
57,500
61,500
66,000
71,500
77,000
82,500
30
58,500
62,000
66,500
72,000
77,500
83,000
31
59,000
62,500
67,500
72,500
78,000
83,500
32
60,000
63,500
68,000
73,000
78,500
84,500
90,000
33
64,000
68,500
74,000
79,000
85,000
90,500
34
64,500
69,000
74,500
80,000
85,500
91,000
35
65,500
70,000
75,000
80,500
86,000
91,500
36
ATA
66,000
70,500
75,500
81,000
86,500
92,000
37
BUMP
66,500
71,000
76,000
81,500
87,000
93,000
38
} } } }
67,500
72,000
77,000
82,000
87,500
93,500
39
68,000
72,500
77,500
82,500
88,500
94,000
40
68,500
73,000
78,000
83,500
89,000
94,500
41
69,500
73,500
78,500
84,000
89,500
95,000
42
70,000
74,000
79,000
84,500
90,000
95,500
43
70,500
75,000
80,000
85,000
90,500
96,000
44
71,500
75,500
80,500
85,500
91,000
96,500
45
72,000
76,000
81,000
86,000
91,500
97,500
46
72,500
76,500
81,500
87,000
92,500
98,000
47
73,500
77,500
82,000
87,500
93,000
98,500
48
74,000
78,000
83,000
88,000
93,500
99,000
49
74,500
78,500
83,500
88,500
94,000
99,500
50
75,500
79,000