Federal Bridge Gross Weight Formula

The difference in weight concentration between short and long wheelbase trucks. The shorter truck is damaging the bridge because all of its weight is concentrated in a smaller area.

The Federal Bridge Gross Weight Formula is a mathematical formula used by truck drivers and United States Department of Transportation (DOT) officials to determine the appropriate maximum gross weight for a commercial motor vehicle (CMV) based on axle spacing. This is necessary to prevent damage to roads and bridges. CMVs are most often semi-trucks or buses, but the formula is of most interest to truck drivers due to the heavy loads their vehicles often carry.

Compliance with the law is checked when vehicles pass through a weigh station, often located at the borders between states or on the outskirts of major cities. There is one exception to the formula which allows the common five-axle semi-truck configuration to weigh the maximum legal gross weight without violating the bridge formula law.

Contents

1 History
2 Usage
3 Bridge collapse
4 The formula
5 Exception
6 Bridge formula table
7 See also
8 References
9 External links

History

The first truck weight limits were enacted by four states in 1914, ranging from a low of 18,000 pounds (8,200 kg) in Maine to a high of 28,000 pounds (13,000 kg) in Massachusetts. These laws were enacted to protect earth and gravel-surfaced roads from damage caused by the iron and solid rubber wheels of early heavy trucks. By 1933, all states had some form of varying truck weight regulation. The Federal-Aid Highway Act of 1956 instituted the first federal truck weight regulation (set at 73,280 pounds/33,240 kilograms) and authorized the construction of the Interstate Highway System.

In the late 1950s, the American Association of State Highway and Transportation Officials (AASHTO) conducted a series of extensive field tests of roads and bridges to determine how traffic contributed to the deterioration of pavement materials. In 1964, the AASHTO recommended to Congress that a bridge formula table be used instead of a single gross weight limit for trucks. The Federal-Aid Highway Act Amendments of 1974 established the bridge formula as law, along with gross weight limits still in use today.

Usage

The formula was enacted as law to limit the weight-to-length ratio of a CMV. The formula is necessary in order to prevent the concentrated weight on a truck’s axle from producing stress on bridge members (possibly producing a bridge collapse). In simplified form, this is analogous to a person walking on thin ice. When standing upright, a person’s weight is concentrated at the bottom of their feet, funneling all of their weight into a small area. When lying down, a person’s weight is distributed over a much larger area. This difference in weight distribution would allow a person to cross an area of ice while lying down that might otherwise collapse under their body weight while standing up. In order for an overweight truck to comply with the formula, more axles must be added, or the length between axles must be increased.

A division of the DOT, the Federal Motor Carrier Safety Administration (FMCSA) regulates all safety-related aspects of the trucking industry.

CMVs are defined by the FMCSA as vehicles engaged in interstate commerce, used to transport passengers or property; with a gross vehicle weight of 10,001 pounds (4,536 kg) or more; designed or used to transport more than 8 passengers (including the driver) for compensation; designed or used to transport more than 15 passengers (including the driver) without compensation; or is used to transport hazardous materials in quantities requiring the vehicle to be marked or placarded under hazardous materials regulations.

The weight and size of CMVs are restricted for practical and safety reasons. CMVs are restricted by gross weight (total weight of vehicle and cargo), and by axle weight (i.e., the weight carried by each tire). The federal weight limits for CMVs are 80,000 pounds (36,000 kg) for gross weight (unless the bridge formula dictates a lower limit), 34,000 pounds (15,000 kg) for a tandem axle, and 20,000 pounds (9,100 kg) for a single axle. Axles spaced less than 40 inches (100 cm) apart are considered a single axle.

In effect, the formula reduces the legal weight limit for shorter trucks with fewer axles (see table below). For example, a 25-foot (7.6 m) three-axle dump truck would have a gross weight limit of 54,500 pounds (24,700 kg), instead of 80,000 pounds (36,000 kg), which is the normal weight limit for a five-axle semi-truck.

Bridge collapse

A bridge weight limit sign, which drivers must heed before crossing a bridge. Notice how the weight limit increases with the number of axles.

The August 2007 catastrophic collapse of the Interstate 35W Mississippi River bridge in Minneapolis has brought renewed attention to the issue of truck weights and their relation to bridge stress.

Federal estimates suggest truck traffic has increased over 200% since 1970, shortly before the federal gross weight limit for trucks was increased by 30,000 pounds (14,000 kg). This is also the period from when many of today’s interstate bridges were built. Research clearly shows that increased truck traffic (and therefore, increased stress) shortens the life of bridges.

Some smaller bridges have a weight limit (or gross weight load rating) usually indicated by a sign posted in front of the bridge and visible to anyone driving over the bridge. These are necessary when the weight limit of the bridge is lower than the federal or state gross weight limit for trucks.

In special cases involving unusually overweight trucks (which require special permits), not observing a bridge weight limit can lead to disastrous consequences. Just fifteen days after the collapse of the Minneapolis bridge, a heavy truck collapsed a small bridge in Oakville, Washington. It was determined that the truck was 145,000 pounds (66,000 kg) over the weight limit of the bridge. However, there was no indication that the truck was in violation of the bridge formula.

The formula

CMVs such as semi trucks are required to pass through weigh stations at the borders of most states and some large cities. These weigh stations are run by their respective state’s DOT, and CMV weight and size enforcement is overseen by the FHWA. Weigh stations check each vehicle’s gross weight and axle weight using a set of in-ground truck scales, and is normally where a truck’s compliance with the formula is checked.

A diagram of truck axle groups which are used to calculate compliance with the formula. Axles 1, 2, and 3 are considered the tractor group; axles 2, 3, 4, and 5 are the trailer group; and axles 1 through 5 are known as the outer group. This truck is not violation of the formula.

FMCSA regulation §658.17 states:

No vehicle or combination of vehicles shall be moved or operated on any interstate highway when the gross weight on two or more consecutive axles exceeds the limitations prescribed by the following formula:

w = the maximum weight in pounds that can be carried on a group of two or more axles to the nearest 500 pounds (230 kg).
l = spacing in feet between the outer axles of any two or more consecutive axles.
n = number of axles being considered.

Two or more consecutive axles may not exceed the weight computed by the bridge formula, even if the gross weight of the truck (or the weight on one axle) is below otherwise legal limits.

Exception

There is one exception to the formula. Two consecutive sets of tandem axles may carry 34,000 pounds (15,000 kg) each if the overall distance between the first and last axles of these tandems is 36 feet (11 m) or more. For example, a five-axle truck may carry 34,000 pounds both on the tractor tandem axles (2 and 3) and the trailer tandem axles (4 and 5), provided axles 2 and 5 are spaced at least 36 feet (11 m) apart.

This exception allows for the standard 5-axle semi-truck configuration to weigh up to 80,000 pounds (36,000 kg) (the legal limit)

Bridge formula table

Distance in feet between any
group of two or more axles 1
Gross weight in pounds 2

2 axles
3 axles
4 axles
5 axles
6 axles
7 axles

Less than 8 3
34,000
34,000

More than 8 4
38,000
42,000

9
39,000
42,500

10
40,0005
43,500

11
40,000
44,000

12
40,000
45,000
50,000

13
40,000
45,000
50,500

14
40,000
46,500
51,500

15
40,000
47,000
52,000

16
40,000
48,000
52,500
58,000

17
40,000
48,500
53,500
58,500

18
40,000
49,500
54,000
59,000

19
40,000
50,500
54,500
60,000

20
40,000
51,000
55,500
60,500
66,000

21
40,000
51,500
56,000
61,000
66,500

22
40,000
52,500
56,500
61,500
67,000

23
40,000
53,000
57,500
62,500
68,000

24
40,000
54,000
58,000
63,000
68,500
74,000

25
40,000
54,500
58,500
63,500
69,000
74,500

26
40,000
55,500
59,500
64,000
69,500
75,000

27
40,000
56,000
60,000
65,000
70,000
75,500

28
40,000
57,000
60,500
65,500
71,000
76,500

29
40,000
57,500
61,500
66,000
71,500
77,000

30
40,000
58,500
62,000
66,500
72,000
77,500

31
40,000
59,000
62,500
67,500
72,500
78,000

32
40,000
60,0005
63,500
68,000
73,000
78,500

33
40,000
60,000
64,000
68,500
74,000
79,000

34
40,000
60,000
64,500
69,000
74,500
80,0005

35
40,000
60,000
65,500
70,000
75,000
80,000

36
40,000
60,000
66,0006
70,500
75,500
80,000

37
40,000
60,000
66,5006
71,000
76,000
80,000

38
40,000
60,000
67,5006
71,500
77,000
80,000

39
40,000
60,000
68,000
72,500
77,500
80,000

40
40,000
60,000
68,500
73,000
78,000
80,000

41
40,000
60,000
69,500
73,500
78,500
80,000

42
40,000
60,000
70,000
74,000
79,000
80,000

43
40,000
60,000
70,500
75,000
80,0005
80,000

44
40,000
60,000
71,500
75,500
80,000
80,000

45
40,000
60,000
72,000
76,000
80,000
80,000

46
40,000
60,000
72,500
76,500
80,000
80,000

47
40,000
60,000
73,500
77,500
80,000
80,000

48
40,000
60,000
74,000
78,000
80,000
80,000

49
40,000
60,000
74,500
78,500
80,000
80,000

50
40,000
60,000
75,500
79,000
80,000
80,000

51
40,000
60,000
76,000
80,0005
80,000
80,000

52
40,000
60,000
76,500
80,000
80,000
80,000

53
40,000
60,000
77,500
80,000
80,000
80,000

54
40,000
60,000
78,000
80,000
80,000
80,000

55
40,000
60,000
78,500
80,000
80,000
80,000

56
40,000
60,000
79,500
80,000
80,000
80,000

57
40,000
60,000
80,0005
80,000
80,000
80,000

1 Calculated values reflect FHWA policy of rounding down when distances fall exactly between 6-inch (15 cm) increments.
2 Calculated values reflect FHWA policy of rounding down when weights fall exactly between 500 pound increments.
3 Tandem axle by definition.
4 Distances between 8 feet (2.4 m) to 8 feet 11 inches (2.7 m) may not be rounded down.
5 __ Maximum legal weight limit based on number of axles. Increased axle lengths beyond these do not increase maximum legal weight.
6 __ Exception to the formula: when the four axles under consideration are two tandem axles spaced at least 36 feet (11 m) apart, a gross weight of 68,000 pounds (31,000 kg) is allowed.
__ Upper blank areas represent unrealistic configurations.

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Federal Bridge Gross Weight Formula

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