Definitions

# Federal Bridge Gross Weight Formula

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.

## History

The first truck weight limits were enacted by four states in 1914, ranging from a low of in Maine to a high of 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 ) 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. The FMCSA regulates the length, width, and weight limits of CMVs for interstate commercial traffic. Interstate commercial traffic is generally limited to a network of Interstate Highways, U.S. highways, and state highways known as the National Network (NN). Provided the truck remains on the NN, they are not subject to the state limits. State limits (which can be lower or higher than federal limits) come into effect for intrastate commercial traffic, provided the vehicle is not on the NN.)

CMVs are defined by the FMCSA as vehicles engaged in interstate commerce, used to transport passengers or property; with a gross vehicle weight of 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 for gross weight (unless the bridge formula dictates a lower limit), for a tandem axle, and for a single axle. A tandem axle is defined as two or more consecutive axles whose centers are spaced more than but not more than apart. Axles spaced less than 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 three-axle dump truck would have a gross weight limit of , instead of , which is the normal weight limit for a five-axle semi-truck.

## Bridge collapse

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. As of January 2008, the National Transportation Safety Board has not yet determined the official reason for the bridge collapse, although design failures are blamed in initial assessments. Reports suggest that as early as 1998, the Federal Highway Administration (FHWA) expressed concern over bridges on the I-35 corridor due to an expected increase of international truck traffic from Canada and Mexico.

Federal estimates suggest truck traffic has increased over 200% since 1970, shortly before the federal gross weight limit for trucks was increased by . 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. Estimates indicate that a single truck does as much damage to roads as 750 cars.

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. Driving a truck over a bridge that is too weak to support it usually does not result in an immediate collapse. The bridge may develop cracks, which over time can weaken the bridge and cause it to collapse. Most of these cracks are caught during mandated inspections of bridges. Most bridge collapses occur in rural areas, result in few injuries or deaths, and receive relatively little media attention. As many as 150 bridges collapse each year, and most of those are the result of soil erosion around bridge supports.

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 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.

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:

$w = 500 left \left(frac\left\{l cdot n\right\}\left\{n-1\right\} + 12n + 36 right \right)$

• w = the maximum weight in pounds that can be carried on a group of two or more axles to the nearest .
• 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. Although this means that any two axles must comply with the formula, experience has shown that axles 1 through 3, 1 through 5, and 2 through 5 are critical and must be checked. This means that the axle group which comprises the entire truck, known as the outer group; and the interior axle groups, known as the tractor group and trailer group groups, must also comply with the bridge formula. If these combinations are found to be satisfactory, then all of the other axle groups on this type of vehicle normally will be satisfactory.

## Exception

There is one exception to the formula. Two consecutive sets of tandem axles may carry each if the overall distance between the first and last axles of these tandems is 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 apart.

This exception allows for the standard 5-axle semi-truck configuration to weigh up to (the legal limit) without being in violation of the bridge formula law. Without this exception, the bridge formula would allow an actual weight of only to on tandems spaced to apart. This exception was sought by the American Trucking Associations specifically so trucking companies could use trailers and gross . It was the only way tank truck operators could reach 80,000 pounds without adding axles.

## 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 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 to 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 apart, a gross weight of is allowed.
• __ Upper blank areas represent unrealistic configurations.