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This diagram illustrates the difference in weight concentration between a short and long wheelbase truck. The shorter truck causes more wear and tear because all of its weight is concentrated in a smaller area.

The Federal Bridge Gross Weight Formula (also known as Bridge Formula B and the Federal Bridge Formula) is a mathematical formula in use in the United States by truck drivers and Department of Transportation (DOT) officials to determine the appropriate maximum gross weight for a commercial motor vehicle (CMV) based on axle number and spacing. The formula is part of federal weight and size regulations regarding interstate commercial traffic (intrastate traffic is subject to state limits). The formula is necessary to prevent heavy vehicles from damaging roads and bridges. CMVs are most often tractor-trailers or buses, but the formula is of most interest to truck drivers due to the heavy loads their vehicles often carry.

Early 20th-century weight limits were enacted to protect dirt and gravel roads from damage caused by the solid wheels of heavy trucks. As time passed, truck weight limits focused primarily on gross weight limits (which had no prescribed limits on length). By 1974, bridges received special protection from increasing truck weight limits. The bridge formula law was enacted by the U.S. Congress to limit the weight-to-length ratio of heavy trucks, and to protect roads and bridges from the damage caused by the concentrated weight of shorter trucks. The formula effectively lowers the legal weight limit for shorter trucks, preventing them from causing premature deterioration of bridges and highway infrastructure.

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, where the vehicle may be weighed and measured. The one exception to the formula allows a standard five-axle semi-truck configuration to weigh the maximum legal gross weight. This exception was specifically requested by the American Trucking Associations to allow tank trucks to reach the maximum legal gross weight without violating the bridge formula law.

History

The first truck weight limits were enacted by four states in 1913, ranging from Template:Convert in Maine to Template:Convert in Massachusetts. These laws were passed to protect earth and gravel-surfaced roads from damage caused by the steel and solid rubber wheels of early heavy trucks. By 1933, all states had some form of truck weight regulation. The Federal-Aid Highway Act of 1956 instituted the first federal truck weight regulation (set at Template:Convert) 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 the gross weight limit of Template:Convert. Current applications of the formula allow for up to 7 axles and 86 feet or more length between axle sets, and a maximum load of 105,500 lbs.

Usage

The formula was enacted as law to limit the weight-to-length ratio of a commercial motor vehicle (CMV). The formula is necessary to prevent the concentrated weight on a truck's axle from producing stress on bridge members (possibly causing 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 crawling that might otherwise collapse under their body weight while standing up. For an overweight truck to comply with the formula, more axles must be added, the distance between axles must be increased, or weight must be removed.

A division of the DOT, the Federal Motor Carrier Safety Administration (FMCSA), regulates safety for the U.S. 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, it is not subject to state limits. These 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 that are used to transport passengers or property: vehicles with a gross vehicle weight of Template:Convert or more; those designed or used to transport more than 8 passengers (including the driver) for compensation; vehicles designed or used to transport more than 15 passengers (including the driver) without compensation; or those 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 Template:Convert for gross weight (unless the bridge formula dictates a lower limit), Template:Convert for a tandem axle, and Template:Convert for a single axle. A tandem axle is defined as two or more consecutive axles whose centers are spaced more than Template:Convert but not more than Template:Convert apart. Axles spaced less than Template:Convert 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 Template:Convert three-axle dump truck would have a gross weight limit of Template:Convert, instead of Template:Convert, which is the standard weight limit for Template:Convert five-axle tractor-trailer. FMCSA regulation §658.17 states: "The maximum gross vehicle weight shall be 80,000 pounds except where lower gross vehicle weight is dictated by the bridge formula."

Bridge collapse

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

The August 2007 collapse of the Interstate 35W Mississippi River bridge in Minneapolis brought renewed attention to the issue of truck weights and their relation to bridge stress. In November 2008, the National Transportation Safety Board determined several reasons for the bridge's collapse, including (but not limited to): faulty gusset plates, inadequate inspections, and the extra weight of heavy construction equipment combined with the weight of rush hour traffic. The I-35 Trade Corridor Study reported that 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, with the FHWA listing it as "high-priority" in 2005.

As of 2007, federal estimates suggest truck traffic increased 216% since 1970, shortly before the federal gross weight limit for trucks was increased by Template:Convert. This is also the period during which many of the existing interstate bridges were built. Research shows that increased truck traffic (and therefore, increased stress) shortens the life of bridges. National Pavement Cost Model (NAPCOM) estimates indicate that one Template:Convert truck does as much damage to roads as 750 Template:Convert cars.

Some smaller bridges have a weight limit (or gross weight load rating) indicated by a sign posted in a visible position in front of the bridge (hence the reference to a "posted 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 discovered during mandated inspections of bridges. Most bridge collapses occur in rural areas, result in few injuries or deaths, and receive relatively little media attention. While the number varies from year to year, as many as 150 bridges can collapse in a year. About 1,500 bridges collapsed between 1966 and 2007, and most of those were the result of soil erosion around bridge supports. In 1987, the Schoharie Creek Bridge collapsed in upstate New York, due to erosion of soil around the foundation, which sparked renewed interest in bridge design in inspection procedures.

In special cases involving unusually overweight trucks (which require special permits), not observing a bridge weight limit can lead to disastrous consequences. Fifteen days after the collapse of the Minneapolis bridge, a heavy truck collapsed a small bridge in Oakville, Washington.

Formula law

CMVs are required to pass through weigh stations at the borders of most states and some large cities. These weigh stations are run by state DOTs, 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 are usually where a truck's compliance with the formula is checked.

Truck axle groups are used to calculate compliance with the formula. Any two axles must comply with the results of the formula, but axle groups 1–5, 1–3, and 2–5 are most critical. This truck is not in 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:

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

• w = the maximum weight in pounds that can be carried on a group of two or more axles to the nearest Template:Convert.
• 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") 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 will usually be satisfactory.

Penalties for violating weight limits vary between states (bridge formula weight violations are treated as gross weight violations), as the states are responsible for enforcement and collection of fines. Some states, such as Connecticut, issue fines on a percentage basis (e.g. 20% overweight at $10 per Template:Convert), which means larger trucks pay higher fines. For example, a truck with a legal gross limit of Template:Convert that violates the limit by Template:Convert would pay a fine of $500, while a truck with a legal gross limit of Template:Convert that violates the limit by 5,000 pounds would pay a fine of $250. Other states, such as New York, issue fines on a per-pound basis (e.g., 5,000 pounds overweight equals a $300 fine). Others, such as Massachusetts, impose a less complicated fine schedule whereby a vehicle that violates the limits by less than Template:Convert is fined $40 per 1000 pounds, while a violation over 10,000 pounds pays $80 per 1000 pounds (e.g. 5,000 pounds overweight equals a $200 fine).

Some states require overweight trucks to offload enough cargo to comply with the limits. In Florida, any vehicle that exceeds the limits by more than Template:Convert is required to be unloaded until the vehicle is in compliance. Florida also includes a scale tolerance, which allows for violations of less than 10% to be forgiven, and no fine issued. Florida also allows for a load to be shifted (e.g., moved from the front towards the rear of the vehicle) for the vehicle to comply with axle weight limits, without penalty.

Exception

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

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

A CMV may exceed the bridge formula limits (or gross weight and its axle weight limits) by up to Template:Convert if the vehicle is equipped with an auxiliary power unit (APU) or idle reduction technology. According to the FMCSA, this is permitted "in order to promote reduction of fuel use and emissions because of engine idling". To be eligible, the vehicle's operator must prove the weight of the APU with written certification, or—by demonstration or certification—that the idle reduction technology is fully functional at all times. Certification of the APU's weight must be available to law enforcement officers if the vehicle is found in violation of applicable weight laws. The additional weight allowed cannot exceed 400 pounds or the weight certified, whichever is less.

Issues

The bridge formula (also referred to as Formula B) is based on research into single-span bridges, and fails to consider multiple-span bridges. Two-span bridges may not be fully protected by Formula B, depending on the truck length, span length, and other factors. Shorter wheelbase vehicles (usually specialized trucks such as garbage trucks and water trucks) have trouble complying with Formula B.

In 1987, the U.S. Congress passed the Surface Transportation and Uniform Relocation Assistance Act, requesting the Transportation Research Board (TRB) to conduct a study to develop alternatives to Formula B. The study recommended several that were never implemented. It suggested that Formula B was too strict for trucks with shorter axle lengths. One of the alternative formulas (later known as the TTI HS-20 Bridge Formula) was developed in conjunction with the Texas Transportation Institute. TTI HS-20 allowed shorter trucks to have higher weight limits than Formula B. For a 3-axle truck with an axle length of Template:Convert, the weight limit increased from Template:Convert to Template:Convert. TTI HS-20 also failed to address the problem of multiple-span bridges.

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

References

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External links

• Bridge Formula Law
• Bridge formula weights calculator