Federal Bridge Gross Weight Formula
Encyclopedia
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
United States Department of Transportation
The United States Department of Transportation is a federal Cabinet department of the United States government concerned with transportation. It was established by an act of Congress on October 15, 1966, and began operation on April 1, 1967...

 (DOT) officials to determine the appropriate maximum gross weight for a commercial motor vehicle (CMV) based on axle
Axle
An axle is a central shaft for a rotating wheel or gear. On wheeled vehicles, the axle may be fixed to the wheels, rotating with them, or fixed to its surroundings, with the wheels rotating around the axle. In the former case, bearings or bushings are provided at the mounting points where the 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
Infrastructure
Infrastructure is basic physical and organizational structures needed for the operation of a society or enterprise, or the services and facilities necessary for an economy to function...

.

Compliance with the law is checked when vehicles pass through a weigh station
Weigh station
A weigh station is a checkpoint along a highway to inspect vehicular weights. Usually, trucks and commercial vehicles are subject to the inspection....

, 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
American Trucking Associations
The American Trucking Associations , founded in 1933, is the largest national trade association for the trucking industry. Through a federation of other trucking groups, industry-related conferences, and its 50 affiliated state trucking associations, ATA represents more than 37,000 members covering...

 to allow tank truck
Tank truck
A tank truck or road tanker is a motor vehicle designed to carry liquefied loads, dry bulk cargo or gases on roads. The largest such vehicles are similar to railroad tank cars which are also designed to carry liquefied loads...

s 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 18000 pounds (8,164.7 kg) in Maine
Maine
Maine is a state in the New England region of the northeastern United States, bordered by the Atlantic Ocean to the east and south, New Hampshire to the west, and the Canadian provinces of Quebec to the northwest and New Brunswick to the northeast. Maine is both the northernmost and easternmost...

 to 28000 pounds (12,700.6 kg) in Massachusetts
Massachusetts
The Commonwealth of Massachusetts is a state in the New England region of the northeastern United States of America. It is bordered by Rhode Island and Connecticut to the south, New York to the west, and Vermont and New Hampshire to the north; at its east lies the Atlantic Ocean. As of the 2010...

. 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 73280 pounds (33,239.2 kg)) and authorized the construction of the Interstate Highway System
Interstate Highway System
The Dwight D. Eisenhower National System of Interstate and Defense Highways, , is a network of limited-access roads including freeways, highways, and expressways forming part of the National Highway System of the United States of America...

.

In the late 1950s, the American Association of State Highway and Transportation Officials
American Association of State Highway and Transportation Officials
AASHTO, the American Association of State Highway and Transportation Officials, is a standards setting body which publishes specifications, test protocols and guidelines which are used in highway design and construction throughout the United States...

 (AASHTO) conducted a series of extensive field tests
AASHO Road Test
The AASHO Road Test was a series of experiments carried out by the American Association of State Highway and Transportation Officials to determine how traffic contributed to the deterioration of highway pavements...

 of roads and bridges to determine how traffic contributed to the deterioration of pavement materials
Pavement (material)
Road surface or pavement is the durable surface material laid down on an area intended to sustain vehicular or foot traffic, such as a road or walkway. In the past cobblestones and granite setts were extensively used, but these surfaces have mostly been replaced by asphalt or concrete. Such...

. 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 80000 pounds (36,287.4 kg), still in use as of 2009.

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
Federal Motor Carrier Safety Administration
The Federal Motor Carrier Safety Administration , established January 1, 2000, regulates the trucking industry in the United States. FMCSA is headquartered in Washington, DC and employs more than 1,000 people in all 50 States and the District of Columbia...

 (FMCSA), regulates safety for the U.S. trucking industry
Trucking industry in the United States
The trucking industry involves the transport and distribution of commercial and industrial goods using commercial motor vehicles . In this case, CMVs are most often trucks; usually semi trucks, box trucks, or dump trucks...

. 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
Interstate Highway System
The Dwight D. Eisenhower National System of Interstate and Defense Highways, , is a network of limited-access roads including freeways, highways, and expressways forming part of the National Highway System of the United States of America...

, U.S. highways, and state highways known as the National Network
National Network
The National Network is a network of approved state highways and interstates for commercial truck drivers in the United States. The Surface Transportation Assistance Act of 1982 authorized the establishment of a national network of highways designated for use by large trucks. On these highways,...

 (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 10001 pounds (4,536.4 kg) 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 placard
Placard
A placard is a notice installed in a public place, like a small card, sign, or plaque. It can be attached to or hung from a vehicle or building to indicate information about the vehicle operator or contents of a vehicle or building.- Buildings :...

ed 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 80000 pounds (36,287.4 kg) for gross weight (unless the bridge formula dictates a lower limit), 34000 pounds (15,422.1 kg) for a tandem axle, and 20000 pounds (9,071.8 kg) for a single axle. A tandem axle is defined as two or more consecutive axles whose centers are spaced more than 40 inches (101.6 cm) but not more than 96 inches (243.8 cm) apart. Axles spaced less than 40 inches (101.6 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 feet (7.6 m) three-axle dump truck
Dump truck
A dump truck is a truck used for transporting loose material for construction. A typical dump truck is equipped with a hydraulically operated open-box bed hinged at the rear, the front of which can be lifted up to allow the contents to be deposited on the ground behind the truck at the site of...

 would have a gross weight limit of 54500 pounds (24,720.8 kg), instead of 80000 pounds (36,287.4 kg), which is the standard weight limit for 63 feet (19.2 m) 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

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
National Transportation Safety Board
The National Transportation Safety Board is an independent U.S. government investigative agency responsible for civil transportation accident investigation. In this role, the NTSB investigates and reports on aviation accidents and incidents, certain types of highway crashes, ship and marine...

 determined several reasons for the bridge's collapse, including (but not limited to): faulty gusset plate
Gusset plate
Gusset plates are thick sheets of steel that are used to connect beams and girders to columns or to connect truss members . A gusset plate can be fastened to a permanent member either by bolts, rivets or welding or a combination of the three . Gusset plates not only serve as a method of joining...

s, inadequate inspections, and the extra weight of heavy construction equipment combined with the weight of rush hour traffic. Reports suggest that as early as 1998, the Federal Highway Administration
Federal Highway Administration
The Federal Highway Administration is a division of the United States Department of Transportation that specializes in highway transportation. The agency's major activities are grouped into two "programs," the Federal-aid Highway Program and the Federal Lands Highway Program...

 (FHWA) expressed concern over bridges on the I-35 corridor due to an expected increase of international truck traffic from Canada
Canada
Canada is a North American country consisting of ten provinces and three territories. Located in the northern part of the continent, it extends from the Atlantic Ocean in the east to the Pacific Ocean in the west, and northward into the Arctic Ocean...

 and Mexico
Mexico
The United Mexican States , commonly known as Mexico , is a federal constitutional republic in North America. It is bordered on the north by the United States; on the south and west by the Pacific Ocean; on the southeast by Guatemala, Belize, and the Caribbean Sea; and on the east by the Gulf of...

.

As of 2007, federal estimates suggest truck traffic increased 216% since 1970, shortly before the federal gross weight limit for trucks was increased by 30000 pounds (13,607.8 kg). 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 80000 pounds (36,287.4 kg) truck does as much damage to roads as 750 3800 pounds (1,723.7 kg) 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 collapse
Schoharie Creek Bridge collapse
The Schoharie Creek Bridge was a New York State Thruway bridge over the Schoharie Creek near Fort Hunter, in New York State. On April 5, 1987 it collapsed due to erosion at the foundations after a record rainfall...

d in upstate New York
Upstate New York
Upstate New York is the region of the U.S. state of New York that is located north of the core of the New York metropolitan area.-Definition:There is no clear or official boundary between Upstate New York and Downstate 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
Oversize/overweight load
In road transport, an oversize load is a load that exceeds the standard or ordinary legal size and/or weight limits for a specified portion of road, highway or other transport infrastructure, such as air freight or water freight. There are also load per axle limits...

 (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
Oakville, Washington
Oakville is a city in Grays Harbor County, Washington, United States. The population was 684 at the 2010 census.-Geography:Oakville is located at ....

.

Formula law

CMVs are required to pass through weigh station
Weigh station
A weigh station is a checkpoint along a highway to inspect vehicular weights. Usually, trucks and commercial vehicles are subject to the inspection....

s 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.
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 (226.8 kg).
  • = 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
Connecticut
Connecticut is a state in the New England region of the northeastern United States. It is bordered by Rhode Island to the east, Massachusetts to the north, and the state of New York to the west and the south .Connecticut is named for the Connecticut River, the major U.S. river that approximately...

, issue fines on a percentage basis (e.g. 20% overweight at $10 per 100 pounds (45.4 kg)), which means larger trucks pay higher fines. For example, a truck with a legal gross limit of 20000 pounds (9,071.8 kg) that violates the limit by 5000 pounds (2,268 kg) would pay a fine of $500, while a truck with a legal gross limit of 60000 pounds (27,215.5 kg) that violates the limit by 5,000 pounds would pay a fine of $250. Other states, such as New York
New York
New York is a state in the Northeastern region of the United States. It is the nation's third most populous state. New York is bordered by New Jersey and Pennsylvania to the south, and by Connecticut, Massachusetts and Vermont to the east...

, issue fines on a per-pound basis (e.g., 5,000 pounds overweight equals a $300 fine). Others, such as Massachusetts
Massachusetts
The Commonwealth of Massachusetts is a state in the New England region of the northeastern United States of America. It is bordered by Rhode Island and Connecticut to the south, New York to the west, and Vermont and New Hampshire to the north; at its east lies the Atlantic Ocean. As of the 2010...

, impose a less complicated fine schedule whereby a vehicle that violates the limits by less than 10000 pounds (4,535.9 kg) 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
Florida
Florida is a state in the southeastern United States, located on the nation's Atlantic and Gulf coasts. It is bordered to the west by the Gulf of Mexico, to the north by Alabama and Georgia and to the east by the Atlantic Ocean. With a population of 18,801,310 as measured by the 2010 census, it...

, any vehicle that exceeds the limits by more than 6000 pounds (2,721.6 kg) 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 34000 pounds (15,422.1 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 gross up to 80000 pounds (36,287.4 kg) (the legal limit) without being in violation of the bridge formula law. Without it, the bridge formula would allow an actual weight of only 66000 pounds (29,937.1 kg) to 67500 pounds (30,617.5 kg) on tandems spaced 36 feet (11 m) to 38 feet (11.6 m) apart; compared to 68000 pounds (30,844.3 kg) with the exception. This exception was sought by the American Trucking Associations
American Trucking Associations
The American Trucking Associations , founded in 1933, is the largest national trade association for the trucking industry. Through a federation of other trucking groups, industry-related conferences, and its 50 affiliated state trucking associations, ATA represents more than 37,000 members covering...

 so trucking companies could use 40 feet (12.2 m) trailers and weigh 80000 pounds (36,287.4 kg). It was the only way tank truck
Tank truck
A tank truck or road tanker is a motor vehicle designed to carry liquefied loads, dry bulk cargo or gases on roads. The largest such vehicles are similar to railroad tank cars which are also designed to carry liquefied loads...

 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 axle weight limits) by up to 400 pounds (181.4 kg) if the vehicle is equipped with an auxiliary power unit (APU) or idle reduction
Idle reduction
Idle reduction is type of automobile emissions control aimed at reducing the amount of energy wasted by an idling vehicle. When a vehicle's engine is not being used to move the vehicle, it can be shut off entirely—thereby conserving fuel and reducing emissions—while other functions like accessories...

 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
Span (architecture)
Span is the distance between two intermediate supports for a structure, e.g. a beam or a bridge.A span can be closed by a solid beam or of a rope...

 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
United States Congress
The United States Congress is the bicameral legislature of the federal government of the United States, consisting of the Senate and the House of Representatives. The Congress meets in the United States Capitol in Washington, D.C....

 passed the Surface Transportation and Uniform Relocation Assistance Act, requesting the Transportation Research Board
Transportation Research Board
The Transportation Research Board is a division of the National Research Council, which serves as an independent adviser to the President, the Congress and federal agencies on scientific and technical questions of national importance...

 (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
Texas Transportation Institute
The Texas Transportation Institute in College Station, Texas is the largest transportation research agency in the United States. Created in 1950, primarily in response to the needs of the Texas Highway Department , TTI has since broadened its focus to address all modes of transportation–highway,...

. TTI HS-20 allowed shorter trucks to have higher weight limits than Formula B. For a 3-axle truck with an axle length of 14 feet (4.3 m), the weight limit increased from 46500 pounds (21,092 kg) to 54000 pounds (24,494 kg). 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 6 inches (15.2 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 in 11 in (2.72 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 68000 pounds (30,844.3 kg) is allowed.
  • __ Upper blank areas represent unrealistic configurations.

External links

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