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Bridge Gross Weight Formula

Three questions are addressed by this pamphlet with regard to the Bridge Formula: What is it? Why is it necessary? How is it used?

What is it?

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W = the maximum weight in pounds that can be carried on a group of two or more axles to the nearest 500 pounds.

L = the distance in feet between the outer axles of any two or more consecutive axles.

N = the number of axles being considered.

This formula limits the weight on groups of axles in order to reduce the risk of damage to highway bridges. Allowable weight depends on the number of axles a vehicle has and the distance between those axles. However, the single- or tandem-axle weight limits supersede the Bridge Formula limits for all axles not more than 96" apart.

Why is the Formula Necessary?

Bridges on the Interstate System highways are used by a wide variety of traffic. They are designed to support expected loadings. However, as trucks grew heavier in the 1950s and 1960s, something had to be done to protect bridges. The solution was to tie allowable weights to the number and spacing of axles.

Axle spacing is as important as axle weight in bridge design. A bridge is analogous to thin ice on a pond. Walking on the ice concentrates a person's weight on the small area covered by the individual's feet, and the ice may break. Lying down, however, spreads the same weight over a much larger area, and the ice is less likely to break. Consider trucks crossing a bridge:

graphic01.gif

In Figure 1(A), the stress on bridge members as the longer truck rolls across is much less than that caused by the short vehicle in Figure 1(B), even though both trucks have the same total weight and individual axle weights. The weight of the longer vehicle is spread out, while the shorter vehicle has all of the weight concentrated on a small area.

The Federal-Aid Highway Amendments of 1974 increased the weights allowed on the Interstate System to 20,000 lbs. on a single axle, 34,000 lbs. on a tandem axle, and 80,000 lbs. gross weight (23 U.S.C. 127). But Congress balanced this concession to productivity by enacting the Bridge Formula. The result is that motor vehicles may be loaded to the maximum weight only if each group of axles on the vehicle and their spacing also satisfy the requirements of the Formula. This prevents the vehicle from overstressing bridges in the same way that a person lying down on thin ice would minimize the risk of breaking through.

Until 1982, Federal law set only upper limits (or ceilings) on Interstate System weight limits. A few States retained significantly lower weight limits which eventually became barriers to long-distance truck traffic. In 1982, Federal law was amended to make Interstate System weight limits, including the bridge formula limits, both the maximum and the minimum weights (i.e., floors and ceilings) that States must allow on the Interstate System.

How is the Formula Used?

Some definitions are needed to use the Bridge Formula correctly.

Gross Weight—The weight of a vehicle or vehicle combination and any load thereon. The Federal gross weight limit on the Interstate System is 80,000 lbs.

Single-Axle Weight—The total weight on one or more axles whose centers are not more than 40" apart. The Federal single-axle weight limit on the Interstate System is 20,000 lbs.

Tandem-Axle Weight—The total weight on two or more consecutive axles more than 40" but not more than 96 inches apart. The Federal tandem-axle weight limit on the Interstate System is 34,000 lbs.

Interstate System weight limits in some States may be higher than these figures due to "grandfather" rights. When the Interstate System axle and gross weight limits were adopted in 1956, States were allowed to keep or "grandfather" those which were higher. In 1975, States were also allowed to keep "grandfathered" bridge formula limits which were higher than those established for the Interstate System.

Bridge Formula calculations yield a series of values usually referred to as Bridge Table B. However, the single-axle weight limit replaces the Bridge Formula weight limit on axles not more than 40" apart, and the tandem-axle weight limit replaces the Bridge Formula weight limit for axles over 40 but not more than 96 inches apart. At 97" apart, two axles can carry 38,000 lbs. and three axles 42,000 lbs., as shown in Figure 2.

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Federal law provides that any two or more consecutive axles may not exceed the weight computed by the Formula even though single axles, tandem axles, and gross weight are within legal limits. In other words, the axle group that includes the entire truck—sometimes call the "outer bridge" group—must comply with the Bridge Formula. But interior combinations of axles, such as the "tractor bridge" (axles 1, 2, and 3) and "trailer bridge" (axles 2, 3, 4, and 5), must also be in compliance with weights computed by the Formula (Figure 3).

graphic03.gif

The most common vehicle checked for compliance with weight limit requirements is shown in Figure 3. While the Bridge Formula applies to each combination of two or more axles, experience shows that axle combinations 1 through 3, 1 through 5, and 2 through 5 are critical and must be checked. If these combinations are found to be satisfactory, all of the others on this type of vehicle will normally be satisfactory.

The vehicle with weights and axle dimensions as shown in Figure 4 will be used to illustrate a Bridge Formula check.

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Before checking a vehicle for compliance with the Bridge Formula, its single-axle, tandem-axle, and gross weight should be checked. Here the single axle (number 1) does not exceed 20,000 lbs., tandems 2-3 and 4-5 do not exceed 34,000 lbs. each, and the gross weight does not exceed 80,000 lbs. These preliminary requirements are thus satisfied. The first Bridge Formula combination is checked as follows:

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Check of 1 thru 3 (Figure 5)

Actual weight = 12,000 + 17,000 + 17,000 = 46,000 lbs.

N = 3 axles

L = 20 ft

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W maximum = 51,000 lbs., which is more than the actual weight of 46,000 lbs., so the Bridge Formula requirement is satisfied.

Example—Bridge Table B

This same number (51,000 lbs.) could have been obtained from Bridge Table B as shown by reading down the left side to L = 20 and across to the right where N = 3.

graphic06.gif

Now check axles 1 thru 5 (Figure 6)

Actual weight = 12,000 + 17,000 + 17,000 + 17,000 + 17,000 = 80,000 lbs.

W maximum, from Table B for "L" of 51 feet and "N" of 5 = 80,000 lbs.

Therefore, this axle spacing is satisfactory.

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Now check axles 2 thru 5 (Figure 7)

Actual weight = 17,000 + 17,000 + 17,000 + 17,000 = 68,000 lbs.

W maximum, from Table B for "L" of 35 feet and "N" of 4 = 65,500 lbs.

This is a violation because the actual weight exceeds the weight allowed by the Bridge Formula. To correct the situation, some load must be removed from the vehicle or the axle spacing (35 feet) must be increased.
 

Permissible Gross Loads For Vehicles In Regular Operation1

 

Based on weight formula formula01-(1).GIF

 

Distance in feet (L) between the extremes of any group of 2 or more consecutive axles [Bridge Table B]
Maximum load in pounds carried on any group of 2 or more consecutive axles2
N = 2 AXLES 3 AXLES 4 AXLES 5 AXLES 6 AXLES 7 AXLES 8 AXLES 9 AXLES
4 34,000              
5 34,000              
6 34,000              
7 34,000              
8 & less 34,000 34,000            
more than 8 38,000 42,000            
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     66,000 70,500 75,500 81,000 86,500 92,000
37     66,500 71,000 76,000 81,500 87,000 93,000
38     67,500 71,500 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 84,000 89,000 94,500 100,000
51     76,000 80,000 84,500 89,500 95,000 100,500
52     76,500 80,500 85,000 90,500 95,500 101,000
53     77,500 81,000 86,000 91,000 96,500 102,000
54     78,000 81,500 86,500 91,500 97,000 102,500
55     78,500 82,500 87,000 92,000 97,500 103,000
56     79,500 83,000 87,500 92,500 98,000 103,500
57     80,000 83,500 88,000 93,000 98,500 104,000
58       84,000 89,000 94,000 99,000 104,500
59       85,000 89,500 94,500 99,500 105,000
60       85,500 90,000 95,000 100,500 105,500

1The permissible loads are computed to the nearest 500 pounds as required by statute.

2The following loaded vehicles must not operate over H15-44 bridges: 3-S2 (5-axle) with wheelbase less than 38 feet; 2-S1-2 (5-axle) with wheelbase less than 45 feet; 3-3 (6-axle) with wheelbase less than 45 feet; and 7-, 8- and 9-axle vehicles regardless of wheelbase.

 

Tandem Axle Weight (See pages 4 & 5)
Within Interstate Gross Weight Limit
Exception

 

State Contacts

  Overweight/
Oversize Permits
Interstate 80,000 lbs.
unless otherwise stated
State
Highway
State
Maximum
Alabama (334) 834-1092   > B 84,000 on 6 axles
Alaska (907) 345-7636 Exempt from interstate weight regulation   Up to 145,000 on 11 axles
Arizona (602) 255-7346 LCV B 80,000
Arkansas (501) 569-2381   B 80,000
California (916) 654-4828   B 80,000
Colorado (303) 757-9539 LCV > B 85,000
Connecticut (860) 594-2880   > B 80,000
Delaware (302) 739-4374   < B 80,000 on 5 axles
Dist. of Columbia (202) 727-7050   > B 80,000
Florida (904) 488-4961   > B 80,000
Georgia (404) 656-5435   > B 80,000
Hawaii (808) 587-2185   > B 88,000
Idaho (208) 334-8420 LCV > B 105,500 on 6 axles
Illinois (217) 785-1477   < B 73,280 non-NN highway
Indiana (317) 486-5500 LCV B 80,000
Iowa (515) 237-3264   B 80,000
Kansas (913) 266-2040 LCV B 85,500
Kentucky (502) 564-7150   B 80,000
Louisiana (504) 343-2345   > B 88,000 Tri or Quad axle
Maine (207) 287-8632   > B 90,000
Maryland (410) 787-4088   > B 80,000
Massachusetts (508) 624-0819   > B 80,000
Michigan (517) 373-2120   > B 164,000 on 11 axles
Minnesota (612) 405-6000   < B 80,000 on 6 axles
Mississippi (601) 359-1148   B 80,000 (57,650 on highway class)
Missouri (573) 751-2871 LCV < B 73,280 (2,000 tolerance)
Montana (406) 444-6130 LCV B 80,000
Nebraska (402) 479-4775   B 95,000 on 7 axles
Nevada (702) 687-5410 LCV B Uncapped
New Hampshire (603) 271-2691   > B 80,000
New Jersey (908) 247-0900   B 80,000
New Mexico (505) 827-0383   > B 86,400
New York (518) 457-1155   > B 80,000
North Carolina (919) 574-6683   > B 80,000
North Dakota (701) 328-2621 LCV > B 105,500 on 7 axles
Ohio (614) 777-0224 LCV B 80,000
Oklahoma (405) 425-2390 LCV B 90,000
Oregon (503) 945-7903 LCV B 80,000
Pennsylvania (717) 787-5367   > B 80,000
Rhode Island (401) 277-2986 (overweight),
(401) 277-3175 (oversize)
  > B 80,000
South Carolina (803) 737-1279   > B 80,000
South Dakota (605) 773-4578 LCV B Uncapped
Tennessee (615) 741-3821   B 80,000
Texas (800) 299-1700   B 80,000
Utah (801) 965-4508 LCV B 80,000
Vermont (802) 828-2070   B 80,000
Virginia (804) 786-2787   B 80,000
Washington (206) 753-6554   B 80,000
West Virginia (304) 348-0384   < B 65,000 (73,500 some highways)
Wisconsin (608) 266-7320   B 80,000
Wyoming (307) 777-4376   > B 117,000 on 8 axles

LCV = Longer Combination Vehicle

 

Exception to Formula and Table B

Federal law (23 U.S.C. 127) includes one exception to the Bridge Formula and Table B—two consecutive sets of tandem axles may carry 34,000 lbs. each if the overall distance between the first and last axles of these tandems is 36 feet or more. For example, a five-axle tractor-semitrailer combination may carry 34,000 lbs. 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 apart. Without this exception, the Bridge Formula would allow an actual weight of only 66,000 and 67,500 lbs. on tandems spaced 36 to 38 feet apart.

Bridge Formula Application to Single Unit Trucks

The procedure described above can be used to check any axle combinations, but several closely spaced axles usually produce the most critical situation.

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The truck in Figure 8 satisfies the single axle weight limit (12,000 lbs. is less than 20,000 lbs.), the tandem axle limit (30,000 lbs. is less than 34,000 lbs.) and gross weight limit (57,000 lbs. is less than 80,000 lbs.). With these restrictions satisfied, a check will be made for Bridge Formula requirements, axles 1 through 4.

Actual weight = 12,000 + 15,000 + 15,000 + 15,000 = 57,000 lbs.
W maximum for "N" of 4 and "L" of 23 feet = 57,500 (From Table B).
Since axles 1 thru 4 are satisfactory, check axles 2 thru 4:
W (actual) = 15,000 + 15,000 + 15,000 = 45,000 lbs.
W maximum for "N" of 3 and "L" of 9 feet = 42,500 lbs. (From Table B).

This is a violation. The load would have to be reduced, axles added, or spacing increased, to comply with the Bridge Formula.

 

Caution

This pamphlet paraphrases the actual provisions in 23 U.S.C. 127 and 23 CFR 658 for the sake of clarity. In case of a dispute, the statute and regulations will govern.

Previous editions of this pamphlet released under the title "Bridge Gross Weight Formula," dated April 1984, remain valid. Neither the Formula nor any resulting maximum gross weight values (table entries) have been changed.