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

1
17,000 Ibs. 12,000 Ibs.
17,000 Ibs. 1

| —20 t—| Figure 5

Check axles 1 through 3 (Figure 5)

Actual weight = 12,000 + 17,000 + 17,000 = 46,000 pounds.
N= 3 axles

L = 20 feet

W=500 [ AN 1a + 36]
NA

w=500 [ 20x3). (1213) +26 = 51,000 Ibs,

Maximum weight (W) = 51,000 pounds, which is more than
the actual weight of 46,000 pounds. Thus, the Bridge Formula
requirement is satisfied

Example From the Bridge Table (pages 5 & 6)

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

Gross Weight - 80,000 Ibs.

a 17,000 Ibs. ]
17,000 Ibs. 17,000 Ibs.
J 17,000 Ibs. | 12,000 bs

| Sift |

Figure 6

Now check axles 1 through 5 (Figure 6)

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

Maximum weight (W) = 80,000 pounds (Bridge Table for “L"
of 51 feet and "N" of 5 axles).

Therefore, this axle spacing is satisfactory.

©@ Soll

1
17,000 Ibs. 17,000 Ibs. 17,000 Ibs.
J 17,000 Ibs.

| 36 ft. —|

Figure 7

Now check axles 2 through 5 (Figure 7)

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

Maximum weight (W) = 65,500 pounds (Bridge Table for
"L" of 35 feet and "N" of 4 axles).

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



Permissible Gross ds for Vehicles in Regular Operation’

Based on weight formula W = 500 [ AN tans 26]
Distance in feet (L) N-1
between the extremes
Mowe cSaadeatve axles [——— Maximum toad in pounds carried on any group of 2 or more consecutive axles* —

t N= 2 AXLES

34,000

BAXLES 4 AXLES 5 AXLES 6 AXLES 7 AXLES 8 AXLES 9 AXLES

Tandem

‘Aile 34,000
Mom 34,000
pages 34,000

34,000 34,000
jore than 8/less than9 38,000» 42,000
39,000 42,500
40,000 43,500

ezenoan

44,000
45,000
45,500
46,500
47,000 52,000
48,000" 52,500 58,000
48,500 53,500 58,500
49,500 54,000 59,000
19 Example 50,000 54,500 60,000 saunas
20. (see page 7) 55,500 60,500 66,000
51,500 56,000 61,000 66,500
52,500 56,500 61,500 67,000
53,000 57,500 62,500 68,000
54,000 58,000 63,000 68,500 74,000
54,500 58,500 63,500 69,000 74,500
55,500 59,500 64,000 69,500 75,000
56,000 60,000 65,000 70,000
57,000 60,500 65,500 71,000
57,500 61,500 66,000 71,500
58,500 62,000 66,500 72,000
59,000 62,500 67,500 72,500
60,000 63,500 68,000 73,000 84,500 90,000
64,000 68,500 74,000 85,000 90,500
64,500 69,000 74,500 85,500 91,000
65,500 70,000 75,000 80,500 86,000 91,500
Exception { esc | 70,500 75,500 81,000 86,500 92,000
(eee pages) { 66,500 71,000 76,000 81,500 87,000 93,000
. 67,500 71,500 77,000 82,000 87,500 93,500
68,000 72,000 77,500 82,500 88,500 94,000
68,500 73,000 78,000 83,500 89,000 94,500
69,500 73,500 78,500 84,000 89,500 95,000
70,000 74,000 79,000 84,500 90,000 95,500
70,500 75,000 80,000 85,000 90,500 96,000
71,500 75,500 80,500 85,500 91,000 96,500
72,000 76,000 81,000 86,000 91,500 97,500
72,500 76,500 81,500 87,000 92,500 98,000
73,500 77,500 82,000 87,500 93,000 98,500
74,000 78,000 83,000 88,000 93,500 99,000
74,500 78,500 83,500 88,500 94,000 99,500
75,500 79,000 84,000 89,000 94,500 100,000
76,000 80,000, 84,500 89,500 95,000 100,500
76,500 80,500 85,000 90,500 95,500 401,000
77,500 81,000 86,000 91,000 96,500 101,500
78,000 81,500 86,500 91,500 97,000 402,000
78,500 82,500 87,000 92,000 97,500 102,500
Interstate Gross -) 79,500 83,000 87,500 92,500 98,000 103,000
Weight mt |’ 80,000 83,500 88,000 93,000 98,500 104,000
a2 84,000 89,000 94,000 99,000 104,500
85,000 89,500 94,500 99,500 105,000

85,500 90,000 95,000 100,500 105,500

"The values in this table reflect FHWA's policy of rounding down when calculated weights semitrailer with a wheelbase of less than 38 feet), 2-S1-2 (S-axle semitrailer com-

fall exactly halfway between 500-pound increments. Because the Bridge Formula is bination with a wheelbase of less than 45 feet), 3-3 (6-axle truck trailer combina-
designed to protect highway infrastructure, FHWA determined that this conservative policy tion with a wheelbase less than 45 feet), and any truck with 7 or more axles.

{s consistent with the statutory mandate, H15-44 bridges are designed for a specific vehicle load; H15 refers to a 15-fon 2-
"The following loaded vehicles must not operate over H15-44 bridges; 3-S2 (S-axle tractor axle truck; 44 refers to the year AASHTO published the loading information. See

AASHTO Standard Specifications for Highway Bridges.


xception to Formula and Bridge Table

In addition to the grandfather rights noted on page 3, Federal
law (23 U.S.C. 127) includes one other exception to the
Bridge Formula and the Bridge Table—two consecutive sets
of tandem axles may carry 34,000 pounds 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 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 apart.
Without this exception, the Bridge Formula would allow an
actual weight of only 66,000 to 67,500 pounds on tandems
spaced 36 to 38 feet apart.

Bridge Formula Application
to Single-Unit Trucks

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

4.
¢
15,000 Ibs. 12,000 Ibs.

15,000 Ibs.

15,000 Ibs.

__ 33>
Figure 8

The truck shown in Figure 8 satisfies the single-axle weight
limit (12,000 pounds are less than 20,000 pounds), the tan-
dem-axle limit (30,000 pounds are less than 34,000 pounds)
and the gross-weight limit (57,000 pounds are less than
80,000 pounds). With these restrictions satisfied, a check is
done for Bridge Formula requirements, axles 1 through 4.

Actual Weight= 12,000 + 15,000 + 15,000 + 15,000 =
57,000 pounds.

Maximum weight (W) = 57,500 pounds (Bridge Table for “L”
of 23 feet and “N" of 4 axles).

Since axles 1 through 4 are satisfactory, check axles 2
through 4:

Actual weight = 15,000 + 15,000 + 15,000 = 45,000
pounds.

Maximum weight (W) = 42,500 pounds (Bridge Table for “L”
of 9 feet and "N" of 3 axles).

This is a violation because the actual weight exceeds the
weight allowed by the Bridge Formula. The load must either
be reduced, axles added, or spacing increased to comply with
the Bridge Formula.

Quality Assurance Statement

The Federal Highway Administration (FHWA) provides high-
quality information to serve Government, industry, and the
public in a manner that promotes public understanding.
Standards and policies are used to ensure and maximize the
quality, objectivity, utility, and integrity of its information.
FHWA periodically reviews quality issues and adjusts its pro-
grams and processes to ensure continuous quality improve-
ment.



Note

This pamphlet paraphrases the provisions in 23
U.S.C. 127 and 23 CFR 658 for the sake of clarity. In
case of a dispute, the statue and regulations take
precedence.

Previous editions of this pamphlet, entitled Bridge
Gross Weight Formula (April 1984) and Bridge
Formula Weights (January 1994), remain valid.
Neither the Bridge Formula nor any resulting
maximum gross weight values (table entries) has
been changed.

Bridge
Formula
Weights

August 2006

U.S. Department of Transportation
Federal Highway Administration

Office of Freight Management and Operations
Phone: 202-366-9210

Fax: 202-366-3302

Web site: http://www.ops.fhwa.dot.gov/freight
August 2006

FHWA-HOP-06-105

co)

US Deparment of ransperration
Federo! Highway Administration



Bridge
Fo r m TT] I a With a few exceptions noted in this pamphlet,
the Bridge Formula establishes the maximum
Weights weight any set of axles on a motor vehicle
may carry on the Interstate highway system.
This pamphlet describes the Bridge Formula,
why it was established, and how it is used.

What Is It

Congress enacted the Bridge Formula in 1975 to limit the
weight-to-length ratio of a vehicle crossing a bridge. This is
accomplished either by spreading weight over additional axles
or by increasing the distance between axles.

Compliance with Bridge Formula weight limits is determined by
using the following formula:

w=500 | WL + 12N +36
NA

W = the overall gross weight on any group of two or
more consecutive axles to the nearest 500 pounds.

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

N = the number of axles in the group under consideration.

In addition to Bridge Formula weight limits, Federal law states
that single axles are limited to 20,000 pounds, and axles closer
‘than 96 inches apart (tandem axles) are limited to 34,000
pounds. Gross vehicle weight is limited to 80,000 pounds (23
U.S.C. 127).

Bridges on the Interstate System highways are designed to sup-
port a wide variety of vehicles and their expected loads. As
trucks grew heavier in the 1950s and 1960s, something had to

Long 80,000 Ib. Truck

3 aN

(ete) (eXe).@)
ISN ZEST
l] iP
(A)

Short 80,000 Ib. Truck

ash
Re
fi i

Figure 1

be done to protect bridges. The solution was to link allowable
weights to the number and spacing of axles.

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

How Is the Formula Used?

The weight on various axle configurations must be checked to
determine compliance with the Bridge Formula. Three defini-
tions 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 pounds unless the Bridge Formula
dictates a lower weight limit.



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

Tandem-Axle Weight—The total weight on two or more con-
‘secutive axles whose centers are spaced more than 40 inches
apart but not more than 96 inches apart. The Federal tandem-
axle weight limit on the Interstate System is 34,000 pounds.

Interstate System weight limits in some States may be higher
than the figures noted above due to "grandfather" rights. When
the Interstate System axle and gross weight limits were first
adopted in 1956, and amended in 1975, States were allowed
to keep or "grandfather" weight limits that were higher.

Bridge Formula calculations yield a series of weights (Bridge
Table, pages 5-6). It is important to note that the single-axle
weight limit replaces the Bridge Formula weight limit on axles
not more than 40 inches 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 inches apart, for
example, two axles may carry 38,000 pounds (Figure 2A), and
three axles may carry 42,000 pounds, as shown in Figure 2B.

(A)

® @

| ozin, |

38,000 Ibs,

42,000 Ibs.

Federal law states that any two or more consecutive axles
may not exceed the weight computed by the Bridge Formula
even though single axles, tandem axles, and gross weight are
within legal limits. As a result, the axle group that includes the
entire truck—sometimes called the "outer bridge” group—
must comply with the Bridge Formula. However, interior com-
binations of axles, such as the "tractor bridge" (axles 1, 2,
and 3) and “trailer bridge" (axles 2, 3, 4, and 5), must also
comply with weights computed by the Bridge Formula

(Figure 3).

©@ OO’

Figure 3

Figure 3 shows the most common vehicle checked for com-
pliance with weight limit requirements. Although 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, then all of
‘the others on this type of vehicle normally will be satisfactory.

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

Gross Weight - 80,000 Ibs.

©@ OO'

x h
17,000 Ibs. | 10 Ibs.
17,000 Ibs.

17,000 Ibs. 12,000 Ibs.
1-20 ft.
— ft ——4]

—_—_—_ it
Figure 4