Design

# FHWA Bridge Formula

Since an individual set of bridge design computations cannot be done for every type of truck that may use a particular highway, bridge designers use a standard vehicle, the HS20-44, for estimating critical stresses, strains, or deflections in a bridge structure (see Figure 1) (FHWA, 1984[1]).  Federal law requires its use in bridge design for the Interstate system.

The bridge formula calculates the maximum allowable load (the total gross weight in pounds) that can legally be imposed on the bridge by any group of two or more consecutive axles on a vehicle or combination of vehicles.  If a vehicle conforms to the bridge formula then it will not cause bridge structure stresses, strains or deflections to exceed those critical values calculated using the standard HS20-44 design vehicle.  In effect, it helps to ensure bridges are not “overstressed” due to the almost infinite number of truck-axle configurations and weights.  The bridge formula reflects the fact that loads concentrated over a short distance are generally more damaging to bridges than loads spread over a longer distance. It provides for additional gross weight as the wheel base lengthens and the number of axles increases. It should be noted that the number of axles influences pavement wear more than bridge stress (Hendrickson International, no date given[2]).  For a more in-depth coverage of the bridge formula (and Federal bridge laws in general), http://www.hendrickson-intl.com/literature/bridgelaws/Hendrickson International’s web page is an excellent resource.

Figure 1. Standard bridge design vehicle (after FHWA, 1984 [1]). Note: This is a U.S. FHWA formula so the examples use standard English units.

## Example 1

• Five axle truck
• One single axle (steering axle) – 51 ft separation from steering axle to rear portion of back tandem
• Two tandem axles (34 ft separation for tandems)
• Each set centered 4 ft apart

(for the group of axles – steering to rear tandem)

## Example 2

A partial definition of a tandem axle is any two axles whose centers are more than 40 in. but not more than 96 in. apart.  We know the maximum allowable load on a tandem is 34,000 lb.  Calculate the allowable load based on the bridge formula (initially use 96 in. or 8 ft).

Actually, a tandem axle spacing of 48 in. or 4 ft calculates to 34,000 lb.

## Example 3

A partial definition of a tridum axle is three axles whose extreme centers are not more than 144 in. (12 ft) apart.  Calculate the allowable loading according to the bridge formula:

Footnotes    (↵ returns to text)
1. Federal Highway Administration (FHWA).  (April 1984).  Bridge Gross Weight Formula.  Federal Highway Administration, U.S. Department of Transportation.  Washington, D.C.
2. Hendrickson International.  (no date given).  Federal Bridge Laws web page (http://www.hendrickson-intl.com/Bridge-Laws).  Part of the Hendrickson International web site (http://www.hendrickson-intl.com).

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