## Understanding Live Load Distribution Factors (AASHTO LRFD)

## Understanding Live Load Distribution Factors (AASHTO LRFD)

(OP)

Hey all,

I was hoping someone could help me understand how live load distribution (LLDF) factors are applied. The wording in the AASHTO specifications isn't clear and I haven't been able to find any helpful resources online.

My question is: When determining the resultant moment (or shear) in a single girder, do you multiply the LLDF by the max. moment due to a single lane of loading or the max. moment due to the multiple lanes of loading.

i.e. Assume the maximum positive moment due to single lane loading is 100K-ft and that the LLDF is given as g(n) where n is the number of lanes being loaded.

Assuming 1 lane loading, the resultant moment that a single girder experiences is given as Mg = 100K-ft*g(1)

Now, which of the two options below would be correct for two lane loading:

Mg = 200K-ft*g(2)

Mg = 100K-ft*g(2)

I've spoken with two other engineers and they've given conflicting answers. On one hand it intuitively makes sense that the total moment should be multiplied by the LLDF (200K-ft), but it also doesn't make sense given that the LLDF, g, is given in "lanes".

I was hoping someone could help me understand how live load distribution (LLDF) factors are applied. The wording in the AASHTO specifications isn't clear and I haven't been able to find any helpful resources online.

My question is: When determining the resultant moment (or shear) in a single girder, do you multiply the LLDF by the max. moment due to a single lane of loading or the max. moment due to the multiple lanes of loading.

i.e. Assume the maximum positive moment due to single lane loading is 100K-ft and that the LLDF is given as g(n) where n is the number of lanes being loaded.

Assuming 1 lane loading, the resultant moment that a single girder experiences is given as Mg = 100K-ft*g(1)

Now, which of the two options below would be correct for two lane loading:

Mg = 200K-ft*g(2)

Mg = 100K-ft*g(2)

I've spoken with two other engineers and they've given conflicting answers. On one hand it intuitively makes sense that the total moment should be multiplied by the LLDF (200K-ft), but it also doesn't make sense given that the LLDF, g, is given in "lanes".

## RE: Understanding Live Load Distribution Factors (AASHTO LRFD)

The number of lanes will effect both the distribution factor equation chosen, and also the multiple presence factor.

You really need to read chapters 3 & 4 in AASHTO to get an understanding.

I will say, I did a structural concentration in college but it mainly focused on buildings. Bridge live loading was tough to understand at first, but once you understand it it’s easy.

## RE: Understanding Live Load Distribution Factors (AASHTO LRFD)

If one wheel of a truck (0.5 of an axle) is placed directly over a girder, the other wheel of that truck is 6' away, and the girder spacing is 9', then 1/3 of that 1/2 an axle load is applied with the half that's right over it, and the DF is 0.5 + 0.333*0.5 = .667. That DF holds also for all the vehicles in a line (AKA lane) along the length of the bridge.

For multiple trucks, the wheels (or lines of wheels) are assumed 4' apart (assumed 10' wide vehicles, with point loads at 2' in from each side, thus the 6' wheel spacing for a single vehicle). So, for the 9' girder spacing, the DF for multiple lanes = 0.5 + 0.5*5/9 = 0.778.

That's the basic concept. LRFD adds other possibilities, such as the reactions from truck loads acting on a superstructure that reacts as a rigid body, similar the way pier or abutment reactions are applied to group of piles (M/S + P/A).

If you're familiar with the wheel fraction (WF) used under the AASHTO Std spec. it considered individual wheels or wheel lines, rather than axles, or lines of axles, so the WF is theoretically twice the DF. Most software programs handle input WFs by dividing them by 2 to get the DFs used in calculations.

Rod Smith, P.E., The artist formerly known as HotRod10

## RE: Understanding Live Load Distribution Factors (AASHTO LRFD)

It's best to think of the LL distribution factors as fractions or portions of a lane. You have a LLDF for one, two or more lanes loaded, depending on how many design lanes your bridge has. The LLDF is also specific for interior or exterior beams as well as shear or moment. There is also the multiple presence factor depending on the number of lanes loaded.

Calculate the LLDF for moment for the interior beam with one lane loaded, two lanes loaded, etc. Then calculate the LLDF for the exterior beam with one lane loaded, two lanes loaded, etc. Do the same for shear.

Calculate the moment or shear for the beam or girder in question using one design truck placed along the span to create maximum force effects. Continuous spans have slightly different requirements for the double truck. Multiply your maximum shear or moment by the LLDF and the multiple presence factor to obtain the shear and moment for one lane loaded, two lanes loaded and so on.

To answer your question you take the max moment due to the effect of placing one truck on the span and multiply it by the LLDF for the number of lanes loaded and the MPF for the number of lanes loaded. You will end up with a max moment for one lane loaded, two lanes loaded and so on.

Clear as mud?

## RE: Understanding Live Load Distribution Factors (AASHTO LRFD)

Well, technically, as I said, the Std. spec used the "wheel fraction" (WF) - the fraction of a wheel load (or series of wheel loads) applied to a girder, and the LRFD uses a "distribution factor" (DF or LLDF), which is the fraction of an axle load (2 wheel loads) applied to a girder. In both cases, the lane load is the same - 64psf over a 10' width. The lane load can be converted to an equivalent wheel load (64*10/2) to be used with the WF or an equivalent axle load (64*10) to be used with the DF.

The lane load or truck load, whichever produces the greatest load effect, is applied under the std. spec., but under the LRFD both are applied together (truck + lane).

Rod Smith, P.E., The artist formerly known as HotRod10

## RE: Understanding Live Load Distribution Factors (AASHTO LRFD)

Thanks for clearing this up, I'm in agreement and it looks like I need to have a conversation with my superior.

## RE: Understanding Live Load Distribution Factors (AASHTO LRFD)