Understanding Live Load Distribution Factors (AASHTO LRFD) 1

[Bay_ENG]

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 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".

 

[Guest090822]

It actually isn’t too hard once you understand it. The distribution factor is just the percentage of live load a single girder sees but is in decimal form. FHWA has some design examples you can follow.

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.

 

[BridgeSmith]

As TheRick109 said, the LLDF is a portion of an axle loading applied to a single girder. There are LLDFs for single trucks (wheel loads 6' apart) and for multiple trucks (wheel loads of separate trucks assumed 4' apart). Assuming the bridge is not ridiculously short, there will potentially be multiple vehicles on the bridge at the same time, presuambly a truck equivalent to the design vehicle (HL-93 truck loading) and other smaller vehicles (HL-93 Lane Load).

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

 

[OSUCivlEng]

A bit of clarification. The current AASHTO LRFD live load distribution factors are based on lanes. The old AASHTO Standard Spec was based on wheel loads.

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?

 

[BridgeSmith]

A bit of clarification. The current AASHTO LRFD live load distribution factors are based on lanes. The old AASHTO Standard Spec was based on wheel loads.

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

 

[Bay_ENG]

Thanks OSUCivlEng, you answered my question perfectly. What's concerning is that I reached out to a senior structural engineer at my firm and he gave a different explanation of how LLDF are applied. He tried to explain that the max moment due to the effect of placing one truck multiplied by the appropriate LLDF and MPF for the number of lanes loaded should then be multiplied by the integer of the number of lanes loaded. i.e. Moment due to 3 lanes loaded would be max. moment due to loading 1 truck, multiplied by LLDF, multiplied by MPF, multiplied by 3.

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

 

[OSUCivlEng]

Lysergie perhaps he is not as familiar with the LRFD Specs. Some states did not require LRFD design until somewhat recently.