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# Live Load Distribution Factor using Lever Rule for Small Steel Bridges

## Live Load Distribution Factor using Lever Rule for Small Steel Bridges

(OP)
Hello,

- Bridge: Rolled Steel Beam with corrugated metal deck (nearly no overhangs)
- Interested in Exterior Girder
- Girder Spacing 4.5'.
- While placing the left truck wheel load (2' away from railing) right truck wheel load fall beyond the interior girder (hinge location) that is next to the interested ext girder.

In this case, are we supposed to just take one wheel load for that exterior girder or still put P/2 in the calculation. (Please see sketch attached)

Thank you.
Replies continue below

### RE: Live Load Distribution Factor using Lever Rule for Small Steel Bridges

Applying both wheel loads with the deck modeled as a transverse continuous beam may be somewhat unconservative, since the deck may not fully transfer the uplift load of the interior wheel line to the exterior girder. You could use the lever rule and ignore the second wheel line, and it would be a little conservative. Short of a FEA, it's probably the closest you're going to get. That's what I would do - just assume the deck as a simple span between the girders, and apply the portion of the outer wheel load that goes to the exterior girder (.63) as 1/2 the distribution factor (DF for LRFD) or the full wheel fraction (WF for LFD). So the LRFD LLDF = .315, or the LFD WF = .63.

### RE: Live Load Distribution Factor using Lever Rule for Small Steel Bridges

(OP)
@BridgeSmith
Thank you much. I guess I was confused with LFD's Wheel Load vs. LRFD's Axle Load approach for live load distribution. Your response made everything clearer. Btw, where would I be able to find the information for LL Distribution Factor for Deflection and Shear at Supports. Especially for load rating. I know for deflection, it is m × (no of lanes / no of girders). However BrR gives me different results for 1 lane loaded vs. Multi lane loaded. Also, my hand calc for shear at support does not match the BrR result. Any suggestion would be greatly appreciated.

Thank you.

### RE: Live Load Distribution Factor using Lever Rule for Small Steel Bridges

Is that the BRASS software?

### RE: Live Load Distribution Factor using Lever Rule for Small Steel Bridges

(OP)
Sorry for abbreviation. It is AASHTOWare Bridge Rating software

### RE: Live Load Distribution Factor using Lever Rule for Small Steel Bridges

Yes, AASHTOware uses BRASS Girder as the calculation engine.

When you look at the table of calculated DFs, what does it show in parentheses next to the DFs in question? Below the table, it should have notes indicating what the abbreviations in parentheses mean as far as the method it used to calculate the DF.

### RE: Live Load Distribution Factor using Lever Rule for Small Steel Bridges

(OP)
This is the result from BrR

===========================
Shear Distribution Factors
===========================

--------------------------------
Corrugated Deck on Exterior Beams
(Article 3.23.1.2)
---------------------------------
Same as moment distribution factors:

DF = 0.63 Wheels

Two or More Design Lanes Loaded:
DF = 0.63 Wheels

=======================================
Shear at Supports Distribution Factors
=======================================
Use simple beam distribution factors:

DF = 0.63 Wheels

Two or More Design Lanes Loaded:
DF = 0.63 Wheels

===============================
Deflection Distribution Factors
=================================

Compute Deflection Distribution Factors
----------------------------------------
Input:
Number Lanes = 2
Reduction Factor = 1.00
Number Beams = 7

DF = 2.0/Number beams = 2.0/7 = 0.29 Wheels

Two or More Design Lanes Loaded:
DF = 2.0 * Number Lanes * Reduction Factor/ Number beams = (2.0 * 2 * 1.00)/7 = 0.57 Wheels

### RE: Live Load Distribution Factor using Lever Rule for Small Steel Bridges

I don't have access to my AASHTO spec right now, but that's what I calculated using the lever rule. It doesn't look like the output from BRASS Girder, and it seems to be mixing terminology, reporting the LFD (Standard spec) wheel fraction ("0.63 Wheels"), but labeling it as "DF". This is disappointing. "DF" is the LRFD term for is the portion of the axle weight applied to a girder.

The calcs shown for deflection would seem to confirm this, since "2.0" factor in there gets you the wheel fraction, not the LRFD distribution factor.

### RE: Live Load Distribution Factor using Lever Rule for Small Steel Bridges

(OP)
Yeah, I am new to Bridge Design and not very familiar with LFD approach too. Im way too confused with LFD in the calc. I guess LFD approach dont care about 1 lane vs multi lane too right??

### RE: Live Load Distribution Factor using Lever Rule for Small Steel Bridges

I just spoke with a colleague, and apparently the AASHTOware BrR program does not not use BRASS. The predecessor (Virtis/Opis) did. My colleague said some of our guys had tried the BrR program and found horribly difficult to use compared to our BRASS program.

Other than the misleading/incorrect terminology of calling the wheel fraction "DF", it seems to be working

Article 3.23.1.2 (referenced in the BrR output above) states shear at the ends of beams is to be calculated assuming the deck as simple spans between the girders (lever rule).

The standard spec has a Reduction in Load Intensity (Article 3.12.1) of 10% for 3 lanes loaded and 25% for 4 or more lanes loaded, but no reduction for 2 lanes loaded.

The load rating should be controlled by one of the interior girders, anyway, unless the exterior girder is smaller. According to Table 3.23.1, for 2 or more lanes, the interior girder WF = S/4.5, so your interior girder WF = 4.5/4.5 = 1.0.

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