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# Lane Distribution Factor

• To: <seaint(--nospam--at)seaint.org>
• Subject: Lane Distribution Factor
• Date: Wed, 6 Oct 2004 13:46:24 -0500

Mark Spivak <spivak(--nospam--at)research.suspicious.org>  wrote:

"Hi, quick question for our bridge experts:
I have a three-lane bridge that is 70' long and is supported by 5
longitudinal concrete girders.
I have run through AASHTO calculations to find the distribution factor
for 1 girder so I can run my analysis to find the moments in the girder.
My question is, since I have three lanes should I multiply the loads by
3?
For example i am using an HS-20 truck to find the moment envelope. The
front axle is 8kips and 2nd & 3d are 32 kips.
Should I load my beam by DF*8kips, DF* 32kips and DF*32kips?
Or should I use 3*DF*8kips , 3*DF*32kips and 3*DF*32kips? (For 3 lanes).

Note that i calculated the DF based on the "2 lanes or more" formula.

Thanks."

Mark,
I haven't received any Digests since you posted this, so it's probably

The distribution factor is based on beam spacing (for the old AASHTO).
For the new LRFD AASHTO, it's based on beam and deck stiffness and some
other things, in addition to beam spacing.  In any event, when Nathan
Newmark came up with the original S/11 distribution factor, his thought
process went like this:

Envision a multi-lane bridge with 12 foot lanes, and beams at 6 foot
spacing, with all lanes loaded the same (same truck, same location, same
direction).  Trucks are in each lane, with wheel lines 6 feet apart.
Each beam then carries exactly 1.0 wheel line.  If the beams were 12
feet apart, each beam carries 2.0 wheel lines.  If you have a 3 foot
beam spacing, each beam carries 0.5 wheel lines.  You get the picture.

This logic gives you a distribution of S/12 lanes per beam, or S/6
wheels per beam.  Newmark, being a properly conservative guy, bumped
that up to S/11 lanes or S/5.5 wheels per beam to account for everything
he knew he didn't know.

If you have 3 lanes or 20 lanes on a bridge, with beams spaced at S,
each beam still is responsible for S/5.5 wheel lines or S/11 lanes.

Now, this works pretty well for moment, when your trucks are located
near midspan and the load can distribute (because the beams can
deflect).  Many engineers (myself included) consider it less realistic
for shear.  For shear, when the trucks are located near the end of a
span, I put one rear wheel (heavy wheel) at the support and distribute
it by simple-beam distribution.  The other two wheels get the S/5.5
factor.  This is conservative and more realistic than the entire truck
getting S/5.5, especially for beam spacing less than 5.5 feet, because
if a wheel lands directly on a beam near the bearing, it really can't
distribute; that beam supports the wheel alone.

For reactions at a pier supporting two spans, the logic is similar
except you want to put the middle wheel over the pier, distributed by
simple beam.  For different spans, put the rear wheel over the longer
span.

When I was younger, I used to consider this S/11 business one of the
gaping weaknesses of the AASHTO code.  I no longer do.  In fact, this
week's opinion is that the more complex LRFD formula, which (if memory
serves) includes terms for the torsional stiffness of the beam (as well
as the phase of the moon), is falsely misleading of the state of our
knowledge.  My assumption is that it was better at getting some guy a
Ph.D. than at predicting load effects on bridge beams.  Sometimes, we
confuse precision and complexity with accuracy.

One of the things that I still consider a gaping weakness is the Impact
factor.  The pioneering work, if you can call it that, was done by a guy
named J.A.L. Waddell back around the turn of the last century.  The
formula owes its existence mostly to Waddell's purely qualitative
reasoning regarding span length (longer span, less impact).  I'm sure
there have been tests, but I'd bet the scatter would have allowed a lot
of similar formulas.  He had three or four that he liked and used; the
current one represents some deliberative body's best judgement.
However, I don't have a better one, and it's better than not having one
at all.  Don't forget to apply it.

HTH,

TKDA
St. Paul, Minnesota

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