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Lane Distribution Factor
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- Subject: Lane Distribution Factor
- From: "Michael L. Hemstad" <hemstad.ml(--nospam--at)tkda.com>
- 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 already answered, but... 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. Don't multiply your answer by three. 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, Mike Hemstad TKDA St. Paul, Minnesota ******* ****** ******* ******** ******* ******* ******* *** * Read list FAQ at: http://www.seaint.org/list_FAQ.asp * * This email was sent to you via Structural Engineers * Association of Southern California (SEAOSC) server. To * subscribe (no fee) or UnSubscribe, please go to: * * http://www.seaint.org/sealist1.asp * * Questions to seaint-ad(--nospam--at)seaint.org. Remember, any email you * send to the list is public domain and may be re-posted * without your permission. Make sure you visit our web * site at: http://www.seaint.org ******* ****** ****** ****** ******* ****** ****** ********
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