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Re: reducing rod deflection with tension
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- Subject: Re: reducing rod deflection with tension
- From: Scott Maxwell <smaxwell(--nospam--at)engin.umich.edu>
- Date: Thu, 28 Aug 2003 11:52:57 -0400 (EDT)
Ken, As both Roger and Thomas pointed out, you may be more governed by the desired deflection in the beam. In otherwords, in pointing the tension in the cable that you want to achieve the desired amount of sag in the rod, you may end up putting too much compression in the beam causing it to camber too much. So you should be careful about just looking at the tension in the cable to minimize the sag. As a result, Thomas' suggestion of use temperature in a computer program is a good one. After saying that, if you want to just deal with the sag in the cable without considering the impact on the beam, then it becomes basically a matter of statics. I have dealt with a similar but inverted problem in the past...I had a rod for which I wanted tensioned to a certain level. The problem was how was the contractor supposed to know when he had reached that desired tension level. The solution was to tell the contractor how much sag to have in the rod, which then would produce about the desired tension. As I said, it becomes an issue of statics. You would especially have some insight if you have dealt with equivalent loading methods in prestressed concrete. Image your rod. It is going to deflection in approimately a parabolic/circular/arc shape due to its own self weight. If the ends are free to move (as in your case), then the moment at the midspan will approximately be that of a simply supported beam...w*L^2/8. Now, since it is not really a simply supported beam but rather has a tensile force in it, we know that there is a tension force at each end (call it P) of the rod that acts at a tangent to the deflected shape at the end. This P force will be predominately horizontal with a small vertical component. Since, the slope/angle at the ends is rather small, however, we can approximate the horizontal component of the force as the overall force itself. So, we can approximate the horizontal force as being P. Now, at the midspan, that horizontal force is acting through a moment arm of the deflection at midspan...call it e (as in eccentricity in prestressing, but you can use delta if it gives you warm fuzzies). So, you have a moment due to the horizontal force at midspan of P*e. This moment must be equal to the moment at midspan due to self-weight. Thus, you get P*e=w*L^2/8. You know w, L and are defining e, so solve for P. So, by this method, with w=2.67 lb/ft (what I quickly calculated for the self-weight), L=22 ft (per your message) and desired sag of 1/2", you would need about 3900 lbs of tension in the rod (unless I goofed somewhere...always a possibility). So, now you would have consider what effect that would have on your top chord. HTH, Scott Ypsilanti, MI On Thu, 28 Aug 2003, Roger Turk wrote: > Ken, > > It is probably better to specify the deflection of the beam than to specify > the tension in the rod. > > For example, the deflection of the beam under applied loading without the > Queen post is calculated for queen post locations/center of span. Calculate > the load that the queen posts must apply to bring this deflection back to > what you want. From geometry, you can calculate what force is in the rod, > but the contractor does not have to worry about that. You just have to make > sure that the rod is big enough to take that force. > > If you want to specify the force in the rod to prevent the rod from sagging > more than 1/2", you might end up with the beam looking like an arch. > > HTH > > A. Roger Turk, P.E.(Structural) > Tucson, Arizona > > Ken Peoples wrote: > > . > I have a queen post truss with 1" rods for the bottom chord. The spacing > . > between the panel points is 22 feet. According to our calculations, the > . > 1" rods would sag about 10" under their own weight if they are not in > . > tension and free to move at their ends. I would like to find out how > . > much tension will need to be applied to reduce the self-weight deflection > . > to a reasonable amount - say 1/2". > > . > I see from Roark's formulas - Table 12 Case 3 that if the ends can't > . > move, then the force on the ends would be about 1100 pounds and the > . > deflection of the rod would be about 1 1/2". > > . > While this is helpful, this formula does not get me the force required to > . > bring the rod up that remaining 1" to get the deflection down to 1/2". I > . > understand that it is not possible to get the deflection to zero and > . > expect that as one approaches zero the force qets quite high. What I > . > don't want to do is to specify that the erector have to take more sag out > . > of the rod than is reasonable - thus inducing huge tension forces. > > . > Thanks in advance for your help. > > . > Best regards, > > . > Ken > > . > Kenneth S. Peoples, P. E. > . > Lehigh Valley Technical Associates, Inc. > . > 1584 Weaversville Road > . > Northampton, PA 18067-9039 > . > Phone: (610) 262-6345 > . > Fax: (610) 262-8188 > . > e-mail: kpeoples(--nospam--at)lvta.net > > ******* ****** ******* ******** ******* ******* ******* *** > * 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 > ******* ****** ****** ****** ******* ****** ****** ******** > ******* ****** ******* ******** ******* ******* ******* *** * 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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