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Flexural analysis of 3-legged tower

Flexural analysis of 3-legged tower

Flexural analysis of 3-legged tower

(OP)
I've got a 3-legged trussed tower composed of three pipe columns in each corner.  In plan view it is an equilateral triangle.  Between the pipe columns are vertical and diagonal web members.  If I apply a moment to the tower, about an axis that parallels two of the legs, how do I calculate the tension and compression?  Does one column take all the compression and the other two columns take the tension (or vice versa if the moment is in the opposite direction)?  In other words, would one column have double the axial load as the two other columns (except opposite direction)?  Or is it more complicated than that?

RE: Flexural analysis of 3-legged tower

If the load is perpendicular to one side, it is as you described it.  But if the load is parallel to one side, the truss on that side takes all the load.  So equal tension and compression in two columns.  The third column is at the neutral axis, so no load.  In that situation, the third leg and the lacing just provide lateral support.  Whichever way you look at it, all three legs have to be designed for the same force.

RE: Flexural analysis of 3-legged tower

Without disagreeing, if you run this through an FEM program with fixed joints (reasonable for a pipe structure) you will get bending in the bracing members and torsion on the center leg when the wind is parallel to one face, because of the deflection of the wind resisting frame.

Michael.
Timing has a lot to do with the outcome of a rain dance.

RE: Flexural analysis of 3-legged tower

Michael, old friend, I disagree with using fixed joints.  Why would you do that?  Besides, we don't even know what type members the webs are.

RE: Flexural analysis of 3-legged tower

I didn't say that correctly, there will be bending in all of the web members and torsion in all of the columns.

Michael.
Timing has a lot to do with the outcome of a rain dance.

RE: Flexural analysis of 3-legged tower

each leg would react a portion of the applied moment ...

each leg will be in bending (with pinned reactions), the load in each leg will not be axial (which was my 1st guess)

there'll be a set of vertical couples (on the obvious two legs) and a set of lateral couples on all three legs.

not a trival problem !?  made more complicated if there are fixed ends to the legs.

RE: Flexural analysis of 3-legged tower

hokie66, LOL, I assumed the web members would be round HSS. Even with pinned joints, I think there is a torsion resulting when the wind is parallel to the one face.

Michael.
Timing has a lot to do with the outcome of a rain dance.

RE: Flexural analysis of 3-legged tower

(OP)
Thanks for the commments everyone.  FYI, it's a small tower and the legs are only 16" apart from centerline to centerline of each column.  The 3 pipe columns are 1.25" outside diameter.  The web members are 7/16" diameter solid round bars.

I'm mainly trying to confirm that the column axial tension/compression loads can be taken from the moment divided by "d".  In this case, "d" would be (16")x(sq. root of 3)/2 = 13.85".  A colleague felt that I should divide the moment by the distance to the neutral axis, or find the "I" of the entire configuration of columns and do an extreme fiber stress analysis.  That doesn't seem appropriate to me in this case, but it did make me question it.

RE: Flexural analysis of 3-legged tower

IMHO, that's probably alittle simplistic.  I'd draw a FBD of a leg, assume the applied moment is carried by the two (obvious) legs.  I suspect that the reaction to the ground could be a simple couple (which is not axial load in the legs).

btw, if "the legs are only 16" apart from centerline to centerline of each column", why wouldn't you use this as the moment arm for the couple, instead of "(16")x(sq. root of 3)/2" ?

not sure how the web members would affect the solution, obviously they provide an opportunity for load transfer between the legs.  i think a quick FEM would provide insight and a better answer than a mass of assumptions.

RE: Flexural analysis of 3-legged tower

If the tower carries significant gravity load, such as an elevated water tank, the legs can buckle in a torsional mode.   

BA

RE: Flexural analysis of 3-legged tower

Ah...another argument ensues about pinned or fixed connections in a welded truss or space frame!

To  check column buckling with wind perp. to a flat face, use pinned connections.  To check interaction and torsion, use fixed connections or orthogonal springs to model some fixity (probably too much effort for such a small frame).

If you are hand-calculating this, the critical case will be with two columns in tension and one in compression, using your approach without considering extreme fiber stress.

I'm assuming this is a small antenna tower, likely less than 50 feet high.  

RE: Flexural analysis of 3-legged tower

(OP)
rb1957,

The center-to-center distance at the perimeter of the triangle is 16" between the columns.  The distance from the midpoint between two columns to the third column is 13.85".  I'll run this (or something like it) through an FEA at some point and see what happens.  Just curious what you mean by a couple not being axial loads in the legs.  Isn't the definition of a couple two axial loads acting in opposite directions separated by a certain distance?

Ron,

What you said made sense.  I was just checking column buckling.  It's a 120 foot tower supporting a small wind turbine, but is guyed near the top and at the 1/3 points.

 

RE: Flexural analysis of 3-legged tower

i had pictured the moment applied so that one leg was under the moment axis, therefore unloaded, and the moment was reacted by the other two legs.

instead the moment is applied so that one leg reacts one of the couple loads and the other load is reacted by two legs.  then 13.85" is the right couple arm.  the reactions are vertical, not inclined along the leg.

i suggest you draw a FBD of a legs ... the one leg normal to the plane of bending (reacting P = M/d) is straight forward (i think !?) but the inclined legs are seeing some less obvious secondary effects (i think).

RE: Flexural analysis of 3-legged tower

Guyed towers such as you described are often used for communication towers.  It is also true that they are notorious for collapsing.  Be sure to leave plenty of clear space around the tower.  

RE: Flexural analysis of 3-legged tower

I believe the critical case is the one I sketched where 1 leg is in tension, 1 leg is in compression and the other leg doesn't seen any force because it is located at the neutral axis.

I agree with your colleague suggesting that you calculate I values to calculate reaction forces.

I would neglect the stiffness increased by the web members.

This is a spreadsheet I worked on for bolt groups but it can be used to calculate reactions.

RE: Flexural analysis of 3-legged tower

kikflip,
How can that be the critical case?  The loading is less and the lever arm is greater.

Calculate I and use Mc/I, or just use M/d, you get the same result.

RE: Flexural analysis of 3-legged tower

The guys change everything. It takes the problem out of the engineering realm into that of the black arts.

As I look at it, the wind on the structure's leading leg is the worst case, all of the horizontal load is resisted by one set of guys and all of the vertical component from those guys goes into that lead column. The other guys are slack since the tower tends to move towards them.

All of this, without considering ice and temperature differences. Definitely black art territory.

Michael.
Timing has a lot to do with the outcome of a rain dance.

RE: Flexural analysis of 3-legged tower

Frustrating, isn't it, Michael?  It took 13 posts before we found out this was a guyed mast.

RE: Flexural analysis of 3-legged tower

Hokie, I almost shouted "The guys change everything." in bold, upper case.

Michael.
Timing has a lot to do with the outcome of a rain dance.

RE: Flexural analysis of 3-legged tower

You almost shouted, in bold and all caps too???  Is that some sort of internet etiquette issue?   I was going to use all double bold, all upper case letters, in 28 point print, and was thinking that would be just a grumpy whisper, given my feelings on the matter.  You guys waste your time and effort to try to help someone with what appeared to be some kind of a real structural problem, and then after 13 posts or so he says; by the way here's the important info. and details about the problem, and it changes almost everything you guys were guessing about my problem.  Where is the internet and forum etiquette in these kinds of questions which waste your time, effort and willingness to pass on your knowledge and experience?  Particularly, when the OP'er. won't waste his time to fully lay out the problem, in the first place.

I think we should all take a few weeks off, let every OP go 20 or 30 posts, by which time we might have a better idea what the real problem was, from all the back and forth B.S.; even determine if the participants had a vague idea of the scope and nature of the problem was.  Some of you more experienced fellows waste your time giving such good sound basic advice, and then have it turned on its head when all the cards are finally laid on the table.  Someone on these forums has a sign-off which says something to the effect, 'first define and be able to fully describe the problem, then solve it.'  Let's all start doing that!

RE: Flexural analysis of 3-legged tower

dhengr,

I agree with you.  Members of this forum are too eager to jump to the assistance of the OP without fully realizing the extent of the problem.  In this instance, the very least we should expect is a sketch showing the tower, its supports and the loads acting on it.   

BA

RE: Flexural analysis of 3-legged tower

Well, at least I think we gave some good answers to the original post, which could have been the real problem, but turned out not to be.  And better yet, we might possibly have frightened the OP about trying to design a guyed mast with inadequate experience.  

RE: Flexural analysis of 3-legged tower

the 3 struts 16" apart (on a tower 120' high) are going to be in equal compression and the moment is carried by the guys ... it's usual practise to pin the mast at the ground, i'd expect that you'd want the rotational freedom and i'd expect that if you did fix it, the moment it'd react would be a tiny portion compared to the guys.

RE: Flexural analysis of 3-legged tower

(OP)
I think I gave everyone too much information.  The tower has already been designed; I was just helping the contractor figure out the pick point locations when he lifted the tower.  So I was only checking the maximum distance that the tower could cantilever when being lifted by the crane (moment in the tower and resulting column buckling as well as bolt capacity where the column pieces are spliced).  My original question covers that issue, I believe.  Of course the guys change everything for the in-place condition.

I apologize and I didn't mean to waste anyone's time.

RE: Flexural analysis of 3-legged tower

(OP)
By the way, I essentially got the same result when calculating the overall "I" and using Mc/I as when I used M/d.

RE: Flexural analysis of 3-legged tower

IMHO, you didn't "gave everyone too much information" ...

it would have been helpfull if you'd said ... "i'm lifting a tower" ... that would've stopped several posts about loads (wind, etc).  then we'd've known there is a distributed load (weight) and a single reaction (the crane) ... ok, probably two reactions (assuming a sling).

you could calc the max moment as a function of inclination, and the critical loading is probably with a single leg in compression and two legs in tension (possibly a single leg in tension, and one leg going along for the ride).

RE: Flexural analysis of 3-legged tower

The top set of guys should probably be more than a blade length below the top of the tower.  On this tower, that wind turbine better not be to big.  The thrust from the turbine will induce a fairly significant bending moment at the elevation of the top set of guy wires and this will tend to force the shape and orientation of the buckled shape, along with the guy wire system.  The pinned base is a good idea too.  All fairly obvious comments.

There has been a good deal of sound general advice given here, depending upon what the real problem is, and that keeps changing and getting more complex every 13 posts or so, but the best advice of all was hokie's, which was in essence that the OP'er should clear about 140 or 200' radius around this tower, for when it falls over.  And, low-and-behold, the question and the problem have changed again.  Bjcure...  That wasn't too much info., it was just all the wrong info. for your real problem.  And, you sent a bunch of very good, experienced, advisors on a goose chase, unrelated to your real problem, because of your bad problem definition or description.

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