Unbraced compression truss chord
Unbraced compression truss chord
(OP)
I am being asked to design a custom truss with a completely unbraced bottom flange. The dead load on the truss is so light that there is a net uplift with wind load. This puts the bottom chord in compression. I don't like this condition, but I would like to have more than "I don't like it" for a answer, and if there is a safe way to design for this condition I would like to know how. I checked the bottom chord as a unbraced column the length of the joist and it worked fine. Also, KL/r would be less than 200 if K is 1.0. Is there some reason that K would be more than 1.0? Is there some reason other than structural stability to brace the bottom chord? The truss is basically a bar joist made out of tube steel. I have two competing ideas in my mind. The one is bar joists where any joist with uplift always has uplift bridging. The other is a crane beam where the compression flange has no bracing. Is there a way to calculate a stiffness that would make compression chord bracing unnecessary?






RE: Unbraced compression truss chord
RE: Unbraced compression truss chord
RE: Unbraced compression truss chord
RE: Unbraced compression truss chord
RE: Unbraced compression truss chord
I'm not understanding why the bottom chord has to have the "ends fixed" in order for it to go into compression. Obviously the top chord on the common bar joist is the bearing element, with the bottom chord stopping short of any support. The two are connected via diagonal webs. When I picture a common truss with a uniform or point load going up, I can easily see how the bottom chord develops compression.
WCW, it sounds like a stick model (computer model) is the next step. Your k = 1.0 question is not apparent to me since the bottom chord is connected to the top chord by webs. I would venture to say that k = 1.0 since there is no bracing, but where I'm confused is if part of the bottom chord goes into tension and part does not (unbalanced loads?) I think I'm reading to far into your post and starting to guess, so I'll stop at that.
RE: Unbraced compression truss chord
I didn't say anything about fixing the bottom chord in order for it to go into compression. I didn't even say anything about fixing the bottom chord. I'm not even sure how to respond because I don't understand your comment based on what I wrote in previous posts.
Also, he is asking about the bracing because of using k=1. You can't assume k=1 if the ends are braced.
RE: Unbraced compression truss chord
RE: Unbraced compression truss chord
by the sound of it, you've got bracing in one plane. for the chord to move in the unbraced plane the bracing in the other plane has to bend, no ? but clearly this in not a particularly effective way of providing a bracing effect. so the chord could attempt to buckle like an euler column, with some restraint at the out-of-plane bracing; i suspect that the critical mode of failure is the lower chord deflecting mid-span in the unbraced direction.
RE: Unbraced compression truss chord
If you don't have a brace point at any location along the compression chord then what would be the buckled shape (for either of the top two sketches in the attachment)? If you have no brace, you can't have a buckled shaped, it will just move as a rigid body and is inherently unstable.
RE: Unbraced compression truss chord
That is exactly what I was talking about looking at several posts ago. The diagonals are bracing it in the plane of the truss. The only conceivable braces for the out-of-plane condition would be those same diagonals bending (acting as cantilevers off of the top flange) out of the plane of the truss.
RE: Unbraced compression truss chord
Why can't you bring the bottom chord over to where the truss is supported (Column or wall) and brace the chord out of the plane of the truss there?
Otherwise, design the system so there is no net uplift on the truss (it may be possible).
RE: Unbraced compression truss chord
RE: Unbraced compression truss chord
There is no bending (or very little bending) in the bottom chord. The bending is in the entire truss. k can not be 1 if it is not braced. That is just inherently unstable. Even in the case of beams (which want to buckle out-of-plane) all of the AISC equations are based on the assumption that the section is prevented from twisting and lateral displacement at the support points.
RE: Unbraced compression truss chord
Sorry! I re-read your post and understand what you were saying. My apologies. You were talking about bracing not fixity. The freebody diagram of a segment of the truss turned on end would indeed show the bottom chord "cantilevering" off the top chord. Sorry for the repeat, I just want to clarify.
WCW,
The bottom chord will be a beam-column and would need to be checked for interaction, with possible moment amplification. I'm assuming you did this.
Regarding bracing of the bottom chord, compression members can be unstable in an overall sense, or locally. This instability is a function of the slenderness properties of the flange and web. AISC Table B4.1 does not include "stiffness" terms (EI), but only Fy and E. This is best illustrated in bridge girders where you can have a lot of stiffness with a lot of slenderness and instability. Also KL/r < 200 is not a requirment but a recommendation in the AISC (sort of a mute point to most of us, but perhaps that would make a difference for you).
RE: Unbraced compression truss chord
Consider, for example, an HSS shape of length L sitting on a frictionless surface, say a sheet of ice. Attach a cable centrally at each end with suitable end plates. Throughout the length of the HSS there is no contact between cable and member. Now apply a tension to the cable. The HSS goes into uniform compression. The effective length of the HSS is L even though there are no lateral supports at either end of the member.
Or, consider a continuous beam in which there are points of inflection in two adjacent spans. There is no lateral brace at either point of inflection, yet the effective length of the compression flange, it seems to me, is the length between inflection points.
So, I believe the effective length of your bottom chord is the distance between supports even without lateral bracing. But I don't like it and wouldn't do it.
Perhaps you could provide adequate lateral support with an end vertical rigidly attached to a member tying the joists together at the top chord.
Best regards,
BA
RE: Unbraced compression truss chord
I would make the following comments. I sort of see your point with regard to the pretensioned cable, but........ that only works because the loads (reactions at both ends are always in line with each other (because the pretensioned cable is always straight). That is a perfect system of sorts. If you applied a very small end moment to one end (as would be the case for any construction tolerance), then you can easily see by statics that the system is unstable and would just rotate endlessly from that end moment.
Regarding a continuous beam with inflection points, all current literature says that it is quite WRONG to assume an inflection point acts as a brace point. This is covered in A&J, Structural Stability of Steel (by Galambos), and by Yura, and AISC. The unbraced length of the compression flange is the physical length between brace points on the compression flange regardless of the location of inflection points.
RE: Unbraced compression truss chord
I agree that the cable represents a perfect system in the sense that the end forces are lined up precisely. Any external moment would require horizontal reactions at each end of the member.
I agree that an inflection point in a beam is not a braced point for the compression flange. If it were, the effective length of flange would be from inflection point (I.P.) to column which is or should be a braced point.
But it should be conservative to take the effective length of the compression flange from I.P. to I.P. even though neither is braced. My reasoning is that, beyond these points, there is no compression in the flange to cause buckling.
In any event, I agree with you that a compression flange should be laterally braced and that the spacing of those braces becomes the effective length for buckling.
Best regards,
BA
RE: Unbraced compression truss chord
This is to explain why k = 1.0.
When the bottom chord subjects to compression, at the moment it starts to buckle sideway (sway in weak axis), it is geometrically liking a simply supported beam in bowed shape with Mmax (max deflection as well) in the middle, and zero at ends. For such condition, K = 1.0.
RE: Unbraced compression truss chord
RE: Unbraced compression truss chord
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RE: Unbraced compression truss chord
A bow has an eccentric compression load induced at each end, but it doesn't endlessly rotate. There is a equilibrium point.
RE: Unbraced compression truss chord
RE: Unbraced compression truss chord
That's the same issue as the pretensioned column. The applied load is via a tension force which is inherently stable.
Try THIS, have two infinitely rigid concrete walls 10' apart (horizontally), now place a horizontal HSS in that 10' space. Let's say that the HSS is placed on small ledges that support it vertically and both ends have rollers that allow it to slide along the length of the wall (the small ledge keeps it in place along the height of the wall) - this is now braced in one plane and not in the other. Now, let's say the walls start to get closer, thereby compressing the HSS. Lets also say that the installer put the HSS in so that it is at an angle of 89.9 degrees to the walls, and not 90. Once the HSS feels any compression, it will rotate as a rigid body (not take a buckling mode) and will just become unstable.
Do you see that? Do you agree? I believe there is a difference between an externally applied load and an internal load. The two examples that seem to say it's ok (the prestressed column and the bow) have no external load or reaction to be resisted. The forces are completely internal from the prestressing of the cable or bowstring. This is why you can have internal forces in a prestressed beam but not have any external reaction due to the prestressing, because the forces are all internal, not external.
RE: Unbraced compression truss chord
Interesting discussion. I agree the last panel point of your truss bottom chord needs to be braced. Suggest thinking about it as like a "pony truss" in a road bridge. That is, a truss with its top, compression chord unbraced except by the truss webs cantilevering from the bridge deck members.
RE: Unbraced compression truss chord
Excellent suggestion! This avoids having unsightly bracing on the bottom chord. Each end of the bottom chord would be laterally braced by a vertical member fixed at the top to a rigid member spanning between joists.
Best regards,
BA
RE: Unbraced compression truss chord
RE: Unbraced compression truss chord
Best regards,
BA
RE: Unbraced compression truss chord
The spreader beam shown in the attached photo is in compression. Neither end is laterally braced, yet the effective length is the length of the beam. Like the prestressed HSS mentioned in an earlier post, the compressive forces applied to each end are precisely aligned. But that is also true for the bottom chords of the joists in question.
Under uplift loading, the end diagonals, acting in compression transfer all of the uplift to the supports. Assuming these members to be pin-ended, there is no resistance to overturning. It is the same situation as a bottom bearing joist under gravity load. There is nothing to prevent the joists from racking.
So we all seem to be in agreement that bridging is required at each end of the joist but for different reasons.
Best regards,
BA
RE: Unbraced compression truss chord
Another example like your spreader bar is the boom on a jib crane, the far end is laterally unbraced and the other end at the column is pinned. The k for the boom in compression is 1.
It just goes to prove that the things we build don't always fit neat little engineering models but they work....
RE: Unbraced compression truss chord
I would prefer to say that if applied theory does not agree with actual behavior, then it is misapplied theory.
Best regards,
BA
RE: Unbraced compression truss chord
I would be interested in hearing others' opionions if you get a chance to read the paper and play around with some examples.
RE: Unbraced compression truss chord
RE: Unbraced compression truss chord
RE: Unbraced compression truss chord
I am thinking as the BM changes from center to end the compressive force in bottom chord also changes with maximum at center (assuming ss) and zero at ends. So this case is not exactly similar to a column in uniform compression. What are your thoughts about zero force at ends does that mean this "free" end does not displace lateraly?
In my opinion the simplest solution, if the architect is opposed to continuous bridging, is as suggested by StructuralEIT (5th post from top) i.e. to extend the ends to supporting column or wall with a sloted connection to avoid tension transfer (similar to joist bottom chord extention at column osha requirement).
Another solution would be to provide kickers extending from bottom end panel point to top of adjacent truss panel point.
RE: Unbraced compression truss chord
The example of the truss in the Nair paper is not exactly the same scenario as we have here. His truss is continuous with the columns, developing compression in members L1L2 and L6L7 under gravity load applied at the top of the truss.
In the case we have, the load is upward. Members L1L2 and L6L7 are unstressed axially. The remainder of the bottom chord is in compression throughout, increasing toward midspan. If you assume, as Nair did, that all truss connections are pinned in both directions, then we require lateral bracing at every panel point on the bottom chord.
The best locations for bracing in the problem at hand is at the bottom of the end diagonals. Then the bottom chord does not have to be extended to the support. This, of course, would not please the architect.
Whether or not more bracing is required between these points is a question we cannot answer without knowing the geometry and the loading. If additional bracing is not required, then the bottom chord must be continuous between braced points (no pins) and we would be relying on the buckling capacity of the bottom chord over the length between braced points.
Best regards,
BA
RE: Unbraced compression truss chord
However, he admits ".., in most ordinary situations, adequate bracing has been provided BY DEFAULT, because designers have followed bridging and bracing requirement based on the slenderness criteria of AISC and SJI, which may inherently provide the necessary bracing strength and stiffness."
What is "BY DEFAULT"? My take is follow the traditional design approaches to design the compression members with K = 1.0 for all truss members, the result is a set of well/properly-sized members with adequate strength in the plan of loading. Then apply resulting compressive forces on the full length chord (again, with K=1.0) to ensure it will yield prior to buckle under side sway mode. The longer the span, the lower the allowable compressive stress, thus, it often results in adding braces to reduce the unbraced length. The "DEFAULT", therefore is to simply keep stress (compression) low in the compression members, the INHERENT stiffness will likely to prevent catastrophic failure mode -buckling.
After all said, as Fisher pointed out, K maybe greater than 1.0. Given consideration to side sway mechanism, it can be 1.2, 2.0..., the result (with larger K) is bigger member size, which is not necessary, nor economical. So, for practical reasons, I stick to K=1.0 for designing truss members. Fisher's method provides excellent means to check the final design to ensure laterl stability.
Thanks kbbandw for providing the excellent reference.
RE: Unbraced compression truss chord
Fisher is saying that, in most situations, adequate bracing has been provided "by default".
Default is defined as:
failure to perform a duty;
failure to pay on time;
failure to appear in court.
I would interpret this to mean that, without performing the necessary calculations (failure to perform a duty), most engineer's designs will work satisfactorily because they followed the simple rule of L/240 for bracing spacing on the bottom chord. Perhaps we should all take a closer look at this situation in the future.
In my opinion, open web steel joists should always be braced at the junction of the end diagonal and the bottom chord and at maximum L/240 beyond. Otherwise, the joists may be unstable. This is a tough message to get across to the joist suppliers who are reluctant to comply.
Best regards,
BA
RE: Unbraced compression truss chord
RE: Unbraced compression truss chord
The questions have answered by Shankar & Fisher, except K for truss design - Fisher implies 1 < K < ?, Shanker explicitly indicates K (conservatively) = 1.
Practically, what K value would you suggest in the begining of a truss design? Or would you design the bracing prior to the truss so that the K is exact?
RE: Unbraced compression truss chord
If the bottom chord is totally unbraced, the value of k cannot be determined. It could be argued that it is infinite.
Probably not, but I can't think of a better reason.
The K value for web members may be taken as 1.0. The K value for the bottom chord may be conservatively taken as 1.0 when L is the length between brace points. When considering uplift, the axial load in the bottom chord should be the maximum axial load in any panel within the length L unless a more detailed analysis is performed.
Such an analysis may be found in "Theory of Elastic Stability" by Timoshenko and Gere. Practicing engineers usually do not go to such lengths, however.
Best regards,
BA
RE: Unbraced compression truss chord
Please read my posts/responses again, I was disputing the notion that K shall be taken greater than 1.0 for truss design. You have confirmed my point, for all practical reasons, K = 1. Some call it conservative, some not, but it is the magic number to use, which usually leads to satisfactory designs.
"K" is a 2D geometry factor of defelected column. A stright wire subjects compression (by finger tip), it deflects into sine curve that conform to column with ends pinned, this observation leads to the believe, K is somewhere close to 1, if not exact. I agree, for unequal end forces the K value can't be determined by simple observation, but it is one special case beyond "oridinary".
Structural instability is dependent of member stiffness, to derive which requires reasonable assumptions to begin with. I firmly believe K = 1.0 fits the task (truss design). While I have no question about the need of stability investigation for unbraced compression chord, I do have reservation on tension chord requirement (except for construction purpose), especially for the case with free end pannel joints. I wouldn't offer any thought before I read/understand all justifications.
Your ending sentence cleared a lot of air. AGREED.
RE: Unbraced compression truss chord