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?
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Unbraced compression truss chord 2
- Thread starter WCW
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If it's not braced at the ends, how did you do a design check? You have to brace the ends or else it's like a gravity column that is supported on a horizontal roller at the base. The only thing you can really do is look at the end vertical (or diagonal) and check it for out-of-plane stiffness and strength as a cantilever off of the top chord to see if that will provide adequate bracing per AISC. I wouldn't like that, though, and would really push for the bracing at the ends.
What is it framing into? Can you run the bottom chord to a column/wall and have a knife plate off of the column/wall that gets slotted into the HSS (but not attached), to provide the out-of-plane stiffness without restraining the movement in-plane?
StructuralEIT,
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.
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.
bigmig-
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.
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.
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When there is wind uplift on the truss the entire bottom chord is in compression. The compression starts where the first web member connects to the chord and reaches a maximum at mid-span. My question is how do you design a compression member that has no bracing in one plane? Since there is no more compression after the last web member can I take L as the physical length of the bottom chord? What should I use for K? 2.1 or 1.0 or is K something even greater since I don't have even one end of the member braced in one direction. I thought about using K as 2.1 and L as the length of the member. I think my chord would still work because the size was chosen more for looks than stress levels. We design simple span beams without any flange bracing. Why can't a truss be designed without any chord bracing?
bracing (obviously) provides lateral stability. maybe you can provide some moment capability (not to say "cantilever").
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.
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.
You can design a beam without flange bracing because the section is restrained against twisting (and translation) at the ends, hence the unbraced length. If you have a compression member (e.g. a compression chord in a truss), you have to look at that member individually in addition to the overall member.
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.
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.
rb1957-
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.
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.
You will need some form of bridging at each end in or to prevent movement of the end joint otherwise you have no compression capacity in the bottom chord. Even steel joist companies provide a row of horizontal bridging at the ends of joists subjected to uplift.
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).
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).
For question of "k", if I remember correctly, it is determined by looking at the curvature in direction of concern (bending), and adjusted by moment veriations at the ends and within the member span. If you use the L as entire length of the bottom chord, then k = 1.0 is justified. (M = 0 at ends, single curvature)
kslee-
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.
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.
Structural EIT,
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).
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).
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- #16
This is an interesting question. I would feel pretty uncomfortable with no lateral bracing at each end of the bottom chord, so I guess I would insist on it even though I'm not sure it is theoretically correct.
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
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
BA-
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.
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.
StructuralEIT,
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
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
StructuralEIT:
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.
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.
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