Flange brace force

[ajnweb]

I have a question regarding the flange brace force on a beam. Lets say I have a beam in bending due to gravity loading, the flange brace force on the compression flange is 1% to 2% of the flange force (moment/depth). So I have applied a gravity load to a beam and now have a lateral load to resist, and since we all know that we cannot apply a gravity load and get a net lateral load, where does the equal and opposite force to the flange brace force come from? Is it taken by the flange brace back up to a lateral beam that is attached to the tension flange, and is it the tension flange that then provides the equal and opposite force? Thank you for any and all responses.

 

[JAE]

The lateral force that resists the lateral buckling force in your beam is usually taken into the floor/deck diaphragm system..it is outside of your beam system.

 

[ajnweb]

In a multiple beam system, would the flange force be cumulative then? This could be quite a large force. If it is cumulative and it winds up in the deck diaphragm, it would then have to be braced out, is this correct.

 

[UcfSE]

Note that there is no lateral force until the beam actually buckles. Once it does buckle or tries to buckle, whatever bracing is available will provide the reaction and transmit the force to the foundation.

The buckling force is cumulative when the framing consists of multiple beams. While it sounds like a lot, it usually is quite small compared to the LFRS forces. Thats why we normally see braces that tie into or kick back to the diaphragm or some other part of the LFRS. The diaphragm acts somewhat like a "load sink" for these brace forces.

 

[JAE]

I don't think so - the force is resisted by the "interior" stiffness of the diaphragm. There is no net lateral force developed in the whole floor.

An analogy:
Its like taking a beam and having a point load of P at midspan and two upward point loads (-P/2) on either side of the concentrated load, 2 feet away. The reactions are cancelled out as far as the beam end reactions go. But the beam feels a shear within its length.

So the diaphragm has interior shears and stresses, but no exterior reactions.

 

[ajnweb]

In large span beams with large moments, the cumulative brace force could far exceed the LFRS forces, which is the case I have. Since the lateral force is generated from lateral movement of the flange during buckling, and the direction that it buckles could depend on materal inconsistencies, internal stresses, fabrication tolerences, and loads slightly eccentric, it would seen to make sense that the forces would cancel internally. It would seem to be highly unlikely that all of the beams would buckle in the same direction.

 

[UcfSE]

JAE, what supplies the equivalent of the two upward point loads from the example? It seems like the diaphragm should resist the buckling load internally, not supply another external force to balance it.

 

[JAE]

UcfSE - first off, My statement "I don't think so" was directed at the earlier question by ajnweb...just wanted you to know that - you popped in your response before I did and it sounds like I'm disagreeing with you.

As far as your question - my analogy was weak - I admit. But what appears to me is that the lateral force from the buckled beam is lost in the "load sink" (love that term) of the diaphram. I small beam in the large field of the diaphragm is simply trying to distort a small portion of the diaphragm internally and I just can't see that the cummulation of all the floor beams on that level would add up to some large lateral force that would have to be taken out of the structure via braces to the ground.

 

[sundale]

I concur with JAE that the individual beam bracing forces will tend to cancel out within a given diaphragm or subdiaphragm.

The cumulative bracing force is best considered in terms of the total horizontal column bracing forces required at that story for the sum of the gravity forces at that story. This is the "stiffness" and "strength" necessary to call a frame system "braced" as opposed to "unbraced" (sway).

UcfSE correctly makes the point that this strength and stiffness demand (for stability) is usually quite small in relation to the building's overall lateral requirements for wind and/or seismic forces.

 

[UcfSE]

It looks like we're saying about the same thing. I've never worried about the diaphragm takign buckling load or tried to figure it up to see what happens. I guess I was taking the academic point of view that a 20-pound buckling force should find its way to the ground, though that force would never be seen anywhere nor matter with anything.

What made me think of that is the design of bracing for light-gauge stud walls. When you're bracing with very small straps and angles, that cumulative force can add up to be something you need to consider, though it's seldom very large in the grand scheme of things. Along that same note, I would expect a floor system to behave in a similar manner. Brace forces may add up and may need to be considered though in the big picture they still aren't much.

 

[ajnweb]

So would it be safe to say that the lateral brace forces are somewhat localized, and tend to cancel themselves out internally, as opposed to seismic bracing forces that have to be added together and braced out directly to the foundation? In my example I am dealing with a 5 kip brace force at 3 points along a beam, with 11 total beams. If added together this would produce a 165 kip total force, which is over twice the wind force. But, if these brace forces tend to cancel out, then I would only have to consider the local effects of the brace forces, and maybe compare a 5 or 10 kip brace load to the cummulative wind load at any given flange brace location.

 

[aggman]

I read this thread earlier and at first I couldn't really see how the brace loads would just "cancel out". So I dug into the Stability Design Criteria for Metal Structures (SDCMS) to try and look into it further to satisfy myself. My take is this. When we say that a beam is "braced" what we mean is that the top and bottom flange will not translate with respect to each other (no torsion). They can move laterally, but as long as they move the same amount then the beam is still braced. This is why it is satisfactory to put x-bracing between the top and bottom flanges of two beams and consider that braced. If we build frames in the structure and brace the compression flange using relative bracing then I think that force would have to go into the LFRS. Yes this would require all beams to reach maximum moment at the same time and all beams have a tendency to rotate in the same direction (not likely), but I don't see how you could guarentee that it wouldn't happen. You could assume live load reduction, etc to help the situation but I don't think it will go away. On the other hand most bracing methods on beams are more of a direct torsional bracing system or a discrete system. This to me would cancel itself out in the slab by applying small (insignificant) bending moments in the slab or resolving into small increases and decreases in vertical loads on adjacent beams. This reasoning comes from some of the examples in SDCMS. One particular example (ex. 12.4) describes a relative (truss built in the floor bracing the top flange). The calculated bracing forces were resolved into brace loads. In order to satisfy equilibrium then the beam bracing loads must be resolved into the end reactions of the truss. In order for the system to fail all beams would have to reach their buckling load and have a tendancy to want to buckle in the same direction. Intuitivly I can not really see this happening, but I also can't prove that it couldn't happen.

 

[JAE]

aggman - thanks for the thoughts.

I just try to imagine, however, a floor of beams braced by a concrete diaphragm, and supporting ONLY vertical gravity loads, with no sideway in the overall system due to rigid braces on the sides of the diaphragm. If you take this sytem (i.e. a free body diagram of the floor) and calculate [Σ]F in the horizontal direction how would you get any net lateral reaction to occur?. I think it would have to be zero.

 

[aggman]

I agree with what you are saying in regards to the concrete diaphragm. I also can not see how you would have any net force with this case. The case that I would be concerned with is when you have no concrete diaphragm or anything else. Consider a floor system with no topping. Just the beams and girders. Place a truss through the floor (in the horizontal plane) from one side of the building to the other. (Consider Fig. C-A-6.1, pg. 16.1-422 of the 13th edition AISC manual for relative bracing.) If you are truely depending on the lateral bracing to brace the beam then their will be a forces in the truss which have to be resolved into the LFRS. In the same figure mentioned in the AISC manual you have the torsional "cross frame" brace. This brace resist buckling by torsion and thus their would be no net out of plane forces to resolve. The concrete diaphragm is a torsional brace as specified in the SDCMS.
I also think that the relative system is quite idealized because the typical floor system has beams with connections that are as a minimum 1/2 the T dimension of the beam. Because of this they provide significant torsional restraint to buckling (significant in terms of the applied buckling loads). I think that in 99.99% of the cases this is not something to worry about. I guess I just feel that you have to be aware of the possibility of it being an issue and design accordingly.

 

[DaveAtkins]

I think it gets down to engineering judgment (doesn't almost everything???). If there is a large diaphragm (concrete, steel or wood--doesn't matter), then designing the diaphragm (and the rest of the lateral force resisting system) for wind or seismic forces should result in a structure that is stable enough to handle the various beam and column buckling forces WITHOUT ACCOUNTING FOR THEM IN THE DESIGN. On the other hand, if you are trying to brace two beams with no diaphragm and diagonal bracing between them in the horizontal plane of the top flanges, then I would certainly design this horizontal "truss" and account for the axial forces in the two beams, the end reactions, etc.

DaveAtkins

 

[miecz]

The horizontal force in the brace has an equal and opposite horizontal force in the top flange of the beam being braced. Otherwise the beam would fly away. These two forces end up in the diaphragm and cancel each other. Net force, zero. There is tension in the diaphragm between the top flange and the end of the brace.

 

[ajnweb]

Here is a follow up to the above questions. If I have a rafter that sits on top of a carry beam (the carry beam top flange is in compression) and I have a flange brace that runs from the bottom flange of the carry beam back up to the rafter (to restrain the bottom flange for uplift loads), what restrains the flange brace force from the carry beam's top flange? The moment is about 4500 kip-ft which produces a 16 kip flange force. Do I have to design the rafter to resist the 16 kip flange force, or do I have more of a torsional restraint and have to design the rafter for a concentrated moment per appendix 6 of the 13th AISC?

 

[cap4000]

ajnweb

Assuming you have a diaphragm, I suggest you get the ASCE "Lateral Bracing of Beams and Columns" article by George Winter published in 1960. Essentially it says virtually any metal roof deck has enough stiffness to prevent the beam from buckling. There are column tests even done out of cardboard strips to verify that 2% is a typical conservative bracing load. Depending on your uniform load even the friction force between the deck and beam could be enough. The everyday typical elastic structural analysis engineers perform is not the basis of these formulas. Marvin Larson even uses hydrualic jacks to simulate the shear forces transmitted to the deck diaphragm. His typical 30 ft by 12 ft bay has no reaction forces shown at his columns but he does give the critical shear-deflection formula you would need. His deck also does slightly deflects. Without a deck diaphragm a different analysis would be reqiured. Nice thread. Good Luck.

 

[UcfSE]

Out of curiosity, what kind of load, span and beam do you have that's giving you 4500 k-ft of bending moment?

The connection between the rafter and the top flange is what will carry the top flange force of you carry beam. I believe you should definitely account for this given the magnitude of your load. How that load is taken care of by the rafter depends on the rest of your framing and the load path for that buckling force.

To what code are you designing? If you are using the AISC steel code, there is a section concerning the design of bracing for strength and stiffness concernes.

 

[ajnweb]

UcfSE,

I have a rafter (moment frame) that spans 207' with 18' bays, 12 bays total. To help reduce thrust, there is a carry beam located about 70' in from one sidewall. This carry beam is 90' long and supports 4 rafters, each imparting about an 80 kip point load on the carry beam. The carry beam is about 6' deep, so the flange force = .02*4500/6 = 15 kips. Unfortunatley I am thinking that this lateral load would have to be added to the moment frame rafter along with the vertical snow load.

I am designing to the 2003 IBC with 9th edition ASD. I have seen the bracing strength and stiffness deisng in the 13th edition, but I do not recall seeing it in the 9th edition. I guess I could design the rafter for the 16 kip load, and make sure that it has the stiffness per the 13th edition code. It seems to me that this type of brace would qualify as a relative brace, and not a nodal brace. Or with the carry beam bottom flange brace back up to the rafter, would it qualify more like a torsional brace, and therfore just design the rafter for a concentrated moment as opposed to a concentrated force. Probably 6 to one, 1/2 dozen to the other?