AISC Appendix 6 - Beam Bracing
AISC Appendix 6 - Beam Bracing
(OP)
Through past work by Yura the AISC specification has added appendix 6 which provides requirements for bracing.
Section 6.3 is for beams and includes both relative and nodal bracing requirements. The general concept I understand but we've been trying to understand the explicit application of this section to brace designs.
The main issue is that the brace strength equations ((A-6-5 and A-6-7) provide values for required brace strength, Pbr. This is given as a force in pounds as a function of bending moment and beam depth (ho).
But if we provide braces at 4 feet on center, we get a Pbr value. If we put braces at 8 feet on center we still get a similar Pbr value since the moment is the same. The beam might be a bit deeper since Lb would be larger, but that means that the brace force actually gets smaller since ho is in the denominator....and that seems counter-intuitive...fewer braces means less brace strength required.
Anyone have any views on this?
Section 6.3 is for beams and includes both relative and nodal bracing requirements. The general concept I understand but we've been trying to understand the explicit application of this section to brace designs.
The main issue is that the brace strength equations ((A-6-5 and A-6-7) provide values for required brace strength, Pbr. This is given as a force in pounds as a function of bending moment and beam depth (ho).
But if we provide braces at 4 feet on center, we get a Pbr value. If we put braces at 8 feet on center we still get a similar Pbr value since the moment is the same. The beam might be a bit deeper since Lb would be larger, but that means that the brace force actually gets smaller since ho is in the denominator....and that seems counter-intuitive...fewer braces means less brace strength required.
Anyone have any views on this?






RE: AISC Appendix 6 - Beam Bracing
One thought: I hate App. 6 because it doesn't make sense about 1/2 the time I try to use it!
RE: AISC Appendix 6 - Beam Bracing
I can see the brace force decreasing as ho increases (for the same moment), because the force in the flanges will be smaller.
One other thing about App. 6. The very first paragraph says, "Beam bracing shall prevent the relative displacement of the top and bottom flanges, in other words, twist of the section.", but the spec specifically says that beam bracing needs to prevent lateral translation of the compression flange OR twist of the section. Which is correct?
RE: AISC Appendix 6 - Beam Bracing
To be quite honest, I don't really know how you could prevent twist and not prevent lateral translation of the compression flange.
RE: AISC Appendix 6 - Beam Bracing
If you have a beam subject to pure moment such that you have a brace at the top flange only, no where else on the section, I can see the bottom flange curling up toward the laterally restrained compression flange. The only thing preventing it is the weak axis bending strength of the thin web.
Isn't this similar to the sidesway web buckling phenomenom when a beam is subject to a high concentrated force, and the reason that a stiffener is required even if braced laterally?
RE: AISC Appendix 6 - Beam Bracing
Again, it LTB is driven by the compression force.. if you prevent the compression flange from moving, you've prevented the buckling..
RE: AISC Appendix 6 - Beam Bracing
The AISC forumla gives the req'd brace strength in lbs. But it doesn't give guidance on the spacing of those braces and that doesn't make sense.
Any ideas?
RE: AISC Appendix 6 - Beam Bracing
Could it be interpretated that the brace force (lateral load) calculated is for a particular point along the beam.
For example if the beam is subjected to a UDL then the maximum moment is at midspan and the lateral force is also applied to the beam at midspan hence a brace at midspan would have to take the entire load.
If you needed additional braces because the unbraced span of the beam was still too long, the brace force for each would be dependent on the moment in the beam at each brace location.
RE: AISC Appendix 6 - Beam Bracing
RE: AISC Appendix 6 - Beam Bracing
Suppose, though, that you design a beam spanning 30 feet taking a total distributed load w, with a single brace at midspan. The moment is wL^2/8 and you get a beam size based upon Lb = 15 feet.
You use the AISC forumlae to get a Pbr capacity for your brace at that point. So far so good.
But now if you look at using 3 brace points, the Lb now equals 10 feet, and you get a new beam that is perhaps a bit smaller in weight but the same depth.
With the second design, AISC implies that you need almost 3 times the brace strength of the first design since the Pbr's for each brace will be approximately the same as for the single brace.
That, to me, just doesn't make sense. I can see the three braces, together, providing a similar Pbr capacity, but all three needing that much capacity compared to the single brace?
This is what has me questioning this issue.
RE: AISC Appendix 6 - Beam Bracing
I don't have access to the formula you are talking about, so it is difficult to comment on that. I am attaching a page from CSA S16-01 for your comparison.
You said:
That would be for two brace points which divide the beam into three sections. In the CSA formula, delta(0), the initial misalignment, is based on the length of beam between brace points...if L is reduced, so is delta(0). The term beta increases from 2 to 3 for one and two braced points respectively. Also, note that for two or more braced points, the forces Pb alternate in direction.
BA
RE: AISC Appendix 6 - Beam Bracing
You calculate a single bracing is liking introducing a pin/spring in that location, it has a strength to prevent lateral displacement at that particular location. Then you calculate the second pair of braces, the analogy above repeats again, with the required strength reduced. Isn't that similar to adding supports to a simply support beam, one at a time? The math may not work out (I don't have the paper), but concept is valid.
RE: AISC Appendix 6 - Beam Bracing
The attached sketches show the statics for one and two brace points using that simplification. It is conservative as continuity would require a lesser Pb. Please excuse the scrawl.
BA
RE: AISC Appendix 6 - Beam Bracing
I see what you are saying. But kslee1000, the AISC equation for Pbr only depends upon moment, M, and flange to flange distance ho. There is no first or second pair of braces developed in a sequential order according to AISC. You simply calculate a brace strength for a moment and a beam depth. No mention of brace spacing, number of braces, etc.
BAretired....sorry I goofed - its Saturday and I cannot divide properly. For three braces that would be four segments and less than 10 feet - but the question still remains...how do you apply a single brace strength equation, Pbr, in AISC (and Canadian code similar) to a beam in a way that makes sense.
Your statement, "the analogy above repeats again, with the required strength reduced" I don't see in the AISC spec. How would the required strength be reduced using the AISC equation?
Another way to put this is: What if I put a brace at every single foot spacing? I'd have 28 braces on a 30 ft. span all with strength requried based upon the simple span moment diagram. That would be a LOT of brace strength compared to one or two braces otherwise. It just doesn't seem to make any sense.
RE: AISC Appendix 6 - Beam Bracing
Your response came only 9 minutes after my last post, so I assume you did not have time to review it. As stated previously, I believe the magnitude of Pb (Pbr in AISC) can be calculated from statics if hinges are assumed at all braced points. Please look at the two sketches in my last post.
I do not have the AISC equation. Could you kindly post it?
BA
RE: AISC Appendix 6 - Beam Bracing
But, I think you know well, all this bracing business is due buckling induced side sway mechanism, and all is based on Euler column theory. In column, the buckling is more clearly caused by compression force. For beam, it is essentially the same, but the buckling state is reached from compressive stress introduced by bending. I mentioned similarility between concepts of bracing and continuous beam support, can you confidently calculate one single support that equals sum of all other supports, and been able to work out intermediate support spacing by one general formula?
Again, without read the material, I am not qualified to get too deep into this. It could be very well worthless as pointed out by several responders, but I think a review on the previous works, then compare the similarility and dis-similarility should be helpful in advancing understanding.
Similar to all codes, the use of code specified formulas, equations, coefficients, requires understanding on the underlay concepts, which are often not so obvious before dig into the background materials. Give it a try if you care.
RE: AISC Appendix 6 - Beam Bracing
Thanks for your interest and help on this.
RE: AISC Appendix 6 - Beam Bracing
On the continuous beam analogy, code won't tell the number of supports required directly, the engineer works it out through indirect means (strength, servicibility). Same can be said for bracings.
RE: AISC Appendix 6 - Beam Bracing
The Structural Stability Reasearch Council's "Guide to Stability Design Criteria for Metal Structures" has an article that describes the development of Chapter 6. I have an old version of the Guide, so I'm looking at Article 9.11. From what I can tell, the early development was for nodal bracing, and the brace strength is derived from the stiffness requirement. The stiffness requirement starts by determining the stiffness required to create a nodal point at the brace location. Wioth that as the definition, it makes sense that the ideal stiffness has the brace spacing in the denominator. With this as a starting point, it follows that the required force goes up as one adds braces.
Apparently, you're not the first to question the result. An article in the AISC Engineering Journal, 4th Quarter, 1985 by Lutz and Fisher proposed an alternate approach that was never incorporated into the code.
RE: AISC Appendix 6 - Beam Bracing
For relative bracing, this strength is reduced somewhat to only 0.8%.
There is nothing magical or overly scientific about these equations. It is just putting into code what everyone always used before...
RE: AISC Appendix 6 - Beam Bracing
Mr (required flexural strength) changes for the braces at the first and third points for a UDL, SS beam. The brace force required at these locations will be less than the center brace and you now have the advantage of being able to use a lighter beam. Though you have to install 3 braces instead of 1.
RE: AISC Appendix 6 - Beam Bracing
RE: AISC Appendix 6 - Beam Bracing
Here's an example design:
Span = 30 feet
Factored uniform load = 1.5 k/ft.
Cd = 1.0
Case 1 - Brace only at midspan
Factored moment at midspan = 2025 in-kips
Lb = 15 feet
Required beam size = W16x40
ho = 15.49 inches
Per AISC Equation A-6-7,
Pbr = 0.02MrCd / ho
Required brace strength Pbr= 2.61 kips
Required brace stiffness βbr = (1/φ)(10MrCd)/(Lbho)
Required brace stiffness βbr = 8.07 kips/in.
Case 2 - Braces at 1/4 points
Factored moment at midspan = 2025 in-kips
Factored moment at 1/4 point = 1519 in-kips
Lb = 7.5 feet
Required beam size = W16x36
ho = 15.47 inches
Required midspan brace strength Pbr= 2.62 kips
Required 1/4 point brace strength Pbr= 1.96 kips (this is based on the 1/4 point moment)
Required brace stiffness at midspan βbr = 16.16 kips/in.
Required brace stiffness at 1/4 points βbr = 12.12 kips/in.
So for Case 1 we need a brace with strength = 2.61 kips and a stiffness = 8.07 k/in.
For Case 2 we need just a bit smaller beam, but the brace strengths required are 2.6 and 1.96 kips - almost the same individually but in total almost 3 times that required of the single brace.
For the stiffness in Case 2 - we need a lot more stiffness due to Lb being in the denominator and being 1/2 as much as case 1.
I guess I can go with this - but again, it seems strange that for simply adding braces, we need twice as much stiffness and in total three times as much brace strength. But I guess the moment in the beam is the moment in the beam and at any point it requires 2% or so strength capacity and the key is to optimize your braces through trial and error.
RE: AISC Appendix 6 - Beam Bracing
The brace stiffness is derived by Pbr/d (d=lateral displacement), let's exam the center brace, as Pcr remains constant, however, "d" becomes much smaller from effect of adding brace at 1/4 point, thus the brace stiffness increases. Work out?
RE: AISC Appendix 6 - Beam Bracing
Building codes recognize that no beam can be erected perfectly straight, so a tolerance is permitted. The permissible deviation from a straight line may be expressed as k*L where L is the clear distance between braced points. The value of k may vary amongst codes but is likely to be in the order of 1/500. So D0 = k*L is simply the permissible deviation from a straight line for any beam.
If single point bracing is chosen at midspan, the brace must resist a moment of Cf*D0 where Cf is the compressive force in the flange and D0 is the permissible deviation from a straight line. But, in resisting that force, the brace must deflect a bit more. Let us assume that, at equilibrium, the additional deflection is Db. Let us say the force applied at the brace point is Pb.
It is a simple beam. The reaction at each end is Pb/2. The moment at midspan is Pb*L/2. But the moment is equal to Cf*(D0+Db). So Pb*L.2 = Cf(D0+Db) and Pb is found to be 2Cf(D0+Db)
The beam size may be further reduced by bracing at more frequent intervals. If the beam is braced at an infinite number of brace points, a point of inflection will occur at the midpoint of a typical interior span. The shear at the inflection point will be Pb/2 and the moment at the typical node will be Pb/2*(L/2) = Pb*L/4. But the eccentric moment from Cf is still Cf(D0+Db). So Pb = 4*Cf(D0+Db)/L.
In all cases, the spring stiffness is given by Pb/(D0+Db).
That is why the brace force is larger with multiple brace points.
BA
RE: AISC Appendix 6 - Beam Bracing
RE: AISC Appendix 6 - Beam Bracing
RE: AISC Appendix 6 - Beam Bracing
RE: AISC Appendix 6 - Beam Bracing
The forces in Case 2 are alternating in direction, so the total brace force acting on the whole beam is 2(1.96) - 2.6 = 1.32 kips which is only half the force required in Case 1.
If a beam requires more than three braces in order to satisfy the moment, individual forces will be larger but the sum of all brace forces acting on the beam will be close to zero.
BA
RE: AISC Appendix 6 - Beam Bracing
WillisV - I can see that with additional braces on a column, that the resulting column "design" would allow more axial load...perhaps a lot more, and that would kick up the brace requirements...so the light is beginning to shine a bit on my befuddled brain based on that.
But if you have a column with the SAME axial load, but add more braces, the formulae present much higher brace requirements that don't seem necessary and this has led me to suggest that the designer can use these brace formulae to economize the design by using the minimum number of braces to offer the lowest cost.
miecz - yes, that is the sort of conundrum that I see in these specifications. In my Case 1 above I have one brace with Pbr = 2.61 k and βbr = 8.07 k/in. It works with a W16x40.
Now if I still use a W16 x 40 beam and add two additional braces at the 1/4 points, both with the same strength and stiffness, the equations say that I need a strength Pbr = 2.64 kips at the center (which now doesn't work) and 1.96 kips at the 1/4 points (which works).
For stiffness, I need 16.33 k/in and 12.1 k/in at the center and 1/4 points respectively, neither of which work now....before, with one brace, it worked. This makes NO sense to me.
RE: AISC Appendix 6 - Beam Bracing
RE: AISC Appendix 6 - Beam Bracing
One suggestion. Make a simple beam model with parameters identical to those used in the cal you provided, and set the stiffness as spring support with schemes as in the cal. Now apply an unit load in the center, then observe the change in reactions and deflections. Take a long walk and think it again. Hope this would help.
RE: AISC Appendix 6 - Beam Bracing
I agree with you to a considerable extent. If you have a 30' beam, say W16x40 which works with one brace in the middle, it cannot be made more critical by adding quarter point braces. In fact, the quarter point braces should help alleviate the stress on the midspan brace.
In that situation, the quarter point braces are not "required" braces. You can add them if you wish but the code does not recognize that they help the midspan brace. In fact, there is no code requirement to be satisfied for the two added braces.
If, on the other hand, the beam needs quarter point braces to carry the moment, then all three braces are "required" braces. In that case, AISC dictates that each brace carry 2% of the flange force at the brace point.
So where is the problem?
BA
RE: AISC Appendix 6 - Beam Bracing
I know the Appendix 6 is an appendix and so maybe needs some maturing before making it into the full body of the specification - I was just struck by the fact that the section doesn't attempt to deal with multiple braces along a span directly but forces you to play around with it a bit to get a feel for it. In this instance, the "feel" I was getting didn't feel right at all.
Thanks again all of you.
RE: AISC Appendix 6 - Beam Bracing
RE: AISC Appendix 6 - Beam Bracing
Sorry, you are one step late. I have already stole the star :)
RE: AISC Appendix 6 - Beam Bracing
RE: AISC Appendix 6 - Beam Bracing
Thanks for bringing this up. A beam with three braces cannot be weaker than the same beam with one brace. I think the solution is to ignore some of your braces if the beam works with less braces than you provide. So, if a beam/bracing meets the code with one brace and not with more, ignore all the braces but one.
RE: AISC Appendix 6 - Beam Bracing
The required brace force, Pbr, is only a function of the axial load in the member, Pr for columns and Pr=Mr/ho for beams. For beams, Mr does vary with the length of the beam according to the moment diagram.
The stiffness of the brace has the units k/in. The "inch" part of the units is the lateral movement perpendicular to the member. See commentary Figure C-A-6.3(a), it shows a little diagram relating the axial force P=Pr, and the braced length L=Lb, the brace force Pbr and delta. It looks to me, for the same axial load P, as the length of the "member" increases it becomes less rigid and therefore requires a lower force, Pbr, less stiff member, to resist that lateral movement. Again, no relation to the bending unbraced length, the member size, etc.
RE: AISC Appendix 6 - Beam Bracing
RE: AISC Appendix 6 - Beam Bracing
The column stability formulae considers the effects of gravity "leaner columns" on the overall stability of columns in lateral elements, e.g. braced frames or moment frames. Depending on what stability methodology you use, you can either ignore the notional load Ni (0.2% of the total gravity load) if it is smaller than wind or seismic or sometimes you consider the notional load Ni to be additive to the the transient wind or seismic lateral loads.
Is the notional load concept really a proper way to view the summation of beam bracing forces on the lateral system?
RE: AISC Appendix 6 - Beam Bracing
I do not fully understand you post, but if I understand correctly, the brace force, Pbr, calculated is not additive for multiple bracing members for the same beam. For example, for a simply suported beam with the max moment at the center, with 3 braces at quarter points. The max brace force would be at the max moment, center brace. That force goes into the diaphragm. If you have adjacent beams, all with the center brace, then you would add that center brace force for all the adjacent beams into the diaphragm, but you would not add the brace force of 3 per beam.
RE: AISC Appendix 6 - Beam Bracing
Thus, if there were 4 beams, Pb per beam would be 0.2 + 0.8/2 = 0.6 Pb for a single beam.
When there are two or more brace points, the forces, Pb alternate in direction so adjacent brace forces are not cumulative.
BA
RE: AISC Appendix 6 - Beam Bracing
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RE: AISC Appendix 6 - Beam Bracing
Chapter 7 on page 311 in the 2008 Galambos Structural Steel Stability Book he does exactly a beam braced with two perpedicular beams framed into shear walls. Where he differs from you is that the stiffness of the 2 braces is B=AE/L. He then calculates the A value or area of steel required with a 15 foot long brace combined with the Pbr value. The bottom line is the area of steel is very small so many shapes will typically brace a 30 foot long beam with a moment of 465 kip-feet braced at the 1/3 points. Hope this helps.