AISC Appendix 6 - Beam Bracing 5

[JAE]

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 (h_o).

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 h_o is in the denominator....and that seems counter-intuitive...fewer braces means less brace strength required.

Anyone have any views on this?

 

[271828]

Nothing useful.

One thought: I hate App. 6 because it doesn't make sense about 1/2 the time I try to use it!

 

[Lion06]

You only get a smaller brace force if you have a deeper beam, right? If you keep the beam constant, then the brace force stays the same regardless of the number of braces. That is the part that didn't make sense to me.

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?

 

[frv]

Twist needs to be prevented. The driving force behind LTB is "buckling" of the compression flange (similar to column buckling). By preventing lateral translation of the compression flange you are, in essence, preventing twist.

To be quite honest, I don't really know how you could prevent twist and not prevent lateral translation of the compression flange.

 

[Lion06]

I don't think you can prevent twist without preventing translation of the compression flange, but I think you can definitely prevent lateral translation of the compression flange without preventing twist.

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?

 

[frv]

The tensile force in the bottom of the flange prevents it from twisting, much like an axially loaded member does not twist..

Again, it LTB is driven by the compression force.. if you prevent the compression flange from moving, you've prevented the buckling..

 

[JAE]

OK - but getting back to my question....

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?

 

[tclat]

Hi,

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.

 

[kslee1000]

tclat has a valid point.

 

[JAE]

tclat, that makes sense and goes along with what I was thinking - The brace force equation is implied to be for a singular point on the beam - with the moment that occurs at that point.

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.

 

[BAretired]

JAE,

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:

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.

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 P_b alternate in direction.


BA

 

[kslee1000]

tcalt's thinking is still valid to me.

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.

 

[BAretired]

CSA S16-01 makes the simplifying assumption that the beam is hinged for lateral bending at the ends and at each brace point.

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

 

[JAE]

Hey thanks for the interest in replying.

I see what you are saying. But kslee1000, the AISC equation for Pbr only depends upon moment, M, and flange to flange distance h_o. 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.

 

[BAretired]

JAE,

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

 

[kslee1000]

Since I have no clue what is the "appendix" about, all my response is generated from your writing. I could have miss read though.

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.

 

[JAE]

On Monday - I'll post the formulae.

Thanks for your interest and help on this.

 

[kslee1000]

Add'l thought:

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.

 

[miecz]

JAE-

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.

 

[enginerding]

I think everyone is missing what the equation is actually doing. Consider the nodal bracing equation for brace strength. This gives 2% of the force in the compression flange. Sound familiar?

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...