Steel Beam Bearing - ASIC J10.4 Web Sidesway Buckling 5

[RFreund]

I am trying to clarify J10.4 in AISC - Web Sidesway Buckling. I might be a little picky here, but I want to make sure I understand this correctly.
AISC gives two different equations depending on whether or not the compression flange is restrained against rotation. Here is my confusion:

J10.4 -
"This section applies only to compressive single-concentrated forces applied to mem-
bers where relative lateral movement between the loaded compression flange and the
tension flange is not restrained at the point of application of the concentrated force."

J10.4a
"If the compression flange is restrained against rotation"
J10.4b
"If the compression flange is not restrained against rotation"

"When the required strength of the web exceeds the available strength, local
lateral bracing shall be provided at both flanges at the point of application of the
concentrated forces."

Comm J10.4
"The web sidesway buckling provisions (Equations J10-6 and J10-7) apply only to
compressive forces in bearing connections and do not apply to moment connections.
The web sidesway buckling provisions were developed after observing several unex-
pected failures in tested beams (Summers and Yura, 1982; Elgaaly, 1983). In those
tests, the compression flanges were braced at the concentrated load, the web was sub-
jected to compression from a concentrated load applied to the flange, and the tension
flange buckled (see Figure C-J10.2)."

Comm J10.4a
"For flanges restrained against rotation (such as when connected to a slab), when.."

Comm J10.4b
"For flanges not restrained against rotation, when"

Alright, so my questions:
[ol 1]
[li]In my first snippet AISC states this limit states only applies to beams where relative lateral movement between flanges is not restrained. However, Figure C-J10.2 (or J10.3 depending on edition) defines the unbraced lengths used in the web sidesway buckling equations. The last figure shows the top and bottom flange braced at the location of the concentrated load and defines the unbraced flange length as L/2. Shouldn't the limit state not apply?[/li]
[li]AISC states for flanges "restrained against rotation", do they mean - the local compression flange is restrained against rotation or the entire section is restrained against rotation? Or do they mean that the compression flange is restrained against lateral translation? In figure CJ10.1 they show the compression flange as being braced against lateral translation. Also in the commentary they state "(such as when connected to a slab)".[/li]
[li]Would this apply to the end of a uniformly loaded beam? I want to say no, because it states the "loaded compression flange". In the case of the end of a beam, you would have a "loaded tension flange".[/li]
[/ol]

Thanks!

EIT

http://www.HowToEngineer.com

 

[KootK]

Something like that. I'd start by investigating the web distortional stiffness. (As per Appendix 6.)

I'd be inclined to adjust the original J10.4 equations since they include the web distortion. I don't disagree with the validity of the approach that you've suggested. I'd just go this way because I feel that recycling the original method has a bit more "weight" to it. If they thought it was good enough for J10.4, surely it's good enough for this....

With that, I think that we've pretty much reconciled our respective takes on this. It took some doing but I think that's the ideal outcome. Hopefully my AISC QnA answers don't come back as boat rockers.

I like to debate structural engineering theory -- a lot. If I challenge you on something, know that I'm doing so because I respect your opinion enough to either change it or adopt it.

 

[RFreund]

Whoa whoa whoa, Maybe I'm misunderstanding but I feel like you guys just agreed to something that completely disagrees with the first sentence of J10.4.

"This section applies only to compressive single-concentrated forces applied to members where relative lateral movement between the loaded compression flange and the tension flange is not restrained at the point of application of the concentrated force."
In your example, didn't you state that the top and bottom flanges were laterally restrained?

Also going back a few posts you both agreed to the end bearing case being an issue.

Not for the rotational restraint for the end bearing situation (for example). Without a stiffener (and proper bracing), you are down to web distortion. It's the same thing as what is happening at the center of the beam (except with half the load)....only inverted.

Again J10.4 wouldn't apply as the compressive force (the beam reaction) would be applied to the tension flange, not the compression flange.

Are you arriving at the conclusion that - J10.4 does not address this, it is bad and maybe you could modify J10.4 to check it?

EIT

http://www.HowToEngineer.com

 

[KootK]

Maybe I'm misunderstanding but I feel like you guys just agreed to something that completely disagrees with the first sentence of J10.4.

I apologize for nothing. I've been getting the ever increasing sense that this section of the standard is a hot mess as far as QC goes. That bunk commentary figure has, apparently, been in the standard since the Herbert Walker Bush administration.

In your example, didn't you state that the top and bottom flanges were laterally restrained?

Are you referring the W12/W8 framing plan that WARose posted above recently? If so, then the condition of interest there is the girder end bearing detail where, per the specifications of the example, the bottom flange would be laterally restrained and the top flange would not.

Again J10.4 wouldn't apply as the compressive force (the beam reaction) would be applied to the tension flange, not the compression flange...Are you arriving at the conclusion that - J10.4 does not address this, it is bad and maybe you could modify J10.4 to check it?

My take follows.

1) What the AISC spec tells us to do. I believe that J10.4 is not intended to apply to bearing conditions for three reasons. Firstly, I believe that you're supposed to provide rotational restraint at support locations for LTB and other reasons. So WSB is a moot point there as the restraint required to address it should exist without special consideration. Secondly, as discussed above, the J10.4 equations would not properly address this condition without modification. Thirdly, AISC's help desk response to WARose's questions would seem to imply this.

2) What the theory supports. At a bearing condition with no lateral restraint to the top flange, I absolutely believe that WSB would be a valid failure mode. In fact, I think that it would be more critical at this location than just about anywhere else which is a spiffy reason to avoid it. If you look at it upside down, it's basically a large concentrated load on a poorly restrained cantilever. Ick.
So yeah, I do think that it's bad, I don't think that J10.4 addresses it without modification, and my preferred approach would be to use a modified version of the J10.4 provisions as I feel that's the best way to stay somewhat true to the original intent of J10.4.

3) Terminology. I think that any reference to tension flange, compression flange, top flange, or bottom flange should be dropped from J10.4. There should only be "loaded flange" and "unloaded flange". Anything else causes confusion and, when you review the derivations of the J10.4 provisions, it's clear that no account was given to which flange was in tension/compression. I suspect that the "compression flange" mention probably just came about because the whole WSB thing came about as a result of a surprise failure that occurred during some Yura research where the condition was load applied to the compression flange.

4) Does it really matter which flange is in tension/compression? Almost certainly. My take is that the situation would be much worse if the flange that is restraining the web "kickout" is simultaneously in compression. If you imagine yourself as such a flange, you're clearly working harder when you need to worry about bracing not just the web but also yourself. In the literature, I've encountered discussion about the effect that normal flexural plastification would have on WSB. Once the web/flange joint plastifies, that joints ability to provide rotational restraint to the web becomes compromised to a degree. In many practical situations, however, I would expect that plastification to affect both the compression and tension flanges equally. So really no tipping of the scales there.



I like to debate structural engineering theory -- a lot. If I challenge you on something, know that I'm doing so because I respect your opinion enough to either change it or adopt it.

 

[WARose]

[blue](RFreund)[/blue]

Also going back a few posts you both agreed to the end bearing case being an issue.

I think it's an issue where you do not have the normal restraint at the support we count on (for LTB). See my sketch for the W12/W8 framing plan.

 

[KootK]

So my AISC responses rolled in this morning. My responses come from the same source as WARose's responses. And the responder is most definitely not a no-name. He's a pretty big deal and, were I RFreund, I would absolutely put more stock in the responder's comments than in mine. Since WArose didn't name names, I'll assume that's an etiquette thing and do the same. It's a bit unfortunate that I got a recycled answer on the whole commentary figure thing as a second perspective may have yielded additional insight. That said, A+ for effort. In all that follows, it's AISC in red and me in black.

I will preface this discussion by stating that there are limits to the conditions that can be addressed using the Specification equations. I believe the limits are provided in the text. Based on your questions I suspect you may be addressing a condition that is not considered in the Specification. If this is the case, then you will have to use your own judgment.

I have commented below in red:

1) My interpretation of J10.4 is that it applies at points of concentrated load and nowhere else. For example, if one chose to address WSB with stiffeners for a beam with a single concentrated load, all that would be require is a single pair of stiffeners at that concentrated load. Can you confirm that this interpretation is correct? Yes. All that would be required is a single pair of stiffeners at that concentrated load – assuming that the compression flange is restrained against rotation as is required to use Equation J10-6 and assuming that J10.4 applies to your condition.

My colleague believes that WSB is also applicable at locations away from concentrated loads wherever shear demand is very high. By that logic, you might have numerous stiffeners along the length of a beam, all intended to address WSB originating from a single concentrated load. The stiffener at the point load will be sufficient to prevent relative motion of the flanges if the assumptions stated above are true.

2) Are there any situations in which WSB could apply to heavy uniform loads? I do not think so – at least not as intended in the Specification.

As I'm guessing that the answer is no, why not? The Commentary states, “The web sidesway buckling provisions (Equations J10-6 and J10-7) apply only to compressive forces in bearing connections and do not apply to moment connections. The web sidesway buckling provisions were developed after observing several unexpected failures in tested beams.” I believe the statement is accurate. The checks were introduced due to unexpected and observed behavior in real beams.

To my knowledge there has been no similar unexpected, observed behavior in beams subjected to heavy uniform loads. Does this mean that such behavior is impossible for the full range of conditions that might exist? No.

Your question could be reworded as, “Is web sidesway bucking an applicable limit state for beams with heavy uniform loads but no concentrated loads?”

This brings up the issue of applicable limit states. As an engineer we must consider all possible limit states or modes of failure. The Specification lists a lot of limit states. I do not explicitly check every limit state for every condition I encounter. I know from experience that some limit states simply will not govern. I decide that these limit states are not applicable. There are also limit states that are not addressed in the Specification that I might choose to check. In the Engineering Journal article, "Torsional and Constrained-Axis Flexural-Torsional Buckling Tables for Steel W-Shapes in Compression," the authors provide design aids related to these limit states. However, you will not find constrained-axis flexural-torsional buckling among the limit states in the Specification. It can, however, be an applicable limit state.

In some cases the Specification tells you a limit state is not applicable. Chapter F, for instance, addresses a number of different limit states. It then sets limits (draws boundaries) around these behaviors and states that some of them only need to be checked under certain circumstances.
In the case of Section J10, the applicability is limited by the statement at the beginning of the Section, “This section applies to single- and double-concentrated forces applied normal to the flange(s) of wide-flange sections and similar built-up shapes.” These are the conditions that these conditions that these equations were developed to address.

If you have a wide-flange section or a similar built-up shape (there is some judgment involved in deciding what is similar), then I do not think that web sidesway buckling can govern the strength of the section when a uniform load is applied. I have not proven this mathematically (and I am not certain it is possible to do so given the term “similar”) but I am unaware of any test or analysis that indicates that this will happen. I suspect something else will govern the strength of the member.

There will always be some gray areas. At what bearing length and magnitude (relative to the other loads) can a concentrated load be treated as a uniformly distributed load? I do not think there is a clear answer to this question, so some judgment must be applied. If a condition looks odd, then some additional care and conservatism are probably in order.

If you get beyond the scope of the stated limits of the Specification equations, then their applicability should be reevaluated. Given a particular geometry (outside the range considered in the Specification) a behavior that looks like web sidesway buckling might occur when the member is subjected to a uniform load.

To give as example Jim Fisher wrote an Engineering Journal article entitled, “The Importance of Tension Chord Bracing”. A truss is certainly not a wide-flange section. Most engineers would also not consider it a built-up shape similar to a wide-flange section, though in some respects it is and in others it is not. However, Jim apparently decided that something similar to web sidesway buckling was an applicable limit state for this condition and developed a way to perform rudimentary calculations to check it. Some of his examples approach uniform loads.

In the absence of bracing, it seems that a demand for stability could accumulate over the length of a beam and add up to something significant.

I do not believe this kind of instability could accumulate in the case of a uniform loading for conditions addressed in the Specification. The Specification addresses web sidesway buckling specifically as it relates to concentrated bearing loads, and I believe this could be attributed to the stress distribution in the web. Yura found that this failure mode is due to the presence of a critical compressive stress field in the web. Generally a uniform load on a beam would produce governing limit states that are covered in Chapter F of the Specification, Flexure.

There will always be some gray areas. At what bearing length and magnitude (relative to the other loads) can a concentrated load be treated as a uniformly distributed load? I do not think there is a clear answer to this question, so some judgment must be applied. If a condition looks odd, then some additional care and conservatism are probably in order.

Also if you have an unusual condition behavior resembling web sidesway buckling could govern.

If you feel this is an applicable limit state for your condition, then you should check it in some manner that makes you comfortable.

3) I've attached figure C-J10.3 to this query. I believe the last beam in that figure to be in error as it gives a braced length of L/2 for a condition where relative flange displacement is laterally restrained at the load application point. I feel that the Lb value is not applicable since the load is stabilized at it's application point and the the web, therefore, does not require further stabilization from the bottom flange. Can you confirm that the figure is in error as described?

I have provided the following in response to a similar question:

“I agree that this is confusing. I believe I actually brought this issue up some time ago as well, but I never followed-up on it. I will bring it up with the Committee and make sure any changes that are necessary are made. Note that sometimes sketches and/or discussions are used to illustrate a specific point. I believe some of the conditions shown in Figure C-J10.2 are very “bad” conditions and I would not apply them in practice, though correctly illustrate the variable discussed. I further believe that some of the conditions shown are explicitly not considered in the Specification. Such conditions should be avoided if at all possible. If they cannot be avoided the Engineer is on his or her own relative to the applicable checks.

This Figure has appeared in the Commentary since 1993. I believe that what is required in the bottom figure is that the bracing can remain unchanged, but the point load needs to be moved. Potentially more dangerous, if misinterpreted, is the first figure. Though it correctly illustrates the intent relative to the length considered for web sidesway buckling, I do not think that this condition is otherwise considered in the Specification.

There will always be some gray areas. At what bearing length and magnitude (relative to the other loads) can a concentrated load be treated as a uniformly distributed load? I do not think there is a clear answer to this question, so some judgment must be applied. If a condition looks odd, then some additional care and conservatism are probably in order.“

4) My understanding is that, as far as the WSB design provisions go, stiffeners add no benefit at any location along a beam if the loaded flange is not rotationally restrained. That, because the web/stiffeners essentially cantilever downwards from the loaded flange and you can't have a cantilever with a pinned support. Can you confirm this?

I believe your understanding is correct. The Commentary for Section J10.4 states, “If flange rotation is permitted at the loaded flange, neither stiffeners nor doubler plates are effective.” This is why when the strength is governed by Equation (J10-6) “local lateral bracing shall be provided at the tension flange or either a pair of transverse stiffeners or a doubler plate shall be provided,” but when the strength is governed by Equation (J10-7) the stiffener are no longer given as an option and “local lateral bracing shall be provided at both flanges at the point of application of the concentrated forces” is the only way to address the problem.

5) In reading the research that led to the WSB design provisions (Yura etc), my understanding is that there are two buckling modes being considered based on the (h/tw)/(Lb/bf) ratio. The first is the bottom of the web kicking out laterally against restraint provided by the unloaded flange. The second is the web compression buckling between the flanges. I'm confused in that the WSB provisions don't provide any guidance for this second buckling mode. There are separate provisions for compression web buckling but they only apply where the compression load is applied to both sides of the beam which is not the case for WSB. Can you provide guidance on this aspect of WSB? I am not sure I understand your intent. The Summer and Yura paper addresses several conditions. Let’s look at Chapter 4.

Section 4.1 addresses conditions with braced flanges. Local buckling of the web subjected to compression is addressed in Chapter F. When the proper substitutions are made Equation 4.2 (in The Behavior of Beams Subjected to Concentrated Loads by Summers and Yura) you get something very close to Cases 15 and 16 of Table B4.1b of the Specification.

Equation 4.1 provides a web buckling strength in the absence of bending moments, but this is based on a model where both flanges are restrained.

Equation 4.4 includes the combined effects.

In Section 4.2 the authors suggest that 80% of the Equation 4.1 value can be used for the unbraced case. I believe the 80% is derived empirically and is one of the reasons there are limits to the conditions to which this equation can be applied.

I believe when values consistent with the stated limit in the Specification are substituted, Equations (J10-6) and (J10-7) will always produce values less than Equation 4.5. This does not appear to be the case for all I-shaped members, but it does appear to be true for rolled wide-flange sections. Therefore, it seems that Section J10.4 accounts for both effects.

I may be misunderstanding you intent.

Please let me know if you have any further questions.


I like to debate structural engineering theory -- a lot. If I challenge you on something, know that I'm doing so because I respect your opinion enough to either change it or adopt it.

 

[WARose]

Thanks for posting Kootk. Interesting answer on the distributed load situation. I still will always keep an eye out for it. (As I said before, I've seen a few situations where the sidesway buckling capacity is very low.)

Thanks for the discussion.

 

[KootK]

Thank you WARose. It was a wild ride and I learned much.

I like to debate structural engineering theory -- a lot. If I challenge you on something, know that I'm doing so because I respect your opinion enough to either change it or adopt it.