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Web Sidesway Buckling from Column Reactions on Continous Beam Helpful Member! 

kar108 (Structural) (OP)
5 Jun 09 17:58
I am designing a 30 ft long (3) span continuous steel  beam  for a residential  basement.  The floor joist system provides continuous support for  the top flange.   The beam is bolted to the top bearing plates of (2) adjustable steel columns spaced approximately 10' apart.  The column reaction creates a concentrated load acting on the bottom flange of the beam.   This load must be analyzed for concentrated loads acting on the Flanges and Web as described in section J10 of the AISC Steel Construction Manual (13th Edition).  Using equation (J10-7),  I want to design the lightest possible beam for web sidesway buckling  without using a web stiffener.

My question is what should I use  for "l"(the largest unbraced length along either flange at the point of load)---
What is the proper choice for the unbraced length???

(1)    The entire length of the beam – ~30ft? (I am assuming that the columns do not provide lateral bracing), or
(2)    The maximum span between columns and/or foundation walls --- ~10ft?,
or
(3)    The distance along the bottom flange where the moment is negative ( measured from each column location to the point of zero moment)--- ~5' for the fully loaded condition; ~12.5 when the live load is removed from the center span?  (Since the floor system fully braces the top flange which has a positive moment, we only need to consider the unbraced portion of the bottom flange subjected to a negative moment)

 
KootK (Structural)
5 Jun 09 18:44
This is a great question.  One I've been meaning to ask myself for some time.

As for the value to use for "l", my interpretation -- based on diagram C-J10.2 given in the commentary - is that you should use the full length of the beam (~30).

Based on the commentary info, it sounds as though adding stiffeners wouldn't improve matters anyhow.

I have a few related questions of my own:

1) In kar108's case, there are two point loads (reactions) causing sway buckling withing one length of unbraced bottom flange.  Does anything additional need to be done to account for the fact that two loads may now contribute to the sway buckling?

2) It has always seemed to me that, if one provided full height stiffeners and a stiff cap plate connection, you could consider the stiffener / web combination to simply be an extension of the column below.  In this way you could claim to have braced the beam using the column.  Is this rational?  Does anyone know of a procedure for checking the cap plate connection in this scenario?

Usually, when I ask this question around the office I get a big fat "Just brace the damn flange".

Adam
Helpful Member!  JAE (Structural)
5 Jun 09 18:54
I may be a bit of an old fogie, but I always put stiffeners on beams when they go over the top of a column.

I know AISC provides a nice check for sidesway web buckling for these conditions but over the years, the main structural collapse mechanism that I've seen is simply beams without stiffners over the columns.

Due to tolerances in sweep and web plumbness, installation variability in column plumbness, and unbalanced loads from one side of the beam, you can get a pretty unstable condition without them.

Now to answer the first question - l is defined in section J10.4 as the "largest laterally unbraced length along either flange at the point of load."  

So you would go essentially the full length of the beam in your case.  One unstiffened column point doesn't brace another.

 
Lion06 (Structural)
5 Jun 09 19:23
I believe that if you provide stiffeners - which AISC requires at points of support - that it would be 10' (if the top flange is braced like you say).  The top flange being braced along with the stiffener will brace the bottom flange.  The is the same as bracing the bottom flange at a seat support (maybe on a concrete wall) and providing stiffeners or an end plate.  That provides rotational restraint, and braces the section.  If you provide a stiffener and the top flange is braced then you have the same condition.
Lion06 (Structural)
5 Jun 09 19:24
I also wanted to say that it's also the only way your column will be braced in both directions.
KootK (Structural)
5 Jun 09 19:25
Where does AISC say that stiffeners are required at all points of support?
Lion06 (Structural)
5 Jun 09 20:06
I apologize.  It doesn't require stiffeners, but it does require that the section be restrained against rotation at points of support.
BAretired (Structural)
5 Jun 09 21:59
I agree with SEIT up to a point.  You must use stiffeners or other form of rotational restraint over each column.  If you do, the unbraced length is from point of inflection to point of inflection.  It is not the 10' span of the beam, no matter what the so-called experts say, but if you want to use 10' as your unbraced length, you will be on the safe side unless you get negative moment all the way across the span.

In that case, the unbraced length is equal to the span plus the distance from the column to the point of inflection on each side of the span.  If the point of inflection is at 2' each side of the column, the unbraced length is 10 + 2 + 2 = 14'.

Such a condition is not likely to occur in residential loading, but it is important to understand the principle involved.

Most codes recognize that, when the moment is variable across the unbraced length, another factor comes into play which acts in your favor.  I believe AISC calls it Cb.

BA

BAretired (Structural)
6 Jun 09 9:37
Sorry, I spoke without thinking on the matter of unbraced length.  If the beam is continuous and torsionally restrained at all supports, the unbraced length would be 10' max.

If the beam was a 10' span with a 2' cantilever each end, each loaded with a concentrated load at the tip, then the unbraced length of the bottom flange would be 14'

BA

csd72 (Structural)
8 Jun 09 5:18
This is a classic failure mechanism that is often overlooked - put in the stiffener!

I disagree with BA, the deflection points are not points of restraint and your effective length is between points of restraint no points of zero moment.
ishvaaag (Structural)
8 Jun 09 6:02
A traditional detail to prevent lateral buckling of deep beams in the bottom (compressed) flange is to provide struts at 45 deg upwards to the floor. I think rarely the floor is checked for these rotation prevention forces (not seen in the books, or don't remember). The point here is that technically is assumed that the rotation prevention provided by the floor, maybe even unchecked, has been accepted in practice. Using a stiffener may, depending the detail, signify as well the same kind of introduction of rotational forces to the floor than by the struts, only that bigger. Hence, seeing the cost of adding details to simple straight members it looks natural some try to use simply the beam, without stiffeners. And in the books there are formulae for concentrated loads without stiffeners for a number of cases, maybe one as the described as well.

So, technically, since it is the rotation prevention by the floor what is accepted in many cases as the stabilizing mechanism against the lateral buckling of the referred bottom flange, and seeing the books contemplate the case, one may think it is acceptable practice to go for the beam without stiffeners, since, once the stabilizing rotational loads are passed to the floor, there must not be much difference between a rigdized and not rigidized support point, as long its capacity is proven.

And so one might start to think in what width of the web could be taken for such check. 18 times -9 times each side- the thickness of the beam web plus the width of some quite stiff plate supporting the beam?

Of course, all forces, vertical compression and bending stressses in plane and out of plane (bracing required) force need be taken in to account for the accepted collaborating segment of web. If the loads are small, it might work.

There is also the question on how the working notional panel is working. Given the small dimensions, maybe just a stresses approach might work; you may see the implications and assumptions that need to be taken to analyze one of such panels in whatever the way.

And as well, beyond the science of construction, the crystallized mode of it, code and pathology of construction experience. So one might elect not enter somewhat uncharted territory and put stiffeners.
 
Teguci (Structural)
8 Jun 09 9:12
Without the stiffeners you have a double pin connections at the top.  Rotation is allowed at the floor to beam connection and at the beam web to beam bottom flange. If one of these pins is not elliminated, then the column reactions are variable and subject to redistribution due to high deflections.
CentrePACE (Structural)
8 Jun 09 12:03
In regards to the unbraced length, "l", and beam rotation restraint at supports: If an adjustable steel support column is embedded in a 4" concrete slab at the bottom and the top bearing plate is bolted or welded to the bottom flange of the beam, could the beam be assumed to be braced or "restrained against rotation" at that point (with continuous bracing of the top flange from the floor system)?
Lion06 (Structural)
8 Jun 09 12:19
CenterPace-

I would tend to say NO.  You can certainly check to see if the cantilevered column is adequate (for both strength and stiffness) for bracing the bottom flange of the beam, but that detail, in and of itself, doesn't brace the bottom flange. I would just provide the stiffener and call it a day.    
KootK (Structural)
8 Jun 09 12:52
Technically, you have to provide a stiffener AND a brace though right?  According to the AISC provisions, the stiffener by itself doesn't do anything for you in this situation.
Lion06 (Structural)
8 Jun 09 13:14
What brace?  If the top flange is braced as you say, and the bottom flange is positively connected to the column, then the stiffener itself does brace the bottom flange of the beam AND it provides a brace point for the column in a direction that is perpendicular to the longitudinal axis of the beam.  The only way for the beam to buckle in a LTB fashion would be for the stiffeners to fail.   
CentrePACE (Structural)
8 Jun 09 13:20
I am referring to a beam without stiffeners at the support.  Could the positively connected column, along with the top flange bracing, together act as a restraint against rotation without the need for a stiffener?
Lion06 (Structural)
8 Jun 09 13:25
No.  At that point you have to rely on bending of the web and that won't cut it.  miecz recently posted a calc showing that it is possible to get that work, but there is no point in going through that mess.  

The basic problem is that without the stiffener, you are counting on the beam to brace the column, so you can't count on the column to brace the beam.  Unless, like I said, it is a cantilevered column (not a pinned base) and you actually check the strength and stiffness of the column to brace the beam.  

Providing stiffeners takes care of both issues.
kar108 (Structural) (OP)
8 Jun 09 14:19
Is anyone aware of any documented steel beam failures in residential basements due to unreinforced point loads?

I ask this question, because my own observations (and also responses from several steel suppliers) indicate that residential  steel basement beams are typically not reinforced at column supports in our area (PA – low seismic risk).   

Is this possibly because  basement beams are subject to gravity loads only (no wind loads to create drift in members above and eccentric loading situations, and no seismic in the area).  The beams are supported by relatively  short steel columns (4"x11Ga),  only 7' to 8' long that are embedded in 4" of concrete and either bolted or welded to the beam.?
 
Lion06 (Structural)
8 Jun 09 14:34
I'm not aware of any, but I only have 3 years of experience.  I would tend to think that there are several reasons for a lack of a ton of failures.  The design loads are rarely seen - especially in residential construction.  When is the last time someone had 40 psf LL in their house?  The connection to the column does offer some benefit (though difficult to quantify and not reliable).  You start eating into your factor of safety.

kar-
Where in PA are you?
BAretired (Structural)
8 Jun 09 16:00
kar108 said "I want to design the lightest possible beam for web sidesway buckling  without using a web stiffener".

You could determine the maximum flange force as a result of the load.  Apply two percent of the flange force laterally on the bottom flange at each column.  If the beam web tributary to each column has the strength and the stiffness to resist the lateral force in accordance with the bracing requirements of the code, it should be adequate.

 

BA

Lion06 (Structural)
8 Jun 09 16:06
I'm not even sure I am buying that this is a web sidesway phenomenom.  Web sidesway is when the tension flange moves laterally as a result of a large concentrated force on the compression flange.  Your situation is not the same, because your tension flange (top flange) is braced.  This is a LTB issue.  What is the problem with providing the stiffener?
KootK (Structural)
8 Jun 09 16:41
Structural EIT:

I'm not sure that I agree with your assesment regarding stiffners / braces.  AISC J10.3 commentary reads "If flange rotation is permitted at the loaded flange, neither stiffeners nor doubler plates are effective."

To me, this implies that a discrete brace is required, whether you choose to install stiffeners or not.

I agree, however, that if the top flange is not just braced laterally but torsionally as well, then the stiffeners would provide lateral restraint to the bottom chord.  This would be reasonable if the top flange were embedded in concrete and connected to the slab with studs etc.  The wood framing situation described here would not provide the necessary rotational restraint in my opionion.  It would really only be the dead load on the beam preventing it from rotation.  The same dead load, mind you, that may be encouraging the system to buckle in the first place.

If you're going to count on stiffeners for beam bracing, I think that it needs to be via the mechanism that I described in my post near the beginning of this thread.

I've never seen a failure of this sort of system.  I have seen a couple that seemed to be barely holding on for dear life however.  Always at the beam over column connection too.

I suspect there are two main reasons for the lack of failures in residential construction:

a) Steel members used in residential construction tend to be grossly oversized.

b) Usually residential steel members have stringent depth limitations on them (often why they're steel in the first place).  This leads to stocky, shallow members that tend to be relatively stable.
KootK (Structural)
8 Jun 09 16:46
The sidesway phenomenon is about the two flanges moving relative to one another.  Whether it is the tension or compression flange that does the physical moving, it's still sidesway buckling.
BAretired (Structural)
8 Jun 09 19:42
The stiffener is an extension of the column through the beam.  In effect, the column spans from footing to top of beam by virtue of stiffeners or the beam web if it is stiff enough.  This prevents rotation of the bottom flange about a horizontal axis.  A stocky beam may provide a web stiff enough to achieve this without a stiffener.

The cap plate of the column must be capable of resisting the moment resulting from the brace force acting horizontally at the bottom flange.   

BA

csd72 (Structural)
9 Jun 09 4:54
I think Kootenaykid is spot on with regards to the reasons why these dont fail in residential construction.

In commercial construction I have read of a few failures contributed to a lack of stiffener over columns.

The one thing that has not been mentioned so far are all the second order effects that could result from the sidesway of the beam web. Short of an FEM analysis these would be hard to truly account for.

We need to remember that codes are only an approximation of reality and there are rare situations where merely following the code will not necessarily make a safe structure. This is the reason why we are taught to understand and not just to know.
CentrePACE (Structural)
9 Jun 09 9:59
StructuralEIT:  
Unless, like I said, it is a cantilevered column (not a pinned base) and you actually check the strength and stiffness of the column to brace the beam.

Thanks. I have analyzed this column as a cantilever (fixed base and free top) and applied a lateral load at the end of 1% of the axial load (which is 310# based on a 31k axial load in one specific case).  The column does not fail, but it deflects 1.044".  Can I consider this as a lateral brace or is the deflection to high?  If not, what degree of deflection would be a limit?
ishvaaag (Structural)
9 Jun 09 12:28
All elements in one structure brace -stabilize- ones to others. The overall general buckling of a framed structure, a reality for weak ones, is generally omitted from consideration in our piece by piece designs, by methods usually safe. Notional loads by diverse derivations, not all consistent in the proposed value, or different in-member imperfections from fabrication or construction are applied. Relative bracing is accepted, yet for some cases (not precisely for those it is recommended) the path of the forces appearing as a requirement of stabilization are not properly followed to foundations. In all, that if not for enough safety, for proper understanding, we need a thick to be seen two tomes manual to fix the many shortcomings generally appearing in the field. Whilst, keep tight to the code, but even this is no easy task, for as we see here, interpretations vary even between seasoned and well taught engineers.
KootK (Structural)
9 Jun 09 16:44
CentrePACE,

I don't think that you want to use your column as a cantilevered member to brace the bottom flange of your beam.

Effective bracing is about strength AND stiffness.  And, in the majority of cases, stiffness is far more important.

While your column might be able to muster the 2% strength required to act as bracing, it is likely woefully inadequate with respect to stiffness.  Your deflection estimate would seem to support this conclusion.

I believe that the 2% rule is intended to be an indirect way of providing brace stiffness.  I suspect that the rule was also derived assuming discrete, strut type bracing.  I'm not sure that ANYTHING (column, beam flange, slinkys)that can support the two percent rule can be considered bracing.

An interesting example of this is when engineers try to brace steel framing with wood members.  In my opinion, the wood bracing should be designed for the 2% load multiplied by E(steel)/E(wood).  Without scaling up the load in this fashion, I don't see how adequate brace stiffness can be ensured.
Lion06 (Structural)
9 Jun 09 17:03
CenterPace-

I don't think 1% is a good number.  Use App. 6 in AISC 360-05 - I believe it works out closer to 2% of the compression force in the flange of the beam.  When you get that load, apply it laterally to the top of your column and check it for strength (may not be a problem), and stiffness (this is where the problem will likely be).  For the stiffness, just apply a 1k lateral load to the top of the column, check the deflection, and invert it (1/delta) - this will give you the stiffness in K/in.  Compare this to the required stiffness per AISC 360-05 App.6.   
OzEng80 (Structural)
10 Jun 09 19:00
Structural EIT - Would you mind listing the stiffness requirements from AISC App.6? My code (Australian) has a 2.5% bracing requirement with no provision for stiffness. I would appreciate it if I could be armed with some figures for this obvious requirement.

Regarding the main post, I always provide stiffeners in these situations. I believe the calculation of the web bending (to restrain the bottom chord) should also account for the large compressive load at this point (support) ie, the web is already tending to buckle under compression prior to adding additional bending stresses.
 
Lion06 (Structural)
10 Jun 09 19:31
Oz-
I'll post it tomorrow morning.  I was out of the office today.
apsix (Structural)
10 Jun 09 20:40
OE80
AISC 360-05 can be downloaded from here;

http://www.aisc.org/content.aspx?id=2884
 
OzEng80 (Structural)
10 Jun 09 20:58
Thanks! Got some reading to do. I must confess i was hoping for something along the lines of: brace deflection limit of beam depth/1000 or column height/500...

Cheers
  
csd72 (Structural)
11 Jun 09 8:29
OzEng80,

Just as a curiosity, look at the references on page 439 and you will see reference to the old Australian Standard AS1250.

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