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Cantilevered Beam Backspan- Unbraced Beam Length

Cantilevered Beam Backspan- Unbraced Beam Length

Cantilevered Beam Backspan- Unbraced Beam Length

(OP)
- Have several cantilevered steel beams which naturally have negative moment over a portion of its backspan.

- The top flange is continuously braced by a composite slab. However, the bottom flange (currently) is unbraced.

- Trying to determine what unbraced length should be used when checking if the beam has the capacity to resist the negative moment.

- Attached you will find a partial framing plan, bending moment diagram, and a blow up detail which illustrate the condition and the unbraced length I'm trying to determine.

Any help you could provide on this would be greatly appreciated.

Thanks

RE: Cantilevered Beam Backspan- Unbraced Beam Length

Good question, chief45.  I have a feeling you are going to get a few different answers from the forum. Theoretically, it is a difficult question to answer, but there are some safe routes to take.

The safest route is to brace the bottom flange at the tip of the cantilever, at the column and near the point of inflection.  Then the unbraced length is the length between braces.

If you brace the bottom flange only at the column and not at the other two points, then in my humble opinion, the unbraced length is from the point of inflection to the tip of the cantilever.  I suspect others will disagree.

If you do not brace the bottom flange at the column, your structure is unstable and prone to lateral buckling.  It is not clear what the unbraced length is or even if it can be determined.



 

BA

RE: Cantilevered Beam Backspan- Unbraced Beam Length

I would provide tranverse beam at the column to make it a fully braced point. Then consider the cantilever, and the back span seperately. Otherwise, BA's method seems logically correct.

RE: Cantilevered Beam Backspan- Unbraced Beam Length

According to AISC 360 6.3.1

"Lateral bracing shall be attached to both flanges at the brace point nearest the inflection point for beams subject to double curvature bending along the length to be braced"

I guess the nearest brace point for you is the column if you dont add any other brace point and that is also the spot that has both flanges braced, so i guess the unbraced length is the whole backspan in your case.

If you add full-depth stiffeners at the inflection point than the unbraced length is from inflection point to column.

But BAretired is right you are going to get alot of different answers.

i don't think I would use the whole length as Lb for negative moment, but who knows.

RE: Cantilevered Beam Backspan- Unbraced Beam Length

I believe that an inflection point cannot be considered as a braced point. Right?

RE: Cantilevered Beam Backspan- Unbraced Beam Length

I would say that an inflection point should NOT be considered as a brace point.  This is explicitly stated in the 13th edition AISC manual and in various texts.  The unbraced length should be the distance between actual brace points for the bottom flange.

What are the beams supporting?  Is it concrete filled metal deck?  If so, provide shear studs and a full depth stiffener near the inflection point and this will brace the section there.  Otherwise, the unbraced length is the length between the columns.  You can get a lot of help from Cb for this situation.  Maybe that will solve your problem and you won't have to worry about unbraced lengths.  I just did a back-of-the-envelope check and using Cb (I'm getting about 2 without diving too far into the moment diagram) you can use the full plastic moment, so unbraced length shouldn't be an issue.  You really only need Cb to be about 1.3 to get up to Mp.

RE: Cantilevered Beam Backspan- Unbraced Beam Length

I agree with slickdeals and StructuralEIT that an inflection point is not a braced point.  But it does represent the extent of compression in the bottom flange.  If the bottom flange of the beam is braced only at the columns, then the length subjected to compressive stresses is the backspan length plus the cantilever length and that is the length I would consider unbraced.

Because the inflection point can move under checkerboard loading, its location should be determined with reduced live load on the span and full load on the cantilever.

In my opinion, your cantilever length of 7'-6" is too long compared to the span.   

BA

RE: Cantilevered Beam Backspan- Unbraced Beam Length

Guide to Stability Design Criteria for Metal Structures, T.V. Galambos ed., P. 168, mine is 4th. ed.

RE: Cantilevered Beam Backspan- Unbraced Beam Length

I agree with BA Retired here, but do consider inflection points as "braced" points for exactly the same reason - the compression is no longer in the bottom flange - exactly what what we are bracing for the compression stresses seen.   

Mike McCann
MMC Engineering

RE: Cantilevered Beam Backspan- Unbraced Beam Length

I always assume the unbraced length is the entire length of the backspan, and I do use the Cb factor.

DaveAtkins

RE: Cantilevered Beam Backspan- Unbraced Beam Length

You design both beams for the 815'-k moment and you need to consider the full 27'-6" length as unbraced unless you have other secondary filler beams which would physically brace the beam.  If the cantiliver beam is a separate beam then the unbraced length would be the 7'6" length.

In this specific example the unbraced length does not matter since the beam is ovestressed even when assuming a fully braced compression flange. The allowable bending stress is 0.6Fy for an unbraced length up to about 14 feet after which the allowable stress starts decreasing.

It seems to me that filler beams should be provided to support the concrete slab and thansfer the loads to the monster w30 beams.

 

RE: Cantilevered Beam Backspan- Unbraced Beam Length

Brace at columns, then use the cantilever and backspan as your unbraced lengths.

The slab will restrain the backspan to some degree, but it's not straightforward to work out, so I would just ignore it.

Inflection point does not equal a braced point. Just because the flange has gone into tension doesn't mean the beam can't fall over.

RE: Cantilevered Beam Backspan- Unbraced Beam Length

Tomfh,

You said

Quote:

Brace at columns, then use the cantilever and backspan as your unbraced lengths.

If you mean cantilever plus backspan = unbraced length, then I agree with you.  But for large moments such as this, would it not be better to brace the bottom flange at the end of the cantilever and at the point of inflection?

Also, what is the advantage of having such a long cantilever?  Why not use 4' for the cantilever?  It would seem to make more sense to me.
 

BA

RE: Cantilevered Beam Backspan- Unbraced Beam Length

"Inflection point does not equal a braced point. Just because the flange has gone into tension doesn't mean the beam can't fall over."

No, but if the new compression flange (top flange) after the inflection point IS braced, then a brace point can be considered at the inflection point.  

Realistically, all we are dealing with here is providing some form of bracing to stabalize the compression flange, whatever it is.  If a beam of equal depth is provided at the inflection point anyway as BAretired initially mentioned, all this becomes a moot point.   

Mike McCann
MMC Engineering

RE: Cantilevered Beam Backspan- Unbraced Beam Length

The 7' 6" cantilever is most likely an architectural requirement. I do not think adding a beam at the inflection point and end of cantilever would make any difference. Which inflection point would consider? the one under the dead load, live load or combined? If this were an actual project, I would then strongly recommend adding more framing to properly support the concrete slab, shift the load more to the columns and reduce flood bouncing and most likely reduce the size of the relatively heavy beams (eventhough they do not figure for the current configuation)

The unbraced length stops at the column. you do not design the beam for an unbraced length of 35 feet. The beam is effectively braced at the column.  

RE: Cantilevered Beam Backspan- Unbraced Beam Length

I would use the inflection point that gave the longer unbraced length of the two.

Mike McCann
MMC Engineering

RE: Cantilevered Beam Backspan- Unbraced Beam Length

w12x26,

I doubt that the 7'-6" was an architectural requirement.  Usually in a Gerber system of beams, the location of the splice points for the drop-in spans are the responsibility of the structural engineer.  

However, if I am wrong about that and it was an architectural requirement, it can be resolved by simply bracing the bottom flange as required.

You say "if this were an actual project I would then...".  I believe it is an actual project (chief45 can advise on that).

You then say:

Quote:

The unbraced length stops at the column. you do not design the beam for an unbraced length of 35 feet. The beam is effectively braced at the column.
I partially agree with you.  You do not design the beam for an unbraced length of 35 feet.  I agree with that.  The part that you have wrong (in my mind) is that the unbraced length stops at the column.  It does not.  The unbraced length is equal to the backspan plus the cantilever span because that is the portion exposed to compression.  The fact that the bottom flange is laterally braced at the column does not prevent it from deflecting as I attempted to show in an earlier sketch.  That would be the failure mode.   

BA

RE: Cantilevered Beam Backspan- Unbraced Beam Length

Yura has written (sound of thunder) that an inflection point is NOT a brace point.  

The correct steps here (per AISC) are:

Cantilever Design
Design should be based on its full cantilever length using Cb = 1.0 and providing bracing of the cantilever end on the TENSION flange (look it up - AISC recommends the tension flange end of a cantilever for bracing).  Design for the Lb = cantilever length, Cb = 1.0 and the moment at the end of the column.

Bracing at the column
Provide some sort of bracing against rotation at the column - usually vertical stiffners in the beam web and a positive connection between beam and column cap plate to prevent rotation.

Main back span negative moment design
If there are no intersecting beams along the backspan, use Lb = FULL BACK SPAN LENGTH and calculate a Cb value based on the Ma, Mb, Mc and Mmax along the span per chapter F of AISC's 13th edition specifications.  With these, use the negative moment at the column for design.

If there are intermittent beams along the back span, and if they can be considered as braces, use the Lb = beam spacing and Cb = 1.0 (or calculate a Cb for each of these segments) and use the largest negative or positive moment for the design check.

Main back span positive moment design
If the top flange is braced by decking then Lb = 0 and design for yielding only.  

If there are joists on the top flange, or intermittent beams, use Lb = beam/joist spacing, and check the positive moment design - again using Cb = 1.0 or calculating Cb for each segment and using the maximum moment of each segment (usually don't go to that extreme)

AISC does suggest bracing at the inflection point but if you have intermittent beams that probably isn't required.

I do disagree with using the inflection point.  I admit that in years past I used that length (column to IP times 1.2 for yucks) only with Cb = 1.0.  But per previous seminars by Yura and others they've suggested that this isn't proper to do and isn't always conservative.  

 

RE: Cantilevered Beam Backspan- Unbraced Beam Length

In that case, you are dealing with "rollover" of the tension flange, which is an entirely different animal than compression flange failure.  Timoshenko addressed this too, years ago...

Mike McCann
MMC Engineering

RE: Cantilevered Beam Backspan- Unbraced Beam Length

In thinking about this further, with the small deflections seen, you are really approaching the "snapthrough' analysis of an arch section with a very shallow curvature.  This is a combination of tension induced rollover and compression induced lateral buckling.  

Mike McCann
MMC Engineering

RE: Cantilevered Beam Backspan- Unbraced Beam Length


"The fact that the bottom flange is laterally braced at the column does not prevent it from deflecting"

Sorry BAretired, but I can't agree with you. The whole purpose of a lateral brace is to stop it deflecting (laterally) isn't it?.

JAE's procedure is in basic agreement with the design procedure to AS4100 (Austalia's steel code).

RE: Cantilevered Beam Backspan- Unbraced Beam Length

BLACKPOT-

It looks like they didn't provide a stiffener at the beam over column connection.  That is the reason for instability.  If you provide that stiffener then the beam is braced (at the compression flange) over the column.


w12x26-

The beam is not overstressed for a fully braced compression flange.  Furthermore, if you take advantage of the Cb factor you can use the full plastic moment for the unbraced length of 27'-6".


BA-

If you provide a stiffener at the beam over column connection, why wouldn't the compression flange be braced there?

RE: Cantilevered Beam Backspan- Unbraced Beam Length

I think the whole thing needs not to be stretched out without end. Go back to any respectable text to review what is the definition of compression buckling, what is the cause, and what is the aftermath. It's a clearly defined phenonmenon, but many have chosen to deviate from.

RE: Cantilevered Beam Backspan- Unbraced Beam Length

I ran a quick calculation on Enercalc and found the beam to be overstressed even for the fully braced compression flange condition. I may be missing something then. This was a pure ASD check and I am not sure I want to introduce plastic design into this exercise. I also usually design for deflections.

The sketch does show a stiffener albeit partial and this I think does effectively brace the bottom flange against lateral buckling.

 

RE: Cantilevered Beam Backspan- Unbraced Beam Length

apsix,

What I said was

Quote:

The fact that the bottom flange is laterally braced at the column does not prevent it from deflecting as I attempted to show in an earlier sketch.

In that sketch, I indicate a deflection of the bottom flange of the beam.  At each column, the flange does not deflect because it is laterally restrained.  But please note it is not rotationally restrained about a vertical axis. The flange is capable of rotating about the column axis and when buckling starts, that is precisely what it does.

The inflection point deflects in a direction opposite to that of the cantilever.  That is necessary in order to maintain the same rotation angle at the column.  

StructuralEIT,

You are absolutely correct.  There was no lateral bracing over the column in the Station Square collapse in Burnaby, B.C.  That is a different kettle of fish than what we are talking about.

You then ask "If you provide a stiffener at the beam over column connection, why wouldn't the compression flange be braced there?"

As I have stated, the compression flange IS BRACED THERE .  It is braced against translation, but not rotation about a vertical axis.  In buckling, the bottom flange does not move laterally because it can't.  But it can rotate about the column axis unless the column is torsionally stiff and the beam is torsionally connected to it.
 

BA

RE: Cantilevered Beam Backspan- Unbraced Beam Length

w12x26-

This is a good lesson not to trust Enercalc without doing the check yourself.  Do the calc for yourself and you will see that the section is ok for a fully braced flange.  Use Fb=0.66Fy=50*0.66=33ksi.  Sx=329in3.  Thereforfore, the allowable moment is 33ksi*329in3=10857k-in=904.75k-ft.  This is greater than the 815k-ft moment in the diagram.

Additionally, using the full plastic moment isn't introducing plastic design, it's using LRFD for a fully braced compression flange.  It's the whole reason that you can use 0.66Fy iunstead of 0.6Fy.  

RE: Cantilevered Beam Backspan- Unbraced Beam Length

I have modified a sketch made on an earlier thread by moving the hinge support to the position of Column A.  The deflected shape of the buckled flange is shown.  

The deflection is zero at each column.

The inflection point deflects in the opposite direction to the cantilever.

At Column B, the bottom flange rotates about a vertical axis.

BA

RE: Cantilevered Beam Backspan- Unbraced Beam Length

StructuralEIT,

I used 36ksi steel and that may be the reason the beam did not figure.  

RE: Cantilevered Beam Backspan- Unbraced Beam Length

Quote (chief 45):

The top flange is continuously braced by a composite slab.

I read that to mean that the top flange has shear studs into the slab. Couldn't it be shown that the bottom flange has a Continuous Torsional Brace, according to 6.3.2b? In this case, doesn't the compression flange have full lateral restraint?
 

RE: Cantilevered Beam Backspan- Unbraced Beam Length

miecz - how does a "fixed" top flange of a WF shape rotationally brace a bottom flange in compression?  

The web probably doesn't have the necessary stiffness (weak axis bending in the web) to do any good.

I wouldn't count on it as a designer that's for sure.

RE: Cantilevered Beam Backspan- Unbraced Beam Length

JAE,

The restraint would have to come from the web.  I'm not sure the web has enough stiffness, but it might.  Other structures are designed this way: A through truss braces the top chord by the verticals; and AISI has provisions for the web contribution to the bracing of hat sections where the brim of the hat is unbraced and in compression.

AISC 6.3 says that lateral stability may be provided by torsional bracing.  Article 6.3.2 says torsional bracing may be continuous and need not be attached near the compression flange.  Formula A-6-13 appears to account for the flexibility of the web.  I haven't run the numbers, but it seems to me that the web might provide the required stiffness.

RE: Cantilevered Beam Backspan- Unbraced Beam Length

Perhaps I am missing something here.  We are told that "The top flange is continually braced by a composite slab".  If the slab is composite, doesn't that mean that the beam is composite too?  Why are we talking about the bare steel beam carrying 815'k.  Wouldn't that be carried by the composite section?  But then, why are we using such a long cantilever?

Or do we mean the deck is composite with the slab, but the beam is non-composite?  I don't know.

 
 

BA

RE: Cantilevered Beam Backspan- Unbraced Beam Length

BAretired...no.

A composite slab does not mean that the beam is composite.  You can use a rippled composite deck and have the deck/concrete act compositely as a spanning element between beams.  But the deck-slab might not be shear connected to the beam to create a beam-slab composite action.

 

RE: Cantilevered Beam Backspan- Unbraced Beam Length

Quote (miecz):

but it seems to me that the web might provide the required stiffness

It is the "might" in your statement that would push me to not consider the web as a bracing element.

RE: Cantilevered Beam Backspan- Unbraced Beam Length

Thanks, JAE.  So the beam is non-composite.  Under those circumstances, it is recognized that some lateral support comes from the web due to torsional restraint at the top flange, but reliance on this to prevent bottom flange buckling is not acceptable practice.

The moment diagram should show maximum and minimum positive and negative moments due to alternate span loading.  Maximum positive and negative moments do not occur simultaneously with one load pattern.

If the cantilever remains 7'-6", the prudent course of action is to brace the bottom flange at the end of the cantilever and also at the point of inflection most remote from the column.

 

BA

RE: Cantilevered Beam Backspan- Unbraced Beam Length

(OP)
Thanks for all the great responses and assistance.  To answer a few questions:

-  The 7'-6" cantilever is due existing conditions.  Our structure is directly adjacent to a 25 story office/parking garage structure on deep foundations. We had to offset our foundations as to not foul with the existing foundation.

-  All the cantilevered beams are being designed as non-composite.  Typical beams are indeed composite.

It appears that the general consesus is that there isn't one.  Seems that a conservative approach would be to design the beam to work unbraced the entire backspan for the maximum negative moment...

Thanks again to all

RE: Cantilevered Beam Backspan- Unbraced Beam Length

(OP)
Also, I just realized that I forgot to include in my sketch (see top of thread) that there are beams framing into the end of the cantilever (from the north and south).  

Wouldn't these intersecting beams brace the beam at the end of the cantilever?

RE: Cantilevered Beam Backspan- Unbraced Beam Length

Yes, they'd brace the end of the cantilever.

As far as "no consensus", I just have to say that your design shouldn't be based upon the consensus here at Eng-Tips but on the governing steel code and standard of practice (which in the US is AISC).  AISC requires what I listed above in living color.

 

RE: Cantilevered Beam Backspan- Unbraced Beam Length

Agreed.  The code is a minimum standard which must be satisfied.

BA

RE: Cantilevered Beam Backspan- Unbraced Beam Length

I've gotten into this discussion with many folks over the years.... most of whom thought that the RISA program should have automatically recognize the inflection point as a brace point.  

The code provisions are now pretty clear that inflection points cannot be considered a brace point. Hence the "proper" design would be to use the entire backspan length as the unbraced length.  

That being said it was a common design practice for years and years to consider the inflection point as a brace.... But, only if you also used a Cb of 1.0. That is an important caveat.  

Since Cb is fairly large for beams with a moment diagram like this, the old design practice is not necessarily un-conservative.

RE: Cantilevered Beam Backspan- Unbraced Beam Length

I am curious to see the load diagram for this problem. Obviously this a building structure and I really do not understand the relatively high loads.  

RE: Cantilevered Beam Backspan- Unbraced Beam Length

JAE-

Without the beam size, beam spacing, deck thickness, deck, reinforcing, and concrete strength, I can only say it "might" work.  I'm not even sure there are shear studs on this beam.

chief45-

It's still not clear to me.  Are there shear studs connecting the beam to the slab?

RE: Cantilevered Beam Backspan- Unbraced Beam Length

If it is a concrete slab and composite deck, the deck could be simply spot welded to the beam flange.

BA

RE: Cantilevered Beam Backspan- Unbraced Beam Length

Even if the intent was not to design this beam as composite, the designer could detail studs for the top flange.  Those studs might be cheaper than adding bracing to the system.  The attached sheet shows how the slab could then provide a continuous torsional brace, according to Appendix 6.

RE: Cantilevered Beam Backspan- Unbraced Beam Length

miecz,

Interesting idea.  I would not have thought it would have been possible to get enough stiffness out of the web of the beam.

I am impressed with your calculation but still prefer a brace at the inflection point and at the end of the cantilever.

BA

RE: Cantilevered Beam Backspan- Unbraced Beam Length

If you can provide shear studs into the slab, just add a full depth stiffener at the inflection point and the bracing is taken care of.

RE: Cantilevered Beam Backspan- Unbraced Beam Length

StructuralEIT,

The op stated that typical beams on the project are composite with the slab.  I agree that a full depth stiffener can work, but that sidesteps my assertion that the system can meet Appendix 6 without a stiffener.   

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