Cantilevered Beam Backspan- Unbraced Beam Length

[chief45]

- 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

 

[BAretired]

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

 

[kslee1000]

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.

 

[ash060]

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.

 

[slickdeals]

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

 

[Lion06]

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.

 

[BAretired]

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

 

[connect2]

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

 

[msquared48]

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

 

[BAretired]

chief45,

I attach a sketch showing my version of unbraced length and buckled shape of bottom flange when braced only at the columns.

BA

 

[DaveAtkins]

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

DaveAtkins

 

[w12x26]

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.

 

[Tomfh]

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.

 

[BAretired]

Tomfh,

You said

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

 

[msquared48]

"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

 

[w12x26]

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.

 

[msquared48]

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

Mike McCann
MMC Engineering

 

[BAretired]

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:

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

 

[JAE]

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

The correct steps here (per AISC) are:

[red]Cantilever Design[/red]
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.

[red]Bracing at the column[/red]
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.

[red]Main back span negative moment design[/red]
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.

[red]Main back span positive moment design[/red]
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.

 

[msquared48]

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