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

 

[msquared48]

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

 

[apsix]

"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).

 

[Paperandpencil]

The attached might be worth a read when thinking about if the beam compression flange is restrained at the column.

 

[Lion06]

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?

 

[kslee1000]

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.

 

[w12x26]

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.

 

[BAretired]

apsix,

What I said was

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

 

[Lion06]

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.

 

[BAretired]

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

 

[w12x26]

StructuralEIT,

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

 

[miecz]

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?

 

[JAE]

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.

 

[miecz]

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.

 

[BAretired]

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

 

[JAE]

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.

 

[JAE]

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.

 

[BAretired]

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

 

[chief45]

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

 

[chief45]

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?

 

[JAE]

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.