Continous Beam Unbraced Length (Sorry)

[ToadJones]

Say you have a beam continuous over 3 supports with a cantilever at each end under 'assumed' uniformly distributed loading.

This beam is supporting bar joists at 4ft o.c. but the joists are not part of a diaphragm or braced in the plane of a diaphragm so only offer marginal lateral support to the top flange.

As you can picture, the beam is in negative bending over the supports and for some distance on either side of the support and it is assumed that the beam is braced at the support.

Say the beam spans 20' between the supports and the top flange is in compression beyond the inflection and assume that 60%, or the center 12', of the span has the top flange in compression.

Do you assume that the "unbraced length of the compression flange" is still 20'?

Or is the unbraced length to be considered to be the length of the compression flange which is unbraced?

Of course this problem is what it is because the bar joists are not part of a diaphragm or a braced system....in other words they are just framing between girders at 90 degrees.

 

[msquared48]

Toad:

Long a point of consternation here - the inflection point / lateral brace issue. I will not go there...

Personally, I would take the conservative approach here and use the 20 feet, unless the ends of the joists in question are linked back to another diaphragm that could then let the joists provide lateral stability, if you know what I mean.

Mike McCann
MMC Engineering

http://mmcengineering.tripod.com

 

[wannabeSE]

Appendix 6 of AISC 360-05 is fairly clear: "In members subjected to double curvature bending, the inflection point shall not be considered a brace point."

 

[ToadJones]

Mike- I apologized in my thread title b/c I know this subject has been beaten to death here.

The problem I have with it all is....
The maximum moment in the continuous span is over top the support, it is considered braced at that point, but you determine the moment capacity of the beam based on an unbraced length = the full span. It seems overly conservative.

 

[amec2004]

In members subjected to double curvature bending, the inflection point shall not be considered as a brace point.

The inflection point shall not be considered as a brace point, on the contrary, it’s the most unstable point.

This is an old topic and there are many similar discussions before.
Some of the references are:
* Structural Stability of Steel: Concepts and Applications for Structural Engineers P307
* Metal Building Systems: Design and Specifications P102
* AISC EJ 2001 Q1 Fundamentals Of Beam Bracing by Joseph Yura

For your case, there are TWO unbraced length Lu for LTB calc, one for top flange and one for bottom flange.
In STADD they are called UNT and UNB. The value of UNT and UNB all depends how the *COMPRESSIVE* flange get braced. Please note the *COMPRESSIVE* flange will change between top and bottom flange with changing of positive/negative moment.

Say your joist has floor deck and can be taken as horizontal diaphragm, so for the mid span positive moment, top flange get compression and it’s fully braced by the deck, so top flange Lu=UNT=0
Since you run the joist continuously over support column, on top of column you get negative moment and bottom flange get compression. If your joist bottom doesn’t have brace, you shall count the beam full length as unbraced length.

The similar scenario happens to building moment fame rafter beam where we have positive moment at mid span and negative moment at beam-column MC joint, and at the top flange we purlin braced but at bottom flange we don’t have brace

The similar scenario happens to building moment fame column where we have reverse moment due to crane point moment, or lateral wind or seismic load, and at the column exterior flange we girt as brace but at the interior column flange we don’t have brace

For above two similar scenario we can run flange brace to bring down the unbraced length.

anchor bolt design per ACI 318-11 crane beam design

http://www.civilbay.com

 

[ToadJones]

AMEC-
I have used STAAD and RISA for years.
RISA has similar parameters for the unbraced length of the compression flange; instead of UNT and UNB, they use Lcomp Top and Lcomp Bot.
But this seems to muddy the waters even further.
In order to properly apply these parameters it seems as though you have to apply different UNT or UNB parameters on different segments of the beam depending on which flange is in compression even though its all the same beam.
Yet, if I were to blindly follow the rules of thumb would I not be forced to call UNT and UNB both = 20 ft?

 

[amec2004]

>> apply different UNT or UNB parameters on different segments of the beam depending on which flange is in compression even though its all the same beam.

Below are the steps you can follow to define UNT & UNB correctly

1. Check the member's local axis to determine which flange is Top and which flange is Bottom. This is critical otherwise you will mess up everything

2. Break the member by *virtual* segments, not *physical* segments by placing a break node, based on the Top flange’s lateral brace condition
Say you have composite deck it shall be fully braced and set UNT=0 for all physical segments in the member, or you have two secondary beams tie in at 1/3 point with connection above 1/3 of beam depth, you set UNT = 1/3 L physical segments in the member. Again, you need not to physically break the beam, just to re-define the existing segments’ UNT value

3. Repeat step 2 based on Bottom flange’s bracing condition

Please note you won’t know which segment has positive or negative moment, they are changing with different load combination cases and it’s impossible for you to know correctly.

Just define UNT & UNB based on the member’s local axis and the program will take care of the rest.

anchor bolt design per ACI 318-11 crane beam design

http://www.civilbay.com

 

[ToadJones]

AMEC-
I am not sure what breaking the beam into sub-elements is achieving in what you describe above.
You can assign UNT & UNB without breaking the beam into sub-elements, no?

" Please note you won’t know which segment has positive or negative moment, they are changing with different load combination cases and it’s impossible for you to know correctly."-->

Isn't the entire point of what you are saying about breaking the beam up into smaller beams just to allow you to assign different UNT & UNB values to the beam along its length?
If this is the case, one would have to run the analysis and observe where along the length of the beam the moment changes from positive to negative then do a second analysis with the beam broken up in to smaller elements.

 

[amec2004]

Unfortunately most of my sayings are interpreted in the opposite direction. Anyhow ...

>> I am not sure what breaking the beam into sub-elements is achieving in what you describe above.

I said you need NOT to break the beam for setting UNT & UNB

>> You can assign UNT & UNB without breaking the beam into sub-elements

Yes

>> Isn't the entire point of what you are saying about breaking the beam up into smaller beams just to allow you to assign >>different UNT & UNB values to the beam along its length?

No

>>If this is the case, one would have to run the analysis and observe where along the length of the beam the >>moment >>changes from positive to negative then do a second analysis with the beam broken up in to smaller >>elements.

You need NOT to do this and you are NOT able to do this as the positive and negative moment are changing with different load combinations. If there are 100 LCBs, it’s not practical for you to do this.

All you need to do is to assign UNT & UNB based on the member’s local axis. By observing the member’s local axis, which is static all the time, you will know which flange is TOP and which flange is BOTTOM, and where to grab the bracing condition for UNT and UNB


anchor bolt design per ACI 318-11 crane beam design

http://www.civilbay.com

 

[JAE]

You use the length between brace points for each flange and calculate a Cb factor to apply to that unbraced length. The Cb factor adjusts the value of the moment capacity to account for member curvature and lateral torsional stability. ToadJones, this (the Cb factor) is what takes care of the "conservatism" that you mentioned in your earlier posts.

So for your first example - a continuous beam with non-diaphragm braced joists at 4 feet, assuming that the joists apparently can't laterally brace the beam due to lack of diaphragm, the unbraced length is the full span both for the top and bottom flanges as this is the full distance between brace points (those brace points being the columns. The columns would have to brace the beam against twist/rotation.
With this condition, the Cb factor would be calculated and with that it would derive your [φ]M_n capacity. This [φ]M_n would be checked against the +M_u and the -M_u values.

If there was a diaphragm, then the positive moment check would be for a [φ]M_n value derived from an unbraced length of 4 feet (the joist spacing) and a Cb factor calculated from the moment values across the 4 foot length (Ma, Mb, Mc, and Mmax)

 

[JAE]

I'm assuming the original question is generally directed for AISC in the US. If not my apologies.

 

[amec2004]

I love this forum when JAE mentioned the Cb factor in AISC, which is call Omega-2 factor in Canadian CSA S16-09.

Yes, Cb and UNT , UNB are all the factors you shall take care to do an accurate steel member design.

If you don’t handle UNT & UNB correctly, you collapse the structure.

If you don’t take care of Cb (AISC) or Omega-2 factor (CISC) in the past, that factor was default to 1.0 by all programs and you just waste some steel, you are on the conservative side.

I frequently told my colleagues that it’s painful to be a structural engineer. There are too many things we have to take care of, and the code is getting more and more complicated thanks to the cheap and fast running personal computer.

For seismic we do pushover and time history, for base plate and water tank we do FEM, for steel frame we do DAM, for a tiny anchor bolt it takes me 3 years to know what’s going on … On the positive side, these complexities create some business opportunities.

Attached PDF is the paper explaining how Cb (AISC) or Omega-2 factor (CISC) shall be applied or calculated properly in STAAD.

All comments are welcomed.

anchor bolt design per ACI 318-11 crane beam design

http://www.civilbay.com

 

[JAE]

I think this original question doesn't have anything to do with STAAD or any other computer program.
Cb factors have been around for decades and we used to (and I still do at times) hand-calculate beam capacities using them.

 

[amec2004]

>> Cb factors have been around for decades

Agreed, but it seems to be difficult to benefit from it if there are, say 30 or more locad combinations ?

anchor bolt design per ACI 318-11 crane beam design

http://www.civilbay.com

 

[JAE]

I guess I was just suggesting that it would be easy to answer ToadJones' question without reference to UNT, UNB, STAAD, etc.
(I always thought STAAD was a difficult program to use anyway - much better products out there - but I digress and shouldn't have).

 

[ToadJones]

JAE-
Yes, question had nothing to do with STAAD but it did come up because I was using RISA and checking the code check it provides.
I just happened to notice that the max moment is over the support, where the beam is in fact braced, but the beam capacity is based on the max unbraced length of span...if that makes any sense.

I will say this, I have used STAAD, RISA and several other programs.
If you are doing some cookie-cutter beam and building design, RISA is probably the least difficult to use. I think STAAD is a better piece of software for designing other "non-standard" structures. I think RISA was developed strictly with building design in mind.

 

[JAE]

I have to admit that I used STAAD about 20 years ago in parallel with another program on a significant and unique project - both matched OK on the solution but when STAAD reported an explosion to infinite moment at one end of a major member, and when we called the STAAD office to get help only to be rudely told not to bother them, it left a bad taste.

The more important question is - did your question get answer by all the above to your satisfaction?

 

[ToadJones]

Actually, No.
I consider myself an adequate structural engineer, but this one has me puzzled.

In the code check in RISA, RISA calculates the bending capacity based on an unbraced length of the member of say 20', or the full span. But in the code check it uses the max moment over the support where the beam is in fact braced.

 

[JAE]

Well, the beam isn't "braced" at the column - rather - that is a "brace point". There is still unbraced length on either side of that brace point that needs to be considered. The bottom flange can still buckle laterally beyond that column brace point.

AISC's use of Lb = span length (for negative moment - unbraced bottom flanges) and Cb factors to account for the member moment profile are intended to provide you with a good estimation of the moment that would induce LTB in that condition.

 

[amec2004]

>>AISC's use of Lb = span length (for negative moment - unbraced bottom flanges)

Should it be top flange for negative moment ? Please correct me if I am wrong.

>> and Cb factors to account for the member moment profile are intended to provide you with a good estimation of the moment that would induce LTB in that condition.


The caluculation of Cb depends on the moment diagram. We have to rely on program to do it if there are more load combinations.

anchor bolt design per ACI 318-11 crane beam design

http://www.civilbay.com