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.

 

[amec2004]

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

Sorry I find I am wrong, it should be bottom flange

anchor bolt design per ACI 318-11 crane beam design

http://www.civilbay.com

 

[ToadJones]

Page 16.1-304 of AISC 360-10 provides some insight.
"The maximum moment in the unbraced segment is always used for comparison to the nominal moment".

Can Cb equations from AISC be used for a continuous beam? (EQ. F1-1) ?

If so, does one just use the moments at the quarter points of the span?

 

[amec2004]

>>Can Cb equations from AISC be used for a continuous beam? (EQ. F1-1) ?

One beam may have many Cb with different values on different segments depending on the lateral brace conditions.

The above mentioned many Cb are dynamicly changing with the changing moment diagram with different load combinations

anchor bolt design per ACI 318-11 crane beam design

http://www.civilbay.com

 

[BAretired]

Having a cantilever at each end complicates things substantially. If the cantilevers are unusually long, it is best to brace them top and bottom near the tips as well as at the column. For some reason which I do not yet fully understand, an unbraced tension flange in a cantilever can initiate lateral torsional buckling.

For a continuous beam without cantilevers, the unbraced length of the bottom flange can be no longer than the distance between the two inflection points on opposite sides of the column because that is the length of the material in compression. It is recognized that inflection points are not brace points, but to consider the unbraced length of the bottom flange to be the full span does not make sense to me.

Notwithstanding the above, it is good practice to brace both flanges at or near all inflection points.

BA

 

[amec2004]

>> it is good practice to brace both flanges at or near all inflection points

We use flange brace for this. Tie the roof beam/truss bottom flange/chord to both side of purlin using angle.

anchor bolt design per ACI 318-11 crane beam design

http://www.civilbay.com

 

[JAE]

BA - In the "old" days we used to use inflection points as "brace points" and for negative moment checks we used Lb = column-to-inflection distance and then kicked that up by a factor of 1.2 just for feel-good.

I sat in a seminar given by Yura some years ago in Texas and asked the question - "can we use that IP to column distance for negative moment unbraced length". He paused a minute and then said yes - as long as you use Cb = 1.0. Within a couple of weeks after that - I learned that he back-tracked on that and he and others spent efforts revising the Cb formula to its current form we see in the AISC spec today.

Based on that - the current "correct" method is to use the full span for Lb for negative moment checks and calculate a Cb ratio for that particular check....with the Cb using moments at quarter points between points of bracing. The Cb factor does get fairly significant and appears to work fairly well but it is sort of counter-intuitive when you see that the compression flange typically jumps up to the top where you have joists resisting lateral translation.

amec2004 suggests that there will be a vast number of Cb values for each unbraced length segment and this is correct - each load combination will have different quarter point moments resulting in different Cb values - but that issue is not relevant to this thread topic.

ToadJones - the Cb value is calculated based on the quarter point moments and the M(max) across the Lb distance...each unbraced segment will have its own Ma, Mb, Mc, and Mmax values and resulting separate Cb values.

So for negative moment maximum at a column in a typical continuous span condition you will have two unbraced segments - one going west of the column and one going east. Each will have a Cb value for each load combination and each will result in a moment capacity based on those Lb and Cb values. The Lb value would be the full span unless you add braces to the bottom flange per BAretired's suggestion above (i.e. at inflection points).

 

[JoshPlumSE]

This is a question that comes up frequently with RISA tech support. Though, it is really an engineering question more than a question about program behavior.

Test out the AISC code by doing the following:

Create a fixed-fixed beam with an unbraced lenth of the full length and a Cb = 1. What is the moment capacity?

Compare that to the moment capacity of a beam with an un-braced length equal to the distance from support to inflection point using a Cb of 1.0. What is that moment capacity?

Does the ratio between the two approximately correspond to the Cb factor you should have used for the unbraced length? Is it higher or lower?

When I did this test, I got a ratio of moment capacity of a little more than 3.5 compared to a Cb factor of 2.3.

So, doing it this way is approximately 30% more conservative than the old way (using the inflection point and a Cb of 1.0). It's in the same ballpark, so it seems rational. I'll let the academics argue why one method is more accurate than the other.

 

[Portcullis]

Toad, your second paragraph/sentence is the most important. Regardless of how you decide to handle the beam unbraced length, the stability of the beam at the column support is critical. If the beam is not adequately braced against roll over lateral buckling at the columns, then any value you assign to the beam unbraced length (top or bottom flange) would not be correct.