Inconsistency in calculation of Lr for LTB 1

[Italo01]

Hello,

I always had a problem with the derivation of the length Lr in AISC spec. (Which is exactly equal to the Brazilian code). I never understood why the factor Cb is not considered in the calculation of Lr, since Lr is defined as the length at which Mcr= Mr.

I Friend of mine, which is a member of the Brazilian code revision comission, talked recently about this question and he proposed that the factor Cb be included in the calculation of Lr. I'd like to know your opinions about this matter.

The image above from Salmon shows that, as defined today, Lr is the length for which Mcr = Cb*Mr, which doesn't make sense, since Cb shouldn't affect Mr.

The chart below shows the proposed curves.

Thanks for your opinions.

 

[Italo01]

In the Link below, he shows the derivation of the equations.

https://www.linkedin.com/posts/albe...8-u3yE?utm_source=share&utm_medium=member_ios

 

[chris3eb]

I think that the AISC methodology was to design the moment strength vs unbraced length curve specifically around the case where Cb = 1.0 and then to amplify the moment strength values based on the calculated Cb.

They may have done this just for simplicity, but I think there also may be a safety reason for it. If your loading condition ends up being different and the real Cb factor is smaller than you calculated, your capacity would be overestimated by a maximum of the ratio of those Cb factors. But if Cb was also incorporated in Lr, you could have a case where the capacity could be overestimated by much more than that - if you calculated the beam as being in the inelastic LTB range, but it was actually in the elastic LTB range.

Here is some commentary language which doesn't address Lr specifically but does mention that Lm incorporates the moment gradient while Lp does not and also states that Lp only has physical meaning when Cb = 1.0. So it's not a mistake that Lp and Lr don't incorporate Cb -it's deliberate.

 

[Italo01]

Hello chris3eb,

Thanks for your opinion but i don't think that the current approach is more conservative that the approach i posted. If you look at the chart with the proposed curves, all of them converge to Mp at Lp.

P.S.: The charts show M as a funcion of λ instead of L but the principle is the same since λ=L/ry.