Laterally unbraced length of beam column capacity

[designrider]

Consider a two-span continuous beam (L=span length, 2L=total length) with uniform loading and a axial force along the axis of the beam. The top & bottom flanges have stability bracing at the support locations only. What are the values of Lb(lateral-torsional buckling for bending capacity), and KL (euler buckling for axial capacity) that are appropriate for use in the interaction equation?

Conservatively, a designer could use Lb=L and KL=0.8L (K=0.8 for fixed-pined buckling shape assuming the center support produces a 'fixed' end condition for the spans on each side). I believe this is appropriate for would for positive moment regions, but I am not convinced for negative moment regions. Notably, the maximum moment occurs in the negative moment region right over the intermediate support, and in my opinion makes KL=0.8L is excessively conservative to use for evaluating interaction capacity at this section. Arguably one could even assume continuous support at this instantaneous location, thus eliminating the threat of euler buckling. However, what happens incrementally away from the support? Do I need to immediately use KL=0.8L or is there some interpolation value I can use as I check combined stresses along the beam length? It is my understanding that the equation for euler buckling evaluates column capacity based on the section most susceptible to buckling. It seems intuitive to assume this would be more near midspan rather than at the support. Thus, the most highly stressed moment section (at center support) and the weakest axial capacity (near midspan) will not coincide and therefore need not be checked as such. But if not, what interaction capacities should be checked?

I expect most responses will tell me to just use the conservative values and just move on. However, I am designing a waler for a 72ft deep cofferdam that has 54klf uniform load, a 2585kip-ft moment, and 980kip axial load, so any justifiable reduction in the analysis is worth finding.

Thanks in advance!

 

[JAE]

I would use KL with K = 1.0 as the double beam could potentially buckle in a pure "S" shape - where each span would mimic a pure simple span bending shape. If the double span cannot possibly bend into an "S" shape then the 0.8L would work in my view.

The unbraced length for bending, Lb, would be equal to the full span, L unless there are other attachments/braces along the span, in which case the KL would reduce as well.

 

[RFreund]

You can possible use the Cm factor to increase your bending capacity.

EIT

 

[designrider]

Thanks for the comments.

The loading is hydrostatic, thus no load patterning required it is essentially a dead load, and thus 'S' shape bending will not occur.
Cm is indeed a good way to increase moment capacity, I have explored that already, good tip though. I am more interested in how to improve the axial capacity, at least the evaluated axial capacity at the negative moment region.

 

[designrider]

It seems highly improbable for the beam-column to buckle due to axial force near the negative moment region, even though the stress combination is the highest here. It seems the inherent stability provided by the proximity of the center support bracing should grant improved capacity.

Consider the interaction equations in AISC chapter H
Pr/Pc+8/9(Mr/Mc)<1.0

RFreund commented a way to improve Mc, but how can I improve Pc?

Thanks again

 

[ishvaaag]

You can investigate the effects of intermediate or central restraint of some column in the literature of bracing.

Is your structure suitably braced?
SSRC 1993
Ricles, Walsh Eds.

has a pair of articles on that. Most surely Galambos or later Ziemian also have.

Certainly the asymmetrical mode of failure must be preferred in general; in strong bending it is prevented by the loading but except you have mechanical restraint on weak axis bending it could also form.

 

[BAretired]

RFreund commented a way to improve Mc, but how can I improve Pc?

I don't think you can consider Mc and Pc separately. If Pc is large enough so that there is no inflection point in the beam, you must take the full length L as the unbraced length but consider the variation in stress along the compression flange when computing buckling load.

BA