Elastic critical moment of cantilevers

[stancrst]

Hello,

I am curious to know if there is any particular way in which RSA 2016 deals with lateral torsional buckling of cantilevers, more specifically the calculation of the elastic critical moment. Using EN1993-1-1 as a design code, I am aware that the formula and coefficients used for other types of members are taken from ENV (Annex F). Since this (pre)standard refers to BS5950 for cantilevers, I am having difficulties in deciding parameters (critical lengths, bending moment diagram) for a cantilever and then trusting the result. I give a simple example below and compare Mcr results from RSA with (correct) results from another software. (Theoretical) critical lengths are based on BS5950 / NCCI document SN009a-EN-EU (Effective lengths and destabilizing load parameters for beams and cantilevers - common cases). Bending moment diagram case used is uniform load.

For the case of a free tip of the cantilever, Mcr should be 129 kNm. Theoretical critical length 1 x L. RSA result is fine for Mcr assuming a bending moment diagram as from a uniform load on a SS beam, see picture below. I feel however that this correct result is perhaps just a coincidence.

Using a critical length in RSA of 2 x L then naturally results in an over-conservative value.

If my cantilever is assumed to have a torsional restraint at its tip, the theoretical critical length is 0.8 x L. Mcr should be around 211 kNm. RSA give a critical moment of 139 kNm and furthermore the C1 coefficient in this case is 0.97, as shown below. This coefficient should not theoretically go lower than 1. 

So, is it possible to calculate cantilever with the Eurocode as a design standard?

I would have one final question, not related to cantilevers, but to the critical moment of simple beams. In the general formula used, there are two 'k' coefficients. I assume 'k' (effective length coefficient for end rotation on plan) is calculated just as L0/Lcr and that 'kw' (sort of effective length coefficient related to warping) is always taken as 1. Is this correct?

Thank you in advance. 

[stancrst]

Bump. 

At least is there a confirmation for the last question in the original post?

[Artur.Kosakowski · Accepted solution]

HI,

I'm sorry for not being able read and to confirm what you wrote but actually this topic have already been discussed on the forum in this thread.

Currently for cantilevers Robot uses the same approach as for beams. 

I would have one final question, not related to cantilevers, but to the critical moment of simple beams. In the general formula used, there are two 'k' coefficients. I assume 'k' (effective length coefficient for end rotation on plan) is calculated just as L0/Lcr and that 'kw' (sort of effective length coefficient related to warping) is always taken as 1. Is this correct?

Yes, this is correct.

If my cantilever is assumed to have a torsional restraint at its tip, the theoretical critical length is 0.8 x L. Mcr should be around 211 kNm. RSA give a critical moment of 139 kNm and furthermore the C1 coefficient in this case is 0.97, as shown below. This coefficient should not theoretically go lower than 1.

Could you attach the corresponding Robot file? 

[stancrst]

Thanks for the answer, Artur. I did some searching before posting, but somehow missed that thread. It is all clear now. I attach the Robot file.