Bracing of Beams against lateral buckling

[ajk1]

My question relates to the CSA S16.1-94 steel design code, Clause 20.2 (I know that there is a later Standard but I do not have it here at home).
The formula kb = (beta Cf / L) x (1 + do / db),
where L is the length between brace points, and beta is a factor that increases with the number of equally spaced braces. It is 2, 3, 3.41 and 3.63 for 1, 2, 3 or 4 equally spaced braces, respectively.
The force in the brace equals kb db. Sorry I don't have the alt codes handy for the Greek letters.

This seems to mean that the closer the braces are spaced, the smaller L becomes, the larger kb becomes and the larger the force in the brace becomes (do and db are based on the length of the member that is being braced). How can this be? I would have thought that the closer the braces are spaced, the smaller the force in each brace.

 

[BAretired]

I don't have the latest S16 either, but in the 8th Edition printed in 2004, the following formula is given:
Pb = β[Δo + Δb]Cf/L

Since Δo is a function of L (Δo = 0.002L), the required brace force is not getting larger with smaller spacing beyond four equally spaced braces.

You can find Greek letters and other symbols if you click on the Ω icon in the line above"Submit Post".

BA

 

[ajk1]

In the example in the 7th edition of the CSA Handbook, which is what I have at home, they calculate Δ based on the total length of the column compression member: In the example, the braces (wall girts) are at 2000 mm spacing and the column length is 3 x 2000 = 6000 i.e. 2 braces. They then calculate the column Δ = 6000/1000 = 6.0 mm. So for say 3 braces instead of two, Δ remains the same since it is based on total length of member in this example, and β increases from 2 to 3.

So following this example, for braces at third points of a member there would seem to be a larger force per brace than a single brace at mid-length? What am I doing wrong?

Thank you for the tip on how to find the symbols on here. That makes things much easier!

 

[ajk1]

I spoke just now to the Canadian Institute of Steel Construction and this is what they told me. Seems to make sense and puts the issue to rest in my mind.

My question has been asked before, and the formula does give a greater force per brace when 2 braces are used than when 1 brace is used. That is correct, because with a single brace you are trying to force the member into 2 half sign waves, but with 2 braces you are trying to force the member into 3 half sign waves and that requires more force per brace than to force it into 2 half sign waves.

 

[BAretired]

Yes, the β factor increases with the number of braces up to four but does not increase after that. That does not account for the discrepancy that you are using the full length to determine Δo when you should be using the brace spacing or more correctly, Δo = 2L/1000 which is the permissible deviation from a straight line permitted by code for a member having a length of 2L.

BA

 

[ajk1]

I am unclear why you seem to be saying that I have not used the correct calc for Δ[sub]0[/sub]. The example in the CISC Handbook shows the calculation for Δ[sub]0[/sub] as based on the full length of the member. For a single brace, that is 2L, where L is the spacing of the braces. So I have used 2L/1000 which is what you say should be used. I don't have G40.20, but I am assuming that it says that the permissible out of straightness is the member length divided by 1000.

 

[BAretired]

If you have four braces spaced at 1000mm o/c, L = 1000 and span = 5000. Δo = 2mm, not 5mm. If your handbook says otherwise, it is wrong.

In the case of only one brace at L = 2500, Δo is of course 5mm because 2L = span.

BA

 

[ajk1]

The example in my handbook must be wrong then. Thanks for the heads up. That's what I get for not having the latest Handbook at home.

 

[Hokie93]

This topic has been addressed by Joseph Yura in the attached document, taken from the notes of one of his short courses. Yura's discussion is based on a column but the same concept can be extended to a beam. That is, use the required brace spacing (that spacing which would provide the required flexural strength) rather than the actual brace spacing. The response you received from CISC is true only if the load on the column is such that column must be fully braced at one-third points in order to provide the required strength. For a constant column load, providing more braces does not increase the brace stiffness requirement.