The origin of the 2% bracing force? 4

Salmon and Johnson mention it in "Steel Structures--Design and Behavior", but they did not originate it.

DaveAtkins

No idea - but it seems to work. Also have heard 5%

Err - error in the original post, meant to say 0.2% as opposed to 2% for out of plumbness.

Clansman

"If a builder has built a house for a man and has not made his work sound, and the house which he has built has fallen down and so caused the death of the householder, that builder shall be put to death." Code of Hammurabi, c.2040 B.C.

Try this?

You might also read Appendix 6 of the AISC Specifications for Structural Steel Buildings 2005 edition

Clansman:

It may be related to the 2% minimum crown slope for Highways. Anything is possible.

Mike McCann
MMC Engineering

Mike:

Draw a smiley at the end, will you ! Kind nice to find little tickling around on a Friday afternoon. Have a nice weekend.

He got me going, but only for a second!

Clansman

"If a builder has built a house for a man and has not made his work sound, and the house which he has built has fallen down and so caused the death of the householder, that builder shall be put to death." Code of Hammurabi, c.2040 B.C.

I don't know, but it was 2%, 1% and 2% for the 1969, 1984 and 2001 editions of CAN/CSA S16-01 respectively. I don't think it has any sound theoretical basis.

Best regards,

BA

Winter's seminal papers in 1958 and 1960 on column bracing are the first widely known treatment of the subject that I am aware of. The % force required for bracing in those was in the range of 1% - my guess is the "double that and you won't have to worry about it" effect came into play to arrive at the 2% "rule". On a side note, I've found very rarely in practice that the strength controls bracing though - almost always stiffness.

Professor Theodore von Schwarzenhoffen developed the theory.

If you have a copy of "Steel Mill Buildings" by Ketchum, he has a discussion on the subject; although he suggested 2.5%.

Wasn't Theodore von Schwarzenhoffen a character in a Laurel and Hardy movie?

This is either a very unfortunate coincidence, or the old Prof. Milo's idea of a joke...

I have a number of Ketchum's texts back in Ottawa, but not here with me in New Zealand. I would really love for someone to post the appropriate pages!

Cheers,

YS

B.Eng (Carleton)
Working in New Zealand, thinking of my snow covered home...

I tip my hat to you YS for knowing the that the good professor was indeed a character in the Laurel & Hardy short "The Music Box". I was wondering if anyone would recognize the name. I believe he was also one of Mike McCann's professors in engineering school.

I attached the relevant page from the 1921 edition of Ketchum's Steel Mill Buildings. I download this from books.google.com. I have a print version of the 1932 edition(same discussion on the 2.5% as the 1921 edition) but the scanned pages were too large to post.

AS 4100 uses 2.5% (i.e. P / 40). Its predecessor (AS 1250) also used P / 40, and also had a stiffness requirement that the maximum permissible lateral deflection was L / 400, if I recall correctly. The stiffness requirement has been withdrawn in AS 4100. According to the commentary (AS 4100 Supp 1 Clause C6.6.2):

The restraint is required to be able to transfer 2.5% of the axial compression force in the member being restrained, where this is greater than the force specified in Clause 6.6.1. A stiffness requirement is not given even though there is a theoretical solution (Ref. 27). This follows the finding (Ref. 28) that the requirements for centrally braced columns are satisfied by practical braces which satisfy the 2.5% rule.

27 Mutton, B.R., and Trahair, N.S., ‘Stiffness Requirements for Lateral Bracing’, Journal of the Structural Division, ASCE, Vol. 99, No. ST10, Oct. 1973, pp. 2167-2182.

28 Mutton, B.R., and Trahair, N.S., ‘Design Requirements for Column Braces’, Civil Engineering Transactions, Institution of Engineers, Australia, Vol. CE17, No.1, 1975, pp 30-36.

I don’t have a copy of the cited references, but I recall an explanation which goes something like this:

Consider a classic Euler column, with a lateral spring restraint at mid-height. Consider the buckling load in the column as the spring stiffness varies from zero to infinity.

At zero stiffness, the column will be unbraced, with a buckling load of:

Pcrit = pi^2 * E * I / L^2 = P0

At infinite stiffness, the effective length is halved, and the buckling load will be 4 times higher:

Pcrit = pi^2 * E * I / (L / 2)^2 = 4 * P0

At intermediate stiffness, the buckling load will lie between these limits. Therefore, the theoretical objective of a lateral restraint is to be sufficiently stiff that the buckling load approaches the upper limit. The question is – how stiff does the spring need to be?

If you conduct a series of buckling analyses, and plot the result of normalised buckling load (Pcrit / P0) vs. normalised spring stiffness (expressed as spring stiffness / column section stiffness, or k / (E * I / L^3) ), you get a graph something like the attached.

I suspect there is a general closed-form expression, but the important thing to note is that once you have a lateral spiring stiffness greater than about 175 * E * I / L^3, the column is effectively fully laterally restrained. Making the spring even stiffer does not increase the buckling load.

If we return to the old AS 1250 provisions, the implied required lateral spring stiffness is:

k = (P / 40) / (L / 400) = 10 * P / L

Assuming we are designing for the full compression capacity of the braced member (i.e. P = 4 * P0), this expression reduces to:

k = 10 * ( 4 * pi^2 * E * I / L^2 ) / L

which is approximately 395 * E * I / L^3 , which comfortably satisfies the theoretical requirements.

As noted above, the spring stiffness requirement is no longer explicitly stated, but the argument is that “the requirements for centrally braced columns are satisfied by practical braces which satisfy the 2.5% rule”. Personally, I still do a stiffness check as well (i.e. lateral deflection no greater than L / 400 when subject to a lateral load of P / 40, because this is the REAL theoretical requirement.)

Hope this helps!

So in summary, it appears as though someone, somewhere has determined that 2.5% of the axial load justifies a stiff enough brace to supply full restraint to the section.

I think Julian's answer is a lot better than that. The papers by Mutton and Trahair from the 1970's are on subject.

Hokie,

No offence, but you may have missed the point. After trawling through the theory, you/we still don't know where "2%" is from. Which is the original question. And it still isn't answered.

The concept has always been the same - applying some manner of spring stiffness theory. But as others have said, the % axial force varies from code to code.

The logical question is - how and where is the 1.5%, 2%, 2.5% concluded as satisfactory! (?)

Case still open as far as I'm concerned.

@SlenderBeam:

No, I don't know who, where and when the 1% / 2% / 2.5% first originated. I suspect it is a lot like a lot of other empirical "rules of thumb" which end up being found to be so useful that they end up being codified; such as maximum permissible stress = 2/3 tensile strength; shear strength = 40% of tensile strength, 2% cross fall on roads (thanks msquared48!), and so on. A lot of these principles have been developed and refined over many years from the 19th Century onwards (or even earlier).

Later research may find a real theoretical association, such as I have outlined that the real requirement for a brace is actually the spring stiffness rather than the design load, but this can be rationalised against the original rule of thumb (such as designing for a lateral load of P/40 and a lateral deflection of L/400 in fact yields an appropriate stiffness). However, in this case the original "rule of thumb" seems to have been found to be so simple and practical that it has survived in the codes, rather than the "real" theoretical requirement.
Hope this helps!

In "The Design of Typical Steel Railway Bridges" by Thomson, 1908

He suggests that lattice bars have a thickness of 1/50 of their length, which would be 2%. No reason given for the rule. Who knows, perhaps this 1/50th might have morphed into the 2% rule.

I looked in some older books but they didn't have any discussion on latticed columns. My guess is that it's an empirical method that someone came up with and it just kept getting passed along. It's sort of like the NYSDOT "unofficial" standard sheet containing the criteria for rivet replacement. The drawing has been floating around for 30+ years but no one knows who actually came up with it.