The origin of the 2% bracing force?
The origin of the 2% bracing force?
(OP)
Does anyone know the origin of this rule of thumb? Where does it come from? It seems everyone knows the 2% rule but no one knows where it comes from! Is it in any way related to the 2% that the code allows for out of plumbness? <scratch head>
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.






RE: The origin of the 2% bracing force?
DaveAtkins
RE: The origin of the 2% bracing force?
RE: The origin of the 2% bracing force?
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.
RE: The origin of the 2% bracing force?
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RE: The origin of the 2% bracing force?
RE: The origin of the 2% bracing force?
It may be related to the 2% minimum crown slope for Highways. Anything is possible.
Mike McCann
MMC Engineering
RE: The origin of the 2% bracing force?
Draw a smiley at the end, will you
RE: The origin of the 2% bracing force?
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.
RE: The origin of the 2% bracing force?
Best regards,
BA
RE: The origin of the 2% bracing force?
RE: The origin of the 2% bracing force?
If you have a copy of "Steel Mill Buildings" by Ketchum, he has a discussion on the subject; although he suggested 2.5%.
RE: The origin of the 2% bracing force?
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...
RE: The origin of the 2% bracing force?
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.
RE: The origin of the 2% bracing force?
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!
RE: The origin of the 2% bracing force?
RE: The origin of the 2% bracing force?
RE: The origin of the 2% bracing force?
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.
RE: The origin of the 2% bracing force?
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!
RE: The origin of the 2% bracing force?
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.
RE: The origin of the 2% bracing force?
If it's no longer available, perhaps it is also appropriate for SlideRuleEra's website?!
Cheers,
YS
B.Eng (Carleton)
Working in New Zealand, thinking of my snow covered home...
RE: The origin of the 2% bracing force?
RE: The origin of the 2% bracing force?
A star for the sheet bridgebuster!
Cheers,
YS
B.Eng (Carleton)
Working in New Zealand, thinking of my snow covered home...
RE: The origin of the 2% bracing force?
It's probably the best source for this type of question. I took a quick look at it, but do not particularly care to read the whole chapter right now. But, here are some quotes:
"For stiff brace systems the brace force approaces Fbr=Po*Delta_o/L. The brace force is a linear function of the initial out-of-plumbness".
They give a lot of technical references for the chapter that probably give you a better response than I am capable of.
Josh
RE: The origin of the 2% bracing force?
"The lateral bracing of the compression chords or flanges of trusses and deck girders and between the posts of viaduct towers shall be proportioned for a transverse shear in any panel equal to 2-1/2 percent of the total axial stress in both members in that panel, in addition to the shear from the specified lateral forces."
There was no citation or reason given in support of the 2-1/2 percent number.