The origin of the 2% bracing force (part #2) 7

[ForestMoon]

Hi all,

I was reading the original thread (Link) regarding the origin of the 2% bracing force and no definitive answer was given as to its origin, which led me to reading the Guide to Stability Design Criteria for Metal Structures 6th Edition (2010) by Ronald D. Ziemian.

Chapter 12 seems to offer an approximate answer to this question in its first paragraph (whilst still not definitive):

Stability bracing requirements first appeared in the early 1900s related to the design of lacing in the built-up members of trusses (Waddell, 1916). Numerous railroad truss failures prompted the development of the 2% rule—the lacing shear force equals 2% of the force in the column. The lacing rule was most likely simply extended by structural engineers to all stability bracing situations, primarily as a result of steel design specifications in the United States not containing general bracing requirements until 1999. In the 1970s, the New York City building code contained the 2% rule for stability bracing but no stiffness requirements.

In Chapter XVI of Bridge Engineering (1916) by Waddell, the following equation is given to calculate the shear S to be carried by the lacing in percentages of P, the total load on the member, as a function of the slenderness l/r of the compression member:

S = (200P)/(16,000-60 l/r)

For a typical l/r = 75, S/P = 1.7 %.

Hope it can help someone in the future.

 

[KootK]

Fun. This is what I've got.

 

[phamENG]

which led me to reading the Guide to Stability Design Criteria for Metal Structures 6th Edition (2010) by Ronald D. Ziemian

If you read the entire thing on account of that question, then kudos to you. It's on my shelf, but I haven't had time to penetrate it too deeply.

Yura has contributed quite a bit to this area of study, and AISC appendix 6 is based largely on his work and Ziemian's. There, column bracing is 1% of axial, but beam stability bracing is maintained at 2% of the axial force in the flange. But this these are also coupled with a minimum stiffness value, which would make up for the required capacity reduction as compared to the rule of thumb.

 

[ForestMoon]

@KootK:

Interesting... Waltz (1998) goes deeper into that explanation. As they said, the 1/100 initial slope is quite arbitrarily chosen.

@phamENG:
I haven't read it all yet, just looking for this specific answer. But it seems like a great reference for the subject matter, will definitely keep it close.

 

[NorthCivil]

My guess is some old boy licked his thumb and held it to the wind. "2%! sounds about right."

it seems to work.

some numbers nuts along the way have tried to put some numbers behind it, to give it a logic that they felt was missing.

In the end of the day, like so much we deal with. before the maths and the quantity take offs, there is an equally important interpretation and practical understanding of the geometries we deal with that cannot be appropriately expressed with equations.

thus, 2% it is.

 

[JoshPlumSE]

I just wanted to expand on the references others have mentioned. If anyone wants to look them up / purchase them.

Throop, C.M. 1947. Suggestion for safe lateral bracing design. Engineering News-Record, pp. 90-91

Nair, R.S. (1988), “Simple Solutions to Stability Problems in the Design Office,” Proceedings of the 1988 National Steel Construction Conference, AISC, Chicago, IL.

Nair, R. Shankar (1992). "Forces on Bracing Systems," Engineering Journal, American Institute of Steel Construction, Vol. 29, pp. 45-47.

R. H. Plaut, 1993 ASCE Journal of Structural Engineering REQUIREMENTS FOR LATERAL BRACING OF COLUMNS WITH TWO SPANS

Plaut, R. H., and Yang, J.-G. (1993). "Lateral bracing forces in columns with two unequal spans." J. Struc. Engrg., to appear.

Stanway, G. S., Chapman, J. C., and Dowling, P. J. (1992). “A simply supported imperfect column with a transverse elastic restraint at any position. Part 1: behaviour.” Proc. lnstn. Civ. Engrs., Strucs. and Bldgs., 94(2), 205-216.

Waltz, Miles E. 1998. Discrete Compression Web Bracing Design for Light-Frame Wood Trusses. MS Thesis, Oregon State University, Corvallis, Oregon.

 

[human909]

My guess is some old boy licked his thumb and held it to the wind. "2%! sounds about right."

Interesting.... This seems to get even more arbitrary in the codified strength for LTB.

I'll speak about the Australian code here as that is what I know, here we use 2.5% as wind must have been a little stronger on the day the "old boy licked his thumb and held it to the wind". EG:

"The lateral restraint ..... shall be designed to transfer a transverse force acting at the critical flange (...) equal to 0.025 times the maximum force in the critical flanges"

This seems to be a case of. "This LTB is damn complicated. Let's just pretend it is the same as Euler column buckling and design our restraints with the same strength requirements as we did earlier in the code. Ok job done, lets got to the pub!"

From playing around with computational LTB the 2.5% seems grossly excessive. Though LTB is arguably an even a more fickle beast than compression buckling, so a healthy bit of conservatism is warranted.

Yura has contributed quite a bit to this area of study, and AISC appendix 6 is based largely on his work and Ziemian's. There, column bracing is 1% of axial, but beam stability bracing is maintained at 2% of the axial force in the flange. But this these are also coupled with a minimum stiffness value, which would make up for the required capacity reduction as compared to the rule of thumb.

Hmmmm... I only saw this after my above post. I really need to read more from Yura as he really seems to have done some of the better work here. Do you know if Yura gave a good reason for the choice of 2%? (The stiffness requirement is something that really should be required in all codes IMO.)

Also surely somebody has done further research since Yura?

 

[phamENG]

I don't recall. I'll have to dig out some of his papers and go back through them.

In terms of more recent work - not that I know of. I just took a stability course a little over a year ago (trying to finally finish my MS), and most of it was based on Ziemian, Yura, and Galambos. Galambos if for no other reason than he was my professor's doctoral advisor, though Structural Members and Frames has some really good stability stuff in it.

 

[human909]

I don't recall. I'll have to dig out some of his papers and go back through them.

In terms of more recent work - not that I know of. I just took a stability course a little over a year ago (trying to finally finish my MS), and most of it was based on Ziemian, Yura, and Galambos. Galambos if for no other reason than he was my professor's doctoral advisor, though Structural Members and Frames has some really good stability stuff in it.

I'll have a look when I can.

If you missed it the first time and if you have the patience there is lengthy discussion in a previous post linked below. Half the discussion is more AS4100 (Australia Code) specific but the general idea explored could be quite informative. (at least it was beneficial to me) It also exposes quite a big flaw in AS4100, albeit it is a flaw that is likely to only be problematic in rare circumstances.

Rafter without fly brace?

Agent666 Blog Post Series on the topic

 

[Agent666]

Point 1:-
Restraint bracing really has almost nothing to do with force in a practical sense.
Point 2:-
Restraint bracing is really a stiffness requirement/problem in disguise.

Your bracing points need to be stiff enough to force a higher mode of buckling. It's that simple. The force is almost arbitrary, but it gives you something to practically design for.

Many older codes had stiffness requirements (in addition to strength), but these seem to have gone over time in favour of only having some % of the flange force on the basis that most practical braces essentially offer sufficient stiffness to force a higher mode of buckling (either FTB or axial buckling, concepts are similar).

However, this opens things up for abuse in terms of you could put the absolute minimum strength required (say a single 6m long wire each way off a beam flange to something solid which acted in tension with 5kN capacity to restrain a 5kN force, it might stretch a considerable amount so would not be stiff enough), but it may not be stiff enough (but then you'd argue potentially that's not a practical detail anyway and warps the intent the code had in mind regarding you providing practical restraints).

The reality is you're bracing with global or localised bracing which has often been provided for some primary purpose other than only providing the member restraint. In practical term it does double duty as also locally stabilising the member, from twisting or displacing laterally. For example think about a roof with bracing at discrete points, these are the points where you would consider axial buckling restraint, and the global roof bracing forces are likely to be an order of magnitude higher than the bracing 2.5% forces if you were to add them in. Specific details like fly braces and so forth are practically a minimum size to allow bolting, and as such often have considerably more strength than required for just restraining members. So practically you have sufficient stiffness without actually evaluating it. The issue is people sometimes convince themselves that inappropriate details provide sufficient restraint and throw the underlying stiffness requirement out the window!

 

[human909]

Well put Agent666. The strength requirement really covers things in most cases unless you try hard. And if you don't inquire too much or aren't a pedant then it isn't a problem.

If you are too inquisitive you can quickly make problems for yourself. Case in point is a 23m 250UC column as part of a building I designed recently that lacks any flange restraint that fit the textbook view of a flange restraint. Yet if you consider it unrestrained for 23m then even a small moment will quickly reach the columns capacity. I spent too long hand wringing over whether extra restraint was required. But even a rudimentary buckling analysis shows that connections that might normally be considered 'pinned' are more than stiff enough to provide sufficient restraint.

(Context: A steel framed building with open spaces for further expansion. Without meaningful floor diaphragms connecting beams with should not normally be considered as flange restraints.)

 

[Settingsun]

 

[Settingsun]

 

[Settingsun]

It's American, but I wonder if this is the origin of the British and Australian 2.5%

 

[ForestMoon]

Here's an extract from Throop (1947) article regarding this matter:

 

[HTURKAK]

Your bracing points need to be stiff enough to force a higher mode of buckling....And a pink star for this explanation..

The following document Stability of Steel Beams and Columns ( by GARDNER ) is very useful to get the concept. The document is SCI publication and free of charge.

 

[engineering_patrol]

imperfections are always considered in non-linear analysis types.