Weff Effective Section Modulus for Class 4 CHS (Circular/Tubular Hollow Section) (Eurocodes)

[emilywalters]

Could anyone direct me to the formula for the calculation of Weff (effective section modulus) for a CHS. I need this and the Aeff (effective area) to perform a verification check for local buckling in accordance with BS EN 1993-1 and BS EN 1995-1. I have the following equations but no idea where they came from:

Aeff = A * [( 80*t / do) * (275N/mm-2 / fy) ]^0.5

Weff = Wel * [( 140*t / do) * (275N/mm-2 / fy) ]^0.25

Where:
A - area
Wel - elastic section modulus
t - thickness
do - outside diameter
fy - steel yield strength

 

[ishvaaag]

I have looked at the question and I have not managed yet to find an exact answer. One of the references I saw says it was not providing the formula or values for circular section yet astonishingly immediately gives one for elliptical sections, of which the circular is just a particular case. Then 93-1-1 seems to be directing to 93-1-6 (chimneys and alike) and I think to remember this sends you as well to the european recommendations for shells. I am not yet finished with the matter and if I find something neat will post.

Whilst as help to work a practical case of a pipe column under compression and uniaxial bending -biaxial can be vectorially reduced to it- with shear I post a printout of a Mathcad 2000 worksheet dealing with the problem, based in information in Galambos guide V. I may provide as well the zipped worksheet if interested, I lately provide mostly printouts because as pdf people has easier access to the content.

I have also a number of other worksheets dealing with related matters, most in setup closer to the american practice.

 

[ishvaaag]

This is a printout of the same worksheet with the calculations blackboxed, er, collapsed, in Matchad language, as it appears normally for its use. I add it because it makes more understandable the process.

 

[ishvaaag]

A good reference

http://www.google.es/url?sa=t&rct=j...-4GADQ&usg=AFQjCNHwAbV_d00qA5-Xvzpe9oI7eUZqEw

 

[ishvaaag]

This image composed from BS 5950-1 and Steelwork Design Guide to BS 5950-1: 2000 confirming your equations...

 

[ishvaaag]

BS 5950-1 2000 not exactly "confirming" since using Z in notation. Somewhere I found yesterday elastic section properties (and on effective) should be used for Class 4, I may find again.

 

[ishvaaag]

From the english version of EAE (a Spain's standing steel code -there are others, mainly CTE- you see, all is being normalized ...)

"sections of class 4 (slender) are those in which local buckling also inhibit the development of their elastic resistance capacity, and the yield strength cannot be reached in the extreme compression fibre."

"hence" use of effective section properties

"For slender sections of class 4, the reduction in their resistance capacity in ultimate limit states, as a result of local buckling, may be estimated using ideal effective sections ..."

(still trying to find the original source)

 

[ishvaaag]

In BS EN 1993-1-1:2005 Incorporating Corrigendum No. 1 (see image inserted with this link)

any reference to the formulas (present as you see in the BS 5950-1:2000, see previous image quote) is absent.
As you see, then, for Class 4 section, it refers to EN 1993-1-6, that again fails to quote the formulas.

BS EN 1993-1-1:2005
5.5.2 Classification
"Class 4 cross-sections are those in which local buckling will occur before the attainment of yield stress in
one or more parts of the cross-section.
(2) In Class 4 cross sections effective widths may be used to make the necessary allowances for reductions in resistance due to the effects of local buckling, see EN 1993-1-5, 5.2.2."

So one can argue that is what is made through the formulas, yet EN doesn't give any validation to such formulas, since absent.

In short, the formulas seem to never have been (nor in 2000 since not EN, nor in 2005 by absence of explicit quote in EN) part of the Eurocode specification, and by its use, even if someone can prove technically correct, one can't claim the check to be in accord to Eurocodes. Or, maybe, one can claim, but it can be arguably denied.

To claim that one is forced to follow EN 1993-1-6 (or EN 1993-1-3 if cold formed).
(EN 1993-1-3 is for plated structures and in this irrelevant to the case).

Now we can proceed to identify the origin of the equations, that seem be related to BS 5950 (or you can apport the precise origin of the same). I'll still pursue the matter to where I can.

 

[ishvaaag]

Sorry forgot the insert, here goes:

 

[ishvaaag]

errata 2nd link from here

(EN 1993-1-3 is for plated structures and in this irrelevant to the case).

should read

(EN 1993-1-5 is for plated structures and in this irrelevant to the case).

 

[ishvaaag]

Steel Guide to BS 5950-1 :2000 (7th edition) dismisses any potential doubt of Zeff referring to any kind of plastic modulus when saying ...

"For class 4 slender sections the effective elastic modulus Zeff ..."

so as of now we know your stated formulas were correct in a BS 5950 environment.

 

[ishvaaag]

This article even referring to elliptical sections identifies the formulas as BS 5950, extends them to the elliptical section cases, shows the formulas be conservative in charts for both CHS and elliptical sections ... and still doesn't identify the original derivation of the Class 4 effective section properties for CHS.

http://www.istructe.org/technical/files/young/TakMingChan.pdf

 

[homostructural]

You may find an answer here!

 

[ishvaaag]

Thanks homosructural, I understand that ... but I am still going around the original problem of finding the source for the formulas quoted, that seem not be from eurocodes.

Some other interesting info

http://www.eagle.org/eagleExternalP...ing&UltStrengthAssessOffshoreStructures/Guide

 

[ishvaaag]

You can also see critical loads for the compressed and bent thin cylinders in Table 20-15 of the Formulas for Stress, Strain, and structural matrices by Walter D. Pilkey. These are neither your eqs.

 

[emilywalters]

I have finally found the origin of the formula I stated above, they can be found in BS 5950-1:2000 3.6.6 (and before this there are effective areas for other cross sections)

It is strange however that the Eurocodes that supersede this standard instruct you to use "effective area" and "effective section modulus" and yet there is no mention of the equations to do so (despite there being several looping references to where you should look - driving you round in circles between 3-5 and 3-1 and 3-1-6)

I have decided to use the BS 5950 equations and will do so until Eurocodes inform me otherwise. The only slight concern is that the equations are not valid for very large, very thin sections (and no alternative is provided, which may imply these sections are totally unsuitable for this use) Additionally, the classification of sections differs slightly between BS 5950 and BS EN 1993 and I am unaware as to whether this renders the equations inaccurate for certain cross sections.

 

[ishvaaag]

Well, I also found the equations in BS 5950, yet not the technical info on where they were derived (except that one could reinvent the wheel with some thin wall section program providing the axial and bending strength, but to get the same results we should be using the same sources for such, that we have not yet identified.

Respect the technical info provided by eurocode and what is expected from the designer, I started a thread in the design according to eurocodes forum. Essentially my position is that the code should only be mandatory for the items a solution is provided therein, which not always is the case; with that understanding and the code not providing, you would be justified enough to use the BS 5959 formulation -that is, if you don't find how to better proceed in EN 1993-1-6, which I doubt is the case, for there different modes of failure are treated and how to be combined them mandated ... eurocode then simply directs you to a more complex check, I think, but stills at least provides a "how to".

 

[ishvaaag]

And when I say mandatory, always to be understood with acceptable alternatives as provided and justified by sound engineering judgement to be accepted by the approving authority.