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Warping Constant - Back to Back Lipped Cold Formed C Sections

Warping Constant - Back to Back Lipped Cold Formed C Sections

(OP)
Hi, I am trying to calculate the warping constant for back to back lipped cold formed section as shown in attached file. The values of the section is also provided.

I have used the formula which is provided in the thread linked below but I believe the formula provided by tennist doesn't account for the stiffeners? My value is coming out to be 4.7 vs 4.9 given (using spacing on 0.1mm). This small margin is probably OK for thinner sections but as I increase the thickness of members the difference also increases.

On the other hand, I do not get a value anywhere close to those mentioned above on the section builders on FEM sofware.

RE: Warping Constant - Back to Back Lipped Cold Formed C Sections

Quote (123SP123)

I have used the formula which is provided in the thread linked below but I believe the formula provided by tennist doesn't account for the stiffeners

Stiffeners oriented perpendicular to your channel webs will not contribute appreciably to the torsional stiffness of the cross section and certainly should, in my opinion, be disregarded for determination of the warping constant.

RE: Warping Constant - Back to Back Lipped Cold Formed C Sections

KootK, I'm guessing the stiffeners in the context of cold formed sections are the channel lips, the 'c' dimension return is classified as a stiffener.

The only real way to work out the torsion and warping constants accurately is to resort to first principles and FEM approaches. You have not indicated how they are connected and this matters I think. This paper has a formula for channels that are welded back to back. If they are connected together at discrete locations far apart, like is normally the case with them being connected where there are bracing channels. Then I suspect they are more likely to act as two separate channels that are braced to one another at these locations, but in between they are behaving as individual members

Any equation is only ever going to estimate the properties, especially as they often never take into account complexities such as properly accounting for the corners. I'd assume as you assume that the equation presented in the other thread neglects the channel lips, I suspect it more appropriate for hot rolled sections given the parameters it contains.

See below regarding FEM approach:-

Using this excellent python package, with back to back with no gap I get most properties in good agreement except for the warping function and torsional constants, I suspect its to do with the fact that in reality its a gap and they are not actually glued together like the mesh indicates.

Double Channel (1.16mm thickness, hard against one another)
Section Properties:
A = 578.081
rx = 56.699
ry = 18.007
J = 697.946
Iw = 1145173485.288

adding a 0.1mm gap with a small linking 1mm section to tie things together at one location results in the following results, much closer on J as you'd expect J to be 2 times a single channel in this configuration (which it is), but warping constant still miles off compared to your published value. So probably not correctly being determined based on linking the sections into one composite member:-
Section Properties:
A = 578.181
rx = 56.701
ry = 18.035
J = 259.504
Iw = 1071245662.119

So basically I'm of no help here... I suspect if you find anything related to separate but composite or touching members and their combined warping constant then post back, just a guess but I suspect it may be something similar in nature to the parallel axis theorem or similar type of thing to "add" them together.

I'm getting the following properties for the single channel for comparison purposes:-
A = 289.040
rx = 56.699
ry = 14.522
J = 129.275
Iw = 279775483.894

Work through the equation I posted in the paper, and post back to see if it agreed with your value (it still neglects the corners but its probably close enough to compare assuming your sections are welded together top and bottom).

RE: Warping Constant - Back to Back Lipped Cold Formed C Sections

I'd point out, tables in an old AISI standard I just found for welded back to back channels seem to suggest a ratio of around 3.5-4.5 times the individual channels Cw, my ratio above is 1071/279 = 3.83 for what its worth.

RE: Warping Constant - Back to Back Lipped Cold Formed C Sections

(OP)
Hi Agent,

I went through the publication "Numerical Evaluation on Warping Constants of General Cold-Formed Steel Open Sections" linked above and calculated the Warping constant for two channels with stiffened flanges back-to-back welded the value I got is 1171 x 10^6 which is similar to what you got I guess but my section is going to be bolted at certain spacing.

Can you please let me know what page number and which AISI publication mentions the ratio?

RE: Warping Constant - Back to Back Lipped Cold Formed C Sections

Quote (Agent666)

KootK, I'm guessing the stiffeners in the context of cold formed sections are the channel lips, the 'c' dimension return is classified as a stiffener.

Of course... thanks for the correction as well as as the excellent contribution.

RE: Warping Constant - Back to Back Lipped Cold Formed C Sections

Check this document, I was looking at an earlier version with tables and simply comparing the values to work out the ratio.

Now the later version linked to above states that Cw for back to back channels connected at the middle of the web should be taken as being double that of a single channel (refer to clause 3.3.3). There's some examples in example III-8 that uses screws and doubles the single channel Cw.

Hopefully that gives you confidence to work it out by hand. The published value is 1.76 times the value I calculated for the single channel, so nearly 2 times I guess. Could just be my value is slightly different because they used an equation with approximations to derive.

RE: Warping Constant - Back to Back Lipped Cold Formed C Sections

For what its worth, I think the original published properties are definitely based on ignoring the corners. So published properties are an estimation at best.

The following properties are for a single channel with very small exterior radii (nominally square). Note that 2xJ=266mm^4 for J of two channels. Note also that 2xA=592mm^2 for two channels. These agree exactly with the published values so they are clearly ignoring the effect of the corners noting the slight differences to working it out exactly via the FEM approach. Goes back to my original suggestion that you really have to use FEM as you don't necessarily know how the published values have been calculated in some cases.

Section Properties:
A = 296.218
rx = 57.213
ry = 14.750
J = 133.060
Iw = 297157625.216

python script here to work out single channel using the package referenced if you need to evaluate others quite easily. Refer to the readthedocs page for any further information regarding the parameters

RE: Warping Constant - Back to Back Lipped Cold Formed C Sections

(OP)
Hi Agent!

Thanks again for the response above.

I have gone through what you did above and also the AISI example. Everything seems fine there.

I just wanted to add I think I have now figured out how they came across the value of 4.93 x 10^8. For warping constant they treated the back to back beam as I beam (ignoring the stiffeners). I used the formula from xcalcs and got the same value as 4.92 x 10^8.

Link: https://www.xcalcs.com/cgi-bin/tutti/x3calcs.cgi?a=o&d=i_0_0_6_1_0&f=1&l=en options - show formulas

Now the question is would you recommend to use 4.93 or 5.93 (2x 2.97).

RE: Warping Constant - Back to Back Lipped Cold Formed C Sections

Well I guess if you didn't start off with their value, then following the code verbatim and used the FEM result you'd use the 5.93*10^85.59x10^8 mm^4 value and be none the wiser. So I think there is you answer.

Your xcalcs link isn't working for me so I cannot see the formula/derivation. But I think the fact you are having to fudge/use equations for an equivalent I section that then ignores the stiffeners/lips (and maybe doesn't account for the doubled web thickness potnetially), it all starts sounding like its so far away from what you really have in reality that it cannot be relied on for accuracy. Use the FEM result as this is more true to the actual theoretical value, provided the 2Cw thing is valid. Using the lesser value will obviously be conservative.

Results for a single channel with no lip (otherwise the same), for comparison you can see the lips have a large effect on Iw/Cw. Note due to the way in which the author has formulated the CeeSection, you need to put l=1.16, and r_out = 0.1 to get the flange tip correctly laid out if you are playing with the python module I posted.
A = 264.099
rx = 55.900
ry = 11.526
J = 118.355
Iw = 141642874.221

Sounds like the original person working out the properties just cherry picked answers/approximations from all over the place instead of using a more correct theoretical approach.

I'd check the latest version of AISI to make sure it still contains the 2xCw approach just to be certain though. I just went with whatever I could find with a quick google search.

RE: Warping Constant - Back to Back Lipped Cold Formed C Sections

Actually I just noted something, you should take 2 x 279775483.894 = 5.59x10^8 mm^4
(you used the square corner value which overestimates the true Cw comparing that to my first post with the rounded corners)

RE: Warping Constant - Back to Back Lipped Cold Formed C Sections

Hi 123SP123, I finally remembered to get onto that xcalcs link using a different browser (wouldn't work in Chrome for me).

But using the following formula which I assume you are referring to for an I beam I get I_w = C_w = 5.48 x 10^8 mm^6. So I still don't quite see how you matched with the manufacturers published value of 4.92 x 10^8 mm^6 using a formula from this site? Could you elaborate?

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