HSS Beam Section Modulus 2005 3

[jcox]

Does anyone no how to get the effective section modulus for hss columns for Slender flange and web elements. I have tried calculating the I(effective) with the b(effective) removed from the compression side. TheI calculate the new section modulus based on the new area and displaced NA. I'm really not horribly off what the manual says I should get for an allowable moment in the beam tables, but I'm off enough that it's bugging me. I'm trying to write a spread sheet that can reproduce the tables. The tables inform me that the non-compact/slender elements have been taken into account, but they never show an example of how they were arrived at. If anyone has any idea of how this has been calculated please let me know.

 

[dik]

Most manufacturer's have tables of section properties and the sections are proportioned to meet min b/t ratios. What is it that you are trying to calculate?

Dik

 

[jcox]

There is a fair amount of tubes that do not met the requirements. HSS8x8x3/16 is an example. Once the section goes past the non-compact region, I'm having difficulty determining the rational to get the same results shown in Table 3-13 of the new manual. The CD of examples that came with the manual actually runs the HSS8x8x3/16. However, they are testing for a required moment. They caculate S(eff) conservatively (i.e. easier) and show that the HSS8x8x3/16 works for the moment they are requireed to resist. They state that if you want a more precise answer that you can take only compression side out, calculate a new S(eff) with a shifted neutral axis. I'm willing to do this, I just don't seem to be able to reproduce the table. I figure that they are somehow manipulating the radius of the bend differently for different thickness--or something. I wish they would run a full example that would show their reasoning that reproduces the same number in the tables.

Any help explaining this would be great. I like to write spreadsheets that can reproduce the manual's numbers, or at least be able to understand why I'm not getting their numbers.

On a side note: What's up with the manual's only rounding the depth of the member to 0.1" (See WF's)? I use to be able to run a simple macro that could take all the decimal dimensions, convert them to the detailing dimension, and write to a text file. Now I'm having to check everyone of the sections against the manual value. Check out the the W14X22 (d=13.7, 13 3/4) vs the W14X43 (d=13.7, 13 5/8) its the same decimal depth with different fractional depths. Would it have killed them to tack on the extra decimal place? For $350 you think you could have sprung for the extra ink.

 

[dik]

I'm not sure how the .188 wall thickness falls out in your environs. The Canadian steel code S16 considers the member as a Class 4 section and directs the design to CSA S136, the code for Cold Formed Sections. CSA S136 is endorsed in Canada, US and Mexico.

Dik

 

[jcox]

I got this response from the AISC.

I wish there was a way of verifying the table numbers. I guess the best you can hope for in rectifying the equations to the table is to get close.

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The tables in the Manual are not meant to be reversed engineered, as that defeats the entire purpose of using such tables. However, you should be close. Be sure you are using 0.93 times the nominal thickness for all section properties, such as area, section modulus, moment of inertia, etc.

Be sure to use the Section F7 expressions found in the 2005 AISC Specification. There you will find three limit state expressions. The one with the smallest Mn governs.

The Section F7 limit states contain a Mn expression for slender flanges and a Mn expression for non-compact webs, hence I am confused why you asked this question. There are three Mn expressions for each limit state (namely, yielding, flange local buckling and web local buckling). The smallest Mn value from these three is the Mn that will be used for the design and allowable strength determination. The tabulated values are based on a LRFD design strength of 0.9Mn and an ASD allowable strength of Mn/1.67.

 

[dik]

S136 is endorsed by the AISC. You could run through the calcs and see how they compare to the tabular data. Hopefully they are close <G>.

Dik

 

[WillisV]

jcox - I have been working on this issue for the past few days and will post here when I get a resolution. I believe that the tables in the AISC Manual are likely in error for HSS members with slender flanges. For the HSS8x8x3/16 example, I believe the correct capacity to be approximately 43.5ft-k.

 

[WillisV]

Resolution: There was a minor error made in the calculation of flexural capacities for SLENDER HSS sections in Table 3-13 (square HSS sections). This does not affect any of the other tables (rectangular HSS etc) nor does it affect the compact or non-compact shapes in the table.

In the creation of the table the nominal wall thickness (tnom) was inadvertantly used instead of the design wall thickness (0.93tnom). This error will be corrected whenever the next errata for the Manual is released.

The table below lists the affected sections and the corrected values. Note that I generated this table and that it did not come from AISC, therefore it is subject to any errors I might have made, however I went to all reasonable lengths to ensure its accuracy.

I also feel it is helpful to see the exact process used in the calculation of the table. The calcs shown below go through this process step-by-step for an HSS8x8x3/16 for the corrected version, as well as show the steps required to replicate the incorrect printed values.

Have a Merry Christmas!