Risa-3D - Confirmed error with calculation of hp for singly-symmetric beams AISC 360-16 Sect. F4 1

[RattlinBog]

TLDR: Risa-3D calculates hp as a negative number anytime the PNA is within the compression flange of a singly symmetric beam cross-section. This causes a noncompact web and messes up flexure Section F4 equations, reducing bending strength. AISC 360-16 (or -22).

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Risa support confirmed that the below issue is an error in the program, and they have a ticket out to fix it. Risa-3D (v22.0 and earlier)

If you ever need to design a singly symmetric I-shaped beam with unequal flanges per AISC 360-16 (or -22) using Risa's "tapered WF" shape dialog or by importing a shape from RisaSection, then be aware of this issue.

In the uncommon scenario of having a cross-section with a plastic neutral axis (PNA) located within the compression flange, Risa-3D will calculate the variable hp to be a negative number, which is wrong. The variable hp is defined in AISC 360 as, "Twice the distance from the plastic neutral axis to the inside face of the compression flange."

The variable hp is needed to calculate the limiting width-to-thickness ratio, λpw, for Case 16 in AISC 360-16 Table B4.1b for the web of a singly symmetric I-shaped member. When hp is negative, λpw becomes a large negative number, which automatically classifies the web as noncompact. A negative λpw also causes issues in flexure Section F4 equations (F4-9b), (F4-13), and (F4-16b).

The AISC Specification commentary on Section F4 states this about hp: "Otherwise, in extreme cases where the plastic neutral axis is located in the compression flange, hp = 0 and the web is considered to be compact."

In my personal opinion, I think it's okay if hp is a positive, absolute value instead of 0. It just can't be negative. If it's 0, it causes a dividing by 0 issue in the λpw equation.

I compared a hypothetical test beam with a large compression flange in both Risa-3D and a comprehensive Mathcad worksheet I built:

Risa-3D: hp = -0.181", λpw = -2661.2, LRFD design bending strength = 151.4 kip-ft
Mathcad: hp = +0.181", λpw = 137.3, LRFD design bending strength = 183.2 kip-ft

 

[JoshPlumSE]

Thanks for the warning. I'm kind of interested in the dimensions of the Tapered WF that you were using that produces this problem?

No criticism for using such a section. I'm just curious how close this sect might be to sections that I've used in the past.

 

[bones206]

Good catch. I am currently working through a PEMB tapered frame reinforcement design, using channels to build up the compression flange. Trying to leverage RISA Section and RISA 3D for this, but it seems to require a lot of workarounds.

 

[RattlinBog]

Thanks for the warning. I'm kind of interested in the dimensions of the Tapered WF that you were using that produces this problem?

No criticism for using such a section. I'm just curious how close this sect might be to sections that I've used in the past.

The only reason I caught the hp mistake in Risa was because I was using it to check the accuracy of an Excel design aid I was developing for my M.S. project (see thread in the structural forum). I was checking 12 different cross-sections, and 2 of them had the hp issue. Those 2 were a (1) W12x40 reinforced with a C10x15.3 channel cap and (2) W12x40 reinforced with a 1/2" x 10" top flange cover plate. Both of those sections pushed the PNA into the compression flange.

When I emailed Risa support, I created yet another hypothetical built-up beam to show them the issue. That time, I used Risa-3D's built-in "Tapered WF" shape creation tool, and created a shape with the following dimensions: 3/4"x10" compression flange, 1/2"x6" tension flange, and 1/4"x10-3/4" web. See below snip. Ag = 13.1875 in2.

I checked Risa's results with my comprehensive Mathcad worksheet. See attached for the Mathcad pdf.

Good catch. I am currently working through a PEMB tapered frame reinforcement design, using channels to build up the compression flange. Trying to leverage RISA Section and RISA 3D for this, but it seems to require a lot of workarounds.

I'm guessing your PNA will end up in the compression flange, so you'll likely have the negative hp issue in Risa-3D then. Thankfully, the issue in Risa-3D reduces bending strength per Section F4, so it should be conservative, but it's still an issue...

I don't know if you've noticed this bones206, but Risa-3D does not use the section properties that were calculated in RisaSection! If you import a RisaSection file to analyze in Risa-3D, open up the shape in Risa-3D and compare with RisaSection. If the shape has any additional elements besides 1 web and 2 flanges, the properties will likely be different. That's because Risa-3D only uses the dimensions of 1 web and 2 flanges to re-calculate all section properties, no matter what they were in RisaSection. For a Tapered WF, this should be fine. For something reinforced with a channel cap, WT, etc, Risa-3D will have no idea that the additional reinforcement shape exists! Ask me how I know...lol

 

[bones206]

This is my first rodeo with RISA Section. I bought it to help tackle this project. I was able to import my built up section, but I haven’t checked that the properties matched. So thanks for the heads up!

 

[RattlinBog]

Bones, be sure to read through the RisaSection Help document. Especially important to understand how it takes vertical slices through the section to determine flange dimensions. You can overwrite flange and web dimensions if it's giving you an average due to unequal flanges.

Also, before you import to Risa-3D, make sure to select the RisaSection "shape type" as either Wide Flange for doubly symmetric shapes or Tapered WF for singly symmetric shapes. Tapered WF can technically work for both. The reason this is important is because it tells Risa-3D which AISC 360 sections to use. If you have a singly symmetric shape but select Wide Flange shape type, Risa-3D will only code check using section F2 and F3.

I could share my mathcad sheet with you if it would be helpful? The Excel design aid I'm building would be great for this, but I want to wait to publish it until I'm completely done.

 

[bones206]

Thanks for the tip, I completely overlooked the option to export as tapered WF. Maybe this will work out after all, aside from the little hp error.

I don’t have mathcad anymore, but appreciate the generous offer.

 

[JoshPlumSE]

Rattlin Bag -

Thanks for sharing. Honestly, that Tapered Member looks reasonably normal to me..... I was hoping the ratio of the two flanges was going to be worse than that!