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LTB of Wideflange with Wideflange Cap Plate

LTB of Wideflange with Wideflange Cap Plate

LTB of Wideflange with Wideflange Cap Plate

(OP)


"Cap Plate" = W10X19
Other wideflange = W12x26
Lb = 210 inches
Cb = 1.67
Cantilever Column
Gravity Loads < 0.05 Compressive Capacity

All loads are delivered concentrically through the "Cap Plate" wideflange.

For bending about the Y-Y axis, I'm simply using the "Cap Plate" wideflange properties, and consider it to be fully braced against LTB. The W12x26 in strong axis bending provides the LTB bracing.

For bending about the X-X axis, I am using the provisions in F4 in the AISC-360 with the combined section properties of the two wide flange beams. When the "Cap Plate" side is in tension and the bottom in compression, Iyc / Iy < 0.23 so I am required to take J as 0. Because of this, my capacity of the combined section is even less then the capacity of the "non-cap plate" wideflange taken in isolation. I think that the F4 provisions are over-conservative, and that the capacity should be at least the capacity of the single wideflange member, so I'm using the single member's capacity instead of the combined section.

Do you agree with my thought process for Y-Y bending?

Do you agree with my thought process for X-X bending?

RE: LTB of Wideflange with Wideflange Cap Plate

Quote (OP)

Do you agree with my thought process for Y-Y bending?

I do and would expect this to be conservative.

Quote (OP)

Do you agree with my thought process for X-X bending?

I think so. Are you able to tell us the compression flange stress for both the composite and stand alone scenarios? I'm not able to convince myself that the composite stress would always be lower than the stand alone stress although that may well be the case.

I like to debate structural engineering theory -- a lot. If I challenge you on something, know that I'm doing so because I respect your opinion enough to either change it or adopt it.

RE: LTB of Wideflange with Wideflange Cap Plate

Do you agree with my thought process for Y-Y bending? Yes

Do you agree with my thought process for X-X bending?
For positive bending (top of shape in compression) I get a ΦMn = 179.8 ft-kips (vs. 139.5 for the W12 alone)
For negative bending (bottom of shape in compression) I get a ΦMn = 86.66 ft-kips (vs. 139.5 for the W12 alone)

So for the negative bending of the combined section - I agree that the capacity is less than that of the W12 by itself.
But it seems to me that because of the drastic shift in the centroid, and the PNA, you have a little compression flange far away that could be more susceptible to LTB failure than the W12 shape alone.
So I'm not sure you can just ignore the combined shape effect on LTB.

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RE: LTB of Wideflange with Wideflange Cap Plate

(OP)

Quote (KootK)

Are you able to tell us the compression flange stress for both the composite and stand alone scenarios?

Composite - Sxc = 38.2 , Stress = 17.7 ksi
Stand alone - Sx = 33.4, Stress = 20.3 ksi

Quote (JAE)

For negative bending (bottom of shape in compression) I get a ΦMn = 86.66 ft-kips (vs. 139.5 for the W12 alone)

Interesting, I got 74.6 ft-k and 113 ft-k

Quote (JAE)

So for the negative bending of the combined section - I agree that the capacity is less than that of the W12 by itself.
But it seems to me that because of the drastic shift in the centroid, and the PNA, you have a little compression flange far away that could be more susceptible to LTB failure than the W12 shape alone.
So I'm not sure you can just ignore the combined shape effect on LTB.

That is a great point, unfortunately for me. Might need to upsize my W12

RE: LTB of Wideflange with Wideflange Cap Plate

(OP)
50. I get Fl = 32 ksi, not 35ksi. Sxc = 38.2, Sxt = 59.6

RE: LTB of Wideflange with Wideflange Cap Plate

(OP)
Oh shoot. I was using Sxc / Sxt to get FL. Not Sxt / Sxc. But that still doesn't explain the discrepancy in our W12 standalone calcs...

RE: LTB of Wideflange with Wideflange Cap Plate

It might be some of the input variables...not sure.
Here's the input I used:

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RE: LTB of Wideflange with Wideflange Cap Plate

1) I don't think that you really have a problem here. It's just a matter of demonstrating that.

2) In general, I'm pretty skeptical of any situation where adding more material decreases capacity. There are some valid instances of that, but not many.

3) It is very much my suspicion that the lower capacity here relative to the capacity of the W12 alone is really a spurious result emanating from incongruities in the math and the theory. As you know, the math on this stuff is over the moon complex and simplifications have been made.

4) I take the Iyc/Iy ratio business to be getting at this: let that ratio get too low and it means that your shear center and center of torsional rotation will be further from the compression flange.

5) With the shear center further from the compression flange, we start to worry about flange raking, flange distortional buckling, and all of the other voodoo that amounts to: we're no longer convinced that flange rotation equates to section rotation so we're not going to count on St. Venant torsional resistance. Check.

6) One way to get J back in the mix, I feel, would be to add stiffeners within the section to get back to a place where we can confidently say that flange rotation = section rotation. If this is the same column that was the subject of a previous thread, there may, in fact, be several good reasons to consider stiffeners. On the other hand, it may be that the cost of the stiffeners is more than the cost of upsizing the beam.

7) It may be right that the F4 business is neutering your St.Venant torsional stiffness. There is a significant source of additional capacity, however, that F4 is neglecting in your case. F4 was developed for a singly symmetric I-beam with one little flange and one big flange. The fact that your big flange is actually an I-beam cap changes things for the better. Each of the flanges on the cap will contribute additional warping (Cw) resistance to LTB in a way that is not captured by F4. I'd be astonished if accounting for that extra Cw in your evaluation didn't more than outweigh the loss of J.

I like to debate structural engineering theory -- a lot. If I challenge you on something, know that I'm doing so because I respect your opinion enough to either change it or adopt it.

RE: LTB of Wideflange with Wideflange Cap Plate

I might approach this a little differently: Ignore the outstanding flange tips of the cap member. Essentially assume that they don't help at all. Then treat the member as a WF with a Cap Channel. To me that is a more common and simple calculation.

RE: LTB of Wideflange with Wideflange Cap Plate

(OP)
KootK:

Thanks for the thorough response, it's very much appreciated. The discussion has been great for my understanding.

JoshPlum:

I see how that could help by increasing the Sxc (the tiny exterior flange tips increas c in the equation Sx = Ix / c while not adding much to Ix). I don't understand how treating the member as a WF with a cap Channel makes the calculation more simple? Care to elaborate?

Edit: The tiny flange tips in this case would be in the tension part of the beam (in this case) so actually I think ignoring those tips would hurt Sxc. I still don't see how this simplifies the calculation. It seems to complicate it because I can't use the gross section properties of the "Cap Plate" wideflange, and have to come up with reduced section properties instead.

RE: LTB of Wideflange with Wideflange Cap Plate

Quote (cal91)

I don't understand how treating the member as a WF with a cap Channel makes the calculation more simple? Care to elaborate?

Maybe it isn't much easier.... It's just a configuration that I'm more used to seeing. I've always done these for crane rails where SA bending is governed purely by the wide flange strength alone. But, then weak axis loading is governed purely by the bending of the channel. Simple and conservative. Though I understand you are probably looking for a more exact answer.

Also, I feel like I've seen tables out there for this cap channel configuration. AISC manuals have the properties. But, I remember seeing capacity tables... Maybe a design guide or engineering journal article or something along those lines.

RE: LTB of Wideflange with Wideflange Cap Plate

This section reminded me of the eave beam detail we devised for a domed stadium some years ago - we used three W24's - two vertical and one "cap" on top.

The idea here was to create a slot where the entire roof would skirt along on teflon bearing pads. The sections spanned about 21 ft. if I recall.

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RE: LTB of Wideflange with Wideflange Cap Plate

The paper JoshPlum may be recalling is a fourth quarter 2010 paper in AISC Engineering Journal titled "Singly Symmetric Combination Section Crane Girder Design Aids" by Johnson and Laman. The paper included capacity tables for wide-flange girder sizes ranging from W12x26 + C10x15.3 to W36x150 + MC18x42.7 for both grade 36 and grade 50 steel. The paper is available at the AISC website (www.aisc.org).

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