Polar Moment of Inertia of Weld Group

not my area, but why would you want a polar moi of a weld group ? Particularly for the welds shown. Wouldn't you say the two bolts carry the load ?


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Ahh i see the confusion, here is a plan detail. There is an angle and its bolted to the channel but welded to the HSS column. Im looking at the weld to the column as the bolts are good.
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Ip = Ix + Iy

Have you shown the weld in the wrong place in the first attachment? It looks as though it's shown welded to the PFC instead of the column.

Check out the post from MegaStructures at '30 Aug 20 12:28' in this post:

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Yes the weld is shown in the wrong place in the first attachment. It should be shown at the Column as i show in the second attachment, but still the same weld shape shown in the first attachment. And i know that Ip=Ix+Iy, but how do i get the Ix and Iy when you treat the welds as lines?

Polar moment of inertia of weld group, Ip = ΣIx + ΣIy
For a vertical weld segment, Ix = l³/12 + l(dy)² where dy is the vertical distance from the weld segment centroid to the weld group centroid.
For a horizontal weld segment, Ix = l(dy)²

Attached is an example elastic weld group calculation. Also, see AISC's Steel Construction Manual, Part 8 for more info.

Since you are determining Ip, then I assume you are using the elastic weld group method. For this weld, you are permitted to use the Instantaneous Center of Rotation Method which will get you almost twice the capacity. You can use the Weld Group Coefficients taken from Table 8-10 in AISC's Manual Table 8-10.

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To get Ix and Iy for welds, you ignore the width dimension, and get answers in units of length^3. Eg L^3/12 + L*y^2 instead of B*D^3/12 + B*D*y^2 for a rectangular element.

This assumes the welds are all the same size.

You need to calculate the centroid of the weld group in order to find Ix and Iy...

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Can the weld coefficients found in AISC table 8-10 (14th Ed) be used when the horizontal weld is on the bottom rather than the top as in the case in this thread? Or must you do the calculation using IP or Elastic method when the weld is on the bottom? Thanks

XavierEng05 that table applies to both cases (horizontal weld on top or bottom) if you look at the diagram on the table. I would try to use the ICR chapter 8 tables when possible since the elastic method usually gives overly conservative results.

Seconding the question by XavierEng05. Because you're asking about Ip, the weld group is presumably in torsion like the case in the Manual, not subject to out-of-plane moment.

For Ip, S, etc. calcs, I'd refer you to Salmon, Johnson, and Malhas. They have a great section on the Elastic Method for weld groups.

Finally got around to modifying my SMath program... and just updated...

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and these are the patterns



Rather than think climate change and the corona virus as science, think of it as the wrath of God. Feel any better?

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