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Eccentric Loading of Welded Joint / Torsion

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Well, seems that this topic (eccentric loading) has been working me over the coals recently!

So today my question pertains to welded joints (fillet welds) loaded eccentrically in torsion.

I am wanting to understand the difference between J & Ju. I understand that Ju is the unit polar moment of inertia and it must be multiplied by an area (throat for example) to calculate the stress at that point. I am good with the throat area derivation.

However, I have seen differences between Kennedy, Shigley and the NCEES practice exam.

The way I am thinking about it, if you want to know the torsional shear stress at a specific point (say the extreme fiber for max shear) you would use J= 0.707*h*Ju.

If you want to calculate the average torsional stress, you would use J= Total Weld Area * Ju. For example, two parallel, vertical welds each of length d, would be J= 1.414*h*d*Ju

Why in practice would you look at average torsional shear vs. max torsional shear (if I am understanding this correctly)? Wouldn't you always just check for max shear at the extreme fiber and not care what the average is?

Thanks in advance for your thoughts.



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Hello Ski. I work as a steel connection design engineer. When I run into a situation where the IR method is not easily applicable to a weld group, I default to using the elastic method form Ch. 8 of the AISC Construction Manual.  I've created a slide outlining the programmable logic used to calculate weld forces (kips/in). It's pretty simple to put into an excel spreadsheet, Mathcad, or programming language. Although reliable, this method does not account for directional strength increases for fillet welds, and is very conservative. To be honest, I adopted this method of analysis instead of the simplified/common cases given in PE, SE, or textbook documents because it is more generally applicable. I hope this helps. 

Edit to add the following:

This method calculates the maximum weld force (k/in) at the start/end of a single weld, within a given group. This value is affected by the weld group geometry, and therefore strength parameters like Ix, Iy, and J.

Steel Design FlowCharts - Elastic Method.pdf

Edited by DrZoidberWoop

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Hi Dr. Woop,

Thanks for your reply and for sharing, I appreciate it.

With that being said, can you comment on the fundamentals of my question as it pertains to the PE exam?

I think that the total area is used for calculating the direct shear (F/Atotal), but still don't understand the difference between why you would use J=0.707*h*Ju (seemingly to evaluate max torsional shear at an extreme fiber) vs. J=Total Weld Throat Area * Ju (ie two parallel, vertical welds each of length d, would be J= 1.414*h*d*Ju )

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Ski. Even though I use a much more general form of the elastic method, I use essentially what you have described in your first equation (J= 0.707*h*Ju). For weld sizing, the secondary forces (from moment and torsion) are the key factors for selecting/evaluating critical weld points because forces are not equally distributed (except in maybe a circular weld group without bending or shear). I don't think I've ever come across a situation where this could be reasonably discounted.


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Ski, I am not a pro on this topic but in my notes for the PE exam regarding Ecc. Loaded welded connections it says that welds are treated as lines and that is why you multiple J against just the weld throat thickness. Hope this helps. 

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