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Torsion constant accounting for web/flange fillet welds?

Torsion constant accounting for web/flange fillet welds?

Torsion constant accounting for web/flange fillet welds?

(OP)
Hi All

Is anyone aware of a derivation of the torsion constant (called 'J' in this part of the world, no doubt different symbol elsewhere) inclusive of the fillet welds between web and flanges in a three plate welded beam?
Most texts have derivations for the torsion constant but always state 'ignoring fillets' or word that effect, because its conservative to do so.

Inclusion of the root radii in a hot rolled section can give a small but beneficial boost to the torsion constant which gives benefits for overall lateral torsional buckling strength.

I'm dealing with evaluating a member substitution of welded section being substituted for original hot rolled section which had some larger root radii, so neglecting the welds takes a big hit on the torsion constant to the point where the member doesn't quite work depending on how J is worked out

In the past I've made the fillet into an equivalent root radii and evaluated it this way as solutions are readily available for inclusion of the root radii in the calculation, but really wondering if anyone has ever come across an exact solution for say a triangular fillet at the flange/web interface instead of the rounded root radii present in a hot rolled section.

The way I've allowed for it in the past is to say the root radii is equal to the leg length on the weld, this allows for less metal in the derivation of torsion constant than is really present in reality when evaluating it with the root radii method vs true fillet (which should be conservative). Contractor has worked out area of weld and made metal at root the same area for an equivalent diameter and then evaluated.

While we can go back and increase plate size a little to compensate, the question is really is there an exact 'fillet' solution?

Solution for root radii for comparison if anyone is interested is here

thanks

RE: Torsion constant accounting for web/flange fillet welds?

Appendix C to AISC Design Guide 9 (Torsional Analysis of Structural Steel Members) provides equations for the torsional constant ("J" in AISC terminology) that includes the fillet in the case of wide-flange, channel, and Z-shapes.

RE: Torsion constant accounting for web/flange fillet welds?

(OP)
Thanks, I do believe that is the same equation I posted for a circular root radii, I was specifically wondering if there was similar derivation for a triangular fillet (representative of a fillet weld).

RE: Torsion constant accounting for web/flange fillet welds?

Alas, I don't have a specific answer to your specific question. Frankly, I'm surprised that there's even equations for radiused joints as as I thought that one pretty much had to resort to FEM to figure these things out for non-trivial geometries.

Given that your resistance to LTB comes by way of both St.Venant and warping torsion resistance, what percent difference does weld inclusion make to the sum? If it's less than 10%, I'd be fine with the impact on LTB.

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.

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