Shear Lag Transfer Length

[Lomarandil]

In short, over what distance of a tension member does shear lag need to be considered?

If I have a 20' pin connected member, with a 2' connection at each end, my intuition is that the shear lag effect of that connection (in this case, a knife plate gusset to an HSS) probably only applies to the end 4-5' of the member before tensile stresses are distributed to the full cross section. After this 4-5', it would seem rational to use the yield on gross capacity, especially for combined stress checks.

That said, I can't find any provision of the codes that says this. Am I totally off base?

 

[KootK]

I suspect that you'd be fully distributed, with regard to tension stress, a good deal sooner than that. It obviously depends on the kind of cross section that you have and how you're introducing the load. From a code check perspective, I think that you simply need to satisfy the D3 provisions for effective net area. If you're interested in knowing whereabouts the lag can be thought to be fully dissipated, I'd turn to table D3.1 and look at what it takes to make U >= 1.0.

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.

 

[Lomarandil]

Thanks KootK.. I had considered that, but for rectangular HSS (sorry, should have been more specific) and a lot of other shear lag connections, U=1-x/l asymptotically approaches 1 (and that only at a ridiculous length). So that doesn't get us very far.

 

[KootK]

I see what you mean lomarandil. How about this:

1) Go to the point "l" away from the member that represents the end of the connection proper.
2) Trace your way from the connected element at "l" around the section to the point furthest away, travelling at a 45 degree angle.
3) Assume that the point that you end up at represents the location of U=1.0.

Once you're outside of the connection and into member propoer, load spread should occur very rapidly. I've always assumed that web yielding provisions imply a distribution angle of about 2.5:1. By that measure, 45 degrees should be pretty conservative.

If you want to be more aggressive, you could modify the procedure above such that the starting point occurred a distance across the section that assumes that all of the effective net area is located as close as possible to the connected element.

What are you trying to accomplish here anyhow? I still contend that your D3 check is all that is required for shear lag.



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.

 

[RPMG]

Saint Venant's principle is that if you're a sufficient distance from the connection, stress is constant regardless of the cross section/connection. Shear lag addresses the special case where you're near the connection. I would recommend that you flatten your half of you HSS since it's a knife plate, use the first connector, and use a 1:2 slope (22.5 deg) to establish your uniform stress location. This is based off of research with plates and single pin connectors.

Of course, this may be unconservative for a connection that is infinitely long, so use the most conservative answer when compare's to KootK's response.

The code is meant to express the importance of Saint Venant's principle and shear lag. If you have a special case where this does not reasonably apply (because you understand the code's intent), then the code restriction does not apply. There's always a code provision for best judgement.

EDIT: For combined stress checks: Combined stress checks can be segmented however you choose. They're based on Ma/Mr and Pa/Pr at a specific location because Ma and Pa are at a specific location.

 

[Lomarandil]

Thanks KootK and RPMG. Sorry for the delay in replying -- deadlines.

What I want to accomplish is to know at what location it makes sense to no longer consider the shear lag effect in the combined stress check. It sounds like there may not be a closed-form answer there, but the two suggestions you've offered seem like reasonable places to start.

 

[nutte]

What code are you designing to? I don't think I've ever worried about the tensile rupture limit state (the one where shear lag plays a part) in a combined forces check. Rather, the combined forces check would use the tensile yielding limit state, which is checked on the gross section, independent of the shear lag at the end of the member.

 

[KootK]

Like nutte, it's never occurred to me to do such a check. Of course, just because it hasn't occurred to me, doesn't mean that it's not valid.

Philosophically, it's probably similar to concrete where the sectional checks cease to make sense in the disturbed regions so we switch to strut and tie at the connections. We have tools for both the connections and the Bernoulli regions in steel but not much guidance with regard to the transition length.

My gut feel is that, if the connection works and the combined section checks calc out a few member depths away, you should be alright.

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.