shear center or centroid of weld group?
shear center or centroid of weld group?
(OP)
Why, when analyzing a weld group do you take the torsional moment as the load times the distance from the load to the centroid of the weld group instead of to the shear center of the weld group?
I'm thinking specifically of a C-shaped weld group (as shown in example 5.18.1 of S&J 5th edition, but also shown in many other examples). My understanding is that for zero torsion to exist that the load must be through the shear center. If it occurs through the centroid, and the centroid doesn't align with the shear center, then torsion is introduced. Why is this not accounted for in elastic weld analysis?
Let's say you have a channel cantilevering from a column that is fillet welded on three sides, creating a C shaped weld. Let's, for argument's sake, say that the channel is loaded in a plane through the centroid of that weld group. You would clearly have torsion in the channel, because it isn't loaded through the shear center. Why is it that the torsional moment in that channel doesn't have to be taken out with the connection (the C shaped weld group)? Per typical elastic weld analysis, the weld group is loaded through its centroid, and is therefore not subject to any torsional stresses.
I don't agree with that. Anyone have an opinion on this?
I'm thinking specifically of a C-shaped weld group (as shown in example 5.18.1 of S&J 5th edition, but also shown in many other examples). My understanding is that for zero torsion to exist that the load must be through the shear center. If it occurs through the centroid, and the centroid doesn't align with the shear center, then torsion is introduced. Why is this not accounted for in elastic weld analysis?
Let's say you have a channel cantilevering from a column that is fillet welded on three sides, creating a C shaped weld. Let's, for argument's sake, say that the channel is loaded in a plane through the centroid of that weld group. You would clearly have torsion in the channel, because it isn't loaded through the shear center. Why is it that the torsional moment in that channel doesn't have to be taken out with the connection (the C shaped weld group)? Per typical elastic weld analysis, the weld group is loaded through its centroid, and is therefore not subject to any torsional stresses.
I don't agree with that. Anyone have an opinion on this?






RE: shear center or centroid of weld group?
RE: shear center or centroid of weld group?
RE: shear center or centroid of weld group?
A planar weld shape does not have the same 3 dimensional effects or interplay with longitudinal stresses that occur within the shape itself.
So nutte is correct that it is a distinction between an interal stress "mechanism" and an external effect.
RE: shear center or centroid of weld group?
Is that true? I think about bending stresses and they are internal stresses from an externally applied load. They can be zero at the ends or they can have some magnitude at the ends (obviously depending on the boundary conditions). A beam always must resist torsion at its ends, and, unless the torsion goes from max at midspan to zero at the ends, I don't see how the torsion in the section doesn't have to be resisted by the connection.
RE: shear center or centroid of weld group?
RE: shear center or centroid of weld group?
I'm not sure. You still have to compute e from some point. Why from the centroid of the group?
RE: shear center or centroid of weld group?
Maybe you should visualize the following:
An I beam that has a downwards load applied to the right of its centroid, and connected to a stiff wall by 3 welds - one at the web and 2 flange welds, over the RHS portion only.
The method of sizing the welds for this case is identical to that for a channel. The weld doesn't care what the centroid of the attached section is, only where the load is in relation to the connection.
tg
RE: shear center or centroid of weld group?
I think you make a good point. Reference the Steel Design Guide Series 9, Torsional Analysis of Strucural Steel Members. Example 5.5 of that publication analyzes a channel with fixed ends and a uniform load at the centroid. It goes on to calculate shear and tension stresses at the supports. It would seem as though the weld ought to be designed to carry the forces calculated.
RE: shear center or centroid of weld group?
The flange couple keeps the channel from twisting because the applied load is eccentric to the centroid of the channel.
If you cut a section away from the channel at any point along the span, there would be transverse shear stresses in the flanges. If you cut the beam a small distance from the weld, there are still the shear stresses. So the weld sees these horizontal flange shear stresses as though there is torsion in them.
So your applied load is then applied to the weld group at its shear center location and this develops similar horizontal "flange" stress in the flange portion of the weld group.
If we were to apply a torsional pin at each end of the channel, and load it down its length at its shear center, the channel would spin out of control since there is no resisting shear stress at the ends.
Does that make sense? I agree this is a difficult thing to get your head around.
RE: shear center or centroid of weld group?
RE: shear center or centroid of weld group?
How can you load a channel such that no flange forces are necessary to restrain twist?
RE: shear center or centroid of weld group?
RE: shear center or centroid of weld group?
RE: shear center or centroid of weld group?
RE: shear center or centroid of weld group?
RE: shear center or centroid of weld group?
RE: shear center or centroid of weld group?
Shear center theory was developed for the section free to rotate. Weld group typically is a steel shape attached to the rigid base and cannot rotate at all. Its shear center is the same as a section centroid (just like for the closed sections). In a low stress elastic analysis weld stresses can be found by assuming rotation around centroid. 'Instantenious center of rotation' method was invented for plastic analysis and gives more realistic non-linear stress distribution between the welds. It still has nothing to do with shear center, it treats open and closed sections the same way. Read steel design manual for more information about it.
RE: shear center or centroid of weld group?
RE: shear center or centroid of weld group?
Example 5.5 solves for the stresses in the beam at the support. This can easily be converted into forces by multiplying by the web and flange thicknesses. Solving Example 5.5 with the load at the shear center gives the results outlined by JEA above. Moving the load off the shear center has dramatic results, but not what I expected. There are some small additional shear stresses, but the tension stress at the intersection of the web and flange grows dramatically.
As it may help some to understand Example 5.5, I've attached a mathcad printout that shows the solution.
RE: shear center or centroid of weld group?
I read your printout, and I note that you've assumed Case 7 from AISC Design Guid 9. That case is a torsionially fixed ends. I refer to Appendix C in that design guide:
"...If however, the beam is an isolated span, Ojalvo (1975) demonstrated that a closed box made up of several plates or a channel, as illustrated in Figur C.2, would approximate a torsionally fixed end. Simply welding an end plate or column flange may not provide sufficient restraint."
I can't include Figure C.2, but it is a wide flange with two plates welded top flange tip to bott flange tip, on each side of the W-shape, making an effective tube for a short length at the beam end.
The cantilever channel in the original post does not have this type of box included, so I think that the channel welded to a column flange is not a torsionally fixed end, rather it is a torsionally pinned end. I think the difference between fixed and pinned is the warping, just an end plate doesn't restrain the warping in the section, while th box end does.
chichuck
RE: shear center or centroid of weld group?
You're right, the connection "may not provide sufficient restraint" to be considered fixed. However, the connection will provide some unknown degree of torsional fixety. The design guide is focusing on the design of the beam, not the weld. For the design of the beam, I believe it's conservative to assume the torsional restraint is pinned. For the design of the weld, it would be conservative to assume the torsional restraint is fixed.
RE: shear center or centroid of weld group?