shear center or centroid of weld group? 2

[Lion06]

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?

 

[nutte]

The torsional stress in the channel is an internal force, while the C-shaped weld still sees the load applied at its centroid?

 

[OzEng80]

The torsional stresses would still have to be 'taken out of the channel'. If you forget about shear centres and centroids, and reduce it to just a weld along the web and to the flanges - where is the eccentric load to the welds?

 

[JAE]

The shear center of a singly symmetric shape is off the centroid due to the flow of shear through the section (both transverse and longitudinal shear) in conjunction with its flexural, longitudinal stresses.

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.

 

[Lion06]

JAE-

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.

 

[slickdeals]

Would'nt the Instantaneous Center of Rotation method compute the point of rotation, and hence account for this said torsion?

 

[Lion06]

slickdeals-

I'm not sure. You still have to compute e from some point. Why from the centroid of the group?

 

[trainguy]

Guys,

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

 

[miecz]

StructuralEIT-

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.

 

[JAE]

If you load a channel at its shear center, this develops shear stresses in the vertical web (that resists the vertical load component) and it develops shear stresses in the flanges in opposite directions to the "moment" from the load and the distance between shear center and centroid.

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.

 

[haynewp]

I thought you could use the centroid of the weld group simply because the welds at the flanges are assumed to take a share of the vertical load, whereas the flanges of the channel itself are assumed to balance moment only?

 

[slickdeals]

This is an interesting topic:
How can you load a channel such that no flange forces are necessary to restrain twist?

 

[haynewp]

You would load it through the shear center.

 

[slickdeals]

If you load a channel at its shear center, this develops shear stresses in the vertical web (that resists the vertical load component) and it develops shear stresses in the flanges in opposite directions to the "moment" from the load and the distance between shear center and centroid.

.

 

[haynewp]

Yes sorry, I was thinking how to keep it from twisting. I don't think that you can, once you have bending stresses along the flanges, you will have horiz shears developed to balance them

 

[haynewp]

What about a constant moment case? There is no differential longitudinal force as you go along the length of the flanges.

 

[JAE]

Ahhh..haynewp...you had to go and make it even more complex to think about!

 

[yakpol]

StructuralEIT,
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.

 

[haynewp]

I have been told I do that a lot.

 

[miecz]

I know I'm repeating myself, but I think I found something valuable. Please look at Example 5.5 of the Steel Design Guide Series 9, Torsional Analysis of Structural Steel Members. I realize that this example is not for a cantilever, but it does address the question, "what happens when the load is away from the shear center?" I believe that the weld would have to carry the forces calculated from these stresses.

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.