Zero Channel Torsion 2

[vava1]

When applying a concentrated load onto a single section of channel, at what location would there be no torsion acting upon its cross section – at its shear center or the centroid? I have the flexibility in the design to place the concentrated load where there would be no torsion. Any information would be appreciated. Thank you.

 

[youngstructural]

To employ a cliché: Your picture paints a thousand words...

I was confused by your earlier descriptions and had thought the same as BAretired. However, I do not quite agree with the effect of your sketches:

Slow the problem down. Think about the effect of each portion of the problem:

Let's start with your case 1.

1. Your are loading through the centroid, not the shear centre, so there is a secondary rotation due to shear flow, correct? This means that you now effectively have a supporting shear force AND an applied moment.

2. Sketch the BMD and SFD. At your support you have tension at the top flange, compression at the bottom, and shear in the web. The moment arrives at the support as a couple of shears accross the flanges.

(ASIDE: Yes I'm aware this is an idealisation, but it is quite close to reality and makes the problem easy to handle.)

3. As JAE has been quoted as saying, the situation at the supports is NOT like in the section itself. You already have the forces in the member, so the effect of the shear lag of the section is moot. You can better picture this new situation as being an infinite block where we are shearing one area, pulling and pushing on two others. Your top flange weld must carry tension and some shear, while your bottom flange weld compression and opposing shear, and your web carries your vertical load in shear.

Now, let's look at your case 2:

1. Similarly to Bloggett's discussions regarding the loading of a shelf angle with a rotating beam (see Design of Welded Structures, Lincoln Electric Company), you need to look at what will realistically happen in service. Thus unless you can guarantee that the load will pass through the shear centre, you will be better off considering the loading occuring through the centroid and causing moment. I only use the application of a channel's shear centre saving me from the development of moment when I am applying members and supports to the back of the web (ie: quite close to the shear centre).

2. In my opinion, Design as per one unless you're certain of your loading position and that it cannot shift.

Okay, this is turning into one of my classically long posts, however you have made the point a couple of times that I seemed to be contradicting myself. The previous situation involved joists loading near the shear centre, and the support being a column with the channel's web fixed to the face of the column. The situation you have described is, as I have explained my view above, different in that the support holds moment. I was thinking of a simple shear connection in the prior case.

Happy to keep chatting, but I'm hoping you'll understand where I'm coming from now... I'll be very keen to hear any opposing views, with explanations of why.

Cheers,

YS

B.Eng (Carleton)
Working in New Zealand, thinking of my snow covered home...

 

[miecz]

As JAE wrote in the earlier thread, this is a difficult thing to get your head around.

To try to gain some insight, I built a simple model of elements. It models a C6x8.2 channel, cantilevered 24 inches with a 1 kip load at the end. I looked at two cases: one with the load at the shear center and one with the load at the centroid. This is a simple model that any of you can build. It has nodes in each direction at about 1 inch centers.

Moving the load from the shear center to the centroid has the following effects. The horizontal shear forces attaching the flanges shrink to practically zero. The total vertical shear force in the web shrinks a little, but the peak shear, located at the intersection of the web and the flange, increases 50%. But the real dramatic effect is that the axial force, the force along the axis of the channel, concentrates to the nodes at the intersection of the flange and the web. The 2508 lb force you see in the attached file is only 1335 lb when the force is at the shear center. This large axial force at this location makes sense when you picture the channel twisting under the load applied at the centroid. This 100% increase in tensile force occurs at the same location where the shear increases by 50%.

This is the same effect at the support that you get from the AISC Design Guide for Torsion.

 

[kslee1000]

EIT's 1st case is well understood, at the support, the weld group feels the torsion and the shear both acting on the geometric center of the weld group, which is coincident with the geometric center of the channel. So the welds shall be designed for the combined stresses with respect to its centroid.

The 2nd case (say loaded on shear center) is little trickier. I assume at the tip of the beam the load is placed somewhere like below:
_____
|
F |
--|
|
|_____

Now there is no torsion but shear stress on the channel flanges and web.

Next, let's move just a small distance away from the load point towards the support, the force "F" and the carrying horiz. bar both have disappeared, but the shear stress in the channel. The shear in the flange and in the web will each produce a moment about any vertical axis in between the web and the mid-point of the flange. For simplicity, let's say about the centroid of the channel, in which, the moments are opposite to each other with different magnitudes, thus produce a net moment/twist on the section in concern. The shear, and the stress due to the net moment/twist, therefore is the design stress for the support welds about their geometric center, which is again co-incident with the centroid of the channel.

 

[kslee1000]

There is a little distorsion on the key-pad sketch, but should be understandable.

 

[BAretired]

For a channel to develop maximum flexural stress in the flanges, there must be a shear flow. Shear flows inward from the tip of the bottom flange to the web, then up the web to the top flange and finally, outward to the tip of the top flange.

In doing so, horizontal shears are created in the flanges, towards the web in the bottom flange and away from the web in the top flange. To balance the moment created by these opposing flange shears, load must be positioned outside the web of the channel for equilibrium.

If load is positioned elsewhere, the beam cannot develop its full flexural potential. It will have torsional stresses and will twist throughout its length and its capacity will be significantly reduced.


Best regards,

BA

 

[miecz]

What BA says is true, and I believe it applies to the weld as well as the channel. For anyone who cares to see the results of my RISA finite element model first hand, I've uploaded the model.

 

[kslee1000]

miecz:

Can you upload the results (for both cases - loaded on the geometric center & loaded on shear center) that shown shear stress on the welds (without bending stress)?

 

[miecz]

kslee100-

Here are the joint reactions for flange shear for the two load cases. The top flange reactions are hard to read, but they are simply the reverse of the bottom flange reactions.
I did this quickly, so I didn't model the C6x8.2 with tapered flanges, and so on. Looks to me like, for the load at the centroid, the shears on each flange pretty much add up to zero. The shear forces are small compared to the reactions in the x-direction, which I included, along with the deflected shape.

 

[WpgKarl]

Wow, this thread is a long one....so I'll add some more to it. It is interesting to note that a channel is a very common member, but we didn't seem to cover those sections much if at all in steel design at undergrad.

You should consider the effect of how the channel is connected into the structural system. In some cases, the twisting caused from loading the channel away from the shear center can be taken out of the channel and into the supported structure by a force couple.

If the channel is a cantilever and is free to rotate and translate at the end, then the design of the channel becomes very complex, as it is an open section subject to torsion, which is only symmetric in one direction. I'll see if I can find a link to give guidance for designing a cantilever channel. I agree that the welds become tricky and require additional consideration as well.

 

[BAretired]

miecz,

Nice piece of work.

Best regards,

BA

 

[kslee1000]

Yes, miecz, it is impressive!

If I interpret the results correctly (the load case number at left bottom of the print out has somewhat confused me), the first two results agrees the thinking - when loaded on the shear center, the end support will experience a dimished torsion as compared to loaded in the geometry center. But the fact is there is a torsion there. You may try to place a line load at the shear center, from tip to the support, by doing so, the torsional shear should be "0".

It is good to notice on the last 2 results that the change in axial stresses due to load on the shear center.

Thanks for the info.