Zero Channel Torsion
Zero Channel Torsion
(OP)
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.






RE: Zero Channel Torsion
Place the load at the shear center to eliminate torsion.
Best regards,
BA
RE: Zero Channel Torsion
There is discussion of this in S&J in the chapter on torsion.
RE: Zero Channel Torsion
Channels are the only member I can think of off the top of my head which are best side (or face) connected to a support column; Fasten them with the web flat against the member, toes out from the supported joists/rafters/girts/etc.
Cheers,
YS
B.Eng (Carleton)
Working in New Zealand, thinking of my snow covered home...
RE: Zero Channel Torsion
I recently (about a month or so ago) posted a question here regarding your last post. My question was why a channel welded to a support would need to be designed for torsion, but the connecting C-chaped weld would not be. We never came to a definitive conclusion, but your last post in this thread implies that the connection should also be designed for the torsion (referred to the shear center of the section, and not the centroid of the weld group).
Did I interpret your post correctly?
Do you have any literature on this?
RE: Zero Channel Torsion
YS is talking about torsion about an axis parallel to the direction of the channel. It is a small torsion, but the connection must be designed for it. A channel loaded at its shear center and simply supported on a flat surface with no connecting material would fall over on its web.
Your post at:
http://www
was referring to torsion about a different axis, i.e. an axis perpendicular to the channel web. The weld was in the shape of a "C" and you questioned why eccentricity is measured from the center of gravity of the weld group rather than its "shear center".
The current thinking on this is that weld forces should be taken about an "instantaneous center". Finding the instantaneous center is a trial and error procedure.
Best regards,
BA
RE: Zero Channel Torsion
My post was referring to torsion about the axis of the member. How can you get torsion about an axis perpendicular to a member - isn't that just a moment?
Additionally, for the strength (ICR) method, you only determine the instantaneous center of rotation, but you still take moments about the centroid of the group, not the ICR.
RE: Zero Channel Torsion
On your other point, you may take moments about any point you wish. For equilibrium, the sum of all moments must be zero.
Best regards,
BA
RE: Zero Channel Torsion
Please post again if we need to chat something through... Include the previous thread; I'm not sure which one you mean. I do not believe I posted at the link BA included.
These fundamentals are often the tripping stones that people (myself included) miss small portions of, which can make all the difference in the world.
Cheers,
YS
B.Eng (Carleton)
Working in New Zealand, thinking of my snow covered home...
RE: Zero Channel Torsion
vava1
RE: Zero Channel Torsion
I am attaching two sketches which clarify exactly what I am talking about.
The first one (labeled case 1) has the channel loaded through the centroid. There is clearly torsion on this channel because it is not loaded through the shear center. That being said, do you design the weld for the direct shear (P) and the torsion (Mt) or just the direct shear since the load does go through the centroid of the weld group. Even if you go into the steel manual and use the ICR method, you use the eccentricity as the distance of the applied load from the centroid of the weld group.
For case 2, the load is applied at the shear center of the channel so there is no torsion on the channel, but traditional connection design says to design the weld for the torsion............... so, do you or don't you?
RE: Zero Channel Torsion
If you have a simply supported beam, pinned on both ends, you have a statically indeterminate system, since you have four reactions (vertical and horizontal on each end) but just three startics equations. You would have a vertical reaction at each end (obviously) and a horizontal reaction at each end. These reactions would be equal in magnitude with opposite directions.
But nobody designs connections for such. That's why we assume a pin on one end and a roller at the other, so there are only three unknowns, resulting in a statically determinate system.
Now take our channel. If it's torsionally fixed, we'll have a torsion at the support. I suppose that torsion should be applied to the weld. But is torsionally fixed correct? If it was torsionally pinned, is it stable? The sum of all external forces result in no moment about the member's axis. Is the internal torsion zero at the ends and maximum at midspan?
The comments about vector analysis of weld versus instantaneous center of rotation analysis are moot. Either way you use, you still size the weld for the same forces and moments.
RE: Zero Channel Torsion
There should be torsion at the support regardless of torsional fixity, correct? Torsionally fixed just means it is not free to warp at the ends (while torsionally pinned) means it is free to warp at the ends), right? If there were no torsional support at all, it would be unstable and all of the AISC equations wouldn't apply.
RE: Zero Channel Torsion
Regardless of the internal forces/moments in the member, all of the external forces/moments (support reactions and applied loads) should sum to zero to maintain static equilibrium.
RE: Zero Channel Torsion
RE: Zero Channel Torsion
RE: Zero Channel Torsion
RE: Zero Channel Torsion
RE: Zero Channel Torsion
I misinterpreted your earlier thread. I thought you meant that the channel was connected to a column by a "C" shaped weld group on the back of the channel. The channel was a cantilever loaded on its shear center.
I see now what you meant. I believe that in Case 1 (load at centroid of channel) the channel would twist but the welds would be centrally loaded, i.e. all parts of the three legs of the weld would carry an equal amount of the vertical reaction.
In Case 2 (load at shear center of channel) the channel would not twist but the weld would be subject to a moment.
Best regards,
BA
RE: Zero Channel Torsion
RE: Zero Channel Torsion
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...
RE: Zero Channel Torsion
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.
RE: Zero Channel Torsion
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.
RE: Zero Channel Torsion
RE: Zero Channel Torsion
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
RE: Zero Channel Torsion
RE: Zero Channel Torsion
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)?
RE: Zero Channel Torsion
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.
RE: Zero Channel Torsion
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.
RE: Zero Channel Torsion
Nice piece of work.
Best regards,
BA
RE: Zero Channel Torsion
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.