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.

 

[BAretired]

vava1,

Place the load at the shear center to eliminate torsion.

Best regards,

BA

 

[Lion06]

BAretired is correct. You have to locate the load at the shear center to eliminate torsion.
There is discussion of this in S&J in the chapter on torsion.

 

[youngstructural]

BAretired is right... But remember your complete load path; Next you need to consider the effects at the support. Of course this would need to be done for any beam, however with a channel I often see engineers neglect the eccentricity at the support caused by the shear centre often not alligning with the centre of the support column.

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...

 

[Lion06]

youngstructural-

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?

 

[BAretired]

StructuralEIT,

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.eng-tips.com/viewthread.cfm?qid=237679&page=8

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

 

[Lion06]

BA-

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.

 

[BAretired]

If your post was referring to torsion about the axis of the member, then there can be no question that the weld group must take out the torsion equal to the reaction times the distance from shear center to back of channel. It is a very small moment.

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

 

[youngstructural]

If I follow correctly, I believe BAretired has addressed the issue. Is there anything outstanding to discuss, StructuralEIT?

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...

 

[vava1]

Thank you everyone for your help!
vava1

 

[Lion06]

My question still persists, mainly because the information in this thread is virtually completely contradictory to that in the thread I started. With the exception of 1 or 2 people, everyone who responded to my thread seemed to think that the weld should NOT have to take the torsion for a channel loaded through its centroid.

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?

 

[nutte]

The weld would have to be designed for the reactions at the support. So what are those?

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.

 

[Lion06]

nutte-
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.

 

[nutte]

I'm not talking about ends needing to be torsionally fixed per AISC. I'm talking about basic statics. Let's take a plain old beam with one end restrained vertically, horizontally, against rotation about its axis (torsion), and against rotation about a vertical axis. It is only free to rotate in its strong axis direction. The other end is only restrained against vertical displacement. Now load this beam through its centroid. How can there be any torsion at the support? Your only reaction will be vertical at each support.

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.

 

[Lion06]

I agree that the forces need to sum 0 for statics, but my original question goes back to why are there torsional stresses in a channel loaded through its centroid and not in a weld group loaded through its centroid?

 

[nutte]

That goes to the question of whether or not there is a torsion reaction at the support. If we solve that, we'll have the answer.

 

[nutte]

Sorry, per your original question, I still agree with JAE's response in the first thread.

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.

 

[Lion06]

That seems to go against what BA and youngstructural are saying.

 

[BAretired]

StructuralEIT,

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

 

[nutte]

I agree with BA's post.