Theoretical Torsional Analysis Question 1

[Lion06]

Here is the situation. I have a WF in an existing building that is being modified. The modification is going to introduce significant torsion on WF. I am going to weld the web of a channel to the flanges to create a closed section. In trying to dumb down the torsional analysis, I am only checking the closed section for torsion (assumed HSS with wall thickness = the smallest of the channel web, WF web, or WF flange) and neglecting the outstanding parts of the composite section (i.e. channel flanges, and WF flanges not connected to the channel web).
The member is fine for torsion (as would be expected).

It is my understanding that because it is a closed section the warping stresses are negligible such that there will be no addition to the bending stresses from torsion. Is that a fairly accurate statement?

If it is, would it be reasonable for me to use the WF with just the web of the channel (such that the section looks like this ___ )
_|_|
for flexure and do two seperate checks?

I would do one check for torsion using the conservatively assumed HSS section only and do a second check using the shape above for flexure. Again, my reasoning for assuming the two seperate analyses are valide is that the closed section reduced the warping normal stresses (what would add to the flexural normal stresses) to a negligible amount. I would also design the weld of the channel to the WF using Blodgett - he has a good example of the shear flow in a built up section subject to torsion.

I would really appreciate some opinions.

 

[rb1957]

make sure there is some loadpath out of the closing web; in your biz, probably a weld.

if there are discrete points of torsion input into the composite beam, why not close off the other side of the I-section locally ?

 

[Lion06]

I am assuming you are talking about the weld (per Blodgett) that I mentioned.

Additionally, it is loaded eccentrically from glass as well as acting as a wind girt. It is also loaded eccentrically from the cladding when the wind blows.

It is not discrete locations, but a uniform load (from both wind and gravity - which happen to be additive in this case) at a given eccentricity.

 

[csd72]

The only section that has no axial stress induced by torsion is a pipe. All others have axial stresses induced by warping, for closed sections this is much less than for open sections.

 

[Lion06]

csd,
I know what you are saying, but my steel textbook (Salmon and Johnson) says that for closed sections the normal stresses due to warping are negligible. Is this an inaccurate statement?

 

[271828]

"Is this an inaccurate statement?"

Yes.

Yet again, S&J is the place to look... LOL.

 

[apsix]

Yes, the effects of torsional warping can be neglected for closed sections.

 

[csd72]

Yes, though you need to take them into account to design the welds.

 

[Castigliano]

StructuralEIT:
I think you're fine with neglecting the warping torsional stresses. The Saint Venant shear stresses will be more than adequate for sizing the weld, in addition to the bending shear stresses. If you have access to a simple FEA program, a quick shell model of the beam will confirm your assumptions and maybe give you some additional confidence.

Castigliano

 

[Lion06]

I've used Blodgett's example (Problem 5) on page 2.10-9 before and was planning on using it again. I don't believe that it accounts for warping stresses. It adds the torsional shear stress to the bending shear stress (horizontal shear -> VQ/I) to design the weld.

 

[csd72]

Thats fine to design a perpendicular weld, but what about longitudinal shear?

 

[Lion06]

csd-
I'm not quite following. As far as I can tell, there would only be stresses from the horizontal shear flow, the torsional shear stresses and warping stresses. If we say the warping stresses are negligible then we're left with the horizontal shear flow and the torsional shear stresses.

You are losing me a bit with the perpendicular weld, and the longitudinal shear. As far as I can tell the only longitudinal shear would be the bending shear stresses (horizontal shear flow). The torsional shear stresses are acting perpendicular to the horizontal shear flow stresses such that adding them directly (as done in Blodgett) is conservative, in my opinion.

 

[csd72]

StructuralEIT,

I am not 100% sure of the answer but I think we are missing something here, I will try to explain.

To picture warping stresses then the simplest way to look at it is that each of the four walls is a plate in bending taking their share of the torsion.

Now each of these has a typical linear stress distribution with positive at on end and negative at the other. The positive on one side is adjacent to the negative on the next side and vice versa so the stresses tend to cancel each other out giving you the result that they are negligible.

Now my point is, how do the positive and negative stresses cancel each other out if they are on opposite sides of your corner weld? The only way they can is by additional longitudinal shear in the weld.

There is no cancelling out effect in this case so the effects may actually be significant.

 

[NS4U]

I'm not sure what 271828 means, an explanation more concise than "LOL" might further their statement.... But in my opinion Salmon and Johnson is exactly right. For tube sections warping is most definitely negligible for design. This it has to with the fact (for tubes) shear flow is continuous around the section. Whereas shear flow is discontinuous in flanges of I-beams. Thus producing warping stresses in the flanges. (note that warping stresses in webs are ignored).

S&J's statement is further backed up by the properties of Tubes vs I-beams. The additional “warping torsion” associated with warping is proportional to the warping constant (Cw). For an HSS 8x8x5/8 (As=16.4 in^2) CW=63 in^3. For a W12x58 (As=17 in^2) Cw=3570in^3 (56x's higher!) Warping in tubes is most definitely negligible. Heck Design Guide 9 which is put out by AISC says it can be neglected as well for tubes.

Warping produces additional normal stresses in the flanges only. By boxing your section you are essentially eliminating those stresses. Thus I think your approach is perfectly reasonable.

 

[csd72]

Everyone is talking about axial stresses from warping and not thinking about longitudinal shear stresses from warping.

 

[rb1957]

the point csd72 is making is consider the shear flow around the cross-section, resisting the applied torque. these shear flows also run out-of-plane along the tube, and give rise to warping. the effect of warping at the end of the tube may be negigible, but the shear flow along the beam should be considered, no?

 

[NS4U]

I'm refering to all of the stresses associated with the section.

If your Cw is small therfore,
your warping torque is small therefore,
ALL stresses associated with warping torque are small thefore,
neglecting warping is OK

 

[csd72]

Page 401 gives a basic diagram of the type of thing that I am talking about:

http://books.google.com/books?id=VR...X&oi=book_result&resnum=7&ct=result#PPA401,M1

Also note the last line of point (4) on the following:

http://www.access-steel.com/discovery/ClauseLookup.aspx?id=EC010

 

[dik]

Take a look at your connections and details and try to eliminate as much torsion as possible.

Dik

 

[Lion06]

csd,

From the graphic (and the text), it appears that the longitudinal stress from warping equals the longitudinal stress from torsinal shear. Is this your understanding? If so, is it as simple as adding the torsinal shear stress twice.

That's a good link.

Star from me.