Torsion of a T section

[gkm111]

I'd like to first get confirmation of a torsion question.

1) The shear center is located at the intersection of the flange and web. So if the load is applied at the end of the flange the torque is load x flange width/2?

2) The maximum shear stress is located at a point most distant from the shear center? So if both legs are 2" long then the maximum shear stress will be at the end of the web?

3) If 2 is correct then how can you increase the torsional capacity of the T section?

Thanks for any assistance you can provide.

 

[gkm111]

Btw, I'd like to increase the strength without increasing the thickness of the section, if this is possible.

 

[XR250]

A T section is always going to be pretty flimsy in torsion no matter what you do.

 

[rb1957]

actually i thought the maximum shear stress was at the junction of the two flanges. i thought i read about increased the fillet radius.

the standard formula for maximum stress = 3*T/(b^2*t) (i think) would suggest increasing the summed length of the elements of the X-scetion ("b")

Quando Omni Flunkus Moritati

 

[paddingtongreen]

Can you use a 2"x2" HSS instead, or weld in a 1"x1" angle on the backside of the tee to make a box? Closed sections are much stronger in torsion.

Michael.
"Science adjusts its views based on what's observed. Faith is the denial of observation so that belief can be preserved." ~ Tim Minchin

 

[BAretired]

I don't believe the maximum shear stress occurs at the end of the web but at the fillets where the web joins the flange.

The best way to increase the torsional capacity of a tee without increasing its overall dimensions is to add a couple of plates such that they form a triangle with the flange of the tee resulting in a closed shape. Better still, a pair of angles such that they form a box section with the flange of the tee.

BA

 

[gkm111]

The application is:
- support of granite slabs over a pool gutter drain
- stainless steel plates are being used to fabricate a section
- therefore, I wish to minimize the plate sectional area as well as the amount of welding required
- An HSS would be ideal, but the costs would be prohibitive
Maximum Torsional stress = Torque * y / J

For flat plates J = 1/3 ∑ bt^3

I'm using Roarke's formula to get an exact figure for the b/t ratio.

So given the above, what is the maximum shear stress due to torsion?

I've seen that y = simply the minimum thickness of the flange or web. Is this true or is y the distance to most extreme point in the section?

Also, is there a better way to use 2 plates to minimize the effect of torsion?

Thanks.

 

[gkm111]

This is the detail.

 

[gkm111]

Yes, BA and Excel you are both correct the maximum stress is at the joint.

 

[BAretired]

Your detail seems overly complicated. Can't it be simplified?

BA

 

[gkm111]

I thought the detail is fairly basic. I don't see how it can really be simplified.

 

[BAretired]

You said an HSS would be ideal but the cost would be prohibitive. Would you need a stainless steel HSS or could you use a conventional HSS with epoxy paint or other protective coating?

BA

 

[hokie66]

The question was originally about torsion of a tee section, but the detail shown wouldn't result in torsion in the tee. Only the top plate of the tee extends to the wall connection, so that plate is the only part which could experience torsion, if any. I think it is a non-issue, but wonder about what actually supports the granite slabs. Are they just bedded onto the lath?

 

[gkm111]

Like I mentioned, all the steel is Stainless. Second any profile or section needs to be fabricated, and since it is stainless and the company has basically no options for suppliers to fabricate an HSS would be a very expensive proposition.

@ Hokie, Yes the granite is embedded into the lathe, but is supported by the stainless steel T section. The lathe does not provide any real support. Why wouldn't there be any torsion in the T? The whole section would try and rotate if a person were to jump on one side of the support. Am I missing something?

I agree at the ends the torsion can be ignored as the concrete and connection can absorb any twisting.

 

[hokie66]

There is no torsion in the tee because the ends are not fixed against rotation. You can't have torsion in a member with ends which can rotate. In your case, the stem of the tee just stiffens the plate for bending across the trench, but does nothing to stiffen the plate against twisting.

So are you saying that the granite pavers span between the tee sections? If so, the only way for the tee to be subject to twisting is for the granite to break/crack.

 

[gkm111]

Thank you so much hokie66! You and the rest really helped me on something I didn't know much about.

So if there is no need to check for torsion, all I need to check is the rotation of the section?

 

[BAretired]

If the granite slabs can span between tee sections, why not decrease the width of gutter to provide an inch of bearing for the granite on each side and omit the tee sections altogether?

BA

 

[gkm111]

Great idea BA, but I do not have any power to make those kind of changes and the detail is a standard detail.

I already suggested to use 1'-6" or 2'-0" width slabs and this would not be an issue, however the company wants/insists to have the design like this.

 

[BAretired]

It must be discouraging to work for a company like that.

BA

 

[gkm111]

Well this is just a job I'm doing on the side for a friend, she's with the company. I wouldn't work long for a company that doesn't work with you, even if the details you are coming up with are more economical and durable than theirs.

For instance, there really is no need to insist on stainless steel. If they just eliminate stainless from the equation then a simple 2x2 galv HSS would be so easy to use.