Torsion on Tee Sections

[amecENG]

I was wondering if anyone can offer any advice or a good reference on calculating the torsional resistance of a WT section?

 

[wiktor]

"Roark's Formulas for Stress & Strain" is a good reference book.
You may also use any of the so called "section makers" to calculate torsional resistance. You can use demo version of "Section maker" by Daystar Software from

http://www.daystarsoftware.com/products/demos

It's fully functional. with saving and printing disabled.

 

[amecENG]

What I am looking for more particularly is how to calculate the "Warping Stress".

I have an eccentric point load on a WT section so I am concerned about the normal stress which is a combination of strong axis bending and warping stress as opposed to the shear stress that arises from a pure torsional moment.

 

[Hokie93]

This topic is addressed in AISC Design Guide #9 (Torsional Analysis of Structural Steel Members) in section 4.3. According to the design guide, shear and normal stresses due to warping can be neglected for tee-shaped members of typical dimensions.

Hokie93

 

[csd72]

A T has very very little torsion capacity.

 

[amecENG]

I only have 150lbs point load at an e = 8" in the center of a WT4x6.5 that spans 4' with both ends fixed.

I realize that the torsional resistance of a T is not very high but my loads are not very high either. The T must have some resistance I am just stuck on how to calculate it.

 

[BAretired]

Mt = 150*8/2 = 600"#
J = 18000mm^4 = 0.0432in^4
[θ] = Mt/GJ = 600/(11,165,000*0.0432) = 0.00124 rads/"
total rotation at midspan = 24[θ] = 0.0299 radians

Torsional stress in flange = c*[θ]*G = 3,542 psi

Rosional stress in web = 3,161 psi

There will be a stress concentration at the fillet.

BA

 

[amecENG]

Thanks BA for the calc.

The stress that you calculated is a shear stress that would develop from a pure torsional load. But isn't this also a combined stress problem?

I believe I should have three stresses resulting from three moments;
1. A bending moment on the full cross section caused by gravity load
2. A bending moment on the full cross section caused by lateral load
3. A bending moment resulting from some sort of force couple that I do not know how to calculate for a T section.

The first two moments represent the biaxial effect, whereas the third moment represents the warping effect.

I have ordered a hardcopy of the AISC Design Guide #9 as Hokie93 suggested and hopefully that will clear it up for me when it arrives. But any tips in the meantime would be appreciated.

 

[trainguy]

One of my top 3 rules of structural engineering:

If it's hard to calculate, it's probably a bad idea.

tg

 

[BAretired]

It is a combined stress problem. I did not include the bending on the full cross section for gravity load or lateral load, only for the torsional effect.

Mt stands for torsional moment. The applied torsional moment is 150*8 = 1200*#, but if applied at midspan, 600"# goes to each support. The rotation and shearing stresses for that condition is what I provided.

For a tee section or an angle or a cruciform section, there is no warping because all of the elements intersect at a common point, the shear center.

BA