Torsional Stress on a Channel "[" section

[HighPanda]

I have to check a channel section which is sub to torsional moment.

However, I can't remember the equation for the calculation of shear stress because I have left school for a long time.....

I am wondering whether anybody remembers the equation....

Thanks!!!!

 

[youngstructural]

I'm willing to bet that you're talking about either

For a solid bar:

Tau = Mt/J

Where M = Applied Torque
t = Member thickness
J = Torsion constant = (bt^3)/3 for b/1 >= 10

or

For a hollow section:

Tau = M/(2At)
where A = Area enclosed by the centre line of the hollow section = (b-t)(d-t)


HOWEVER the torsional effects on an "open" section are more complex those for a solid bar or a closed section (such as a hollow structural section). I really think you need to refer to your design code, however here is how the NZS 3404 code tackles this problem...

Design Warping Normal Stresses f*w = Mfy/Zeyf

where
Mfy = Magnitude of Warping Moment
Zeyf = design elastic modulus for the one flange about the minor principle y-axis of the section as a whole

Zeyf ~ 0.5 Zey

Maximum Warping Shear Stress = TauW = (1.5 Vf)/Aw

where
Vf = Flange Shears

And combining these formulas normally requires the application of factors to account for second-order effects as well.

You really need to get a design quide on torsional design of open sections if you're going to check a channel.

Please see my attachment, which is a design procedure from HERA provisions and shows the Torsional design of solid, closed and open sections to NZS 3404.

Cheers,

YS

B.Eng (Carleton)
Working in New Zealand, thinking of my snow covered home...

 

[hokie66]

All good stuff from YS, but you need to start with the knowledge that channels are not much good in torsion. If you can prevent torsion by locating your loading at the shear centre, the torsional problem may go away. But if there is significant torsion, a channel is the wrong section choice.

 

[youngstructural]

Hokie's got your proper solution... I should try not to be so litteral with my help!

You don't necessarily "need" to check a channel at all; I would definately try to get the load through the SHEAR centre, and please remember that this is a point behind the web (ie: falls outside the section). It is not the same as the centroid; There often seems to be confusion on this point when this subject comes up.

Cheers,

YS

B.Eng (Carleton)
Working in New Zealand, thinking of my snow covered home...