Beam section

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Hello,
I would like to know how to calculate rest of parameters manually
without using of program. Below I put simlple picture. I have already
done:
Moment of interia (Iz) = 230192 mm4
Moment of interia (Iy) = 94032 mm4
Area (A) = 816 mm2
section modulus (S2) = 9207.68 mm3
section modulus (S3) = 6268.80 mm3
shear area (SA2) = 600 mm2
shear area (SA3) = 360 mm2
centre of gravity:
Sy=25 mm and Sz=15 mm
Beam lenght L=1000 mm
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And here is my problem, becouse I want to know how to calculate
manually step by step:
Torsional resistance (J1)mm4 = ?

Thanks for help
bross

[John_Holtz]

Hi Bross,

Calculating the torsional resistance depends entirely on the shape of the cross section and whether the cross section is closed (like your tube) or open (if the tube had a slice down one side, or a channel is an open section).

If you can consider your cross section to be "thin-walled", the this formula for Roark's Formulas for Stress and Strain, 6th edition (yes, I'm that old ;-), page 352, can be used:

K = J1 in Sim Mechanical = 2 * t^2 * (b-t)^2 * (h-t)^2 / (b*t + h*t - 2*t^2)

where t = 6 mm

b = 50 mm

h = 30 mm

If you want to pursue it further, there is a book named Design of Welded Structures by Omer W. Blodgett. This book goes into a little bit of theory and many formulas (like the one above) for torsion and everything else related to mechanical engineering calculation for structures.

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Thank AstroJohn for your reply. I also found a model how to calcute the torsional resistance
for profil which I presented in query. There is link to this book:
http://www.scribd.com/doc/52989339/17/Torsional-Resistance-Ixx

I asked you because I would like to know how to calculate manually for the simple model and
to understand.

I have more advanced profile (see attachment-profil alum) and I want to use it as cross
section in the beam in autodesk simulation (static sress with linear material models). All
parameters I can define in cross sectional proporties without torsional resistance (J1mm4)
because I don't know.
Is the other option to define this profile? I saw in nonlinear (Static Stress with Nonlinear Material Models)
in section general type (see attachment frame2 section-where you can import) but i don't want to use it.

I prepared the section in Ansys where you can create both simple cross-section and advanced (see section-ansys)

Best regards,
bross

[AstroJohnPE]

Hi bross,

The formula that I have for the torsional resistance of a closed tube is the same as the one you found: 4*A^2 / integral of (dLength / thickness).

However, A is not "cross-sectional area of the tube" as given in your reference!!! That is, do not use the area of the metal. The area in this formula is the area inside the  mid-thickness outline. See the attached image.

Considering only the closed area of your outline, I calculate a torsional constant of 19320 mm^4. This is about 8% lower than the ANSYS calculation. (Is that affected by the mesh? The sides and bottom of the cross-section are coarsely meshed with just 1 element through the thickness.) The "appendages" do not add very much to the torsional resistance, so you can either ignore them, use the formula from the reference (assuming it is correct!), or use the calculator with Simulation Mechanical to approximate each of them.