Torsional stiffness

[borjame]

I'm trying to get an equation which will give the torsional stiffness of beams with the following cross sections: a trapezoid and a parellelogram (the polar moments of these shapes is enough). These will actually be sections in a composite beam with the end sections being triangles to close out the beam so any info calculating torsional stiffness of a composite beam structure would be a great help too!

 

[GregLocock]

I think you'd be best off to go and read a structures book. eg Roark. Torsion of thin walled tubes of arbitrary cross section is non intuitive to say the least. If you want to pile in regardless then the simple formula is derived by twisting a plane section and adding the contribution of each twisted little piece. Needless to say this can fail horribly in pracice once you have re-entrant shapes, or non uniform wall thickness. for thin walled tubes of arbitrary cross section K=4*(enclosed area to mean thickness)^2*t/(length of mean thickness)

For a rectangular tube of constant thickness then K is 2*t*t*a**b*b/(a+b) if t is small

In your research you will come across the membrane analogy. This tells you that the result for a rectangle is the upper limit for a parallelogram of the same dimensions and thickness.



Cheers

Greg Locock