I think, for a stationary shaft... Assume you're given a stationary shaft lying along the x axis. Assume further that it's under torsion.
To find the applied torque, I think you would want to integrate R x (Txy, Txz) over the surface of a cut through the shaft, where "R" is the radius vector from the center of the shaft to each point on the cut surface, and "x" is the cross product. But I'm not sure; these comments of mine are pretty half-baked. Of course, if the shaft is stationary (or rotating at constant velocity) then the applied torque must be the same no matter where you look along the shaft. Stephen A. Lawrence wrote: > What you just said sounds right, but what you've actually got looks to > me like the torque per unit volume. I think you need to integrate that > over a volume to get the actual torque acting on that volume. > > OTOH if that value is nonzero then your object is spinning up -- it's > not just sitting there. If you're looking at something like a steel > shaft which is under torsion but stationary then T12 = T21 and you need > to look at something more complicated to figure out what the torque on > the shaft is -- maybe the gradient of the stress tensor? > > > David Jonsson wrote: >> On Wed, May 13, 2009 at 9:36 PM, David Jonsson >> <[email protected] <mailto:[email protected]>> wrote: >> >> Hi >> >> Can someone explain to me how to calculate the torque from the >> stress tensor? >> >> >> It seems to be this simple >> >> Torque = T12 - T21 >> >> For a two dimensional tensor >> >> T= T11 T12 >> Â Â Â Â T21 T22 >> >> Right? >> >> Now I will do some nice calculations, but first I would like to have >> this confirmed. >> >> David >> >> >
