hokie wrote, BA replied:
BA, I know warping comes into it, but it is a minor factor. Not always. For short spans, it is a major factor. Fixed at one end with torque applied at the other is close enough to what you described. It is not close at all. Fully fixed at one end means that the top and bottom flanges do not rotate about a vertical axis at the fixed end whereas a torque applied at both ends means the flanges rotate in opposite directions about a vertical axis.
The torsional constant for open shapes is derived so that calculations can be done in the same manner as for solid bars and closed shapes. The torsional constant J for a rectangular bar is βbt3 where β varies according to the ratio b/t. When b/t approaches infinity, β approaches 1/3. When b/t = 6 as in the case of the flange of the 250 PFC, β = 0.299. J for a channel is simply the sum of the J values for the three rectangular cross sections, two flanges and the web. So J = 2*90*153*0.299 + 220*83/3 = 220,000 mm4, slightly less than the 238,000mm4 which you gave earlier.
Usual engineering practice for sections built up from plates is to take β as 1/3 so that J = Σbt3/3. Using that method, I find J = 240,000mm4.
In the case of a PFC, I think if is unrealistic to consider this as a shearing problem, as it is really just flange bending with a bit of warping of the web. Flange bending may occur in the actual setup but is not true in the case of an equal and opposite torque applied at each end of a channel section. If you look at what happens to the shear stresses, they fall off the edge. I don't know what that means. The shear stress is maximum at the middle of the flange but it varies linearly from one edge to the other with zero value at mid depth.
BA
