Convert Strain gauge readings to stress

Tr/J where J is polar moment of inertia only works for closed sections. Long explanation, but the most brief/clear I've seen is Omer Blodgett's in Design of Weldments (and repeated in other texts by the same author) available VERY inexpensively from the J.F. Lincoln Arc Welding Foundation.
(One quick visualization is in applying a torque to a tube, and measure the angular displacement. Then slit one side of the tube lengthwise, and apply the same torque. The displacement will be much larger in the 2nd instance even though the areas and polar moment of inertia will be essentially the same. This is because the torsional shear stress is the same on the plane normal to the axis of the tube as it is on the longitudinal. When you get to the slit, the shear stress has to be zero, because there's nothing there to resist it on the longitudinal plane.)

Young's Modulus and Poisson's ratio depend on the material (and to some degree the form e.g. cast, wrought, etc.). Assuming you have wrought mild steel (structural steel) your Poisson ratio is likely to be 0.295 to 0.3.

 

What is the orientation of your strain gauge(s) on the I-Beam and was the beam subjected to strictly a torque ?