Maybe this could help: "(a) Nomenclature Let d = shaft diameter, in. H.P. = horsepower Km = shock factor for bending loads Kt = shock factor for torsional loads M = bending moment, In-lbs. N = revolutions per minute (RPM) S = shear stress, lbs/in² Smax = maximum allowable shear stress, lbs/in² T = torque, in-lbs. Tmax = maximum allowable torque, In-lbs. (b) Relation Between Torque and Horsepower T = 63,025 (H.P.)/N (1) (c) Torsional Loading For shafts under steady torsional loads (and no bending loads), d = [(5.09 T)^(1/3)]/S (2) In the particular case of a shaft in which Smax = 12,000 psi (for example in the case of #303 stainless steel and a gradually applied load), equations (1) and (2) can be combined to yield: Tmax = 2353 d^3 (3) and (H.P.)max = 0.037 d^3 N (4)" Source and further information: http://www.sdp-si.com/D200/PDF/D200_T12.pdf Further information: - "Rules of thumb for mechanical engineers By J. Edward Pope (page 313/Rotating shafts)": http://books.google.com/books?id=peo1L6abBRAC&pg=PA313&lpg=PA313&dq=maximum+allowable+torque+for+a+rotating+shaft&source=bl&ots=gMI9J2QcaS&sig=q6B0Sg2Vdy7RJ4lehCiAZdRptNM&hl=en&ei=BaF2Suv0L5WMsAbBnIX9BA&sa=X&oi=book_result&ct=result&resnum=8#v=onepage&q=&f=false

We can use Torsion Equation for this. T f - = - J r where T = Torque pi D^4 J = Polar Moment of Inertia = ------- 32 f = Max. allowable shear stress r = radius of the shaft If you know the value of max. allowable shear stress of bearing steel, you can find the max. allowable torque.