orsion shaft calculations

huangyhg

torsion shaft calculations
we had the output shaft of a torque wrench fail.  the torque wrench is rated for 3200 ftlbs.  the square output shaft is practically 1.08 inches square.  according to the formula i used [ max torque = (2/9)x shear stress x(width of square)^3, where shear is .42*yield], the shaft would have to be made of 417ksi material.  hardness testing a new shaft resulted in hrc between 42-46 on the outside, suggesting a yield of around 217ksi at best.
i'm i looking at this wrong, or is the torque wrench over-rated?  we found the same problem with another top brand as well.
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max shear stress in a square section (from roark) is in the center of the flat side,
max. τ = 0.601 t / a3
where 2a is the length of the square side.
so, for a 1.08 square, at 3200 in-lbfff">, the max shear stress would be 12 ksi and a bit; well within the allowable shear for even a mild steel tool (but not much margin there).  at 3200 ft-lbfff">, the max. shear is 146 ksi and a bit; this would require 300 ksi material not to yield, and no margin of safety.
are you sure about the tool's rating?  most common 1" drive socket tools have a max. torque rating closer to 1000 to 1200 ft-lb., though i've seen one rated a little over 2000 ft-lb.
possible strain hardening?