Torsional Stresses

definition

τ = T c / J

where J is the polar moment of inertia (units: in⁴, m⁴).

solid shafts:		J = π d4 / 32
circular tubes:		J = π (do4 - di4) / 32

Recall that torsional bars were said to be in pure shear.

 

limitations

These equations are only valid for bars with circular cross sections (solid or hollow) that remain linear-elastic. stresses must not exceed proportional limit cross sections for noncircular bars do not remain plane maximum stresses for noncircular bars are not located at the farthest distances from the center These equations are not valid near stress concentrations (e.g. holes, notches, fillets, load points).

Automotive Engineering, December 1996, p. 91

 

solid vs. hollow shafts

Circular tubes are more efficient than solid bars in resisting torsional loads. Material near the outside surface carries most of the torsional load, so most of the material in a solid shaft is stressed significantly below the maximum shear stress.