Torsion, ultimate/failure strength

The ultimate/failure strength in torsion, the outer flbers of a section are the first to shear, and the rupture extends toward the axis as the twisting is continued. The torsion formula for round shafts has no theoretical basis after the shearing stresses on the outer fibers exceed the proportional limit, as the stresses along the section then are no longer proportional to their distances from the axis. It is convenient, however, to compare the torsional strength of various materials by using the formula to compute values of x at which rupture takes place. 

A splined torsion-shaft, Fig. 5.52, 2" diameter is subjected to a constant torque M,= 180 KN. The material is high strength carbon steel heat treated to 1,200 MPa ultimate strength and 313 MPa fatigue limit xyin completely reversed torsion. Service experience indicates continuous untimely failures along section A-A in correspondence of a shoulder fillet of radius p — 2 mm. 

---