ON STRESS DISTRIBUTIONS IN ENGINEERING MATERIALS. 285 



As long as the elastic limit of the material of a bar of the diameter 

 d = 2r is not exceeded, the torsional resisting moment is 



M=Se . d^7r/lG = S^ . rV/2. 



If therefore from the observed torsion moment wc estimate shearing 

 stresses S^ as if the material were perfectly elastic, then the plastic stresses 

 arc 



This formula has been used for estimating the plastic shearing limits 

 and drops from the torsion curves. Beyond these limits dM/da is negli- 

 gibly small and the ultimate shearing stresses are therefore 



Appendix II. 

 On (he Hysteresis of Steel under Repeated Torsion. 

 By W. Mason, D.Sc. 



Recent experiments^ have shown that elastic hysteresis becomes 

 rapidly greater with increasing range of stress. At a range of 85 tons 

 per square inch, the width of the hysteresis loop for an annealed steel 

 tube, measured in stress, amounted to 015 tons per square inch. 



The question arises whether the hysteresis found with stress-ranges 

 which extend beyond what are believed to be the natural elastic limits 

 is or is not of the same nature as elastic hysteresis. 



The following set of experiments was one of several made in order 

 to get further information on this point. 



A turned and bored hollow specimen (see figure) of the dead mild 

 steel provided by the Stress Distribution Committee of Section G of the 

 British Association was fixed in an alternating torsion-testing machine 

 wherein the torque, direct and reverse, was applied by a lever which 

 could be operated either by mechanism or loaded by dead weights. The 

 grips holding the ends of the specimen were centred inside ball-bearings, 

 and care was taken to eliminate any friction that might affect the 

 value of the applied torque. The range of the angle of twist was 

 measured by mirrors bolted to the specimen (see figure\ The image 

 of a fixed scale was reflected in turn by each mirror, and was received 

 in a fixed telescope. . The mirrors remained fixed to the specimen through- 

 out, and neither the scale nor telescope was moved during the experiments ; 

 but if any small displacement of these latter, for any cause, did occur, 

 there could be no effect on the range of torsional strain or width of 

 hysteresis loop observed. 



The Table explains the scheme of the experiments. 



The readings in columns o, h, c, d, e arc accurate to within +01 

 scale divisions, and the accuracy of the range of strain and of the width 

 of hysteresis loop is certainly well within +02 scale divisions. The 

 arrangement for observing the torsional strain is intended for measure- 

 ment of comparatively large ranges of angular twist, and not for the 

 accurate measurement of the elastic hysteresis. 



» ' Elastic Hysteresis in Steel,' F. E. Rowett.— Prof. Roy. Soc. A., Vol. 89. 1914. 



