Ductile Materials vnder Combined Stress. 11.7 



maximum stresses due to bending were a compression at the 

 top of the bar, and a tension only at its lowest point ; and 

 these were confined to the mid-section, which was under the 

 maximum bending moment. This system of loading repre- 

 sented the most common example of combined stress in 

 engineering practice, which is a shaft subjected to combined 

 bending and torsion, and it had the further advantage that 

 the critical stresses were produced by comparatively small 

 loads. 



The bending deflexion was measured by means of a scale 

 which rested on the bar, and was guided in a slide provided 

 with a vernier. This simple arrangement was quite satis- 

 factory on such a long beam. The torsion was measured by 

 a pointer clamped to the bar, which moved over a fixed, 

 finely-divided circle. The twist was also measured at three 

 points by clamping mirrors to the bar ; fixed telescopes and 

 vertical scales were used in connexion with these mirrors. 



The Criterion of Strength. 



The theory of elasticity is based on Hooke's law, that 

 strain is proportional to stress. Beyond the elastic limit of 

 a material this law is no longer strictly true, and therefore 

 the usual formula? for calculating the stresses cannot be 

 applied. Consequently it is clear that the elastic limit is the 

 correct criterion of strength. But it is now the usual practice 

 to adopt the yield-point. Guest * stated that Hooke's law 

 holds to the yield-point, and he considered that the first 

 deviation from proportionality of stress to strain was caused 

 by local variations in the material, which altered the stress 

 distribution, and caused local yielding. Thus he assumed 

 that stress was proportional to strain for the main part of the 

 material until the yield-point was reached, and therefore he 

 selected the yield-point as the criterion of strength. Un- 

 doubtedly the yield-point of a material is less affected by 

 special treatment than the elastic limit, and it is more easily 

 determined, consequently other observers, following Guest, 

 have adopted the yield-point. 



Unfortunately opinions differ concerning the exact location 

 of the yield-point, and for comparative purposes, in order to 

 have a well-defined point, the writer also neglected the 

 intermediate state between perfect elasticity and complete 

 yield, and obtained the critical loads from the intersections 



* Proc. Phys. See. London, vol. xvii. Sept. 1900. 



