﻿of Ductile Materials under Combined Stress. 



541 



The principal stresses are T2+ \/fc 2 +T 2 /4r, and the shear 



stress, equal to half the difference between the greatest and 

 least principal stresses, is \ S- + T- 4. 



11. Facts not included in the Table. 



The following- interesting facts may be noticed in connexion 

 with the tests. Considering Test IV., a quarter of the bend- 

 ing load was put on and torque increased to yield. There 

 was simultaneous yielding by bending and twisting (fig. 3), 



but a large addition to the bending load was needed to cause 

 further appreciable yield. When half, or more, of the bend- 

 ing load had been put on originally, the bar gave in both 

 ways simultaneously, and a small addition to the bending 

 load caused farther yield (fig. 3). When the rod could stand 

 a farther load without much deflexion, the bending yield was 

 almost sudden at the critical load, there being none preceding 

 it that could be measured (Test IV.). With larger fractions of 

 the bending load, the yield could be detected before the critical 

 load was reached and deflexion was plotted against twisting 

 moment, in addition to the twist : in fact the specimens gave 

 first by bending in Tests V.. VI., and VII. The yield by 

 twisting, due to the bending load, was small in Test VIII., 

 fig. 1. but the sensitive method of measuring readily detected 

 it. The bar could stand an increase of torque with little more 

 than normal twist. In Tests IX. and XI. the yield was large, 

 and a small addition to the twisting load produced a large 

 twist, the increase of load being unnecessary as the bar was 

 badly deformed in this way without it. The critical load- 

 causing yield in the two ways are given below : — 











Xature of 



Test. 



Original Load. 



Yielded by 

 Bending at 



Yielded by 

 Tvristing at 



Load being 



added and 



stated. 



IV. ... 



4 bending load. 



77 lbs. 



77 lbs. 



Torque. 



V. ... 



A 



715 „ 



7225 ., 





VI. ... 



I „ 



64 „ 



6525 „ 





VII. ... 



9 



TO » J) 



395 .. 



11-5 „ 



.. 



XII. ... 



f „ 



58 „ 



5-5 .. 





VIII. ... 



^ torque. 



356 



341 



Bene ins:. 



IX. ... 



* „ 



308 .. 



310 





X. ... 



1 •• 



223 „ 



194 



• 



