APPARATUS FOR MEASURING STRAIN AND APPLYING STRESS. 289 



ently the maximum stress due to bending was of itself insufficient to cause yield, 

 but the application of a further torque caused the principal stresses to assume the values 



A=f +y# +s ! 



^-v/f + ? ! 



2 V 4 



where p n = normal stress due to bending. 



q = shear stress due to applied torque. 



If we adopt Rankine's theory of maximum stress, then p x in this case passed the 

 working limit of the material, and a set resulted. 

 On the maximum strain theory of St Venant, 



if e x = principal strain, 

 m = Poisson's ratio, 

 then 



in 



m — 1 . m + 1 



and since m has a value between 3 and 4 for steel, it is clear that the addition of a 

 shear stress q would cause an increase in the value of e, which, if below the limit before, 

 might increase sufficiently to cause failure. 



The relation of stress to strain after the permanent set is clearly shown by a further 

 test indicated in the table, column IV. There is now considerable hysteresis in the 

 relation of stress to strain. 



