﻿of Ductile Materials under Combined Stress. 537 



points causes a complete redistribution of stress across the 

 section, and the yield-point stress extends to other areas. For 

 this reason the stress at the first sign of yield should be taken. 

 When a simple tension test is considered, there is still the 

 rounded portion, due to local yielding and eccentricity of 

 loading, although the stress is finally uniformly distributed 

 over the section. When the stress-strain curve become- 

 approximately horizontal there is general yielding, and the 

 corresponding stress should be taken as the yield-point stre— . 

 In the present case there are both causes for the rounded 

 portion of thecurve, local yieldingand redistribution of stress : 

 one operates to cause the first sign of yield, and the other 

 complete yield, to be taken as the limiting condition. As 

 the object o£ the tests is comparative, it matters very little 

 which is taken, the results being in a sense proportional 

 within the limits of experimental error and those arising from 

 taking curve-readings. It is quite impossible to accurately 

 locate the point at which yield first occurs, therefore the 

 selection has been made as described below. This seems quite 

 satisfactory when considering a suitable formula for bending 

 and twisting. The same moments have been tabulated and 

 the corresponding stresses calculated, making the usual 

 assumptions. These have been found to bear a definite 

 relation to the stresses corresponding to the first sign of yield. 

 so nearly as could be read from the curves, when the usual 

 assumptions hold good, and stresses can easily be changed to 

 those calculated on the assumption of a uniform distribution 

 of stress. 



6. Determination of the Yield-Point. 



The yield-point was determined as indicated in fig. 4, 

 test 11. As the intermediate state between perfect elasticity 

 and great flow, or the approximately vertical and horizontal 

 portions on a stress-strain curve, is due to successive yield at 

 various planes of weakness, most elasticians neglect this part 

 of the curve altogether, and there is considerable justification 

 for this course. This has practically been done here, the 

 lines representing the two states being produced to meet in a 

 point. Supposing this course was not justified, at least this 

 is a definite, easily determined point to deal with, and any 

 probable error would not be greater than that which is likely 

 to arise when taking a point less closely defined. 



7. The JVature of the Loading. 



It has already been stated that the most important case of 

 combined stresses with ductile materials is that of bending- 



