1(50 REAL STRESS DIAGRAMS. 



Then the original volume of the bar is 

 = A x L, and 



the volume at the point in question is 

 = a x (L + I). 



But these are assumed to be equal, so that 



A L = a (L + I), 

 or 



a L 

 A ~~~ L + l 



AK 



= TT p > by similar triangles 



Again, the apparent stress is '? ; and the real stress is 



A. 



Load . c , , 

 . So that 

 a 



Apparent stress _ a _ A K 

 Real stress A HE 



Therefore, if, in the diagram, A K or H C represents 



the apparent stress or the , the distance HE, 



Original area 



obtained by the above construction, will represent the 



real stress, or the ^ - . In the same manner, a 

 Present area 



number of other points can be found on the real stress- 

 strain curves. When the maximum load has been passed, 

 local contraction sets in, and the construction is no longer 

 applicable. The last point, F, on the real stress curve 

 must be obtained by dividing the final load by the final 

 area, as obtained from the broken specimen. Thus, 



, ~ ^ Breaking load 



Final stress = O F = ~ =-fi . 



tmal area 



This value must be plotted on the diagram and a smooth 

 curve drawn through all the points obtained. A B E F 

 is then the real stress-strain curve. . 



A similar construction may be applied to compression 



