UNSYMMETRICAL LOADING. 309 



Secondly. When this shortening of the specimen by 

 indentation is carried to excess, an inequality of the stress 

 in the metal close -to the nicks results in the actual break- 

 ing stress being lowered. 



Thirdly. If the nicking is unsymmetrical, the line of 

 action of the load no longer passes through the centre 

 of gravity of the section, and a tensile stress due to the 

 bending action is added to the original tensile stress, and 

 the bar breaks under a smaller load per square inch of 

 section than does the original bar. 



161. Unsymmetrical Loading. The problem involved 

 in the last case is briefly as follows: In Fig. 158 is repre- 

 sented a bar of thickness 6; of width, d; under a tensile 

 load, P, acting at a distance, x, from the centre line of 

 the bar. 



This loading will be productive of a stress on a crosa 

 section of the bar, which will be variable, and will consist 

 of two distinct parts. 



In the first place, there will be a uniform tensile stress, / u 



p 

 where f t = j j, b d representing the sectional area of the 



bar. 



Besides this stress, there will be another caused by the 

 bending action of the force as it is applied, not along the 

 axis of the bar, but at a distance, x, from it, thus causing 

 a bending moment on the bar, which in magnitude is 

 equal to P x. 



The stress due to this bending action is 

 , 6 Pa; 

 / " = T^~ 



The total or resultant tensile stress is the sum of these 

 two, or 



/ = / t + /; 

 JL 6xp 



= b d H b d? 

 The more general expression is 



"A 



H 



A A 



