The Rupture of Steel l>y Longitudinal Stress. 253 



It will now be necessary to enquire how far the appearance of the 

 fracture of a steel bar affords evidence of its having broken by 

 shearing. 



In a bar of circular section and uniform thickness throughout its 

 length, every plane at 45 to the axis opposes an equal resistance to 

 the tarigential stress caused by direct tension. Hence, there is no 

 one plane or planes along which the bar would be more ready to 

 break by shearing than along any other plane, provided that the 

 material was of uniform strength throughout. If, however, the bar 

 be gradually thinned at a certain point, this will no longer be the case ; 

 it has been shown on p. 252, that the area of a plane at 45 to the 

 axis passing through the centre of the narrowed section is less than 

 the area of a plane passing through any other point in that section ; 

 hence, there will be a surface formed by a complete cone of 45, with 

 apex at the centre of the narrowed section, which will oppose a less 

 resistance to rupture by shearing than any other similar cone with 

 apex at any other point. This cone is shown in section in fig. 6 at 

 gof aob. We should then expect to find rupture result in a fracture 

 formed by a cone and crater, or, since there is nothing to determine 

 along which part of the cone rupture will take place, we may expect 

 to find the cone irregularly broken up, part on one end, and part on 

 the other. 



This narrowing of girth at one point always accompanies the 

 rupture of soft steel, and we invariably find such a cone and crater ; 

 figs. 5 and 6, Plate 2, and 6 and 7, Plate 3, are good examples. 



[Note. The rupture of cast iron in compression by shearing is of 

 course well known. Fig. 2, Plate 2, shows the cone of shearing very 

 well.] 



In flat bars of soft steel, this shearing action is still more marked. 

 Here the surface of the least resistance is a plane at 45 to the axis 

 and making 90 with the thin side of the bar ; it is evident that in a 

 bar whose width is considerable compared with its thickness, and 

 which has suffered considerable local contraction, this plane has the 

 least area of all planes at 45 to the axis passing through any point in 



Tension . , 



Shearing 



Sectional 

 area. 



r 1-047 

 \0-980 

 f 0-317 

 \0-327 



Breaking stress. 



Tons per sq. inch. 



10-40 



10-40 



6-14 



4-78 



Mean ditto. 

 10-40 



5-46 



The ratio of the former to the latter breaking stress being 1*9. 



The mean crushing stress was 41'5 tons per square inch ; diameter of specimen, 

 0-875 inch; length, 1'5 inch. 



In the ' Proceedings of the Institution of Civil Engineers,' vol. 90, p. 406, Messrs. 

 Platt and Hay ward give results of shearing and tensile tests of cast iron, from which 

 it appears that the ratio of the breaking stresses is 2'2. 



