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STUDIES FOR STUDENTS 



is that of relief, and after rupture the differential slipping between 

 joints will cause shortening in the direction of maximum stress 

 and elongation in the direction of minimum stress. 



When it is remembered that all the forces at work at any 

 place may be decomposed into three principal directions of stress 



Fig. 4. Cross-section of a bed showing joints. 



.at right angles to one another, it would seem to follow that there 

 would ordinarily be produced only two sets of compressive joints 

 at the same time. To suppose that more than two sets are 

 simultaneously produced would require that the ultimate strength 

 was exceeded at the same moment in two of the principal direc- 

 tions of stress, and this is probably not a common case. One 

 would expect, if the forces in two of the principal directions of 

 stress are equal or nearly so, that the ruptures would be con- 

 •choidal,and this maybe the explanation of some of the cone-in- 

 ■cone structures. Supposing the compressive stresses to be 

 unequal, the ruptures are produced by the maximum stress, and 

 any one of three strains may result : (i ) shortening in one direc- 

 tion, (2) simple shearing, and (3) shortening in one direction 

 combined with shearing. In the first case, that of shortening in 

 one direction and consequent elongation in a single direction, 

 there are produced two sets of joints, but not exactly at right 

 angles to each other. The maximum force probably bisects the 

 .acute angles (Fig. 4).^ Subsequently, however, by differential 

 movement between the fractured parts, it is possible that the joints 

 may be so rotated as to change the originally acute angles to 

 obtuse angles. The two sets of joints would only be at right 

 angles in case the rotation stops at a definite stage. In the second 

 -case, that of simple shearing, there is one set of compressive joints 

 ' Loc. cit, (A), pp. 643, 873; (B), p. 465. 



