42 G.P.BECKER — FINITE STRAIN IN ROCKSi 



to (.[. and a single unbalanced couple, C\ — < ',. The combination of two 

 equal and opposed couples is easily shown to be equivalent to a shear, the 

 axes of which bisecl the angles made by the component forces.* Here, 

 therefore, the balanced couples arc equal to a shear at 45° to Por Q. 



There now remains a single unbalanced couple tending \<j produce 

 rotation of the mass about o z. Unless still other external forces are in- 

 troduced, this couple will merely rotate the mass without strain. If. 

 however, one ol the faces of the cube is compelled to coincide with a 

 fixed plane having the same direction as the forces of the couple,'ag 

 the mass rested on or against an inflexible frictionless support, this 

 couple, together with the resistance, will effect distortion and will convert 

 the square section on the xy plane into a, rhomb with two of it- sides 

 parallel to the fixed plane. The distortion thus produced will consist 

 merely in a tangential shifting of planes parallel to the support and will 

 involve no change of volume. In short, the strain is shearing motion or 

 scission. 



Xo system of forces of constant direction and constant intensity will 

 produce scission. The combination of a couple and an inflexible resist- 

 ance is equivalent to a stress system like that of a simple shear, hut 

 which undergoes rotation relatively to the fixed axes of reference during 

 strain. The dynamic origin of a scission thus differs essentially from 

 that of a shear. 



If a cube resting upon an inflexible support coinciding in direction 

 with "./-were subjected to the force system of figure 4. the couple ' 

 would he inoperative and the stress system would reduce to dilation. 

 axial shears, and the rotational shearing stress which produce- - iission. 

 This last may he called scissive stress. 



No support is absolutely inflexible, and in real cases of supported 

 masses the strains produced will he of a character intermediate between 

 those produced when there is no support and when the support is ideally 

 rigid. Such strains evidently involve both scission and a shear at 45° 

 to the axes. 



On the whole, then, the entire force system, including a resistance to 

 rotation, produces a dilation, a shear in the y z plane, two -hears in the 

 .'■ y plane, one of them at 45° to the axe-, and a shearing motion in the .<• j, 

 plane. Idle most general strain discussed in preceding page- corresponds 

 to any combination of these strains, each of which has been treated in 

 detail. It has also been shown that a general strain of the type here 

 treated i< resoluble into just these components. 



- ie an elementary proof of this proposition in Hull. Geol. Soc. int., vol. 2, 1891, p. 55. 



