UF/nVKKN STKKSS AND DEFORMATION 21 



*'. 



body differs only infinitesimally from the stress at a neighboring 

 point. This is called the law of continuity. 



N \s- consider an infinitesimal cube cut out of an elastic body 

 whii-h is subject to the above assumptions, and let the coordinate 

 axes be taken along three adj;i 



of the cube, as shown in 

 Fig. 6. Then, from the law of con- 

 tinuity, the resultant of the stresses 



4 <>n any face of this cube is 

 equal to their sum and is applied 

 at the center of gravity <>f the face. 

 Consequently, these resultants must 

 all lie in one or other of the three 

 diametral planes drawn through the 



r of the cube parallel to the 



.:iatf plaiH-s. The stresses 

 lying in any one of these planes, 

 say the diametrical plane parallel to ZOX, will then be as represented 



. 



Since the resultant normal stresses on opposite faces of the cube 

 approach equality as the faces of the cube approach coincidence, we 

 may write 



= and = ' 



equilibrium against rotation! 

 tli- r'.Mir >li-aring stresses must! 

 also be of equal intensity, and 

 therefore 



. 7 



'nsidrrin^ the other two 

 diametral planes similar relations 

 U'tw.M-n tlif imniial and slu-arin^ 

 Fio.8 stresses can be estalli si KM 1. Con- 



sequently, the shearing .s 



any point in an elastic bo<f</ in planes mutually at right angles are 

 of equal intensity in each of these planes. 



