CHAPTER II 



FUNDAMENTAL RELATIONS BETWEEN STRESS AND 

 DEFORMATION 



23. Relations between the stress components. In order to d. 

 mine the relation between the stresses and deformations within an 

 elastic body, it is necessary to make certain assumjiti. the 



nature of the body and the manner in which the external forces are 

 applied to it. 



The first assumption to be made is that the material of which the 

 body is composed is homogeneous; that is to >ay. that tl. 

 properties of any two samples taken from different jwirts of tin- 

 are exactly alike. If, more- 

 r, the surface of the Udy 

 is continuous and ti 

 nal forces are di>tiil.ute.i 

 tinuuusly .. 

 or. in ,,thri 



- are no cracks or ot lin- 

 den cha: .11 in the 

 body, and the external forces 

 are distributed over a c 

 erable bearing surface, r 

 lows, in consequence of 

 above assumptions, that the deformation at any j-int of the \x 

 a continuous function of the coordinates of that point In ol 

 words, under the above assumptions the deformation at any IN .JI,I 

 of the body differs only innnitesimally from the deformation' 

 neighboring point. 



Since, by Hooke's law, the stress is proportional to the deforma- 

 tion, it follows that the stress is also distributed continuously 

 throughout the body, -that is, that the stress at any point of 



20 



FIG. 6 



