BARS 



109 



ular sets of planes such that across each of these the stress is 

 in the direction of the normal ; but for a reason already indicated 

 we need not stop to prove this theorem. The planes in question 

 are called the " principal planes " of the stress, and the corre- 

 sponding stress-intensities are called the "principal stresses." 

 They are usually reckoned as positive when of the nature of 

 tensions; we denote them by Pi,p 2 ,p 3 . 



There are certain special types of stress to be noticed. 

 First let j9 1 =j9 2 = PS- The stress across every plane is then in 

 the direction of the normal, and of uniform intensity, as in 

 hydrostatics. 



Next, let^! = pt,=p, say, whilst p 3 = 0. Consider a unit 

 cube whose faces are parallel to the principal planes. The 

 portion included between the faces represented by AB, DA, in 

 the figure, and the diagonal plane represented by BD, is in 

 equilibrium under three forces. Two of these forces are 

 parallel and proportional to DA and A B, viz. the forces on AB 

 and DA, respectively. The third force is therefore along and 



Fig. 40. 



Fig. 41. 



proportional to BD\ and its amount (CT) per unit area is p. 

 A similar result holds with respect to the diagonal plane A C. 

 A cube four of whose faces are parallel to these diagonal planes 

 is in equilibrium under tangential stresses, in the manner 

 shewn. This type is accordingly called a "shearing stress." 

 Its amount (CT) is specified by the tangential force per unit 

 area on the planes in question. 



