DHE MECHANICAL INTERPRETATION OF JOINTS 7 
postulate of this theory may be stated as follows: The ultimate 
strength of the material is determined by the greatest shearing stress 
im the shearing planes, this limiting shear ttself depending upon the 
normal stress in the planes. ‘The limiting shear 7,, is thus assumed 
to be some function of the normal stress in the plane, 7,,=/(c), 
but the nature of this dependence is not specified by the theory. 
The curve, however, which represents the relation 7,,=/(c) has 
certain properties which may be inferred from Mohr’s graphic repre- 
sentation of stress distributions. In this representation a point 
Fic. 12 
S,, corresponding to a shearing plane (Fig. 12), must lie on a princi- 
pal circle, since the points of this circle have the greatest 7 for a 
given value of co. From this fact we may draw two important 
conclusions: 
I. Since a principal circle is completely determined by the two 
extreme principal stresses, o,, o;, the ultimate strength of a material 
that fails by slippage must be entirely independent of the inter- 
mediate principal stress cy. 
2. Since points on a principal circle correspond to planes 
normal to the xz plane, the shearing planes at any point must pass 
through the y-axis. 
Furthermore, a point on a principal circle corresponding to a 
shearing plane must lie on the envelope of all the principal circles 
