8 WALTER H. BUCHER 
representing ultimate states of stress. For this envelope is the locus 
of all points, which, for a given a, have the greatest 7 for the stress 
distributions in question. ‘The envelope thus represents the relation 
Tn=f(¢) between maximum shear and normal stress. As all 
principal circles have their centers on the c-axis, their envelope is 
symmetric with respect to this axis, and touches each circle in two 
points, S,, S,, corresponding to the two shearing planes for the 
state of stress represented by the circle. Referring to Figure 12, 
we see that the shearing planes corresponding to S, and S, make 
equal angles with the zy plane: ¢,=¢.. The acute angle between 
the planes is therefore equal to 2¢,, and is bisected by the principal 
plane zy. 
Pics 13 
Experiment has shown that the envelopes are roughly parabolic 
in shape. They presumably cut the +o-axis at the point-circle 
representing rupture due to uniform all-sided tension (¢,=0,=0;). 
Mohr also infers from the apparent impossibility of crushing a 
substance by applying uniform all-sided pressure, that if the 
envelope cuts the —o-axis at all, it does so at an excessive distance 
from the origin. 
If the ultimate tensile and compressive strength of a material 
are known, say o, and o2, we may construct the principal circles 
corresponding to these limiting states, namely, 
Ox=Cy=O, Of=O01; Gy=—O2, Oy=—G,=0. 
