* b' b pass 



Figure 13. — Active and passive stress circles and their relationship to 



Mohr's rupture envelope. 



From equation 13 and figure 13, the equation for a leaf of the Mohr rupture 

 envelope can be written as : 



t - atan<f> - c = 0. (20) 



The normal form of equation 20 is the expression for all lines perpendicular to the 

 leaf of the failure envelope: 



a tan (J) 



(21) 



A+tan 2 * A+tan 2 <}> /l+tan 2 <|> 



Because the stress circle is tangent to the failure envelope, the radius of the stress 

 circle, r, is perpendicular to the failure envelope at the point of tangency. Noting 

 that t equals zero, the length of the radius is found by substituting the coordinates 

 for the center of the circle of stresses (° > T ) into equation 21: 



o tanc; 

 o 



A + tan 2 * /l + tan 2 c 



(22) 



13 



