Based on the Mohr Circle in figure 4 answer the following questions.
12.) What is the value of the confining pressure? (5 points)
s3 = 20 MPa
13.) What is the magnitude of the Mean Stress? (5 points)
(s1 +s3)/2 = (60 MPa + 20 MPa)/2 = 40 MPa (The center of the Mohr Circle)
14.) What is the magnitude of the Deviatoric Stress? (5 points)
(s1 -s3)/2 = (60 MPa - 20 MPa)/2 = 20 MPa (The radius of the Mohr Circle)
15.) What is the magnitude of the Differential Stress? (5 points)
(s1-s3) = 60 MPa - 20 MPa = 40 MPa (The diameter of the Mohr Circle)
16.) Determine the values of the normal stress (sN) and the shear stress (sS) for a plane that makes an angle q of 30° with respect to the direction of greatest principal stress (S1). (5 points)
sN andsS can be estimated by reading the values of the graph (30 MPa and 17 MPa respectively) or from the following equations:
sS = [(s1 - s3)/2]sin2q = 20 MPa * .866 = 17.3 MPa
sN = (s1
+ s3)/2 - [(s1
- s3)/2]cos2q
=
40 MPa -(20 MPa * cos60) = 30 MPa