In order to answer the question posed at the end of Chapter 4.3 we use Visualizing Stress. Select StressTensor from the Calculators menu. In the textbox labeled SigmaX type in 20. In the textbox labeled SigmaZ type in 40.
Select Plot. Visualizing Stress calculates Sx, Sz, and sxz (Figure 10) on a set of planes that form a circular fan about point P, each plane being separated from its neighboring plane by 5o (Figure 11).
The magnitude and direction of sxz can be visualized by imagining a line running from each plotted point to the origin of the XZ coordinate system. Note that the distributions of sxz forms an ellipse which structural geologists refer to as a stress ellipse. Moreover note that there are two mutually perpendicular directions of sxz that represent the largest and smallest stress vectors. These two directions are referred to as the maximum and minimum principal stresses. In three dimensions the stress ellipse becomes an ellipsoid with three mutually perpendicular principal stress directions, referred to as s1, s2, and s3 (Figure 12).
Structural geologists refer to s1 as the maximum principal stress, s2 as the intermediate principal stress, and s3 as the minimum principal stress. Thus, if we view a section perpendicular to one of the three principal stress directions, then the section that we are viewing will contain either (s1, s2), (s1, s3), or (s2, s3). Furthermore, as will be discussed in Chapter 5, if we know the orientations and magnitudes of two of the principal stresses, then we can calculate the normal and shear stresses acting on all possible planes oriented at some given angle to the known maximum principal stress.