In a 3-D stress analysis, the third Mohr circle can be smaller than the first and second circles under specific conditions. An example provided involves a stress tensor with values of 50 MPa in the x and z directions, and 0 MPa in the y direction. The x-y and y-z Mohr circles are equivalent, while the x-z Mohr circle reduces to a single point at 50 MPa. This scenario illustrates how differing stress states across planes can lead to varying sizes of Mohr circles. Understanding these relationships is crucial for accurate stress analysis in three-dimensional problems.
