Three-dimensional mohr's circle for shear stress components

The Mohr diagram is a graphical technique that is well known and widely used in stress analysis. Mohr’s graphical construction enables the determination of the magnitude of the normal stress component for a given oblique plane. On the other hand, it only gives the magnitude of the total shearing stress, thus failing to provide its components. This paper is an extension of Mohr’s work to overcome this shortcoming. A proposed method, based on the utilization of Cauchy’s formula, along with vector analysis of both the stress vector and the normal stress component, is suggested. It allows full representation of the shearing stress components in Mohr space. This present technique is mathematically derived and graphically depicted.