Graphical methods of representing the stress components on different inclined planes at one point

The Mohr diagram is one of the most powerful and efficient graphical methods in stress/strain analysis and structural design. However, it cannot be used to determine the direction of the shear stress or shear strain for three-dimensional states. In this paper, a three-dimensional figure is given to describe the variation of normal and shear stress on different inclined planes at one point. Based on a mathematical formulation, the direction of the total shear stress is determined, and a graphical method is proposed to represent both the magnitude and the direction of the normal stress and shear stress together.