Normal Stress

In a rectangular or Cartesian coordinate system (x,y,z), the stress tensor τ is given by:

(1)

where i_x, i_y and i_z denote unit vectors in the x-direction, y-direction and z-direction, respectively. The components of τ may be interpreted thus:

• τ_xx is the x-component of force per unit area exerted across a plane surface element normal to the x-direction;
• τ_xy is the y-component of force per unit area exerted across a plane surface element normal to the x-direction; and so on. (Precisely analogous interpretations can be given to components of stress in any orthogonal coordinate system.)

Each component with identical suffices (τ_xx, τ_yy and τ_ZZ) is called a normal stress since it represents a force in a direction per unit area normal to that direction. Each other component with different suffices (τ_xy, τ_yx, τ_xz, τ_zx, τ_yz and τ_zy) is called a Shear Stress.