Basic Equations: Differential Form - Mechanics of Structures: Variational and Computational Methods - page 5

FIGURE 1.5
Right-handed Cartesian coordinate systems.

FIGURE 1.6
Definition of the components of the Cartesian stress tensor.

of a normal stress indicates that the stress acts on a plane normal to the axis in the subscript
direction. The first letter of the double subscript employed with stresses designates that the
plane on which the stress acts is normal to the axis in the subscript direction. The second
letter in the stress subscript indicates the coordinate direction in which the stress acts.
There are three normal stress components. The shear stress components are symmetric,
so that

τ = τ

yx ,

τ = τ

zx ,

τ = τ

xy xz yz zy

This is a consequence of the equilibrium of moments, which is demonstrated in Section
1.4. Thus the state of stress at a point is completely described by six components. In matrix