» General Stress
When discussing stresses at "a point," one should visualize a cube, aligned with an orthogonal coordinate system. Each face of the cube has three stresses acting on it: a normal (axial) stress acting normal to the face, and two shear stresses acting parallel to the face in the other two directions.

Applying equilibrium, it can be shown that there are only 6 unique stresses on the cube (s_x ; s_y ; s_z; t_xy = t_yx; t_yz = t_zy; t_zx = t_xz ; etc.).

• Stress subscripts refer to (1) the face on which they act, and (2) the direction in which they act. Thus, t_xy is a shear stress on the x-face acting in the y-direction.
• Stresses are positive if they act on a positive face in a positive direction or act on a negative face in a negative direction
• Stresses are negative if they act on a positive face in a negative direction or act on a negative face in a positive direction

» General Strain
For a homogeneous (the same at every point) and isotropic (the same in every direction) material, the Normal Strain in the x-direction, e_x, is caused by the three Normal Stresses: s_x acts directly, while s_y and s_z act via the Poisson Effect:

The Shear Strains do not exhibit a Poisson Effect:

In general, all stresses and strains are non-zero.

» Plane Stress
In some situations an element is generally thin in the third (z-)direction relative to the primary material direction of the structure, and there is no resistance to strain (displacement) in that direction; thus there is no stress in the third direction. This situation is called PLANE STRESS. Under conditions of plane stress stresses can be approximated to act in only one plane:

The non-zero strains under Plane Stress are then:

» Plane Strain
On the other extreme are PLANE STRAIN problems. Here, there is no deformation is allowed in the z-direction:

The non-zero strains under Plane Strain are then:

Plane Strain problems usually occur when the thickness of a structure in the third (z-)direction is large or comparable to the other two thicknesses, or the z-dimension is otherwise constrained (e.g., between rigid supports).

» Special Cases

(Click on description to see illustration)

• Uniaxial Stress: Axial (Normal) Stress on an element that occurs in only one direction; no Shear Stress.
• Biaxial Stress: Axial Stresses in 2 directions; no Shear Stress.
• Triaxial Stress: Axial Stresses in all 3 directions; no Shear Stress.
• Hydrostatic Stress: Equal Axial Stress in all 3 directions; no Shear Stress.
• Pure Shear: Only Shear Stresses acting on an element (usually 2-d).