Plane state of stress or simply *plane stress* we call a special case of loading which usually occurs to solid bodies where one dimension is very small compared to the other two. Consider a very thin solid body as shown in Fig. 1. The normal and shear stresses acting on the two opposite sides normal to are all equal to zero. Due to the fact that the body is very thin, we may assume that , and are approximately zero throughout the hole body:

(1) |

Then the stress tensor takes the form:

(2) |

This type of loading is called plane stress. Very thin solids under this type of loading can be analyzed as two-dimensional. It should be noted that no buckling or bending should occur in order to assume plane stress loading.

**Suggested Bibliography**

L.E. Malvern. Introduction to the Mechanics of a Continuous Medium. Prentice Hall, Englewood Cliffs, New Jersey, 1969.

Y.C. Fung. A First Course in Continuum Mechanics. Prentice Hall, Englewood Cliffs, New Jersey, 3rd ed., 1994.

S.P. Timoshenko and J.N. Goodier. Theory of Elasticity. McGraw-Hill, New York, 3rd ed., 1970.