ABasic Equations of Elasticity

A.1 STRESS

The state of stress at any point in a loaded body is defined completely in terms of the nine components of stress: images, and images, where the first three are the normal components and the latter six are the components of shear stress. The equations of internal equilibrium in terms of the nine components of stress can be derived by considering the equilibrium of moments and forces acting on the elemental volume shown in Fig. A.1. The equilibrium of moments about the x, y, and z axes, assuming that there are no body moments, leads to the relations

Graph depicting stresses on an element of size dxdydz with three dimensions xyz.

Figure A.1 Stresses on an element of size dxdydz.

Equations (A.1) show that the state of stress at any point can be defined completely by the six components images, and images.

A.2 STRAIN–DISPLACEMENT RELATIONS

The deformed shape of an elastic body under any given system of loads can be described completely by ...

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