17.7 : מרכיבי מאמץ

The stress components of a body subjected to multiple loading are analyzed by considering a small cube centered at point O.

The cube has the normal and shearing stress components that act on faces perpendicular to the corresponding axes.

The hidden faces also experience these stresses that are equal and opposite to the ones on the visible faces. So, equilibrium is maintained.

Although the stresses on the cube's faces differ slightly from those at point O, this small error disappears as the cube's side length reduces to zero.

Considering the cube's free-body diagram, the normal and shearing forces acting on the faces are determined by multiplying the corresponding stress components with the area of each face.

Then, by applying the equilibrium equations, relations among the shearing stress components are derived, which implies that only six stress components are required to define the stress condition at a given point.

Also, the shear stress cannot occur just in one plane. So, an equal shearing stress must be exerted on another plane perpendicular to it.