Stress

For complete specification of the stress at any point in a body, we need to know the force per unit area across any plane passing through the point and the direction of the force.

For complete specification of the state of stress in a body, we need to know the stress at every point in the body.

Here we are interested to develop the theory of equilibrium and motion of a body when subjected to body and surface forces.

Surface Traction

Let's consider a given plane S passing through a point O within a body.

Figure 2.1

Let's say is a small area of the plane which is normal to direction . Then if is a force which acts per unit area on the plane along the direction , then it has projections along the three axes of coordinates, so that

(2.1)

and the portion of the body which is on the other side of the plane acts along the following surface tractions on the element of area ,

(2.2)