State of Stress:

From the point of functional utilization of a solid component we might determine the probable loads (forces) to that it might be subjected to, so in which its equilibrium, compatibility and stability are satisfied on the overall. But a more critical analysis will denote the satisfaction of equilibrium at each and every point of the solid. The distribution of stresses over the volume of the solid is analyzed taking within these requirements. At one such a distribution has been arrived at it will provide the state of stress at each and every point in the solid in terms of the stress components. Frequently one is not interested in the state of stress at each and every point in the solid, but is satisfied along with the analysis of the state of stress at the critical locations of the solid. Description of the common state of stress includes the definition of six stress elements namely, σ_x, σ_y, σ_z, τ_xy, τ_yz and τ_zx on the three mutually perpendicular planes of a little element at the requisite location. Therefore, in the initial stages of the course, it is enough to master the concepts with reference to the state of stress in two dimensions. The common state of stress at any point in a two-dimensional element is provided through the stress components σ_x, σ_y and τ_xy as shown in Figure. Of course, any element could just be three-dimensional, but the state of stress is two-dimensional because of the absence of any stress components in the pair of z planes. Therefore, in considering equilibrium of forces, the dimension of the element in z direction is taken as unity; in whatever units another two dimensions are expressed.