State of Stress:

From the point of functional utilization of a solid component we may determine the possible loads (forces) to which it may be subjected to, so that its equilibrium, compatibility and stability are satisfied on the whole. But a more critical analysis will imply 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 into these requirements. Once such as distribution has been arrived at this will give the state of stress at each and every point in the solid in terms of the stress components. Often one is not interested in the state of stress at each and every point in the solid, but it is satisfied along the analysis of the state of stress at the critical locations of the solid. Description of the general state of stress involves the definition of six stress components namely, σ_x, σ_y, σ_z, t_xy, t_yz and t_zx  on the three mutually perpendicular planes of a small element at the requisite location. However, in the initial stages of the course, this is adequate to master the concepts with reference to the state of stress in two dimensions. The general state of stress at particular point in a two-dimensional element is given by the stress components σ_x, σ_y and t_xy as illustrated in given Figure. Of course, any element could only be three-dimensional, however, the state of stress is two-dimensional because of the absence of any stress components in the pair of z planes. Hence, in considering equilibrium of forces, the dimension of the element in z direction is taken as unity; in whatever units the other two dimensions are expressed.