Strength of Materials

2.2 TWO-DIMENSIONAL STATE OF STRESSES

It is convenient to presume one of the principal stresses (or stress components in a particular direction) or principal strains (or strain components in a particular direction) as zero and convert the problem to a 2D state. In many occasions, 2D problems are easy to solve.

Thus, in certain situations, the stress components in a particular direction may all be zero and only the components perpendicular to that direction may exist. This is referred to as case of plane stress.

For example, if p_z = q_xz = q_yz = 0 (i.e., all the stress components in the z-direction are zero) and the components p_x, p_y and q_xy exist, then it is a case of plane stress.

Thus, a state of plane stress may be defined as that condition ...