On antiplane stress in an elastic solid

1—It is usual to apply the term “plane stress” to a stress system in an elastic solid in which all the stress components other than those acting solely parallel to a fixed plane (which may be taken as that ofx, y ) vanish identically. Thus the characteristic of plane stress is thatx͡y = 0,y͡x = 0,z͡z = 0, butx͡x ,y͡y ,x͡y do not in general vanish. We may use the term “antiplane stress” to denote a stress system which is complementary to plane stress, that is, one in whichx͡x = 0,y͡y = 0,x͡y = 0, (1) butx͡z ,y͡z ,z͡z do not in general vanish.