Continuity conditions at bending and shearing interfaces of rigid, perfectly plastic structural elements

Bending and shearing hinges idealised as discontinuity interfaces in rigid, perfectly plastic analysis are two important ways to consume plastic deformation energy in dynamic plastic response of a two-dimensional structural element. The continuity conditions at an interface in a rigid, perfectly plastic beam are examined in the present paper when retaining the transverse shear force in the yield condition. Various continuity conditions are suggested at stationary and moving bending and shearing interfaces which may occur during the early response stage of a rigid, perfectly plastic beam. Both regular and singular yield surfaces give the same continuity conditions. The effects of rotatory inertia on the continuity conditions are discussed. It is shown that transverse shear deformations in a rigid, perfectly plastic beam are always localized in a stationary shear hinge, which may lead to a distinct transverse shear, or Mode III, failure. All conclusions for the beam are extended to axisymmetrically loaded circular plates and cylindrical shells.