Plastic Bending of Plates
In this chapter, we shall be concerned with the yield point state of perfectly plastic plates whose thickness is small compared to the dimensions of its plane faces. The load acting on the plate is normal to its surface and is regarded as positive if it is pointing vertically downward. The vertical displacement of the middle surface is assumed to be generally small compared to the plate thickness, and plane vertical sections are assumed to remain plane during the bending. The deformation of the plate is therefore entirely defined by the vertical displacement of its middle surface, which remains effectively unstrained during the bending. A theory based on this model is found to be satisfactory not only in the elastic range but also in the plastic range of deflections. However, when the deflection of the plate exceeds the thickness, significant membrane forces are induced by the bending, the effect of which is to enhance the load carrying capacity of the plate.