The displacement field and its significance for certain minimum weight two-dimensional frames using the analogy with perfectly plastic flow in metal working

Space and force diagrams are drawn pertaining to some simple two-dimensional, minimum weight frames for particular dispositions of load, which are analogous respectively to slip-line fields and their associated hodographs for certain metal working processes. Displacement diagrams for these frames are drawn, following the well-known method suggested by Williot.¹ It is assumed that the strain in each member of a frame is ±e. A one-to-one mapping between the nodal points of a frame and the corresponding displacement field is observed and certain relevant co-ordinates are given in tabular form. A precise analogy is also established between the displacements of a minimum weight frame and the resultant forces in the corresponding slip-line field. The aim of this paper is to emphasize that the analogy used to define the layout of certain minimum weight frames directly from slip-line fields is valid only for the loaded, i.e. deflected condition of the frame. It is pointed out that for certain classes of frame the unloaded, or constructed form of the frame must be considered.