Synopsis
The Paper extends the plastic theory for plane frames of mild steel to cover the cases in which the detailed loading programmes of a set of independently variable loads are either wholly or partially unspecified and there is no restriction on the number of times each load may be applied.
A general method for analysing framed structures of mild steel, under arbitrary loading programmes, is presented. A two-bay portal frame with rigid joints, subjected to three independent forces, is taken as the basis for discussion, and a complete numerical analysis of the “shake-down” problem for this frame is given to illustrate the general method. Once the elastic analysis has been made, the time required for the “shake-down” analysis will, in many cases, be not much longer than that which would be needed to make the analysis for plastic collapse. Limitations of the present theory are discussed, and some suggestions as to its probable applications to design problems are offered.
