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5. Conclusion. The methods presented above have been applied to more complicated frames and readily give the required solutions for collapse design under constant or varying loads. For shakedown design, the iterative numerical method converges fairly rapidly. It may be found easier for highly redundant frames to obtain a new elastic solution at each stage using the numerical values obtained from the previous analysis, since an analysis with numerically unspecified flexural rigidities is extremely tedious. For all three types of design, the introduction at an early stage of the numerical values of the loads simplifies the work greatly, since it will be found that a large proportion of the inequalities generated become redundant and can be ignored. Only examples of concentrated loads on straight members of uniform cross-section between joints have been examined, making it possible to pick by inspection the critical cross-sections. However, the basic ideas are not altered by the introduction of other variables; the analysis will be more complicated, but aids to calculation may be introduced which leave the basic problem unchanged.

The method of characteristics applied to problems of steady motion in plane plastic stress