A Thesis Submitted to the Faculty of Engineering University of the Witwatersrand, Johannesburg for the Degree of Doctor of Philosophy Johannesburg 1981 / This thesis describes the development of an alternative aooroximate technicue for the elasto—plastic analysis c^ unbraced and partially-braced rigid rrames. The proposed technigue, which allows for the treatment o_ simple portal frames as well as for multi-storey and multibay structures, is not confined to steel to which it has been applied in this research but could also be developed for other materials such as reinforced concrete. In essence, the method represents a refinement and extension of the Merchant-Rankine interaction formula. The proposed concept makes use of a multi-curve interaction principle placing the failure load of the actual frame oetween its plastic collapse load on the one hand and a load related to the elastic buckling load on the other hand. The failure curves in the inelastic range are empirical. The plastic collapse load is obtained using the standard first-order approach. The required elastic parameters are evaluated from an elastic buckling analysis and a second-order elastic load analysis, both performed on suitable subassemblages for the general frame. The mathematical derivations are based on the slope-deflection equations including stability functions. For the elastic analyses a purpose-made computer program has been developed. This program makes allowance for transverse column loads, patterned beam loadings and the special case of sway buckling including bending, termed "Symmetry-Buckling". In this thesis the proposed method has been applied to the structure as a whole. In this case the plastic collapse load of the entire frame is determined, whereas the corresponding elastic parameters are evaluated from as many subassemblages as are contained in the structure. The combination of plastic collapse load and elastic parameters which gives the lowest failure load is significant . It is also possible to calculate failure loads for individual sections of a framework. The plastic collapse load and the salient elastic parameters would then both be examined on matching subassemblages. Furthermore, it has been demonstrated that a graphical presentation of the elastic results is possible, thus allowing a "manual" evaluation of the failure load, i.e. without the need of a computer, once the plastic collapse load is known. The derivation of the plastic collapse load is not included in the scope of this thesis. In addition, an approximate analytical procedure, using established computer methods, has been formulated for the calculation of the elastic values. A number of frames have been evaluated by the proposed method and the results have been compared both, to the Merchant-Rankine solutions and to mathematical solutions obtained using an elasto-plastic, computer analysis. The accuracy of the new method has also been tested against published laboratory results of other researchers. In addition, ten small-scale model frames were analysed and tested for this research to confirm the validity ot the empirically evolved interaction curves. It has been concluded that the proposed method is in good agreement with test results anc discrete mathematical solutions, and thus represents a satisfactory substitute for the more complex approaches, without the loss in accuracy and the restriction in usage which applies to the Merchant-Rankine formula. Some other related aspects such as the application of the proposed method to other materials and structures, deflections at the working load level, in-plane member instability, lateral torsional buckling and additional P - A effects have been identified as areas recommended for future research.