Load-capacity estimation and collapse analysis of thin-walled beams and columns—recent advances

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The present paper is devoted to the recent results of research in the area of load-capacity and post-failure behaviour of thin-walled beams and columns (among them thin-walled cold-formed profiles). It deals with ultimate load and collapse of box-section girders (tubes) of different cross-sections under bending, as well as of lipped and plain channel-section beam-columns. The paper contains the presentation of theoretical analysis and experimental investigation of plastic mechanisms of failure and collapse behaviour of these thin-walled sections. The short review of results obtained in recent years in general precedes those obtained by the Department of Strength of Materials and Structures, TUL. The problem of post-failure behaviour is solved using the rigid-plastic theory adopted and modified for the purposes of the solution taking into consideration strain-hardening of the member’s material. On the basis of experimental investigations theoretical models of plastic mechanisms of failure are produced for different sections. Theoretical analysis is based on the principle of virtual velocities. The problem is solved in an analytical–numerical way. The particular attention has been paid to the influence of the strain-hardening of the material after yielding upon the collapse structural behaviour and also to the influence of cross-section shape and dimensions on the character of collapse. The upper-bound estimation of the load-carrying capacity of analysed thin-walled sections by combining results of non-linear, elastic post-buckling analysis with the results of plastic mechanism analysis is carried out. Results are presented in diagrams showing post-failure curves as well as curves representing structural behaviour in the whole range of loading up to and beyond the ultimate load. Some results are compared with experimental results and those obtained from FE analysis. A comparison of lower- and upper-bound estimation of the load-carrying capacity is discussed and illustrated in diagrams. Conclusions dealing with the influence of strain-hardening phenomenon displayed by the material upon the load-carrying capacity and collapse behaviour of examined sections are derived. Also conclusions concerning different upper- and lower-bound estimations of the load-carrying capacity of analysed sections are presented.