The buckling of structures : with particular reference to structures containing bolted angle-section members and lightweight structures.

Ths work described in this thesis has been carried out in the Civil Engineering Department of the University of Tasmania during the period July, 1956 to February, 1960. The research has been directed at obtaining some fundamental understanding of problems of instability of structures rather than the production of empirical information necessary for design purposes, though it is believed that the groundwork has been laid for the determination of valuable empirical data on certain types of problems. The treatment is restricted in the main to elastic buckling of non-redundant frames, though the problems met with in inelastic behaviour or with redundant frames are mentioned, and have been kept in mind throughout. Chapter One begins with a detailed analysis of an unstable mechanism. This study forms an interesting introduction to problems of instability of structures without introducing the complication of the elastic beam equation. Various methods of analysis of structures have their counterpart, by analogy, in the treatment of the behaviour of this mechanism, and the treatment is rather detailed. The remainder of the chapter is devoted to standard methods of calculation of elastic critical loads. Because of the apparent confusion in some recent papers as to the meaning of various critical loads as determined by the moment distribution convergence criterion and other methods, the treatment is again rather full, and contains some very simple examples. More difficult problems are worked as illustrations and also because their results are used later. Chapter Two is concerned with pin-ended struts and gives an introduction to the use of the Southwell Plot and the information that can be obtained from it. The Southwell Plot on deflections is first discussed. Particular emphasis is then laid on the power of the Southwell Plot on strain measurements. It is believed that the strain plot may have been used to ensure centrality of loading of a column for testing, but otherwise the treatment is new. It is intended that the discussion of single columns should furnish a basis for the arguments developed in Chapter Three, In Chapter Three the Southwell Plot on strains is applied to a number of simple model frames and model or full-size structures. A design method for certain types of structures liable to instability is advanced, based on the equation of the Southwell Plot on measured strains. This work is new. The Southwell Plot on deflections has been used previously to confirm calculated values of critical loads of structures, but the equation of any Southwell Plot, and in particular the plot on strains, can be used to take account of imperfections and to relate the performance of the actual structure to the critical load of the perfect structure. The investigation has followed the method of first establishing criteria analytically in the case of a number of simple frames, followed by experimental verification. More complicated frames were then treated. Chapter Four draws attention to the buckling of bolted angle struts as the research project was initiated with this in view. While carrying out preliminary research on the behaviour of angle-section members under simple loading systems, a particularly interesting phenomenon, the bending effect of pure torque, was discovered. The effect has apparently not been previously noticed. The behaviour is reported here, as there is probably a considerable effect on the torsion buckling of angle-section and similar members. (The general analysis of the bending and shortening effect of pure torque has since been carried out, but is not included in this thesis. See Aust. J. Appl. Science, Vol. 11, No. 3 (1960.) The remainder of the chapter contains the results of studies on model structures containing bolted angle members. A method of attack on the problem of obtaining design data is suggested. It is thought that complementary energy methods will furnish the main means of tackling the problems of redundant frames. In view of the importance of energy methods in structural analysis, Chapter Five contains a brief outline of their application. The treatment is rather short and may be considered as a simple introduction to the problems of redundant frames. A pin-jointed redundant frame is solved by complementary energy, the crookedness of members being taken into account. However, any analysis of the behaviour of even the simplest rigid-jointed redundant frames is a problem of considerable complexity, and the determination of its strength is still more difficult. Nevertheless, it is the author's opinion that energy methods of analysis backed by the empirical information obtainable from Southwell Plots on strains will ultimately give a solution.