A study of the bifurcation behavior of a shallow framework

The concepts related to the understanding of nonlinear bifurcation theory have been presented and examples have been worked which show the effect of imperfections on various types of structures. The effect of these imperfections is related to whether the structure exhibits asymmetric, symmetric stable, or symmetric unstable behavior.;An experimental study as well as an analytical study of a simple, four member shallow framework has been performed to observe the effect of imperfections on its behavior. From both studies, it was observed that imperfections do play an important part in influencing the behavior. The effect of member imperfections was to substantially increase the deflections occurring at the center node of the structure. At a load level equivalent to the maximum stable load for the perfect structure, the imperfect structure, while not collapsing, experienced a maximum deflection amplification factor of four. At this load level, the accompanying stresses for the pin-jointed structure were found to be exceeding the elastic limit of the material. If a structure is to be designed for this range of loads, then only a fully nonlinear analysis will be able to predict the load capacity of the structure.;The analytical studies proved to be time consuming because of the nonlinear nature of the structure behavior. In designing these types of structures, consideration must be made as to how important/unimportant a nonlinear analysis of the structure is. For shallow structures which carry most of their load by axial compression, and when these loads are present combined with flexure, the nonlinear effects are important and should be considered.;In general, the behavior of space frames and trusses that exhibit nonlinear behavior is difficult to characterize. Their behavior not only depends on the structure configuration, but on the types and sequence of loading expected during the structure life. The present study has only studied the effects of imperfections and varying the span to rise ratio in conjunction with a central, concentrated load on a very elementary structure.;Further studies need to be made to assess the effects of these same parameters on a more realistic structure, under the influence of both symmetrically and unsymmetrically applied concentrated and distributed member loads, which in real life result from distributed dead and live loads, and from wind loads.