Abstract:
An investigation is made of the static and dynamic response of simple suspended cable systems to applied load. Both the single suspended cable and certain two dimensional cable networks are treated. Analytical solutions in dimensionless forms are given to a variety of cable problems which have important practical applications. The work is divided into five essentially self-contained chapters. Each chapter has its own introduction. Apart from the first chapter, which is more general, the other four chapters apply only to relatively flat-sag systems. In these cases, which are of most practical importance, a characteristic parameter arises that accounts for profile geometry and elasticity. The value of the parameter can range by several orders of magnitude and the nature of the response is accordingly dictated by it. Chapter 1 treats the static response of a single elastic cable which is suspended between two points that are not necessarily at the same level. The cable is loaded by its self-weight and any number of concentrated vertical loads which may be arbitrarily placed along its length. A Lagrangian approach is used to obtain the solutions for the strained cable profile; the tension and displacements are given as functions of a single Lagrangian co-ordinate. This is an exact solution to a classical problem and consistent with this a more formal approach is made. From the general solution results are extracted for the particular cases of the cable under self-weight alone (i.e., the elastic catenary) and the cable under self-weight and a single concentrated load. These particular solutions are used to make a comparison with the results of simple experiments on a cable of deep profile. Chapter 2 contains an investigation of the post-elastic response of a flat-sag suspended cable; the particular cases considered being the response to a point load and the response to a uniformly distributed load. The problem is completely non-linear because, in addition to the geometric non-linearities which are a feature of the static response of flat-sag suspended cable systems, material property non-linearities are also present. By treating the additional tension as the independent variable, rather than the applied load, the actual stress-strain properties of the cable material may be used directly. Simple, yet accurate, solutions for the load and corresponding deflection are then found for the two limits of interest, namely, the elastic limit and the ultimate condition. The effect of unloading after a post-elastic excursion is also investigated and examples are given that illustrate the often substantial reserve strength capacity inherent in such systems. Chapter 3 is concerned with the linearised, undamped, dynamic response of a flat-sag suspended cable to earthquake-like excitation. The ends of the cable are connected to a rigid foundation which is excited sinusoidally in the plane of the cable. For this symmetric excitation wave-type, modal and steady-state solutions are presented to explore the influence which the characteristic geometric and elastic parameter has on the generation of additional tension and deflection in the cable. In particular the asymptotic properties of the wave-type solution are emphasised and tables are presented for the natural frequencies of the symmetric in-plane modes of vibration and for participation factors for additional tension and deflection, all as functions of wide ranges of the characteristic parameter. Chapters 4 and 5 contain static and dynamic analyses of simple, uniform, pretensioned cable networks. In both cases the actual discrete network is replaced by an equivalent membrane and by suitable rearrangements of these governing membrane equations solutions may be had. In Chapter 4 the membranes are considered to be initially taut and flat and the static response to uniformly distributed applied load is sought. Solutions are given for the rectangular membrane, a hyperbolic paraboloidal membrane (assumed straight along generators initially), the equilateral triangular membrane and the elliptical membrane. A discussion is given of the onset of geometric non-linear behaviour and of the characteristic parameters on which dynamic similitude depends. Particular attention is paid to the generation of additional tension in the membranes and a comparison is made between the theory and some experimental results for the case of a square network. In the final chapter a linear theory is developed for free vibrations about an equilibrium position in which the membrane supports a uniformly distributed applied load - that is, some sag is present in the static profile. A detailed examination is made of the circular membrane and the rectangular membrane, particular attention being paid to the influence that the characteristic geometric and elastic parameter has on the symmetric modes of vibration. Following the summary and conclusions five appendices are included, one for each chapter, that supplement the results given in the main body of the thesis.