Studies in the statics and dynamics of simple cable systems

Abstract

An investigation is made of the static and dynamic response of simple cable systems to applied load. Both the single, suspended cable and the counterstressed double cable system (the cable truss) are treated. More complicated systems, such as cable nets, are not treated. The geometry of the simple cable systems is such that the c able slopes are, and remain, small. For example, the ratio of sag to span of the suspended cable must be about 1:8, or less. Closed form solutions are given to a variety of cable problems which have important applications in practice. The work is divided into two chapters. In the first chapter solutions are given for the response of a single, suspended cable to static loading, and a comprehensive theory is presented for the free, linear vibrations of the suspended cable. Where necessary, in the static analyses, the solutions are given accurate to the second order of small quantities. The results of simple experiments are reported. The second chapter deals with the cable truss and, again, static analyses are given and a theory is presented for the free, linear vibrations of the cable truss. The possible lateral instability of the cable truss under applied load is investigated. An attempt is made to give static solutions which are of general significance. In the part this has rarely been done. It is shown that a parameter which involves cable elasticity and geometry has a very important bearing on several of the theories presented. The parameter does not appear to have been given before and, for this reason, most previous works are of limited applicability and in some cases they are wrong. For example, the linear in-plane vibrations of these simple cable systems can be analyzed correctly only if this parameter is included. The lateral instability of the cable truss is important, not only because previously it appears that it has been ignored, but also because it opens up a new field of buckling problems which are unlike any others.

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