Two-step matrix analysis of prestressed cable nets

Abstract

We consider the behaviour of the cable-net shown in Fig l when arbitrary vertical forces are applied to the nodes. According to linear-algebraic analysis this net has l state of self-stress and 12 modes of inextensional deformation. We show that the applied loading may be de-composed into two parts. The first part does not excite any of the inextensional modes, while the second part is carried by the net through geometry changes associated with these inexten-sional modes. The response of the net is linear to each of these separate parts of the loading, and the analysis is done by means of 2ox2o square matrices of full rank. We compute displace-ments for three different loading cases. We discuss, briefly, interactive effects between the two types of behaviour, and non-linearities due to stretching of the cables during 'large' deflection of the 'inextensional ' modes; and we show that both of these refinements can be accommodated by means of rapidly converging iterative calculations. I