Suspension bridge analysis using lagrangian approach

A general analysis of the static and dynamic responses of suspension bridges in presented. The Cullmann ‘elastic weight’ theory is revisited, and it is shown to be a powerful discretization tool. According to this method, the structure is reduced to a system of lumped masses and elastic springs, so that it can be considered as a classic holonomic system of rigid elements (Lagrange system). The elasticity is reduced to reactive conservative forces in the springs, and the second-order components of the potential energy of the applied forces can be detected by means of the work of these reactive forces. This is an advantage, at least from the theoretical point of view, over any finite element method. Another advantage is the substantial diminishing of the redundants, which allowed us to use a portable personal computer. Finally, this discretization method is quite general, but it seems particularly suitable for suspension bridges, in which the springs are only on the bridge, and must be considered as simple bending cells.Some numerical results are shown, in which we examine one of the possible suspension bridges which is to be built on the Straits of Messina.