Flexible bridge decks suspended by cable nets. A constrained form finding approach

The initial geometry of structures made of cables is steered by the cable tensioning forces. In a cable net the geometrical shape and the internal force distribution cannot be dealt as separate issues: the set of geometries defines also the feasible sets of the internal forces. During the last decades, many different approaches have been proposed to deal with the form finding of cable structures. The most efficient one is the so called Force Density Method (FDM), proposed by Schek, which allows to conforming cable nets for structural applications without requiring any further assumption, neither on the geometry, nor on the material properties. An Extension of the Force Density Method, the EFDM, makes it possible to set conditions in terms of fixed nodal reactions or, in other words, to fix the position of a certain number of nodes and, at the same time, to impose the intensity of the reaction forces. Through such an extension the EFDM enables us to deal with form finding problems of cable nets subjected to given constraints and in particular to treat mixed structures, made of cables and struts. In this paper we consider cable nets interacting with members having flexural behaviour. For a given cable assembly and for a given loading condition, aim of this work is to find that particular pretensioning system which replaces both the static and the kinematic functions of the inner reactions of a flexural elastic continuous beam. It is, for instance, the case of the bridge decks suspended by cables, shaped in various forms. The specialization of the EFDM to this type of problem is presented and a progressive set of examples shows the efficiency and the versatility of this approach in contributing to the design of new creative forms

A parametric subdomain discretization for the analysis of the multiaxial response of reinforced concrete sections

The paper presents an improved sectional discretization method for evaluating the response of reinforced concrete sections. The section is subdivided into parametric subdomains that allow the modelization of any complex geometry while taking advantage of the Gauss quadrature techniques. In particular, curved boundaries are dealt with two nested parametric transformations, reducing the modeling approximation. It is shown how the so-called fiber approach is simply a particular case of the present more general method. Many benchmarks are presented in order to assess the accuracy of the results. The influence of the discretization into subdomains and of the quadrature rules, chosen for integration, is discussed. The numerical tests highlight also the effects of spurious stress distributions in the tensile concrete zone, due the interpolation functions adopted for the Gauss integration. It is shown how balancing the number of subdomains and the number of sampling points such spurious effects vanish. The method shows to be accurate, very flexible in the discretization process and robust in analyzing any sectional state. Moreover, it converges faster than the fiber method, reducing the computational demand. All these properties are of great importance when the computations are iteratively repeated, as for the case of the sectional analysis within a computational procedure for a R.C. frame analysis

A collapse induced by shortening in a multispan viaduct

This paper presents the case of a recent collapse occurred at an intermediate pier of a long tied- deck-slab viaduct. The paper retraces the origins of this collapse and studies, in particular, the singular breakage that happened in the diffusion zone of the bearing supports

The role of prestress and its optimization in cable domes design.

For their lightweight, versatile forms and architectural impact, cable-strut structural systems have been widely used as large span roofs of arenas, stadiums and open squares. In this paper, the matrix theory for pin-jointed trusses is firstly recalled. Then, through an elementary cable dome, the role of prestress is outlined and commented. Finally, a special optimization procedure, based on genetic algorithms, allows a thorough comparison between classical structural schemes, whose bearing capacity is due to the mechanical stiffness, and prestressed structures, whose bearing capacity is also due to the geometrical stiffness provided by the prestress

Prestress optimization of hybrid tensile structures.

Cable structures differ from the conventional ones for their lightness and for the versatility of their shapes. As they work only by axial tensile forces, the structural geometry and the pretensioning intensity applied to the cables are closely related. In this paper, a matrix theory suitable for the analysis of a spatial pinjointed structure is recalled and the role of the cable prestress and the optimization of the prestress distribution and of the prestress intensity is studied. In a second part of the paper an optimization procedure, based on a genetic algorithm, is presented. Such a procedure allows searching a solution at the same time of minimum weight and respecting given technological constraints, as shown trough a final example

Time dependent behaviour of an elementary bridge model in presence of uncertainties

During the last decades the excessive deflections of many long span bridges received wide attention both in the research and maintenance fields. The faults of the original previsions can be attributed to (a) lacks in the models adopted for the structural assessment, (b) weak reliability of some shrinkage and creep formulations used for the analyses and (c) differences between the phases of the actual erection techniques and those planned during the design tasks. In this paper the role of the uncertainty affecting quantities and parameters governing the whole attitude of these structures is outlined. With reference to simple but significant examples, it will be shown how some types of bridges possess low sensitivity to the uncertainties, while others result greatly affected by them, exhibiting divergent behaviors over time

Nondeterministic time dependent mechanics of elementary prestressed and cable stayed concrete bridges models

The time dependent behaviour of two elementary structures, one made of a concrete cantilever beam, suspended at the tip by a pretensioned stay, and the other made of a concrete cantilever beam, post-tensioned through a horizontal cable, has been studied. After a short recall, which would outline how a suitable stay pretensioning or a suitable cable post tensioning, may balance the deflections due to selfweight only under elastic hypotheses, the effects of creep on the tip vertical displacement and on the tension in stay are studied. The influence on such effects, due to different stay slopes, is discussed. As well known, the data needed for these analyses involve many uncertain quantities. Thus, in a second part of the paper, through a probabilistic approach, the effects due to large variations of the tension in the cable are studied. On the basis of the achieved results, we can distinguish between two different kinds of structures: those which have a low sensitivity and those which are greatly affected both by creep effects and by uncertainties