Neste trabalho apresenta-se um estudo do comportamento estrutural de cestas protendidas, tendo em vista a sua utilização em coberturas pênseis de grandes áreas livres. A partir da Técnica do Meio Contínuo obtêm-se as equações que permitem analisar as cestas protendidas quanto a esforços e deslocamentos. Fazem-se considerações sobre o sistema de equações encontrado visando a sua resolução mediante o emprego de programa computacional como instrumento de cálculo. Apresentam-se exemplos numéricos e os resultados são comparados com os obtidos em outros trabalhos. Fazem-se algumas considerações a respeito do projeto e do cálculo de cestas protendidas, além de algumas indicações sobre a continuidade da pesquisa. / This work presents a continuous medium method analysis of cable nets and their applications as suspended roofs for large free spans. lnitially the theory of the method is presented and later applied to get the system of differential equation that represents the problem. Finally this system is numerically solved with computational procedures. Some examples are presented and the results compared with those obtained with others methods and numerical procedures. Some analysis and design considerations and further developments in this subject are also included.

Neste trabalho apresenta-se um estudo do comportamento estrutural de cestas protendidas, tendo em vista a sua utilização em coberturas pênseis de grandes áreas livres. A partir da Técnica do Meio Contínuo obtêm-se as equações que permitem analisar as cestas protendidas quanto a esforços e deslocamentos. Fazem-se considerações sobre o sistema de equações encontrado visando a sua resolução mediante o emprego de programa computacional como instrumento de cálculo. Apresentam-se exemplos numéricos e os resultados são comparados com os obtidos em outros trabalhos. Fazem-se algumas considerações a respeito do projeto e do cálculo de cestas protendidas, além de algumas indicações sobre a continuidade da pesquisa. / This work presents a continuous medium method analysis of cable nets and their applications as suspended roofs for large free spans. lnitially the theory of the method is presented and later applied to get the system of differential equation that represents the problem. Finally this system is numerically solved with computational procedures. Some examples are presented and the results compared with those obtained with others methods and numerical procedures. Some analysis and design considerations and further developments in this subject are also included.

Οι εφελκυόμενες κατασκευές από δίκτυα καλωδίων και μεμβράνες αποτελούν ένα στατικό σύστημα ανάληψης φορτίων που εκτός του ότι πετυχαίνει τη βέλτιστη αξιοποίηση της αντοχής των υλικών δίνει και φορείς μεγάλης δυσκαμψίας λόγω της διπλής καμπυλότητας των επιφανειών τους αλλά και της προέντασής τους από συγκεκριμένα όρια ή σημειακές στηρίξεις. Η εύρεση ισορροπουσών μορφών αυτών των κατασκευών δεν είναι αποτέλεσμα μόνο αρχιτεκτονικής έμπνευσης αλλά γίνεται είτε με τεχνικές φυσικής προσομοίωσης είτε ακριβέστερα με εφαρμογή αριθμητικών μεθόδων βασισμένων σε εξισώσεις ισορροπίας ή κίνησης. Στην εργασία αυτή, γίνεται διεξοδική εξέταση και μαθηματική διατύπωση της μεθόδου πυκνότητας-δύναμης προκειμένου για την εύρεση ισορροπουσών μορφών δικτύων καλωδίων και μεμβρανών ακόμα και για τις περιπτώσεις περιορισμών σχετικά με τη γεωμετρία, την εντατική κατάσταση κλπ.. Γίνεται ακόμη εξέταση των παραμέτρων που επηρεάζουν την ισορροπούσα μορφή όπως, της παραμέτρου πυκνότητας-δύναμης, της αλλαγής της θέσης των οριακών κόμβων, της τοπολογίας δικτύου και άλλων. Τέλος, προτείνεται μία διαδικασία υλοποίησης πραγματικών κατασκευών με καλώδια συγκεκριμένης διατομής και αντοχής ανάλογης με αυτή που προκύπτει από τη μέθοδο πυκνότητας-δύναμης. / Prestressed cable nets and membranes are a static load bearing system which besides achieves the optimal utilization of material strength it also gives forms of high stiffness mainly due to the existence of double curvature surfaces and prestress. Finding forms of these structures is not only a result of architectural inspiration but involves either physical modelling techniques or numerical methods based on equations of static equilibrium or motion. In this study, made a thorough examination and mathematical formulation of the force-density method which results in finding equilibrium forms for both cable nets and membranes even if restrictions regarding the geometry or stress state are included. Several types of these structures are formed in order to understand how parameters such as the force-density parameter, the nodal coordinates of fixed nodes, the network topology etc., affect the equilibrium form. Finally, it is proposed an implementation process for the construction of real structures where it is considered the self-weight of the cable net or membrane in the formfinding process.

Los sistemas flexibles de alta resistencia anclados al terreno son una de las distintas técnicas existentes para la estabilización de taludes, ya sean de roca o de suelos. Están constituidos por una membrana (red de cables o malla de alambre) sujeta al terreno mediante placas de anclaje, cables de refuerzo y bulones. En la mayor parte de los modelos de cálculo existentes se supone un comportamiento activo del sistema, es decir, que evita que se produzcan deslizamientos a través de una supuesta pretensión del sistema y convexidad del terreno. El sistema ejercería una presión normal al terreno que incrementa la tensión tangencial en la superficie potencial de deslizamiento evitando que se alcance la rotura del terreno. En esta tesis se han medido las fuerzas en distintos componentes del sistema desde el momento de la instalación, y se ha comprobado que la pretensión es muy reducida. Por otro lado, la supuesta convexidad del terreno raramente tiene lugar. Todo esto conduce a demostrar la hipótesis de comportamiento pasivo del sistema, es decir, que éste contiene a la masa inestable una vez que se ha producido la rotura. Es por ello que se ha considerado el desarrollar un nueva metodología de cálculo basada en un comportamiento pasivo. La nueva metodología consiste en realizar una simulación numérica dinámica en 2D de la interacción sistema flexible - masa inestable – talud estable. Partiendo de las dimensiones de un círculo de rotura en suelos o una cuña en roca, se deja caer la masa inestable con la fuerza de la gravedad. En su caída, la masa inestable deformará a la membrana, cables de refuerzo y bulones desarrollándose en ellos tensiones que deberán considerarse para su correcto dimensionamiento. En el caso particular de los taludes de suelos, se ha recurrido a la modelización de la masa inestable mediante la discretización por puntos SPH (Smooth Particle Hydrodynamics). / Highly resistant flexible systems anchored to the ground are among the techniques for slope stabilisation, either soil or rock. The system is formed by a membrane (cable net or wire mesh) tightened to the ground through spike plates, reinforcement cables and bolts. In the majority of the existing design models, an active behaviour of the system is considered; which means, that it is able to avoid ground sliding through a pretension of the system and the convexity of the slope surface. The system would exert a normal pressure over the ground that increases the shear stress in the potential slip surface avoiding that failure takes place. In this thesis, forces on different system components have been measured, finding that the pretension force is very low. On the other hand, the supposed ground convexity rarely exists. All this demonstrates that actual system behaviour is passive; which means that it is able to contain the unstable mass once the failure has already occurred. Therefore, a new design methodology based on a passive behaviour has been developed. The new methodology consists in performing a dynamic numerical simulation in 2D of the interaction flexible system – unstable mass – stable slope. Starting from specific known dimensions of slip circle in soils or a wedge in rocks, unstable mass falls only under the action of gravity. During its falling, the unstable mass deforms the membrane, reinforcement cables and bolts. Maximum stresses developed in these components should be considered for their design. In the particular case of soil slopes, unstable mass has been discretised with the mesh free method SPH (Smooth Particle Hydrodynamics).