Limit Analysis of Cable-Tied Structures

Cables are frequently used to strengthen existing framed structures. They are also the main members that support bridge-decks in cable-stayed bridges. This type of structures may be idealised to consist of beam-type members under pure bending and cabled members under pure tension. In order to get an estimate of the strength of such structures a step by step elasto-plastic analysis must be used. This procedure, however, is time-consuming as it has to follow every single plasticization and any deplasticization that may occur up to collapse. Limit analyses, based on the upper or lower bound theorems of plasticity provide a better alternative.

In the present work, a limit analysis procedure, based on the upper bound theorem and leading to a linear programming problem, is followed. Plastic rotation in the form of a plastic hinge at the end of a beam-type member marks the plasticization of the corresponding section when its ultimate moment is exceeded, whereas a plastic extension occurs at one point inside the cabled member when its ultimate axial force is exceeded. The whole approach is formulated within the mesh description of statics which is a generalisation of the force method. This method is known to be the computationally most effective one for linear programming structural problems. The process consists of three distinct parts. The first part deals exclusively with the cabled members of the structure. The influence of their force on the rest of the structure is taken into account by satisfying equilibrium along the shortest path between its two ends. In the second part the indeterminacy of the rest of the structure that now consists of beam-type members is catered for using an existing algorithm, also based on a shortest path technique between two points of a connected planar graph. Cantilevers that follow the shortest path of each load to the ground are used in the third part to satisfy equilibrium with the applied loads. The whole process renders a fully automatic and computationally efficient numerical method to find the limit load of the above-mentioned structures. Two examples of strengthened frames, as well as an example of a cable-stayed bridge are analysed.