Parametric design and optimization of arched trusses under vertical and horizontal multi-load cases

CONGIU, ELEONORA

2020-03-06

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Abstract

This dissertation faces the problem of the optimum design of steel truss arches subject to multiple load cases. Arches are one of the most ancient shape-resistant structures, widely used in both civil engineering and architecture. For instance, arches can be considered as purely compressed structures, provided that their “line of thrust” coincides with the centre line of the arch. The “line of thrust” is the locus of the points of application of the thrusts (internal forces or stress resultants) that must be contained within the cross-section of the arch in such a way that the arch transfers loads to the foundations through axial compressive stresses only. As a matter of fact, the more the “line of thrust” differs from the centre line of the arch, the larger the unfavourable bending moments that arise in the arch. This is the reason why it is fundamental to pay close attention to the choice of the shape for an arch in order to minimize (or avoid when it is possible) unfavourable bending effects. Several analytical, graphical and physical methods are provided to find the optimal shape of a monolithic (single rib) arch subjected to a certain load case (i.e. the “funicular curve” for that load). However, if multiple load cases must be considered, it is not possible to find a proper optimal shape for an arch with single rib. In this case, the choice of truss arches with at least two chords becomes indispensable. Indeed, it has been demonstrated that structural optimization of in-plane truss arches with two chords subjected to a single load case leads to optimal solutions in which upper and lower chords tend to coincide with each other and with the “funicular curve” (i.e. the “line of thrust”) for that load. In light of the above, simultaneous shape and size optimization of steel truss arches with two arched chords linked each other through a bracing system (with variable Pratt-type pattern) has been performed for multiple load cases and different structural boundary conditions. Truss arches are effectively used in arch bridges, especially when the arch span exceeds 200 meters (five out of the six steel arch bridges with a span over 500 m are truss arch bridges). For this purpose, a hybrid optimization routine integrating a parametric definition of the design problem, a metaheuristic optimization algorithm and a code for Finite Element Analysis (FEA) has been developed through a MATLAB program. The proposed optimization method allows to simultaneously optimize a larger set of design variables, notwithstanding their large number and various nature (topology, shape and size, as well as continuous and discrete variables, have been concurrently considered). Third-degree Rational Bézier Curves have been chosen to optimize the shape of the arch chords because they can represent a wide family of curves (including conic curves), depending on a small number of parameters. In so doing, in-plane truss arches with different span lengths and structural boundary conditions have been optimized for multiple load cases, only considering vertical loads (acting on the same plane as the arch), since in-plane arches are not suited to withstand out-of-plane loads. On the other hand, spatial arched trusses with two arched chords lying on different planes have been optimally designed for multiple loadings acting in different directions. In particular, a steel arched truss with a lower arched chord variably inclined in the 3D-space and a horizontal upper arched chord linked each other through a bracing system has been designed and optimized for three vertical load cases and a horizontal seismic action parallel to the upper chord plane. Thus, analysing the obtained results, useful suggestions for steel truss arch design have been deduced and presented in this dissertation.