Optimization of shape and arch cross-section for arch bridges

Arches are structural members which have been developed for a very long time in building field. At the beginning, they were designed with limited materials and a conservative criterion, on the safety side, that led to material wasting and to a limited maximum span length range. Over time, the amount of material used to build them has been considerably decreasing because of new structural materials and technologies have emerged such that, nowadays, there is a better and proper use of materials related to their strength allowing a greater maximum span length range. Currently, engineers deal with a vast range of solutions and materials, therefore, they must look for an optimal solution in terms of cost and resistance. The aim of this work is to find the optimal shape and cross-section of an arch, subjected to self-weight and different load conditions, by minimizing the total volume of the arch and satisfying the design requirements. To achieve it, a code written in MATLAB, which numerically solves the differential equation system of the arch, is proposed in which displacements and internal forces can be obtained and thus analyse how stresses change and minimize the arch volume by varying the geometrical parameters.