Numerical and dimensionless analytical solutions for circular arch optimization

In the design of arched structures, the pre-design phase assumes a crucial and even more evident importance. Once the requirements of the project are determined, via the programming process, the design phase begins. The selection of the most suitable shape appeared to be more and more crucial and represent the pre-sizing of the structure. Preliminary evaluation of the design program, schedule and construction budget needs to restrict the type and the characteristics of the structural shape of the arch that will be used. The aim of the present paper is to propose, firstly, a fast numerical resolution method to optimize the circular shapes via the selection of the best lowering degree and cross-sections for the arch, minimizing the total volume of the structure. To this purpose, a self-made code is proposed, able to solve, numerically, the ODE (ordinary differential equation) of the arch. The results, changing the spans, the shallowness ratio and the cross-section of the arches are considered in order to obtain the minimum employed volume and can be used as a first approximation in the design process. Furthermore, an analytical closed form solution is proposed by a dimensionless approach to identify the maximum stress behavior in the arches by a dimensionless parameter (eta). Also in this case the proposed method is able to offer a valid way to evaluate different arch configurations, and can be used in the pre-design phases (conceptual design) for circular and segmental arches covering different spans.