Preliminary Design and Parametric Study of Minimum-Weight Steel Tied-Arch Bridges Obtained According to a Maximum Allowable Deflection Criterion

In this paper, we present a novel iterative method that minimizes the weight of an all-steel arch bridge during the in-plane preliminary design stage. The behavior of the bridge is assumed to be contained within the plane of the arch. The preliminary design is assumed to be governed by the maximum allowable static deflection at a given checkpoint at the deck under a simplified load combination selected by the designer. The designer can select variables commonly used in preliminary design, such as the web slenderness of the cross-sections of both the arch and the deck and their relative flexural stiffness levels. Moreover, the general method is particularized for tied-arch bridges with vertical hangers: its iterative flowchart is adapted, an approximate analytical formulation that allows manual calculations is provided, and a parametric study that illustrates the effect of the main variables on the weight of the bridge is carried out. The main design recommendations drawn from this research for minimizing the weight of a bridge are as follows: a rise/span ratio between 1/5 and 1/7; cross-sections with significantly different stiffnesses in the arch and deck, ideally with highly flexible arches; and cross-sections with the thinnest possible webs.