Empirical methods for the proportioning of masonry arches

"The determination of the thickness at the springing and at the crown in masonry arches, together with the dimensions of abutments, have been determined in the past centuries by means of empirical methods. The most usual method of verifying the adequacy of an arch proportioned according to these empirical method has been made in the 19th century by means of the static procedures at that time consolidated and based on the line of thrust position.. Recent research have pointed out the strong link existing among modern formulation and pre-elastic theories, laying stress on the fact that “the statics of the arch finally escaped from the labyrinth of empirical methods and theoretical conjectures”. Nevertheless the empirical formulas are the only reference on which the major part of masonry arch bridges actually in service were designed.. The most used empirical formulae in general give the crown thickness as a function of the span or the rise. The analytical structure ranges from the simple linear relation proposed by Leon Battista Alberti to the complex one given by Baker. . This paper presents a reasoned catalogue of empirical formulas reported in the treatises from Renaissance to the first decades of 20th century, together with an evaluation of their reliability by means of modern calculations."