Abstract
In most masonry arches stresses are very low and, therefore, collapse does not occur because of material failure. As a consequence, the safety of arches should not be assessed by means of a safety factor based on material strength as for conventional structures. In 1969 Heyman was the first to state that the safety of masonry arches relies on their geometry and proposed a method for computing the so-called “geometrical factor of safety” based on the comparison between the shape of the thrust line and the profile of the arch. In this context, we have recently developed a method capable of computing the line of thrust closest to the geometrical axis and defining a safety factor based on the comparison between such a line of thrust and the profile of the arch, which we have denoted as “performance factor”. In this paper, that supplements the author ref. (Tempesta and Galassi, 2019 [41]), the Matlab code of our method is provided for unlimited and unrestricted use by researchers as well as academics for educational purposes.•The method (denoted as FRS Method) is inspired by the method proposed by Heyman in 1969•Unlike the original iterative method, the FRS Method computes the line of thrust using a one-step procedure, which is less time consuming and provides the exact solution•The original geometrical factor of safety is replaced by a performance factor, that characterizes the range of the equilibrium thrust lines within the profile of the arch effectively and the safety factor in a targeted way
Highlights
We have recently developed a method capable of computing the line of thrust closest to the geometrical axis and defining a safety factor based on the comparison between such a line of thrust and the profile of the arch, which we have denoted as “performance factor”
Heyman [1] proposed an iterative method for computing the line of thrust closest to the geometrical axis and pointed a factor for assessing the safety, which relied exclusively on geometrical considerations
As the objective of the analysis is the detection of the line of thrust closest to the geometrical axis of the arch, in order to compute the value of the three unknown parameters the function S, which expresses the square of the distances between the vertices of the line of thrust and the centroids of the elements, is minimized (Eq (5)): S 1⁄4 ðfR1g Á K þ fR2g Á Y0 þ fR3g Á Ynþ1 À fYGgÞ2
Summary
We have recently developed a method capable of computing the line of thrust closest to the geometrical axis and defining a safety factor based on the comparison between such a line of thrust and the profile of the arch, which we have denoted as “performance factor”. Heyman [1] proposed an iterative method for computing the line of thrust closest to the geometrical axis and pointed a factor for assessing the safety, which relied exclusively on geometrical considerations.
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