Abstract
The arches were a great advance in construction with respect to the rigid Greek linteled architecture. Its development came from the hand of the great Roman constructions, especially with the semicircular arch. In successive historical periods, different types of arches have been emerging, which in addition to their structural function was taking aesthetic characteristics that are used today to define the architectural style. When, in the construction of a bow, the rise is less than half the springing line, the semicircular arch is no longer used and the segmental arch is used, and then on to another more efficient and aesthetic arch, the basket-handle arch. This study examines the classic geometry of the basket-handle arch also called the three-centered arch. A solution is proposed from a constructive and aesthetic point of view, and this is approached both geometrically and analytically, where the relationship between the radius of the central arch and the radius of the lateral arch is minimized. The solution achieved allows the maximum springing line or clear span to be saved with the minimum rise that preserves the aesthetic point of view, since the horizontal thrust of a bow is greater than the relationship between the springing line of the arch and the rise. This solution has been programmed and the resulting software has made it possible to analyse existing arches in historic buildings or constructions to check if their solutions were close or not from both points of view. Thus, it has been possible to verify that in most of the existing arches analyzed, the proposed solution is reached.
Highlights
The arch is a constructive and structural element whose origin must be sought in the Chaldean architecture of the third millennium BC [1]
The geometry that is known in classical literature and from the constructive point of view, as a structural element
The main effort to be considered is the horizontal thrust of the arch, which can be greater, the greater the relationship between the clear span or the springing line of the arch and the rise
Summary
The arch is a constructive and structural element whose origin must be sought in the Chaldean architecture of the third millennium BC [1]. The variants of the semicircular arch, used by the Romans, are the stilted arch, whose rise is greater than the half of the clear span; and the segmental arch, which differs from the semicircular arch in Symmetry 2019, 11, 1243; doi:10.3390/sym11101243 www.mdpi.com/journal/symmetry lost importance in the Gothic, which gave way to the three-pointed arch, Figure 1E, with its different variants, as an acute arch, Figure 1G, or the depressed arch, Figure 1H [5]. At the end of the Gothic, a new arch spread with force until well into the Renaissance and even in the Baroque: The basket-handle arch [6], Figure 1D. The basket-handle arch is a symmetrical arch composed of a succession of circumferential arches tangent to each other and with the supports, see Figure 2A
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