Abstract
This analytical note shall provide a contribution to the understanding of general principles in the Mechanics of (symmetric circular) masonry arches. Within a mainstream of previous research work by the authors (and competent framing in the dedicated literature), devoted to investigate the classical structural optimization problem leading to the least-thickness condition under self-weight (“Couplet-Heyman problem”), and the relevant characteristics of the purely rotational five-hinge collapse mode, new and complementary information is here analytically derived. Peculiar extremal conditions are explicitly inspected, as those leading to the maximum intrinsic non-dimensional horizontal thrust and to the foremost wide angular inner-hinge position from the crown, both occurring for specific instances of over-complete (horseshoe) arches. The whole is obtained, and confronted, for three typical solution cases, i.e., Heyman, “CCR” and Milankovitch instances, all together, by full closed-form explicit representations, and elucidated by relevant illustrations.
Highlights
The Mechanics of masonry arches constitutes a fascinating theme of research, even in present times, towards the understanding of general and specific functional principles, and resulting features, for this peculiar type of natural and classical form of bearing structures, both from the theoretical and the practical points of view
Several rational studies in “modern” times have considered the investigation of specific critical conditions for the masonry arch, as that leading to the least-thickness form optimization under self-weight, as “recently” codified in the pioneering mechanical works by Jacques Heyman [1,2,3,4,5,6]
CCR and Milankovitch solutions turn out to result very close to each other, for all three basic arch characteristics β, η, h; Heyman solution is still able to locate the main features of the self-standing arch, though fails in predicting the correct position of the inner intrados hinge in the associated purely rotational collapse mode, with an increasing divergence at growing opening angle of the arch
Summary
The Mechanics of masonry arches constitutes a fascinating theme of research, even in present times, towards the understanding of general and specific functional principles, and resulting features, for this peculiar type of natural and classical form of bearing structures, both from the theoretical and the practical points of view. CCR and Milankovitch solutions turn out to result very close to each other, for all three basic arch characteristics β, η, h; Heyman solution is still able to locate the main features of the self-standing arch (and in a much simpler manner), though fails in predicting the correct position of the inner intrados hinge in the associated purely rotational collapse mode, with an increasing divergence at growing opening angle of the arch This becomes much apparent for over-complete (horseshoe) arches, which constitute one rather emblematic arch shape in historic constructions, typically in Moorish architecture, with different forms, like rounded, pointed or lobed (the present work considers just the circular arch shape, with radial joints, in the whole analysis). Conclusions attempt to shortly recapitulate the main achievements of the study, as already above described and outlined, in itemized form, and draw down a few perspectives of possible further research investigation
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