Cracking of masonry arches with great deformations: a new equilibrium approach

Masonry arches crack inexorably after decentering.This phenomenon is well known to any master builder.For small deformations these cracks do not affect the safety of the arch.Indeed, the arch with time may show different patterns of cracking, which lead to different sets of internal forces.Within the frame of modern limit analysis, developed for masonry structures, mainly by Professor Heyman since the 1960s, we know that cracking is irrelevant to safety: indeed, it is the capacity of forming cracks which gives "plasticity" to masonry.Small deformations do not distort the overall form of the arch.A direct corollary of the safe theorem states that if it is possible to draw a line of thrust within the arch, the arch will not collapse, and it is safe.This is independent of the "actual" state of the arch, manifested by a certain pattern of cracks.This pattern will change with very small (unpredictable) variations in the boundary conditions; a tiny spreading of the abutments will produce a complete change.However, when the deformations are large, the geometry of the arch is severely distorted and we cannot study the stability with the original geometry: it is necessary to proceed step by step, considering the deformed geometry.This phenomenon has been rarely studied.However, even these studies consider, as a simplification, that the crack patterns do not vary and the movement is studied under this assumption.That this is not the case can be seen with tests with small models of arches: the position of cracks can be altered, and this may influence the validity of the study.The present contribution proposes a method of analysis which permits us to study the history of cracking until collapse.This has not only theoretical interest; it may be used in the analysis of some critical cases which occur in practice.