Stress-strain state of stone cross vaults

Abstract

Introduction. The calculation of stone vaults in historical buildings employs an approach in which vaults are treated as elements “assembled” from three-hinged, two-hinged, and hingeless arches, with the determination of forces being carried out according to general rules of structural mechanics. However, the capabilities of such an approach to analyze spatially working structures (cross vaults) made of materials exhibiting strength anisotropy (masonry) are extremely limited.

Aim. To establish the regularies in the formation of the stress-strain state parameters of a stone cross vault under uniformly distributed loads, as well as the influence of the strength anisotropy of masonry on the strength of the vault.

Materials and methods. The analysis of the stress-strain state of the stone cross vault was performed using a high-level finite element modeling software in a solid spatial homogeneous formulation. The study assessedthe impact of the strength anisotropy of masonry and the non-uniaxiality of the stress state in specific areas  of the vault on its overall strength.

Results. The most unfavorable stress state was found to occur in the central area of the cross vault beneath the axes of the formwork, where biaxial tension of equal intensity is formed, characterized by extremely low resistance. The stress-strain state is dependent on the ratio of rise f to span L (f/L). The strength of the stone cross vault was revealed to depend, among other things, on the orientation of forces relative to mortar joints in the masonry; significant non-uniaxiality of forces is observed in specific areas.

Conclusions. The most significant factor affecting the formation of the stress-strain state in a stone cross vault, in addition to its span and thickness, is the ratio of rise f to span L (f/L). Strength analysis of cross vaults should consider the orientation of forces relative to mortar joints while accounting for the non-uniaxiality of forces in specific areas.