Safe Estimation of Minimum Thickness of Circular Masonry Arches Considering Stereotomy and Different Rotational Failure Modes

Limit state analysis of masonry arches sets to assess the safety of the structure by determining the minimum thickness that just contains a thrust line. Based on the Heymanian assumptions regarding material qualities and the equilibrium approach to the static theorem it has been explicitly proven for semi-circular arches that both the thrust line and the resulting minimum thickness value is subject to stereotomy (brick or stone laying pattern), while present study demonstrates, that the latter statement holds for pointed-circular arches as well. This is not straightforward, since the number- and arrangement of the hinges at limit state vary subject to the geometry in case of pointedcircular arches, resulting a more complex problem. It is also explicitly shown, that stereotomy might also affect the corresponding (rotational) failure mode (for certain arch geometries). Stereotomy of an existing structure is not always known, hence it is relevant to search for a stereotomy related bounding value of minimum thickness for each of the various failure modes. The potential of the envelope of resultants as a thrust line (resulting from vertical stereotomy) leading to bounding value minimum thicknesses is discussed: as shown elsewhere it bounds the family of thrust lines, hence leads to an upper bound value of minimum thickness in case of semi-circular arches. It is demonstrated however, that this cannot be generalized for other rotational failure modes which occur for circular-pointed arches. The envelope of resultants does not necessarily lead to a bounding value of minimum thickness, and even if it does, it can be either an upper or a lower bound. However, it is found that the range of minimum thickness values is bounded in all possible failure mode types. The necessary conditions are provided for each

General Thrust Surface of the Masonry Domes

Masonry domes are shell-like structures with a no-tension type material behavior [1]. The dome geometry, material behavior and the type of the loading define how the dome balances the load. It is known and proved that the dome could balance the load only by forces, without bending moment but cracks may appear since the material does not resist tension. The surface where the balancing forces are acting is called the thrust surface. The paper introduces the idea of the general thrust surface. It is such a balancing surface where the forces are not acting in the tangent plane of the thrust surface and otherwise it is moment free. A method is shown how to find the general thrust surface for a cracked spherical masonry dome. Numerical example illustrates the usefulness and effectiveness of the proposed method to determine the general thrust surface of a spherical dome when radial stereotomy is considered. By the help of the proposed model the safety of the more than 350 years old, cracked dome of Gol Gumbaz, India can be proofed