Finite element thrust line analysis of cracked axisymmetric masonry domes reinforced with tension rings

Masonry domes under self-weight are subjected to hoop tensile forces in their lower portion, which lead to vertical cracks appearing along the dome's meridian planes. Almost always, a close inspection reveals such hoop tension cracks. At the final extent of cracking, the dome stands as a series of arches with a common key stone. Tension rings put around the perimeter close to the base of a dome are commonly used to arrest these cracks. However, the behaviour of domes with tension rings is not well understood. This paper presents an enhancement of the finite element thrust line analysis in order to analyse masonry domes with tension rings. The development of a new element to include the effect of both hoop and meridian tension cracks, utilising orthotropic material properties and a penalty approach, is discussed in detail. The case study for a hemispherical cupola with fibre reinforced polymer (FRP) hoop rings shows that the proposed method can accurately estimate the thrust line of the dome.