Modelling masonry spires : An investigation

Abstract: Masonry spires are a typical part of church architecture. Since it is rare that masonry is used as a load-bearing material in the western world today, it is important to maintain and increase the knowledge of modelling masonry structures both from a maintenance point of view and to build new masonry structures. The purpose of this master thesis is to look at and evaluate some different methods to model masonry spires exposed to common loads such as gravity, settlement and wind. The spire of the Salisbury Cathedral is used as a template regarding geometry and mechanical properties for the modelling methods. Two modelling methods are used in the master’s thesis. The first one is the limit analysis method applied to masonry. It is used to calculate a critical thickness for the masonry of the spire for a severe wind load. The second method is the Finite Element Method (FEM). The commercial finite element software Abaqus is used to create the model and the discretization used with the FE modelling is the macro-modelling approach. Concrete Damage Plasticity (CDP) in Abaqus is used as the material model and adapted to masonry. The finite element model consists of the spire itself along with the supporting structure beneath it down to the piers. Four different simulations (jobs) are run with varying wind direction and two of them have settling piers. The results from the finite element simulations indicate that the membrane stresses in the spire faces for the various jobs were not significantly different from one another. One of the jobs with settling piers could not be completed because the tensile stresses in the arches reached the tensile strength capacity of the material. The other simulation with a settlement that did complete did not have any significant difference in stress compared with the simulations without settlements. While the arches and the piers underwent plastic straining the spire itself did not. The stress levels there remained in the linear range for all the completed simulations. The finite element results also agree with the limit analysis. These findings call into question some of the modelling choices. The inclusion of the structure beneath the spire in the finite element model, as a way to study the effect of settlements, did not give more insight into the spire’s behaviour. Furthermore, the method to implement settlements was too inaccurate and another approach should be used to study the effect of settlements on the state of spires. Further work needs to be done on that topic. Improvements can also be made regarding how CDP was adapted for masonry.