Reformulation and extension of the thrust network analysis. (1st April 2017) - Marmo, Francesco; Rosati, Luciano
Highlights: Comprehensively description of the procedure for the analysing of thrust networks with free edges and holes. Extension of the method to the cases of networks subject to the combined action of vertical and horizontal loads so as to include seismic actions. Reformulation of the method to enhance computational performances: efficient branch assemblage, flexible node numbering, reduction of the number of conditions involved in the optimization process. Analysis of real vaults subjected to combined vertical and horizontal loads, modeled by network with complex geometry and high number of free edges. Abstract: We address the Thrust Network Analysis (TNA), i.e. the methodology for modeling masonry vaults as a discrete network of forces in equilibrium with gravitational loads, first contributed by O'Dwyer and fully developed by Block and coworkers. Reducing the bias by the quoted authors in favor of a graphical interpretation of the method, we reformulate the original version of the TNA by discarding the dual grid and focusing only on the primal grid, thus significantly enhancing the computational performances. The proposed reformulation of the TNA is also extended by including horizontal forces in the analysis as well as holes or free edges in the vault. Furthermore, the coefficient matrices entering the solution scheme are obtained by assembling the separate contribution of each branch, thus avoiding the ad hoc node numbering and branch orientation required by alternative implementations. Numerical examples, some of which referred to vaults having a particularly complex geometry, show the effectiveness and robustness of the proposed approach in assessing the safety conditions of existing masonry vaults or in designing new ones.