Patterns of force:length ratios for the design of compression structures with inner ribs

Domes and vaults, with or without inner ribs, can be modelled as pin-jointed networks with all their members in compression. The Force Density Method is one of the most widely used form-finding methods for the computation of the equilibrium shape of pin-jointed networks. Mapping in topology, in contrast with other mapping methods, does not need an initial estimate of the equilibrium position as part of the solution process. Patterns of force:length ratios are proposed in the present work with the aim of designing compression structures with inner ribs. These patterns are based on the assignment of a higher value of force:length ratio to certain groups of members (rib lines) in order to obtain ribs in the final shape. In this paper a complete procedure for the design of vaults with inner ribs is proposed. Finally two examples inspired by two vaults of the Cathedral of Granada (Spain) are shown using the proposed procedure.