
Medieval vault builders explored threedimensional
equilibrium, creating complex shapes carefully balanced in
space. The structural properties of these sophisticated
forms are still poorly understood because of a lack of
appropriate analysis methods, i.e. methods relating
stability and form. Understanding the mechanics of these
vaulted structures leads to new insights for both analysis
and design.
This work presents a new methodology to generate
compressiononly vaulted surfaces and networks. The method
finds possible funicular solutions under gravitational
loading within a defined envelope. Based on projective
geometry, duality theory and linear optimization, it
provides a graphical and intuitive method, adopting the same
advantages as graphical analysis techniques like graphic
statics, but providing a viable extension for these powerful
tools to fully threedimensional problems.
Key elements in the proposed process are (1) force networks,
representing possible flows of forces through the structure;
(2) interactive reciprocal diagrams, visualising the
proportional relationship of all forces in the force network
and providing a high level of control for the user to
understand and manipulate locally and globally the force
distributions within the system; (3) the use of envelopes
defining the solution space; and (4) linear optimization,
resulting in fast computation and visualisation of results.
For the input of the vault geometry and the loading
conditions and for the output of the threedimensional
results, implementations are written for existing
architectural software. This allows for clear visualisations
of the results, and the smooth integration of the
formfinding process in the design or analysis process.
The proposed method is applicable for the analysis of
vaulted historical structures, specifically in unreinforced
masonry, as well as the design of new vaulted structures.
Key words:
Compressiononly structures, Unreinforced masonry vaults,
Funicular analysis, Thrust network analysis, Reciprocal
diagrams, Formfinding, Limit analysis.

