introduction  abstract  examples  papers  links

The work presented on this web page is part of Philippe Block 's PhD research in Building Technology at the Massachusetts Institute of Technology under supervision of Prof. John Ochsendorf.

  ABSTRACT                                                                                                                                                                                                    5 top

Medieval vault builders explored three-dimensional 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 compression-only 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 three-dimensional 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 three-dimensional results, implementations are written for existing architectural software. This allows for clear visualisations of the results, and the smooth integration of the form-finding 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:  Compression-only structures, Unreinforced masonry vaults, Funicular analysis, Thrust network analysis, Reciprocal diagrams, Form-finding, Limit analysis.

  EXAMPLES                                                                                                                                                                                                  5 top

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. The following  examples show some of the different applications of the thrust network method. This is a work in progress and we hope to expand this list of case studies later...

Pseudo 3-d analysis of a groin vault

The pseudo 3-d analysis assumes that the loads are brought down via a parallel series of independent arches abutting on cross ribs. The ribs then bring down the forces to the corner supports. Very easily and quickly, the thrust network method can be applied to find the range of horizontal thrust values at these corner supports.

3-d analysis of a groin vault

Fully three-dimensional equilibrium shape...

Dome analysis 

This analysis uses a Nervi-like force pattern. The force diagram produced from this radiating force pattern is quite interesting.

Design examples? 

This series shows different possible compression-only equilibrium shapes, starting from a regular orthogonal grid resulting in a simple pillow shape and slowly adding complexity. For every example, the relationship between the geometry of the force patterns and the internal forces in the system (represented in the reciprocal diagram) are visualized graphically.

  PAPERS                                                                                                                                                                                                         5 top

   updated last: 06-05-07