This dissertation presents Thrust Network Analysis,
a new methodology for generating compression-only vaulted surfaces
and networks. The method finds possible funicular solutions under
gravitational loading within a defined envelope. Using projective
geometry, duality theory and linear optimization, it provides a
graphical and intuitive method, adopting the same advantages of
techniques such as graphic statics, but offering a viable extension
to fully three-dimensional problems. 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. This dissertation introduces the method and
shows examples of applications in both fields. Thrust Network
Analysis, masonry, historic structures, compression-only
structures, limit analysis, equilibrium analysis, funicular design,
form-finding, structural optimization, Gothic vaults, reciprocal
diagrams.

Thrust Network Analysis : exploring three-dimensional equilibrium

https://www.fernandofraternaliresearch.com/publications/mrc_2010.pdf

A thrust network approach to the equilibrium problem of unreinforced masonry vaults via polyhedral stress functions

Traditional unreinforced masonry architecture has disappeared from new building activity in the western world. Nevertheless, the architectural heritage of masonry must be preserved, and this involves structural analysis. The classical theory of structures does not apply well to such heterogeneous structures with unknown boundary conditions. Nevertheless, there exists a theory of masonry structures based in simple assumptions about the material: good compressive strength, almost no tensile strength and a constructive care to avoid sliding failure. The theory was born at the end of the 17th Century, developed during the 18th and was applied in the 19th Century. It was abandoned and eventually forgotten at the beginning of the 20th Century. After half a century, in the 1960s, Heyman incorporated the old theory within the frame of modern limit analysis with its implicit treasure of critical observation and experience. The safe theorem permits using equilibrium equations and simple material statements...

/pdf/the-analysis-of-masonry-architecture-a-historical-approach-qdw9dawvup.pdf

The Analysis of Masonry Architecture: A Historical Approach

The optimum geometry design of geodesic domes presents difficulty due to the fact that the height of the dome keeps on changing during the design process. This in turn makes it necessary to automate the computation of the coordinates of joints in the dome when the height of crown changes. The algorithm presented in this study carries out the optimum geometry design of single layer geodesic domes. It treats the height of the crown as design variable in addition to the cross-sectional designations of members. A procedure is developed that calculates the joint coordinates automatically for a given height of the crown. The serviceability and strength requirements are considered in the design problem as specified in BS5950-2000. This code makes use of limit state design concept in which structures are designed by considering the limit states beyond which they would become unfit for their intended use. This new addition contains revisions adopting European and international standards for materials, processes an...

Optimum Geometry Design of Geodesic Domes Using Harmony Search Algorithm

The present paper makes a critical review of some methods and models, now available in the technical litera- ture and commonly used in the analysis of masonry vaults up to their collapse, by highlighting advantages and drawbacks of each approach. All methods adopted to describe the mechanical behavior of masonry structures, in order to be reliable, must take into account the distinctive aspects of masonry, namely the scarce (or zero) tensile strength, the good resistance in compression and the occurrence of failure mechanisms through rotation-translation of rigid macro-blocks. Classic no- tension material models disregard the small existing tensile strength and make the assumption of (1) infinitely elastic be- havior in compression and (2) isotropy, giving thus the possibility to deal with either semi-analytical approaches (espe- cially for arches) or robust numerical procedures. More advanced but rather complex models are nowadays able to deal al- so with anisotropy induced by texture, small tensile strength and softening in tension, as well as by finite strength in com- pression. Traditionally - and nowadays it is still an opinion commonly accepted, in contrast with step by step complex procedures, Limit Analysis has proved to be the most effective Method for a fast and reliable evaluation of the load bear- ing capacity of vaulted masonry structures: classic lower and upper bound theorems recall respectively the concepts of equilibrium and occurrence of failure mechanisms with rigid elements. The so-called Thrust Network Method moves its steps from lower bound theorems, whereas FE limit analysis approaches with infinitely resistant elements and dissipation on interfaces take inspiration from the upper bound point of view. An alternative to Limit Analysis is represented by tradi- tional FEM combined with either elastic-plastic or damaging models with softening, commonly used for other materials but recently adapted also to masonry. They are able to provide a large set of output numerical information but further studies are still needed to ensure their proper application.

Douglas T. Wright

Papers

Equilibrium of shell structures

Analysis, design and construction of braced domes

Tubular structures V