II. Discrete funicular shells

Discrete element - compressive assemblies

Motivation

These principles have been used since the first half of the 19th century (Huerta, 2001) for the design of unreinforced, discrete masonry structures, such as stone vaults and arches. However, simple geometric rules to find feasible structural shapes for the erection of arches were already used in ancient times (Aita, 2003). Such structures, built with discrete blocks, have been stable, seismic resistant and safe for several thousands of years. However, today, discrete, funicular assemblies in architecture and construction are rarely used despite certain unique properties:

• Longevity

• Faster and cheaper erection

• Reuse and sustainability

• Increased fracture toughness

• Simple Connections

Today, the use of discrete shells is mainly limited to specific applications for infrastructure projects, such as bridges and tunnels with relatively simple shapes. For example, the concrete block systems shown in Figure 2.26 take advantage of the longevity and quick erection times of discrete funicular assemblies. They are structurally inspired by historic stone vaults but do not exploit their rich structural sophistication developed over centuries. Furthermore, little attention has been paid to the architectural, formal and aesthetic qualities of historical masonry structures, which remain to this day the most sophisticated discrete structures ever built. Therefore, to further explore the use of discrete funicular structures in contemporary architecture, it is necessary to review the traditional - and now largely forgotten - techniques of stereotomy and erection developed by master masons over the last centuries.

Reference project: Armadillo Vault, Venice, Italy, 2016

Armadillo Vault, Venice, 2016

Tutorial agenda

week 10	A. Form finding	A0. Introduction to COMPAS_TNA & RV2
		A1. Form-finding for a simple Shell structure
		A2. Form-finding for complex geometries
week 11	B. Discretization of compressive shells	B1. Tessellation
		B2. Blocks
week 12	C. Fabrication	C1. Compute material density
		C2. CNC cutting sequence generation

References

1. Van Mele T., Mehrotra A., Mendez Echenagucia T., Frick U., Augustynowicz E., Ochsendorf J., DeJong M. and Block P.Form finding and structural analysis of a freeform stone vault,Proceedings of the International Association for Shell and Spatial Structures (IASS) Symposium 2016,K. Kawaguchi, M. Ohsaki, T. Takeuchi (editors),Tokyo, Japan,2016 (September).

2. Rippmann M., Van Mele T., Popescu M., Augustynowicz E., Méndez Echenagucia T., Calvo Barentin C., Frick U. and Block P.The Armadillo Vault: Computational design and digital fabrication of a freeform stone shell,Advances in Architectural Geometry 2016,: 344-363,2016 (September).\

3. Calvo Barentin C., Rippmann M., Van Mele T. and Block P.Computer-controlled fabrication of a freeform stone vault,Proceedings of the IASS Symposium 2016,K. Kawaguchi, M. Ohsaki, T. Takeuchi (editors),Tokyo, Japan,2016 (September).

4. "The Armadillo Vault: Computational design and digital fabrication of a freeform stone shell" - Rippmann et al.2016