Lorenz Lachauer

ETH Zurich | ETH Zürich · Institute of Technology in Architecture

This paper introduces a powerful three-dimensional, computational equilibrium analysis method for masonry vaults using funicular networks. Applications of this new approach, based on Thrust Network Analysis and extended with insights from structural matrix analysis, for efficient funicular analysis of complex vault geometries are provided. This met...

This paper presents a novel method for computer-aided equilibrium modelling of structures in early design stages. Based on the force density method, an iterative procedure is developed that enables the generation of spatial kinematic pin-jointed structures that are in equilibrium close to a given input geometry, while satisfying additional constrai...

This chapter introduces Thrust Network Analysis (TNA), an equilibrium method for designing unreinforced masonry vaults. TNA extends the Force Density Method (Chapter 6) for the specific case of vertical loading and networks with fixed horizontal projection. The method uses reciprocal force diagrams, derived from concepts based on graphic statics, t...

This paper introduces a new computational equilibrium analysis method for unreinforced masonry vaults, which extends Thrust Network Analysis using structural matrix analysis and efficient optimization strategies. By identifying independent states of equilibrium of funicular networks with any topology and fixed plan geometry, a robust and efficient...

This paper presents a novel and rigorous approach for the design of efficient spatial support structures for flat slabs. Based on the given dead load of the slab and the topology of the supporting structure, this method allows form-finding of support structures that are in equilibrium with axial compression forces only. During the form-finding proc...

The development of structures with complex, curved geometry typically consists of a series of iterative steps in which formal and structural considerations are addressed separately. Since such a sequential process often results in solutions that fail to realise the aesthetic and structural intentions of the original design, there is clearly a need...

This paper presents a new computational framework based on Thrust Network Analysis (TNA) for the design of funicular structures. Fast and robust solving algorithms enable the interactive exploration of these constrained structural systems. By giving explicit, bidirectional control over the internal force distribution and overall geometry to the des...

This paper presents a novel approach for the interactive design of linear structures in space. A method is introduced, that provides a maximum of formal freedom in the design of funicular, hence efficient, structures. For a given deck geometry, defined by a design driving NURBS curve via parametric modeling techniques, a tailored relaxation routine...

This paper presents a concept for a novel typology of computational design tools which are able to bridge the gap between the intuitive "structural sketch" and sophisticated analysis software. Based on equilibrium solutions and graphic statics, a set of interactive parametric tools have been implemented as a prototype, within an existing computer-a...

This paper describes a precise geometric method for the inscription of structural constraints into architectural form. Based on techniques from graphic statics, the force distribution in building structures is visualized using geometric diagrams. This diagrammatic representation allows a formal description that shows the relationship between the fo...

This paper presents a concept for a novel typology of computational design tools which are able to bridge the gap between the intuitive "structural sketch" and sophisticated analysis software. Based on equilibrium solutions and graphic statics, a set of interactive parametric tools have been implemented as a prototype, within an existing computer-a...

It is common practice in engineering to represent a continuous stress field by a network of discrete forces, e.g. hanging models (Gaudí), cable nets (Otto) or strut-and-tie models (Schlaich) . These discrete force networks allow the user to visualize, grasp and control the flow of forces in an intuitive manner. A recent computational advance in thi...

Scale models can be used to understand the equilibrium of masonry systems – and structural compression forms in general– as they stand not because of allowable stresses, but because of their geometry. This paper demonstrates the use of 3D-printed, structural models, and emphasizes their relevance, not only to assess the stability of complex masonry...