Principles of Lightweight Structures: Descriptiveness, Deformations, Internal Forces
Frei Otto’s exclamation in 1977 „Stop building the way you build!“ is still resonating.His works are continuously published in manifold contributions.How can we apply Otto’s approaches to structural and architectural design using modern design tools?
The fundamental research of Frei Otto and his team on lightweight structures reveals basic principles about geometries in nature and building. Within given boundary conditions, structural shapes with an inherent logic are found. The approach of form-finding can be seen as a different kind of prototyping - with a clear differentiation from classical structural theory: It is not the thinking in elements but the thinking in conditions that sets up the design driver.
In structural teachings and design, this approach is very descriptive and aesthetic in a profound way. Approaching structures through thinking in deformations provides a very good understanding about how structures work and about how they can be designed. Deformations relate directly to spans; the distribution of internal forces, bending moments, principal moments or principal stresses, can be derived from a given design task in order to develop a structural geometry.
A design study based on these principles was carried out in a study at the Biberach University of Applied Sciences. The Neue Nationalgalerie in Berlin, an icon of classical modern architecture designed by Ludwig Mies van der Rohe and first opened in 1968, was taken as role model for the design task to develop a waffle slab with its geometry being derived from the support conditions of a square ground plan. The dimensions in ground plan of approximately 65m span were given as a design constraint; the layout of the waffle slab (with the built one measuring 1.80 m in height) was subject to the design. First studies show the interaction of support positions and the correspondent deformations of a continuous slab.
Fig. 3 Analysis models of a point supported slab with varying position of supports; deformation of the slab (with deformations superelevated)
Translating these deformations into an appropriate structure, the relation between span and deformation becomes clear. The support conditions can be transformed directly as a design driver for structural dimensions. They are of course only one singular aspect in design, since internal forces (here: predominantly bending moments and shear forces) are not a priori taken into account. However, a feasible approach to design is found.
The derivation of a structure from the deformation of a reduced model produces an aesthetic, feasable and understandable geometry, as shown in Fig. 4.
Fig. 4 Structural geometry of a point-supported waffle slab derived from its support conditions and correspondent deformations
Taking into account other aspects such as bending moments or principal moments produces different results for the same design task. Comparing the design results shows a great variety of proposals, while all of them are driven by structural constraints: With a very simple structural approach, a great variety of architectural designs can be developed.
3.2 Principles of Lightweight Structures: Efficiency, Structural Optimisation
Structural optimisation is a very useful tool for the design of cars and aircrafts, since the minimisation of dead load is an economical goal, as well as the complex geometries and loading conditions require modern computation tools. Architectural structures are not in motion and therefore it may not seem obvious to transfer these technologies into the building sector. However, when looking at the life cycle of buildings it becomes clear that from excavation, production, delivery, assembly until deconstruction, recycling or disposal, also here there is material in motion.This leads directly to the responsibility of all planners to limit material input sensibly. Furthermore, the principles of lightweight structures as design attitude open up a mind-set of design drivers that can be very useful in the development and understanding of structural geometries.
Fig. 5 Geometries derived from different structural aspects
The studies presented in this contribution use the commercial software Altair OptiStruct, which is based on the homogenization method and implies a wide range of special issues of structural optimisation. The authors would like to thank Altair Inc.for granting reduced and free licenses for academic studies.
3.3 Structural Parametric Patterns
Patterns, or ornaments, have a long history in building and can be found in all cultures. Traditionally, they are decoratively added elements. Adolf Loos’ essay „Ornament und Verbrechen“ (Ornament and Crime) marks a turning point in contemporary architecture: The elimination of any non-functional decorative elements sets the origin of classical modern architecture.
Studies of parametric geometries base on the systematic variation of geometrical patterns: the variation reveals characteristic elements, be it subjective aesthetical or objective structural qualities. Fig. 6 shows examples of parametric studies: Parametric geometrical studies by D‘rcy Wentworth Thompson dealing with the subject on growth and form (Thompson 1961); form-finding studies with systematic variation of boundary conditions using soap films within differently curved wires carried out by Frei Otto and his team (Bach 1988); and parametric optimisation studies carried out by the author developing optimal shapes within a given volume with varying orientation of the point loads applied to the structrure.
Fig. 6 Examples of parametric design studies
Today, the ornament seems to be back in architecture and parametric design is very fashionable in both architectural and structural design. New tools allow generating geometries adapting to variable boundary conditions - being structural demands, lighting conditions or formal conceptions. Fig. 7 shows examples of modern ornaments (left: exhibition stand Gasser Fassadentechnik, Swissbau 2012; right: Suedwestmetall facade, architects Allmann Wappner Sattler)with their design possibilities and manufacturing conditions directly related to new developments: repetition in patterns is other than some few decades or years ago redundant. Structural necessities as well as manufacturing constraints can be neglected. The focus is set on aesthetical logics and qualities.
Fig. 7 Examples of modern ornamental design
The missing link between pattern and structure can be achieved through use of structural optimisation methods. As an example, the procedure in this study shown in Fig. 8 is
A given design space, here: a flat cuboid volume, with part of the space not being subject to the optimisation.
A given structural system, here: evenly distributed