© Marcus Bredt
Formfinding 13.10.2013


Force and geometry are the two critical factors in the implementation of load bearing structures. Alongside functional and aesthetic considerations, they are of major importance during the design process. Their priority may vary depending on the brief, but the objective is always a holistic approach - a `symbiosis´ of all criteria.
During the form-finding process the top priority is on identifying the geometry that enables the optimum force flow within the structure. During the further development of this geometry the focus shifts towards aesthetic and constructional aspects. The boundaries between these two approaches are blurred, but in the interest of clarity both are illustrated separately in the examples below.


When designing resource-saving structures, the key objective is to optimise material use. Material-efficient construction can be achieved using force-flow-optimised load bearing structures. Generally, bending moments should be avoided in the design of optimised structures. Structural elements bearing axial forces distribute loads evenly. Therefore the full capacity of the material can not be used.  
Tensile forces transfer loads more efficiently than compressive forces. The reason for this is the destabilising effect of compressed components. This phenomenon is easy to understand by imagining a simple ruler under load. But few construction projects can be realised using only structures bearing tensile forces. Hence, even the most efficient structures, such as cable nets and membranes, require compression members. Consequently, the best structure for standard construction projects is an intelligent combination of axially compressed and load-bearing members.
The form-finding process for structures consisting solely of tension members, and thereby defining a self-supporting geometry, can also be applied to hybrid structures. Due to the destabilising effect of compressed members, mentioned above, standard numerical and physical approaches can not be used. schlaich bergermann und partner’s specially developed mathematical model allows the extension beyond common, purely tensile structures. This method enables the efficient analysis of different design options taking into account varying design parameters. In combination with innovative design approaches it allows us to develop unusual structural designs all the way to detailed design and construction.

  • BayArena in Leverkusen: A roof structure which transfers loads to merely 8 V-columns, determined in a form-finding process.
    BayArena in Leverkusen: A roof structure which transfers loads to merely 8 V-columns, determined in a form-finding process.
  • BayArena in Leverkusen: A roof structure which transfers loads to merely 8 V-columns, determined in a form-finding process. © Bayer04
    BayArena in Leverkusen: A roof structure which transfers loads to merely 8 V-columns, determined in a form-finding process.


Methods of modern geometry go far beyond the mere illustration and organisation of space. Together with the objective of designing efficient and aesthetically appealing buildings, it also enables the optimisation of structural, geometric and construction-relevant parameters.
Geometrically equal surfaces can be given great variety in appearance and expression through faceting. Judicious segmentation can enhance the three-dimensional effect of a surface. In the field of architecture, this goes hand in hand with the logistical need for modular components. Using innovative optimisation processes, any surface can be divided into elegant, regular segments, while also taking account of specific requirements regarding the production and detailing of components.

A distinction is made between `bottom-up´ and `top-down ´design processes. In the first method the overall shape is created by lining up predefined elements. The principle of `translational surfaces´ developed by schlaich bergermann und partner divides clearly defined surfaces into regular segments, e.g. planar quadrangles with equal rod lengths. As in the House for Hippopotamus in Berlin - the first example of this “bottom-up” process. The principle has since been successfully applied time and again. In this approach, however, the range of possible geometries is constrained by the choice of structural elements. 

In contrast to this, the “top-down” approach is a design or form-finding process to create the shape of a building. The emerging geometry is then overlaid with a mesh of individual facets. This subsequent net structure of free-form geometries utilises sophisticated mathematical algorithms, which schlaich bergermann und partner have developed further, specifically for use in an architectural context.

Just as with physical components the individual elements of this net structure have to meet the most stringent demands in terms of proportion, dimension and quality of the materials. In addition to systems consisting of triangles, the net structure of quadrangular elements in particular unites technical and aesthetic benefits.
Global optimisation procedures allow us to take account of local requirements,
such as evenness of the elements, standardisation of internal angles or desired rod lengths, and transform them into well proportioned mesh patterns, without deviating from the original geometry.
To close the circle, the emerging geometries can in turn be combined with the optimisation procedures of structural analysis.

Study of design options

The following illustrations show the surface of a glass roof; by modifying the net structure it takes on different characters.

Covered in triangles (1) it forms an intricate net structure with a minimal variation of rod lengths. The rods of the quadrangular mesh on the image (2) follow the main curvature lines of the surface. This strategy pursues a regular structure which features planar mesh elements and minimises torsion in the rods. Compared to a triangular net structure it has a significantly reduced number of nodes. In the last image (3) the rods have been advantageously arranged in the direction of the force flow, considering the dead load. It is therefore possible to select smaller cross-sections which noticeably reduce the material usage.

  • Triangular mesh
    Triangular mesh
  • Quadrangular mesh
    Quadrangular mesh
  • Rods aligned to the force flow.
    Rods aligned to the force flow.
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