# Prototower 02

## DRX 2013

**Cone Derived Structures**

Daniel da Rocha, M.Arch., Isabella Thiesen, Dipl.-Math.

**The Cone Tower: Rigidity in Structure – Flexibility in Design**

The Cone Tower is the result of a design process started from the study of simple methods aimed at devising lightweight structures, later carried over to the realm of high-rise design. Its principles are an adaptation of the basic idea behind any type of structural design: the flow of forces, or the redirection of flows of forces within a building structure.

**The Force Cone Method**

The initial inspiration came from the study of the Force Cone Method, created by Prof. Klaus Mattheck, professor of biomechanics at the Karlsruhe Research Centre. His explorations in shape optimization based on the study of tree structures led to a set of graphical rules that help to compose 2D lightweight structures in equilibrium.

The idea behind it is simple: in a situation with a given set of points, every load application point “pushes” a cone-shaped pressure zone in the direction of the applied load, and “pulls” a tension cone in the opposite direction. Consequently, every support point reacts by “pushing” a compression cone in the opposite direction of the force, and pulling a tension cone behind it. As one drafts these cones, a series or intersections will occur, which will then be used as new nodes within the structure. By connecting these nodes with each other and the original given points, a lightweight structure is created. This structure is supposedly in equilibrium, and should represent the most optimal solution to the initial given situation composed by load application points and reacting support points.

This assumption is later tested via the so-called Soft Kill Option (SKO) method. This method acts by analysing a similar load-support situation on a given search space, and removing “material” from this space which it deems unnecessary for the balance of forces within the systems. In all comparison tests, the SKO method showed results that attested the capacity of the Force Cone Method to generate structures in equilibrium.

**From 2D to 3D**

A simple 2D tool was developed to test the Force Cone Method in varied situations. The next step was the creation of a 3D tool which would take Mattheck’s method one step further and try to generate 3-dimensional lightweight structures in equilibrium.

The success of this second attempt led us to explore different ways in which the FCM could be applied in the design of high-rises. This exposed that the inherent limitations of the Force Cone Method, which basically limited it to a tool for initial design ideas for low-rise lightweight structures. However, a few principles which make the Force Cone Method so successful could be extracted and pushed further, such as the relationship of its structures with the angles between forces, the distances between nodes or the intersections between elements as new structural members. These were relatively basic principles which proved very valuable for the design of the following set of structures in the research.

**Reinterpreting the cones**

The cones as a surface object was kept as the basis for further explorations. By using it as a search space for the creation of structural members, i.e. by discretizing its surface, it allowed the precise control of angles and member lengths within a structural composition. The basic principle of redirecting force flow throughout the building, and controlling resulting load paths, led to the idea of piling cone surfaces alternating apices and bases. This created the basic “cone-column”, whose weak points, where apices came together, would be addressed by a secondary column where at the same height, a base to base connection would be present.

When these two basic cone-columns were placed on a sharing axis, additional intersections would be generated. These new intersections proved essential to the overall stability of the structure. By further pulling the apices of the composing cones along the axis, a round of secondary intersections provided additional stability and, most importantly, vertical space for circulation within the building.

A common triangular base discretization for the cones resulted in tetrahedral elements that composed the main frame of the mega-structure for the tower. As a secondary structure, diagonal members connecting node points on different levels were introduced. This creates not only additional stiffness, but generated structural hierarchies and guides the design process for the façade.

**Load Paths**

The flow of vertical forces can be followed throughout the building along clearly defined load paths. Tying the structure together and back to the core allows for a greater structural efficiency, and also allows the creation of unexpected interior spaces throughout the building.

**Clear Structure**

The simple shape of cones and the virtually infinite possibilities for their discretization allows for the creation complex structural solutions that keep their clarity independent of the amount of composing members. It creates a wide space for exploring different solutions for varied load cases and programmatic requirements.

**Simplicity**

The simple definition of the tower in terms of discretized cones can be easily manipulated by a parametric description of cone opening angles, height of cones, the degree of discretization and the number of main load paths as cone columns. The resulting structures can be then fed into an optimization loop to allow for direct feedback on its structural efficiency.

**Potential Applications of Force Cones in Architecture**

Understanding structural design as the principle of force redirection is an essential thinking tool in the design of complex structures. The 3D Force Cone Method in its original state is a hands-on-approach to designing small lightweight structures, with possible applications for buildings of smaller scale. For high-rise structures with more complex load situations, one is still able to use cones as tool to define distinct load paths and control the force flow within larger contexts. Furthermore, cones appear as a simple and efficient designing tool for creating a wide range of building form with interesting interior spaces and exterior appearance, always combined with structural intelligence.