# Prototower 01

## DRX 2013

**Branching Systems**

Kavin Horayangkura, B.Arch., Samar Malek, Ph.D., LEED, AP., Maximilian Thumfart, Dipl.-Ing

**Introduction**

The design tool developed for Prototower IV creates vertical net structures based on branching. The tool simulates tree branching through a set of rules that describe the varying direction of growth, and the merging of branches. The design tool incorporates architecture and structure and can generate various topologies. The overall structure created is a hybrid of a diagrid and a space frame. There are many architectural and structural and aerodynamic advantages to using tree branching including frame continuity, alleviating vortex shedding with irregular facades, all while creating unique spaces.

**Concept**

The objective was to grow a 450m high-rise by a branching algorithm to create the structure and the spatial configuration. Therefore the structure should grow from one or multiple seed points to one or multiple attraction points like a tree. Parameters and rules of growth were identified by examining abstract natural tree growth. In a natural growth pattern the branches spread out at each node. According to the branching angle its topology changes until it reaches a Diagrid like pattern. This topology doesn’t appear in nature but is one theoretical growth pattern which creates a wide and stable structure because the topology is less hierarchical and less loose members are remaining. This pattern change from tree to Diagrid inspired the idea of growing a high-rise and led to a branching algorithm which creates various topologies.

**Branching Algorithm**

Branching describes the splitting of one element into two, while both – so called - children change the direction of growth symmetrically. The parameters that influence the growth of the topology includes branch iterations, angle between each branching pair, length of the members, number and location of seeds and attraction points.

The set of rules that guide the growth of the high-rise are:

Each pair tries to focus its symmetry axis to the attraction point, this is the focus line; around each tip there is a merging tolerance radius which can force the tips to join if their tolerance circles are intersecting. The margining function results in a triangular grid structure that differs from the tree branching where members are not connected.

In 3D there are two branching modes: one creates two branches of which each tries to grow into the direction of the nearest neighbour. The second mode creates four branches of which two are growing in one plane between the closest neighbours to both sides of the starting point. The other two branches are branching perpendicular to this plane.

Another important tool to control the 3D growth is the checkpoints and Tree zones. The checkpoints force the structure to pass a certain predefined point if the branches are within the attraction radius of the checkpoint. The Tree zones can overwrite the growth parameters for certain areas to influence the structure according to program or else.

**Design Exploration**

The design tool can create various structures through the manipulation of the location and number of seed, attraction, and check points. From this exploration a range of structures from a pure diagrid to a pure space frame structure could be created. The final design is a hybrid of both.

**Key Parameters**

The key parameters for the growth of prototower IV are slightly decreasing member lengths to increase the density at the tip of the tower, static angles for the members (70°) and checkpoints that are changing from radial position at the bottom to square position at the tip.

**Structural Analysis**

The structure was designed for displacement and strength. After investigation between the structural performance of the diagrid and the space frame, the diagrid was placed at the bottom. Placing the perimeter structure increases the lateral stability of the structure. Additionally, the effect of the location of the transition from diagrid to space frame was studied with the conclusion. It was found that it was structurally more efficient to keep the diagrid at least 50% of the height of the structure. Thus the final design transitions to the space frame at half the height. The initial final design was analysed and optimized in Karamba. Based on these results, the members were resized to clearly ensure smaller cross-sectional diameters rested on larger cross-sections.

The design tool has many structural advantages. It can produce irregular facades that helps diminish vortex shedding; it avoids structural frame discontinuity because all members grow from each other; it creates a tapered structure because all branches grow towards an attraction point; and it grows a triangular grid, the most stable topology.

**Program**

The program of the building depends on the structure. At the bottom of the tower, the placement of the structure at the perimeter facilitates an open floor space which lends itself naturally to office use. At the top of the structure, the 3D branching creates unique, individual clusters which are used for residential spaces.

**Conclusions**

The branching design tool can create three kinds of structures: a diagrid, a space frame and a hybrid of the diagrid and space frame. The algorithm has many advantages structurally, aerodynamically and programmatically. Further design and structural analysis would include the thermal and daylighting performance of the structure, and the additional structure (core and floor slabs), loads and load combinations, and a dynamic analysis.