Students of the Ecole nationale supérieure d’architecture de Versailles participated in a workshop titled ‘Intelligent Fabrication – Digital Bridges’ from February 20th to March 2nd where they investigated bridge designs using parametric tools such as Karamba and Grasshopper as well as digital fabrication techniques. In the first week, the students split up into groups of 4 to develop bridge designs through physical model studies and digital 3d modelling in Rhino and Grasshopper. Three of the bridge designs were selected to be constructed at full scale in the second week, while other students further developed their bridges at 1:10 and 1:5 scale utilising 3d printed and lasercut components.

Text from the students of ENSA-V. All images from Stephen Jacquens unless otherwise stated.

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1:1 BRIDGES

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Hyperbolic Paraboloid
The hyperbolic paraboloid presents a simplicity and a lightness in its geometric logic. The idea was to use this double curved geometry to create a bridge integrating both convex and concave curves. The final structure in fact is an asymmetric stretched hyperbolic paraboloid. In order to build it, we first thought of assembling the grid in plan, and then lifting up the edges, thus creating an arch. Each intersection would be bolted, allowing twisting of the beams during the process of the transforming it to its final shape. The bolts would afterwards be tightened. The structure was be kept in the final position by cables connecting the bottom extremities of the bridge and other cables blocking the deformation of the frames along the top curve. Alternatively the method that proved to be more successful was to mount the frames at an angle, and then bolt the diagonal beams to it, and finally bolt each intersection together.

Domestical Wildness
We conceived a bridge that reunites the similar characteristics of our initial bridges we designed in the first week: superposition, frame, and regularity. Our desire was to complexify the project, so we built up a frame that highlights irregularity though well thought out and structurally viable. The main load bearing elements of the bridge are two irregular trusses. The diagonals of each truss are composed of two groups of elements which lean towards each other. Their superposition offers a random appearance of the project. With the help of Karamba, we created a parametric algorithm to obtain a visually random model but with an optimal structure. The project evolved all week long thanks to the simulations of the bridge deformations and also due to the creation of 1:10 models. Indeed, we improved the bridge structure to the maximum. To bring an additional factor to the design, the deck of the bridge is independent from the structure of the side trusses and varies its heights at specific points.All of this allowed us to create a new space easily appropriable for everyone.

Triangle Reciprocal Structure
During the first week, experiments around the triangle and the Leonardo da Vinci bridge were made, with different shapes, sizes, thicknesses, and different assemblies such as notches, nails, joints, etc. The purpose of the first bridge was to create two arches composed of isosceles triangles and to mirror them to make the bridge more stable. In order to build the bridge, we optimized it by having two connected reciprocal structures (making the bridge more stable and blocking the horizontal movement). The bridge deck is created by the space between them. It’s placed on wooden beams that transfer the loads to the structure. Each triangular element rests on the one before and the one after. This disposition generates an arch structure system that transfers loads through interconnected components. A wooden shim is placed to fill the empty space between two triangles. The isosceles triangle elements are made of two four meter beams and a one-meter beam. They are fixed together using a metallic element placed on each corner. There are five triangular components.

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1:5 BRIDGES

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Folding Bridge
Here we were trying to associate the flexibility of a folding structure and the stability of a bridge. A physical model work at scale 1:10 allowed us to manipulate and evaluate the structure in realilty. Thus, with the help of Rhino and Grasshopper, we optimized it in order to reduce dimensions of the folded bridge and minimize the quantity of wood. This principle was also a structural solution as the members closer to the supports are larger than those in the center and insure the stability of the bridge. When the structure is deployed, a movable wooden beam can be fixed to the structure which blocks any relative movement of the parts. Therefore the bridge is totally retractable and can be quickly set up in several environments.

Starking
For our bridge we have multiplied identical modules to create an arch. Each module is composed of sloped beams 12 cm high that lean on the horizontal beams of height 9 cm, creating an angle between separate parts. Each module leans on the 1/3 of the other’s length. The bearing load is transferred along the structure to the supports. The spacing elements are placed between the modules to minimize deflection. The joints are organized in a way as to prevent horizontal sliding of the beams and to give the structure a stability.

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1:10 BRIDGES

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Optimised Assembly
In order to optimize our bridges, we have worked on two aspects: digital optimisation and module design. Our first tries on optmizing the structure  for minimum weight in Karamba in order to lighten the two bridges led sometimes to removing the deck. In order to design the bridge, we first created segments in Grasshopper. Then we generated modules by linking segments to each other. The bridge is then separated in three parts: the two piles and the deck. It is then possible to choose how and how much each part is transformed. The geometry obtained has a basic shape for a bridge: a merely elevated deck base on two equal piles. We worked on Rhino for the bridge shaping so that we could obtain the circulations oriented thanks to the asymetric piles we wanted. The frame made of modules is then ajusted to the global form in Grasshopper. Finally, the structure is optimized in Karamba according to uses and loads.

In another scale, in order to totally systematize the assembly, we made male and female modules. In each category, they are simple and double elements. The latest allow an economy of wood sections. An embedding is produced by the assembly of two modules. It participates to the bridge’s bracing. Stability is reinforced by stair’s decking. The load of the structure itself is weighed down. Module’s elements have the very same measure so that everything can be serially produced. The frame of 40×40 cm allows global stability. At the same time, various uses are possible, as to sitting or experiencing the structure as stairs. This proposal results of a mix between the two initial bridges on the one hand and of double method between 3D design and structural optimization by Grasshopper / Karamba on the other hand.

Inversion
During this workshop’s first week, we were interested in the subject of tensegrity. We were indeed seduced by this kind of structure’s apparent floating, and tried to design a bridge using this principle. However, we soon found out this system has weak forces: such a bridge is unable to support more than its own weight. After coming upon this conclusion, we decided to create a mixed bridge, one that would unite the ideas of the tensegrity and a stable structure. First of all, the cables were replaced by wooden elements, allowing them to work in both compression and tension, unlike the cables that would be inefficient once compressed.

We then designed a primary structure composed of four poles, all tilted toward the ground and away from each other, supporting the deck. Wooden elements connect the ends and middle of the deck to the poles to prevent them from falling. It also keeps the poles from becoming closer to one another under the weight. A single concept kept us moving to change the design: the inversion. We joined the poles to make two V’s then flipped one in order to have only three supports. Our concern was then to make such a bridge stable. With three supports only, the bridge tends to fall. It is thus balanced by elements in compression and elements in tension. Just as in the previous design, the deck is held between the two V’s and at its ends and middle by wood beams working both in tension and in compression. The grounded supports are joined by cables to prevent horizontal thrusts. At the very top of the structure, the same system works in both compression and tension to keep the poles from moving.

DNA
The bridge crosses 10 meters, and is made of two arches. The arches bear the deck, which acts as tie rods between the two arches, passing on the loads to the abutments. The bridge is made of three surfaces: one for the deck and two for the arches. The arches continue over the deck in order to create handrails. The surface thickness is optimized by Karamba and they are thicker on the points where they have to bear the most load. The layers are cut so that their inclination is the same as the arches’ inclination. Five ropes, four going through the end of the archs, and one through their intersection, link the different layers.

Underlying
In the beginning of the project, we decided to use a suspended bridge with an underlying structure, as in the reference that served as our inspiration, the Branger and Conzett’s bridge in Switzerland. After creating our first model in Grasshopper, we were able to design the structure by using variable values and, in this way, define certain elements such as the height of the structure, the width, or even the number of triangles. As a consequence, this 3D model, allowed us to reduce the number of triangles and the height of the structure, in order to adapt it to the given span of the bridge, that of 10 meters.

Following the introduction of the model in Karamba, we could optimize the number of triangles, by reducing it to 6 in the final stage, and we were able to define the cross sections for each beam. At the same time, we replaced the cable connections with wooden elements, thinner than the main beams, and because of the nature of the material and its specific behaviour, we could divide the number of elements by two. In the final stage of the project, our purpose was to analyse and design the junctions between all the wooden elements in our bridge. In order to do this, we first identified the main types of joints-mainly five types, which we then designed as 3D models using Rhinoceros, making them custom joints especially fit to our design. As a final step towards the finalisation of the project, we have built a model of our wooden bridge, at the scale 1:10, and, as a final test, we have managed to introduce the custom joints we created, with the help of the 3D printing technology.

Grid Possibilities
The orthogonal grid was the basic element to answer several architectural and structural challenges such as assembling elements in a tridimensional way to avoid using diagonal wind-bracing. The stairs fit freely within the grid that act as independent lateral beams. The whole structure is lifted up by pillars that are also built up from the frame. Although the whole grid is made from from small wood sections, the original designs were highly material-consuming, and what was our design statement for the first phase of the workshop became our challenge for the second phase: how could we manage to keep the logic of the grid and a free drawing of the deck while cutting out the most useless elements of the grid? Are the useless elements depending on the deck design or are they intrinsically linked to the grid design?

Grasshopper and Karamba helped us to consider and answer these questions. Analyzing the grid showed us a very small displacement when loads are applied (< 0.005). When we asked diagonal elements appeared and vertical elements disappeared progressively. The elements that were added through the optimization process varied according to the deck’s design. Thus it seemed more interesting to us to display different possibilities of the grid instead of a final design. We chose three designs that we found interesting regarding the shape of the deck and the optimization the softwares would suggest us.

Cells Bridge
For the first week, we decided to imagine a bridge which is working in compression. We were interested in the use of the wood to create resistance in the structure. In this context, we quickly chose the supports. The structure is based on the circular arcs and spread in successive tangents. At the intersections are placed triangular constructions made in order to support the deck of the bridge. The deck widens at the supports and narrow towards the center of the bridge. A double-lap joint system is chosen to create the required thickness and insure the connections. The base of the bridge is composed of five fastened beams working with ball joint. With the help of Grasshopper and Karamba, we were looking to optimize the measurements of the bridge in search of sturdiness and lightness.

During the second week, we intentionally chose the measurements of the bridge and began working on a surface structure. The bridge is composed of three curved surfaces. The work realized thanks to Grasshopper and Karamba is focused on the research and establishment of an optimized geometry on the undersurfaces. First, we chose a hexagonal pattern which could be divided in triangles so as to contain the forces on the most constrained zones. The geometry is assigned to a color gradiation: the more red the regions are, the more the surfaces need to be reinforced. However, we decided to steer the project to a more organic geometry which was hollowed out according to the colour mapping. The goal was to remove the material as much as possible while maintaining the stability of the bridge.

Perforation
The work on the wired bridge directed us to an arched structure, on which a partially straight deck rests. The idea being to be inspired by stone bridges of Provence, and to adapt the shape to a wooden structure. This shape then guided our work on the theme of surfaces. Contrary to the first exercise, it was here necessary to leave full surfaces, and to hollow out them according to the structural analysis to get a new shape optimizing the material. This change in the design of the bridge has a precise objective, that of lightening the structure to the maximum.

The use of Karamba in Grasshopper allowed us to understand the structural functioning of the bridge. We then deduced the stress curves of the surfaces. We opted for drilling as a tool for removing material. The circle has been chosen as a lightening pattern while giving consistency to the entire bridge. The pattern then varies according to its proximity to the lines of forces previously traced in Karamba, the circles start from a single point and extend as they move away from the lines. This is why there are large hollow holes in the least stressed parts (the upper apron on which one is walking), whereas there is no hole in the supporting parts (the lower deck). Beyond the visual aspect, this work allows to show a design directly related to the structural aspect of the bridge.

Helix Bridge
Helix Bridge is designed as an assembly of three trussed beams forming a triangular tube; twisted then compressed to have a curved spiral. This deformation system of a triangular trussed beam provides  some qualities which improve the structural performance: the twisting creates arches working in compression and the curvature of the whole spin allows to the bridge to be free-standing.

Through Karamba and Grasshopper, it was possible to modulate the spiral by varying the number of triangles which compose the bridge. So, it allowed us to find structural balance between size of wooden sections and the spacing of triangles. Simulation also revealed that the addition of a cable in tension resumes loads of arches in compression. Finally, the bridge curvature produces at the junctions, a different angle for every connection of wooden sections. To optimize implementation of the bridge, a unique articulated knot is imagined to adapt itself to every case. The knot consists of two embeddings for triangle equilateral sections whose angles are known, then four unstable catchers for both arches sections and both bracings, to be bent when need.

Double Curved Bridge
Our bridge is formed by the intersection of two cones resulting in a V shaped bridge. Its hourglass shape is also useful for stability because it allows a good distribution of the forces within the structure. Initially the bridge was planned with a fully triangulated system, which was rethought in a second step, with surfaces. The structure was developed towards more of a cone so the surface could be developable (a form which could be laid flat without being stretched).

With Karamba we have determined the areas that require less material, and then compared this result with our starting object, which allows us to carry out tests to further lighten the surface structure. During the tests, we tried first to remove thicker areas (the white ones) revealed by Karamba which was dispersed in a heterogeneous way, weakening the structure. Then, removing regularly and ponctually small quantities of surface on the areas. This method allowed a good hold of the bridge and still left a large amount of material. To finish, by dividing the surfaces into different faces taking into account the supporting elements, we were able to finalize our system thanks to a more or less important spacing of surfaces and holes.

Wood & Plastic
The project is based on the design of a bridge whose structure is a geometry that seems asymmetric however it follows a regular and a structural logic. We chose to work with triangles as they are the most stable geometric form and create a combination of triangular-based pyramids. Our research focuses on the junction of several beams at one point. How do we connect the beams? Would it be structural? At what moment do our elements of connections come to restore the forces exerted by the beams?

Then, the joints become the primordial elements of the design of the bridge. The connections are presented as basic joints molded according to the different orientations of the beams. We thought about reducing the amount of material in a tissue and the beams to get a lighter shape. So we started with the idea of a ribbon that winds up on two points – starting from a top of the base joint, it connects all the beams and then returns to the middle in the same way. Finally, it was interesting for us to concentrate on the assembly of the beams by working on the prototypes of links illustrating their direction. Each of the links being unique comes to emphasize the complexity of designing a bridge whose simple geometric structure.

Upturn V
The complexity of the six elements’ assembly into one node is achieved through a distinction of the elements. The V triangles are oversized in order to receive the junction of the sleepers. The connections between the V triangles and sleepers are done so with tie system which is screwed together at the node of every V triangle. Each element of the system offers two ball joints allowing the linking of the sleepers and the adjustment of the positioning according to their angle of inclination. The V structure aims to connect the different elements constituent of the link. The deck rests inside the structure and spans between the V triangles, inviting us to a route similar to a stroll around the structure.

V206
Ou initial model had an arched general shape and a triangular section. Considering our bridge as a plain object which can be sculpted, we drew a more optimal and dynamic shape, lighter in the center. Taking notes of the superfluous material in our bridge, underlined by the work on Karamba, a mesh grid appeared. This grid is getting thicker or thinner in response to the forces applying in the bridge, taking the grid to a three dimensional aspect. We tried different shapes and scales possible for the mesh so it would combine a constructive aspect and an aesthetic aspect. Taking a look at our work as a structural object, the final result is shaped in a more organic way than our first model, less conventional and more artistic but yet structural.

Le Cigare
The twist principle was our starting point: the bridge becomes refined then widens. By multiplying smaller and smaller hexagons towards the center of the bridge, we can connect them by triangles which contrevent the whole structure. Secondly, the spaces between the edges were replaced by surfaces, which we then perforate by a process defined according to the loads and forces in every surface of the bridge.

Tripod
We have worked on a fairly pure form of bridge, composed of large “wings” in the shape of a tetrahedron which support the deck. The structure’s lightness allowed us to add an extra which ables more stabilty. Thus the bridge is actually a tripod where each support is placed in a circumscribed circle of 10 meters diameter.
The bases of the wings are all articulate in a central point where all the elements rest on one another in a key point. As for the vertex, the tetrahedrons are linked by beams which prevent them from collapse. The beams which support the deck join themselves to form a small central platform. Some beams could be replaced by cables. This week, we had to focus on how the beams could be joined in knots. The aim was to model them in order to realize them later using a 3D printer. We therefore had to review the junction of our elements and find a suitable form of connection.
This shape also allows the possibility of creating uses, like hammocks hanging on the wings that would allow to extend above the void. The bridge would no longer be just a crossing point but also a space to meet and relax.

Professor: Klaas De Rycke
Tutors: Louis Bergis, Clément Duroselle, Adam Orlinski, Matthew Tam, Thomas Charil, Dragos Naicu, Ewa Jankowska
Student Assistants: Stephen Jacquens, Florian Bourguignon