The BIC structure has been presented as a structural installation for the IASS (International Association for Shell and Spatial Structures) 2015 symposium. It is made out of 10 000 BIC Cristal pens that are a living symbol of the 1950’ industrial era of consumable engineering. 100 billion pens have been sold since then and half a century later, it is still a mythical pen, affordable, practical and durable. Its tungsten ball point is worth 2km of writing. It is pointless to precise the pen is often lost before anyone can see its ink empty.
The BIC Cristal pen was used in this structurally hybrid project as a structural element. The hexagonal section of the pen, ergonomically designed, reflects light in a particular way that gives to the entire structure an unprecedented texture. The project questions, on a wider viewpoint, the capacity of architecture and engineering to use elements for purposes that were not initially foreseen. It explores the ability of architects and engineers to adapt their process of thinking to use unexpected materials to create, in this case, a hybrid continuous form-found suspended structure.
FORM-FINDING AND STRUCTURAL BEHAVIOR OF A HYBRID STRUCTURE
The goal of form-finding is to identify a geometry in static equilibrium with a given set of design loads . The particle-spring method allows rapid and parameter-depending form explorations  . It also gives a qualitative understanding of structural behavior . This objective is achieved by defining particles, with masses, on which loads are applied, and strings with specified stiffnesses and lengths   . The overall procedure attempts to equalize the sum of all forces in the system .
The structure includes three parts that are defined differently in a single particle-spring model (Figure 2). The initial model includes a rectangular mesh supported on a number of points near its four corners. The central part (red) and the hanging part (blue) are defined similarly (Figure 2). The only difference is the direction of applied design loads (Figure 3). With applied loads upwards, the central part takes the shape of a “perfect” compression vault. On the other hand, with applied loads downwards, the hanging part is a cable net working in tension (Figure 5). Elements in these parts sustain thus only axial loads. In contrary, the intermediate part is designed considering the bending stiffness of the elements through the definition of splines  . In this study, bending is introduced by trying to keep each three consecutive particles in a straight line (Figure 4).
During the form finding process, the values of numerical quantities (e.g. axial and bending stiffness) are arbitrary since it is only their ratios that affect the equilibrium shape. However, for analysis purposes material properties and element dimensions were defined with collaboration with BIC and are given in the table below.
|Specific Weight||11.67 kN/m3|
|Elastic Modulus||2900 N/mm2|
|Shear Modulus||1035 N/mm2|
|Tensile strength||70 N/mm2|
|Compressive Strength||110 N/mm2|
|Bending Strength||100 N/mm2|
The BIC pavilion is thus a suspended pavilion designed as a crossing between a hanging model and a vault with the introduction of an intermediate spline network. The outer part of the structure works only in tension while the central part works only in compression (Figure 6). As a result the intermediate part is designed to sustain bending as transition between these two pure structural systems. Figure 6 shows the hybrid continuous form-found structure, while Figure 7 highlights its three different constructive elements.
In this part, the mesh geometry of the form-found shape is modified, generating a triangular mesh made of equal BIC-Cristal-length segments. Two algorithms are implemented. The first is a customized compass method       . The second uses a spring relaxation method to optimize the segment lengths in the generated mesh     .
The compass method, first proposed by Frei Otto  is a geometric method consisting of tracing a grid with equilateral meshes on a target surface. Two arbitrary curves on the surface are chosen having a common intersection point. These two main curves are then divided. The division points are centers of cirles that intersect each other. The resulting rose pattern generates an equilateral mesh.
In the proposed case, the final mesh geometry is the result of an iterative looping algorithm. To simplify fabrication and construction, the implemented algorithm attempts to approximate the initial surface with a new grid composed of identical equilateral triangular modules.
Starting from an arbitrary point on the surface, a first sphere centered on the latter point – whose radius equals the length of one side of the equilateral chosen triangular – intersects the surface (Figure 8). The intersection results in a curve, called a geodetic (Figure 9). This first geodetic curve is divided into a user-chosen number of points (depending on the squared or triangle grid wanted). A sphere is then placed at each one of these points and returns geodetic curves on the surface (Figure 10). The new collection of points are then found by intersecting with each other the new collection of geodetics.
As the algorithm loops, a rose geometric pattern is created on the whole initial surface, creating a network of equidistant points (Figure 11).
By linking resulting intersection points a new mesh is generated (Figure 12).
However, the precision (identical length modules) of the generated new grid depends on the initial surface curvature and on the chosen size of module. The more curved the surface in either directions the less precise is the new grid. Thus the new grid obtained after this first customized compass method is not exact. For the purpose of the construction of the BIC structure, the end result has to be exact as the main component of the structure – the BIC Cristal pen- cannot have variable lengths.
The obtained grid from the previous algorithm gives a geometry whose meshes are approximately identical. The precision of the approximation is not sufficient for the purpose of our work. On Figure 13 all different modules are colored the same. Thus, the second algorithm works as follows:
Once the rose pattern mesh is generated, a second algorithm is implemented using springs relaxation. The mesh is separated in two parts: springs and nodes. Springs are set to have a rest length equal to the desired triangle side length, while nodes are left free to move in all directions. The spring relaxation optimization algorithm is used to identify a solution where all spring forces are in a static equilibrium. The resulting mesh is thus an approximation of the initial surface, built with identical equilateral triangle modules (Figure 14).
The proposed method’s new grid results from an approximation process. The end result is as close as possible to the target surface. The tool includes a limitation in the movement of nodes far from the initial surface. It could be developed further by linking it to material physical properties.
The final surface generated with the structural form-finding using a particle-spring model, seen in section 2, is here approximated in order to use unique identical modules. However, the level of approximation can be adjusted to avoid changing the global structural behavior reached with the particle-spring model surface. Figure 15 and Figure 16 show the final module arrangement with singular modules in red and the central part in blue.
Figure 17 shows the internal stresses in the structure under its dead load with elements in the outer and central part sustaining only tensile and compressive stresses, respectively. Due to the overall bending action on the middle part elements sustain either tensile or compressive axial stresses depending on their topology. As expected, and due to its extremely light weight, forces in the structure remain always lower than the estimated element yield strength (70 N/mm2). The maximal compression stress value reaches 1% of the yield strength while the maximal tension value reaches 0.7% of the yield strength.
FABRICATION AND CONSTRUCTION
Construction issues concerned essentially means of connecting BIC pens together. Two scales were considered.
The first is the one going from a single pen to a tetrahedron module. The second, links modules together to create the structure. For these two scales we designed connection elements with the required properties for the structure. Two fabrication procedures were considered: 3D printing and laser-cutting. The later solution was chosen, essentially for economic and time-related reasons. Laser-cutting Plexiglas also allowed us to preserve the lightness of the structure and avoid to affect the subtle texture created by the BIC’s transparency effects.
In the central part, the triangles of the base mesh have variable dimensions, per ring (Figure 18). The laser-cut base triangle is the module’s base. It is part of what is called the base mesh. The three edges, linking the vertex of the tetrahedron module to the three vertices of the base triangle, are made of BIC pens (Figure 19). These base triangles are isosceles that interlock to form a ring.
The use of the laser-cut base triangles is necessary because of the overall geometry of the central part. At each vertex a notch in the Plexiglas allows for the insertion of a connector.
In order to link the Plexiglas base triangles with the pens, elements (connectors) fit into a slot in the base triangle (Figure 19). For each connector, two planes are identified: the exterior plane and the interior plane, distanced one from the other, of the thickness of the Plexiglas material. These two planes are intersected with a cylinder whose diameter corresponds to the Bic pens’. Each intersection (one on each plane) constitutes an oval shape. The laser cutting being only held in one plane, perpendicular to the cut object, the two ovals found are unified. Thus, the BIC pen goes through the connector being always tangent to one of the two faces (exterior or interior).
Tetrahedra vertices connectors
In the intermediate part, all edges of the tetrahedron modules are made out of BIC pens (Figure 20). The base triangle being equilateral, and the pens being of the same length, all vertices are identical. Thus, there is only one unique type of connector. The connector is included in a plane parallel to the opposite triangle, situated near the fourth vertex (Figure 20). Let h be the height of the module, the connector’s plane is offset with a value of 0.9h. The connector intersects the three pens. Each connector can only eventually move by sliding along the axes of one of the pens. Yet the three pens are not parallel. Knowing the connectors are placed at the four vertices of the modules, the tetrahedron is geometrically locked. The pens that could eventually slide along their own axis are retained by friction (the connectors are laser-cut without margins). Moreover, if a pen were to slide it would meet at its end the two other pens, keeping the first one from getting out of its position. Thus, a glue-free module is created.
Threading cables: rings and pens
In the cable net part, the pens are without the cartridge and the cap. Pens – that have no structural role in this part – are threaded into cables (Figure 21). The cables – passing through the pen – make the structure. Between each threaded pen, a ring is placed. The ring is of a diameter allowing for the passage of three cables (Figure 21). Each cable goes continuously from its fixed end (connected to the upper frame), reaches the interface with the intermediate part and goes back up to its initial point with a “zig-zag” path (Figure 22). The pens at the interface cable net/intermediate are subjected to high values of flexural stress. Thus these particular pens are replaced by steel tubes of the same diameter.
Connections between modules are called hereafter « butterflies » because of their shape. Their role is essential in achieving a large scale flexible structure, allowing it to adapt to the final form-found shape. The butterfly connections are an assembly of two planar laser-cut elements enabling two modules to rotate one with regard to the other along their common parallel axis (Figure 23).
The butterflies are made of two identical, half-lapped jointed elements (Figure 23). Each element is cut – on its long edge – following a circular arc path. On its short edge, the cut follows a “V” shape. Once assembled, the circular arcs hold the BIC pen. The “V” shaped cut – on the short upper and lower edges – hold a clamp whose role is to connect together two pens and the butterfly connection. This system blocks all translational and rotational movements of the pens, except the rotational movement around the pens’ axis. It creates an articulated connection between modules.
« U »’s
The base mesh is made of identical triangles that are the base of all tetrahedra modules. These base triangles are connected to each other thanks to the butterfly connections. The upper mesh corresponds to a fictive surface linking all vertices of tetrahedral modules (Figure 24). The base mesh is flexible until connections are installed between the modules’ vertices. The upper mesh has the role of constraining the geometry and giving to the structure the overall form-found shape. Connections between the modules’ vertices are “U” shaped: they consist of bars, of variable lengths determined by the 3D model (Figure 25). The two extremities of the bars have branches that are inserted into the tetrahedras vertices connectors (Figure 25). It is only when these “U” connections are in place that the predefined form-found shape is achieved.
The idea behind the BIC structure was to create a structurally innovative pavilion from elements that were not conceived for structural purposes. On social, industrial and commercial basis, the BIC Cristal pen represents a symbol of contemporary modernism. It is definitely not a structural element, yet an object anyone can recognize and probably has used. Creating a suspended structure with BIC pens as design driver resulted in the form finding of a hybrid continuous structure. Employing modern aspects of the design process such as computer-aided design, engineering and manufacturing allowed us to change the function of the BIC pen in a unique way creating a structural paradigm that reflects our culture of recycling, reusing and transforming and relates to IASS.
The University of Miami.
Yousef Anastas, Elias Anastas,
Yann Santerre, Landolf Rhode Barbarigos,
Tim Michiels, Victor Charpentier.
Margaux Gillet, Yousef Anastas,
Elias Anastas, Yann Santerre.
BIC ® Company – France.
École nationale supérieure d’architecture de la ville et des territoires à Marne-la-Vallée.
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