Prestressed composite footbridge

Creteil is a city of 90.000 inhabitants in the southeast suburb of Paris. It started to urbanize itself in the late 50’s, impelled by the French architect Charles-Gustave Stoskopf. In 1976 he designed Notre Dame of Créteil, a modest catholic church made of concrete, which became a cathedral 10 years later. Recently, the diocese of Creteil has undertaken a major architectural redevelopment project of its cathedral, including a timber shell covering the religious area and the creation of a new cultural area. Once transformed, the edifice shall be more visible, more hospitable and livelier for citizens. Inevitably, such a molt takes time and a temporary place of worship was required to ensure liturgical services during the two-years work. In November 2011, T/E/S/S, the structural design office in charge of the cathedral renovation project, made an ambitious proposal to the diocese. Based on a previous successful experience – the construction of a composite gridshell for the festival Solidays (see video [1]) – T/E/S/S suggested that rather installing a basic tent, the parishioners should construct themselves a temporary cathedral (see video [2]). The overall cost of the project is 400k€, about 30% more than a standard tent of the same size that would have been rented for 2 years.

The generation of the form was driven by two objectives that of providing a variety of appropriate internal spaces within which the community could assemble, and externally to be a welcoming and visually interesting form. Today, the internal organization of a Roman Catholic Church is in large part driven by the post Vatican II vision of a religious celebration being a collective gathering of the community around the Eucharist, center of spiritual life. A circular seating arrangement is often considered the most convivial form to create a sense of belonging while minimizing a sense of hierarchy (Fig. 2).

However the community is not only using the building for religious celebration but also for encounters on a more informal manner, for example spontaneous gatherings after religious ceremonies. In the early Roman church, such gathering of the community was facilitated by the presence of an anti-space to the main space called a narthex, through which one passed on entering the church. It was therefore felt appropriate that the formal freedom which the gridshell system offered would be used to explore forms composed of an agglomeration of major and a minor volumes which contain the two functions: formal and informal gatherings (Fig. 3).

Formal explorations were undertaken using modeling clay. The final form is based loosely on two adjacent semi spherical volumes of different size, which are merged into one complex form. Externally the fear of the design team was that the totally convex blob form could look intimidating. It was therefore decided that the two spherical virtual forms, which would be joined to make the final form, would be arranged not in a symmetrical axial manner, but in an asymmetrical curved composition. The resulting form seen in plan is convex on one side and concave on the other. The concave form in plan allows for double curvature to be introduced into what would be otherwise a simpler blob and gives sensuality and visual interest to the building.

The temporary cathedral is located on a land owned by the municipality, which is used for sporting and other communal gatherings. The curve in the building defines an external area where the church community could meet in the open air and this is where the entrance to the church is situated. The building was positioned on the site so that the entrance addresses a grass planted area forming a garden forecourt or “parvis”. A service building housing plant, toilets and vestry are housed in a portacabin positioned to the rear of the building.

It is formally quite difficult to integrate doors, which must be verticals, into a complex geometry. Either the gridshell could be deformed to accommodate the geometrical requirements of doors, or the doors could be integrated into an independent form. The latter approach was chosen. In looking for forms to house the doors, reference was made to the conical monumental doorways with rings of concentric decoration, which welcome the faithful to Romanesque and Gothic churches in France. The conical forms were found to by coherent to the overall geometry of the building. The entrance doors were therefore inserted into a conical hooded form made of rolled steel plates and stiffened by concentric steel tubes, which not only make reference to historic precedence but also refer to the gridshell to be discovered inside.

The cone of the entrance doors was positioned in the concave side of the building giving access directly to the narthex part of the internal volume (Fig. 4). To the rear of the church is situated a service door. The steel hood, which houses this door, is curved tightly around the door and takes up an ovoid form.

The gridshell structure is made of long glass-fiber pipes (∅ext 42mm) pinned together with scaffold swivel couplers. The structural members of the grid, all of different length, are built from one, two or three composite pipes connected with steel sleeves (§6.2). The length of the pipes is restrained to 12m so standard trucks can deliver them. The pipes are organized in three layers. The first two layers are placed perpendicularly on the ground. They form the “quadrangular primary grid”. The distance between the pipes of these two layers is constant so the grid is regular. This primary grid is elastically deformed to obtain the final shape. The third layer of pipes acts as bracing. It gives the structure a shell behavior. Those pipes are fixed to the primary grid once it has been shaped. The structure is anchored to a concrete strip footing with a special steel system, which ensures the transit of loads from the composite structure to the ground. A similar system enables to fix the structure to the doors.

A PVC coated fabric, tailor patterned, covers the structure. It includes transparent strips that bring daylight inside. The fabric is stretched on a devoted peripheral edge beam with a double lacing system (halyard and strap). At the ground, the lacing edge beam is made of a bent composite rod nailed regularly to the concrete slab. At the doors, it is made of a steel arch welded to the doorframes. The membrane is waterproof and as a continuous membrane has no joints except at the perimeter. At the perimeter a continuous strip of membrane is prefixed to the internal face of the membrane and fixed to the ground slab being clamped between the concrete and an aluminum flat bar. At the doors, the flexible strip is riveted to the doorframes.

The gridshell is covered in a PVC membrane, which is opaque. How to introduce daylight into the interior was a major subject of reflection. The simplest way found was to use transparent membrane placed occasionally on the membrane. A small amount of light was required in the interior to create a contemplative atmosphere. The lights would in consequence glow and would be seen as luminous insertions in the vault, like stars in the celestial vault or the apse of some Romanesque churches. The stars were patterned on the joints of the PVC membrane. The almond shape came from simplification of the cutting into the panels either side of the joints and to avoid stress concentrations around cuts in the membrane. This shape, known as Mandela, is frequently used in Marian religious imagery. The distribution of the transparent insertions is quite uniform but gets denser above the pinnacle.

The goal of the design process is to identify a gridshell structure that works and which respect as faithfully as possible the architectural project – a shape and a program. It represents “the path from shape to structure”. Its progress, sequential and iterative, revolves around three major stages: shape, mesh and structure (Fig. 7). It is not trivial to go through this complex process. Indeed, for each step, the method, the tool, the criteria, that offer both a sufficient explorative richness to find out enough candidate solution, and the means to evaluate and compare the suitability of those solution, have to be found.

The first step of the process consists in building a precise geometric model from the sketch of the architect and to evaluate its mechanical potential (Fig. 8). At this stage, the goal is to estimate the probability a given shape would lead to the generation of a structurally feasible gridshell. The figure shows a selection of 3 slightly different 3D shapes, derived from the targeted shape, based on an analysis of their principal curvatures. Stresses in the grid are mainly due to the bending of the profiles. They derive directly from their geometric curvature. Thus, the principal curvatures of the surface – because they give a qualitative measurement of the local curvature of any curve drawn on a surface – are relevant indicators to evaluate the stress rate of a grid laying on it. Particularly, one should ensure the following condition is satisfied everywhere, where r is the pipe’s outer radius, Rmin is the minimum principal radius, E is the flexural modulus, σk,flex the characteristic flexural strength (§5.3) and γlt the long-term partial coefficient of material resistance. Ideally, the shape is controlled by few key parameters. Thus, it can be adapted and optimized through an iterative process, towards this criterion (1).

During the second step, the candidate surface is meshed and the mechanical potential of the resulting grid is evaluated. At this stage, we try to estimate the probability a given mesh could lead to the generation of a viable gridshell structure (Fig. 9). Simultaneously, meshes are compared according to their architectural relevance. This time, the geometric curvature of the polylines drawn on the surface is the criterion to characterize the mechanical potential of the grid. In particular, one should ensure the following condition is satisfied everywhere, where Rspline is the spline’s local curvature radius: The mesh is obtained by the compass method, described in [11], which develops a regularly spaced grid on a surface from two secant directrix. For a given shape there are an infinite number of meshes. The aim is to identify at least one grid, suitable towards architectural and structural criteria (Fig. 9). The figure shows resulting meshes and flat grids, depending the directrix. The laboratory tried various numerical methods to generate such grids [12]. Here, a specific software [13], developed for rhino & grasshopper, allows generating this kind of mesh on any nurbs surface. It performs the following elementary operations: surface meshing with the compass method, trimming, control of geometry’s integrity and flattening of the grid. The tool also generates automatically a text file, which can be imported in structural analysis software, containing all the required information to perform the formfinding of the structure. An add-on facilitates loads application of various complexities (snow, wind, etc.), which is tricky for free forms.

In this project, one can identify 4 major structural details : the swivel coupler for connecting com- posite tubes to assemble the grid (Figure 8a); the steel sleeve for connecting several composite tubes to make long members from initially short piece of tubes (Figure 8b); ground anchorages for fixing the structure to the concrete slab (Figure 8c) and the lacing edge beam of the fabric (Figure 8d). Note that the tricky issue of connecting steel and composite parts is solved in a similar way through sleeve and anchorage details.

Sleeves are major components in the structural system. The presented component is a great innovation compared to the composite gridshells built previously, where members were simply interrupted or overlapped. By establishing mechanical and architectural continuities between pipes, this sleeve brings closer the real behavior and the theoretical behavior of the shell.

The sleeve is a steel system that sets up mechanical continuity between two adjacent composite pipes for both tension and bending. It is made of three parts: two connectors linked by a threaded rod (Fig. 12b). Each connector is a 48.3×2.9mm steel pipe, slightly larger than the composite pipes on which it is put on, with a welded M20 nut at one of his end. The connector is pinned to the composite pipe with three 10mm bolts. Some structural adhesive is also employed to fill gaps and to guaranty a good rigidity of the assembly. However, the sleeve is designed ignoring the adhesive contribution to the mechanical strength of the system. A M20 threaded rod links the two connectors. It allows tension forces and bending moments to pass form one pipe to the other. It cannot transfer any twisting moment.

Tension forces are transferred from the composite pipe to the connector through shear in the pins. Thanks to a lower bearing resistance in the composite than in the steel, each of the three pins can be gradually loaded. When loading the system, at first, only one of the three pins is really in contact with both the steel pipe and the composite pipe, because of inevitable small manufacturing gaps. When increasing the axial load, this pin starts to “eat” into the composite pipe until the second pin comes also in contact (Fig. 13). This scheme is reproduced until another failure mode happened. For this mode of composite failure, which prevails in this case, the total bearing capacity of the assembly is thus three times the capacity of a single pin.

Bending moments are transferred through the threaded rod of the sleeve. This part is designed to reach simultaneously the two following qualitative criterions. Firstly, the rod bending stiffness should be roughly equivalent to the composite bending stiffness itself to preserve curvature’s continuity along the system. Note that this continuity is of prime importance from an architectural point of view. Secondly, the steel quality of the rod should be adjusted so it starts its plastification when the composite pipe tends to approach its maximum design stress (a third of the yield stress). Thus, the rod acts as a “fuse” which concentrates rotational deformations avoiding failures in the critical elements of the structure (the composite pipes).

Beyond the technical difficulties related to both design and structural analysis of the shell, the regula- tory framework was a vital issue for the project’s success. Because it was the first time a structure of this kind would host regularly a large number of people in a long-term period, the question of its re- liability over time was a major issue. To be built the gridshell had to comply with existing standards, which do not take into account such an innovative edifice, all in composite material. The strategy adopted to bypass this obstacle consisted in making the most of the existing regulatory framework to justify the compliance of a structure that would not, at first sight, be taken into account by stan- dards that does not include composite materials. As far as possible, the design was led in compliance with the Eurocodes, where the structural design is made according to limit states under normalized loadings (self-weight, snow, wind, etc.). Despite the Eurocodes do not directly take into account com- posite materials, they propose some probabilistic methods to introduce new materials (Annexe D). As far as possible, the mechanical properties of the GFRP pipe were determined by tests in conformance with these methods. Otherwise, values where taken according to the Eurocomp [16]. In some cases, as the sleeve, the design of the construction details has also benefited from this approach.

Placing & Concrete slab and footing.

Delivery, cutting, gluing, connexions

Delivery, cutting, gluing, connexions