APPLICATION OF FOLDED SURFACES IN CIVIL ENGINEERING

Headnote

Abstract: The paper presents the usage of folded surfaces as parts of a building system. This type of surfaces is not often used in constructions, even though the structures get to have a very special and spectacular design. The authors present some of the most known structures using the folded surfaces as a building component.

Key words: folded surfaces, structure, design, industrial.

INTRODUCTION

Folded surfaces are not widely met in constructions history nor in nature, therefore it is relatively hard to understand their constructive concept by comparing it to existing elements.

The purpose of this research was to better understand the folded elements concept, to analyze the existing structures and the design trends for this topic.

2. FOLDED SURFACES GENERAL CHARACTERISTICS

2.1 Design concept

The design concept for folded surfaces was developed by using small models. Hence, the main steps for developing folded elements will be shortly described hereinafter.

Let us consider a sheet of paper, placed on two supports, on opposite sides one from another. The sheet will fold, since it is not able to sustain its self-weight. Nevertheless, if the same sheet of paper is then folded with parallel slits, perpendicular on the supports, on the direction that it needs more stiffness, the paper becomes rigid and can sustain its own weight. Additionally, it can support a load ten times higher than the value of its selfweight!

Continuing with this experiment and increasing the loading over the load-bearing capacity of the folded paper, it can be observed that the "structural" failure occurs by disjoining the folds. By blocking the unfolding of the sheet, by binding their frontal sides into bracings (called tympani), the folded sheet will successfully bear the load increase. The main condition for this to happen is for the stiffening tympan to lay on the supports.

Hence, the so-called yoke-diaphragm is created, which represents the basis of a folded structure. The only remaining condition for this structural folded element is to be made out of a material that can provide a good flexural behaviour, meaning that it can support both tensile and compressive stresses.

2.2 Folded elements building materials

A short analysis on the main construction materials, with respect to their use for building folded structures, is presented hereinafter:

· Wood - theoretically, wood could be a viable material for folded structures, but, unfortunately, there are several inconveniences that may occur. Creating large wood panels, like the ones needed for creating folded elements, is difficult and expensive. In addition, it is complicated to realize strong bonds between the folded surfaces. Due to these reasons, wood is not used for building such structures.

· Metal (steel or aluminium) - due to its tensile strength, it can be formed into thin plates, but the danger of buckling appears, and this disadvantage prevents metals from being used for large scale folded surfaces.

· Masonry or stone - by its definition, being composed from smaller blocks or, respectively, stones, does not fit the characteristic needed for building folded structures.

· Advanced composite materials - these are relatively new in the constructions industry. Folded elements can be produced from polymeric composite materials, especially for roof components, like skylights, for industrial constructions, Fig. 1.

· Reinforced concrete - is highly recommended for folded constructions, due to its overall structural behaviour, especially for its flexural strength.

Considering this materials analysis, the large majority of folded structures are made of reinforced concrete. Therefore, the case studies presented in this paper will contain folded elements made of reinforced concrete.

2.3 Functional parts

Folded surfaces behaviour can be divided into three functional parts:

· Bearing action of the surfaces between the folds and oriented transversally to them - the surfaces bear between the folds, from ridge to eave, and reversed. They work together like a reinforced concrete plate with continuous supports, the bearing being alternated up and down. The supports are assured by the stiffening capacity, ensured by the superior side of the ridge fold and by the inferior side of the eave. The surfaces in between the folding lines are loaded similar to the inclined plates.

· Bearing action of the surfaces parallel to the folds, on their longitudinal direction - the ridge and eave sustain the loads given by the continuous folded plate. The loads are divided into components and transmitted to the oblique surfaces according to their inclination. The oblique surfaces are this time considered load-bearing plates, on the longitudinal direction. They transfer these loads to the supports, similar to several oblique inclined beams, placed one above the other. The load-bearing capacity of the surfaces increases with their inclination angle and with their height, measured on the inclination. For a small inclination, the folded structure loses its efficiency. Therefore, when laying several folded surfaces one adjacent to another, on their longitudinal direction, an analogy can be made with the real bearing efficiency of beams.

· Tympani behaviour - the folds shape must be maintained at the supports by using frontal tympan. The slits unfolding induce the loss of height and, finally, failure. The most efficient tympan has the shape of a solid frontal wall.

Respecting the three aforementioned functional parts, different solutions can be developed for folded elements. The most important aspect is the folds shape. The ratio between the height and inclination over the span determines the rigidity and the bearing capacity of the construction. The folds proportions and the tympani mode of realisation underline the efficiency of the folded surfaces bearing capacity.

3. STRUCTURAL SOLUTION FOR FOLDED SURFACES

3.1 Structural solutions for stiffening the folds shape

The folded surfaces diversity is given by the slits and tympani realisation mode, so that the three functional parts are simultaneously accomplished.

The tympan can be replaced with a tie-rod, Fig. 2, if the folded structure's supports are at its lowest points, where the tie-rod is applied. In this case, the edges of the folded surfaces thicken, becoming more stiffened, so that the loads will successfully reach the supports through them.

An intermediary solution, between the usage of tympani and tie-rods, is a stiffened double bifurcation, with V-shaped braces (arms), for the marginal border.

3.2 Structural solutions for the folds shapes

The folded structures can have, according to their realization mode, several shapes, Fig. 3. The simplest shape is when the folds are parallel to each other, Fig. 3. a. For a trapezoidal plane shape, the best choice is the fan-shaped folds, Fig. 3. b. Using this arrangement, the distance between the slits increases towards the exterior, together with their height.

Another shape is provided by counter-direction folds. The folds can have lengths equal to the span, Fig. 3. c, or smaller than the span. In this case, the folds intersect each other and create discontinuous lines in the load-bearing structure, Fig. 3. d. Hence, stiff corners are created and the folded structure becomes a frame structure. The danger that must be considered in this case is the unfolding of the slits, at the frames ends.

4. FOLDED SURFACES CASE STUDIES

Concrete folded surfaces have been used throughout history, impressing their viewers and successfully passing the test of time. Some of these architectural and structural masterpieces will be analyzed hereinafter.

4.1 Power Plant from Birsfelden, Switzerland

In the case of this construction, the folded surfaces of the covering appear to be extremely thin at the edges. The unfolding of the slits was stopped by using a different method: the fork-like columns are connected by their ends and become a chain of steady bearing points that prevents any deformation of the folds, Fig. 4.

4.2 UNESCO Headquarters from Paris, France

This building is a remarkable example for folded structures. From the trapezoidal plane shape of the building, an impressive folding system resulted. In addition, from connecting the covering with the folded walls, the framing system was created. The frames have two openings and the columns and beams create the folded structure, Fig. 5 and 6.

4.3 The Church of Saint John Abbey Monastery, from Collegville, Minnesota, USA

The designer used, as structural theme for this church, a folded structure developed in the shape of a double pinned frame, Fig.7.

4.4 Mc. Gregor Memorial Conference Centre, from Detroit, USA

The extremely simple and clear shape of the structure gives the structural solution of the building, Fig. 8.

There are numerous complicated details created by the oblique intersections of the construction, and they are visible, giving a stunning architectural view to the building. This construction presents one of the noblest applications of folded structures. The precise and strong geometry characterizes the whole structure and dominates over its surroundings.

4.5 Notre-Dame Church, from Royan, France

The church has an ovoid in-plane shape, therefore the marginal walls are constructed by using columns with a V-shaped cross-section, opened towards the exterior. The openings in-between the columns are closed by strips of glass. Due to the folded shape, each column is very stiff. All the columns are connected by visible external corridors that spatially unify the building, Fig. 9.

4.6 Sears Tampa Company Store, from Tampa, Florida, USA

The structural material is concentrated at the most flexure stressed areas, meaning at the ridge and eave levels, by intersecting the strips of the horizontal plates. This solution considerably increases the bearing capacity of the folded structure, Fig. 10. Following this same principle, the folded metal sheets were created.

4.7 Exhibitions Hall from Torino, Italy

The load-bearing structure for this construction is composed by arches. Nevertheless, this construction will be considered as an example for folded structures due to the arches stiffening ribs, which are folded elements, Fig. 11.

The folds, visible in the ribs cross-section, provide the rigidity if the arches and they represent material concentration areas, at ridge and eave, similar to the construction presented at point 3.8.

5. CONCLUSIONS

When realizing folded constructions, the architects' fantasy was not enough. Mastering the geometry of the folded bearing structures and understanding the way that they work is utterly important for both the designer and the architect.

As expressed in the examples presented in this paper, folded structures have long service lives, both due to their very good structural behaviour, and to their impressive shape and aesthetical characteristics.

References

REFERENCES

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