ARCHITECTURAL MEMBRANE STRUCTURES,  THE FUTURE TODAY

With the rapid growth in the use of fabric structures in architecture, engineering and recreation, the designer is able to make use of a methodology and family of materials not considered before. 

The modern concept of the membrane structure, one that provides atmosphere as well as shade, is a concept that the designer is keen to encourage. With the advent of materials that allow us to think of architecture in new and different ways, we can use large spans economically for the creation of architectural spaces never possible before. The designer can use the shape to create an effect that is not just structural or form based. For instance, by combining the translucency of the membrane with the inclusion of (for instance) light wells, to achieve new dimensions in the use of space. 

I believe computer technology can contribute significantly to understanding and managing lightweight structure development. Fabric structures present designers with unique challenges; the designer must understand the principles that constrain the form, as the shapes of membrane structures cannot be dictated by looks alone, and must follow engineering principle and practice to work successfully. 

In the design and engineering of fabric membranes, we combine the talents of the artist and the artisan in a very pure and unique fashion. The artist cannot work on looks alone without considering the geometric form of the surface. The artisan cannot reasonably produce a decent form without considering the artistic considerations. The computer is the tool that helps the artisan to create original forms without ignoring the geometric necessities. 

In a future of uncertain tectonic plates, mega corporations and world access to information, the only surprise (if surprises are possible), will be if membranes are not used as a first choice for large structures. Where the climate allows, the tent as housing may become a fashion feature rather than a building requirement or luxury. Curvilinear shapes, a unique and distinctive feature of tent architecture, will allow a world of variables where there was uniformity, will allow shade and translucency rather than rigid barriers, and a freedom of spirit engendered by the soaring shapes. 
The use of 3-dimensional tensioned surfaces in architecture as a popular medium, is almost exclusively the responsibility of one man, the architect Frei Otto. During the 50's he studied models and prototypes, particularly with soap bubbles and stocking models, to experiment and discover what kind of shapes could be realised. As is usual with any avant garde product, Otto's vision seemed, usually, to be far ahead of the ability of manufacturers and engineers to supply engineering solutions and stressed fabrics on the scale that he would have liked. It was only in the late 60's and early 70's that the spans of Otto's reached great sizes of the German pavilion in Montreal for Expo 67', or the Gossamer roofs for the Stadia of the ill-fated Munich Olympics of 1972. Although these cable net structures looked like tents, the use of steel cables allowed for structures that could not be realised with the use of membranes alone. 

 GENERAL DESCRIPTION OF PERMANENTLY INSTALLED FABRIC MEMBRANES

 There can be little if any comparison of membranes and their translucency, textures and shapes, with conventional buildings. Most buildings are basically rectilinear in form, with a heavy emphasis on mass and opacity. The translucent membrane, (not all fabrics are so, blackout materials are common), provides diffuse interior lighting effects. This gives the membrane inherent advantages over conventional materials when trying to achieve the objectives of style, function, and ultimate beauty. Tents also have the advantage of being easily erected and dismantled and of providing an effective barrier to the weather, the second of which is an essential of any building. 

In order to prevent wrinkling and to maintain it's shape, a fabric structure is held in tension in order to be structurally stable. This is achieved by either internal pressure (air supported structure), or by mechanically pre-tensioning the fabric from poles (tension structure) or within a frame. The shape of the roof is paramount, as in both types of structure, curvature of the membrane is required to translate loads (wind and snow), into tension forces. The tension structure can use a double curvature that is anticlastic (in opposite directions), while the air supported structure is synclastic (curved in the same direction). 

The use of permanently installed engineered fabric membranes is increasing all the time. This is not to say that they are a fad, or that suddenly they are being used everywhere. However slowly and steadily there is increasing evidence of the use of these structures for the roofs of grandstands, for sports halls, for canopies and atrium covers. The advantages of using fabric for structures are: 
 

 Freedom of artistic and architectural expression Visual Impact Energy Efficiency Translucency Prefabrication off site Low Maintenance Cost
 

Fabric membranes can provide an appearance that cannot be achieved any other way. They can provide simple cover where there is none, or generate complex shapes to subtly alter the space they cover. In extreme cases, they can achieve large clearspans that might not be feasible in other ways. The restrictions of self weight, slenderness ratios or uncertain or unstable foundations can all have a bearing on the design of any large span structure, and sometimes, (not always!), the fabric structure can satisfy the requirements of the design. 

Fabric roofs have been used for stadium covers, particularly in America, even being used for the 1994 football (soccer), world cup grandstand covers. Air supported roofs are gradually being replaced with the cable supported variety, as the usefulness of the R Buckminster Fuller 'Tensegrity' inspired cable supported roofs is being proved. The Florida Suncoast Dome is an excellent example of the latest designs. In Arab countries, the tent has a special significance, as the stricture that 'all important events in a persons life' should take place 'in the family tent' has ensured the rapid take up of modern fabric architecture. Two of the most excellent examples of fabric structure design in the world are the Haj Terminal at King Abdul Aziz international airport, covering 418,000 square metres, (4.5 million square feet), and the King Fahd international stadium in Riyadh, surely the most beautiful stadium of all. 

Permanently installed structures can be specified for as simple a reason as the fact that they can be removable, and this means that some local authorities do not necessarily require planning permission or charge local taxes (rates), for their use. Types include simple tubular frameworks with a fabric covering. This type of construction basically uses a similar form of fabricated steel framework as any normal building, but has the rigid roof sheets or skin replaced with a fabric skin. If the shaped roof is tensioned adequately the building will not collect snow or be troubled with ponding. The framework and torsional bracing must be slightly different to allow for the lack of stiffening from the sheet skin. 

Another type is to use a standard anodised portal frame which has channels let into the legs and corrugated steel sheets inserted, this provides vandal free and extremely secure storage. Normal doors and roller shutters can be fitted into this and any other frame. The fact that the roof is a fabric membrane doesn't cause too many problems, the thinking here is that if a potential thief is going to climb on the roof of a building he is going to get in anyway. 

 TENSIONED MEMBRANE'S

 Traditional building's have several elements that determine their form. First, the foundations, then the structure (of whatever material), thirdly, the services, the external cladding, and the interior decoration. A tensioned membrane can also incorporate all these items, but in a way that makes for truly unique structures. The foundations are usually focused on the areas of the supporting structure, (typically masts), and the restraining guy's (tie-back's). The self weight of the structure is minimal compared to (for example) a bricks and mortar building. Instead, the foundations are required to carry the internal forces of the membrane, such as pretension in the skin, or loads in the boundary cables, which can be severe if the structure is required to carry snow loads. 

The membrane or skin, is fastened to the lifting rings (conic's), by bolts or clamping strips. At this point on the roof, the skin is reinforced, gradually more and more, as these small areas of the roof have to carry the loads of the whole structure. Normally the panels of fabric are radiated out from the conic or conic's in the shape of the spokes of a bicycle wheel. This generates triangular panels that are easily cut from rolls of fabric, satisfying the requirements of commercially and ease of handling. These panels have their loads fed into a series of catenary (or boundary), cables. As with the shape of the membrane itself, the curve of these cables can be determined by calculation, and for each and every catenary there is an optimum curve to carry the imposed loads with the least tension in the cable. It is also possible to have fixed, straight boundary's such as walls or channel type eaves which can collect the rainwater runoff. Otherwise, the rain can be diverted to the catenary points by welding small (25-40 millimetre diameter, 1 inch to 1 1/2 inch) flexible tubular guides around the catenary arch. 
 

 CONSTRUCTION

 Membrane roofs use panels, usually laid across the lie of the fabric so that forces fed into the roof fabric are fed bi-axially (at 45 degrees to warp and weft), with surface loads being transmitted evenly across the entire membrane into a catenary, boundary or perimeter wire around the outside of the membrane, and to a heavily reinforced lifting point at the centre of the membrane roof. 

One of the hardest parts of the manufacturing process for tensile structures is not always exactly understood by the layman, which is, to achieve the required geometry for the final structure, every single component, weather it be cables that support the boundaries of the membrane or the membrane surface itself, has to be designed and manufactured to a size equal to the unstretched state of the material. This is achieved through calculation of the materials to be used. These calculations are extremely complex and not easily undertaken. The reduction in size will be exactly equal to the amount that each material stretches under load. Obviously compression members do not have to be made larger as they do not compress enough to make any difference. Therefore, the structure in question has to be modelled, usually with the help of 3-dimensional computer aided design software, to give finite and precise measurement of the structure in its intended state. 

 INSTALLATION

 The final task of the design engineer, apart from examining the structure on site, is to establish a method of erection for the intended structure. Quite often, some form of temporary support, weather they be stays or temporary guys, will be required until all the internal tensions of the structure are in place. The inhibiting factors of site requirements, or conditions, such as existing walls, boundaries and foliage, can also affect the erection process.

 FORM AND FUNCTION - FORM FINDING

 "He who wonders discovers that this in itself is wonder. " 

                                      M. C. Escher 

Although small scale models can be easily made to demonstrate the intended proposal using scaled down masts, string and nylon stockings, they cannot be used to generate the accurate geometrical shape, nor provide the engineering justification for structures that may be 30 or 40M or greater in span and covering 1000Mý or more. In order to achieve such large structures, the engineering designer must have a full understanding of how the structure will behave under differing weather conditions. This is not the same as with a simple space frame or timber beam. This more complex analysis is relatively easily achievable, but with a 3-dimensional surface that carries it's loads in the plane of the skin, normal engineering design methods cannot be used. 

The single most important factor in the load bearing capabilities of a surface is it's form (shape). It is only with anticlasticly (doubly curved) surfaces such as a saddle, that it is feasible to produce structures that resist loadings through deflection, (ignoring air supported structures, which are synclastic, i.e. spherical). 

The surface must have opposing curvatures, (concave and convex), at every point on it, Thus, all imposed forces, irrespective of which side they come from, can be transferred as a tensile force into the plane of the membrane. If the axis of the two opposing curvatures coincide with the patterning, not only has the material the highest load bearing capacity, but variables that come from loading the bias disappear. 

The three dimensional surface of a membrane structure can be made from any shape that allows the surface to counteract the forces applied upon it. It is necessary to design the surface so that only tensile forces are present. Such a surface may have one of two related but opposite forms, either a surface curving in the same direction (as a sphere), or in two opposing directions (such as a saddle surface). The extreme and seldom achieved example of the anticlastic form is the minimum surface. This shape is defined by the smallest possible area between discretionary formed closed lines. Each point on the surface equates the negative or positive curvatures at zero values. 

 USING COMPUTERS TO CREATE THE SHAPE

 On any defined surface there is an optimum curvature that will carry any load, (that may be imposed), with the least strain in the plane of the surface. By using the opposing curvatures of an anticlastic surface it is possible to control the loads with the membrane surface itself. 
Large firms of consulting engineers have developed the immensely complicated software over many years to find the ultimate form for given applications, with and without loads imposed. In contrast to this, my colleague Bruno Postle developed and wrote the basic shapefinding software to provide simple resolution of an extremely difficult and complex task. Shapefinding software can optimise (or relax), the curvature of opposing sign; this balances the potential forces using the optimum curvature that results. 

Some of the simplest structures are based upon square boundaries or bases rising to a point, or variations thereof. A simple hyperbolic paraboloid can be created by four or more straight boundaries, the shape can be added to, and more or less boundaries created to alter the plan of the intended shape. The three dimensional surface can then be 'nudged' and pushed or pulled, with the use of conical rings or catenary arches or curved members to eliminate point loads. Variations of this technique are used to create almost any surface. 

As a rule of thumb, the larger the change, from a flat plane, the more efficient the surface will be. Analysis regularly shows that areas needing higher rigidity also need greater curvature. This shape or 'model' is then assigned the required geometry for the structure in question. Pole heights, and the boundary geometry, (the rim band or catenary curves), are calculated in relation to the level of strain in the fabric, ( to achieve equilibrium in the specified prestress of the various parts of the membrane ). Compared to a flat plane structures, the anticlastic form gives the membrane out of plane stiffness. 

The shape can satisfy both artistic and engineering requirements if the radii of the anticlastic surfaces are small enough to resist out of plane loads. If a good shape is chosen, the membrane will have low tension in the plane of the surface, and deflection will be reduced as the surface has a form that will resist loads. 

When loads are imposed upon an anticlastic surface, one dimension of the curvature tightens and it's opposing curve relaxes, causing local unstability (and possibly wrinkling or ponding). This is prevented by prestressing the membrane in it's unloaded state to a level that precludes wrinkling. A popular misconception is that prestressing is added to the total load. In fact, under certain conditions it decreases as loads are applied to the membrane. 

ANALYSIS 

" Mathematics, rightly viewed, possesses not only truth, but supreme        beauty, a beauty, cold and austere, like that of sculpture." 

                          Bertrand Russell 

The quantitative analysis of the behaviour of fabric structures under severe loadings, has developed to the point where they can now, be engineered in every way to the same performance criteria as a permanent structure. With the assistance of computers and very high level of engineering, the consulting engineer is now able to provide analysis on even the most complex of fabric shapes. 

Because fabric membranes undertake relatively large shape changes under wind load, ( in comparison with other structures ) the analysis must prove the surface form under load in it's pretension state, and in its loaded state. This means the membrane must be analysed in a series of unequally different geometry's to prove non-linear performance. On a conventional structure, if the loads increase, then the stresses increase proportionally. On a non-linear structure, the resultant load is not constant. 
Ultimately the maximum load that can be imposed upon a membrane is that which matches the maximum tensile strength of the skin. As the skin is 2 dimensional, (or effectively so), and the thickness of the material is minimal, (to the extent that it effectively has no thickness), there can be no bending or compressive resistance. 

The skin must remain in tension at all times. Therefore the maximum stress that can be accepted by the membrane is the ultimate tensile resistance in the skin. The fabric roof, (once the equilibrium shape has been determined), is, under analysis, given a loading equal to the highest pressure expected, which deforms the initial equilibrium state. This deflection is taken up by the fabric membrane in response to the load. 
Because the fabric membrane has a certain give to it, which acts as a shock absorber, the membrane redistributes the load across the whole surface, and higher wind loads can usually be taken by membranes than by traditional tented structures. In this way, with loading on one corner of the membrane and lift on the other corner of the membrane, the deflective shape transmits load from one high down force area, to the other high lift area, without too many problems. 

It is nessesary to allow for a given pre-tension in the erected structure as a value during the initial form finding. This pretension, sometimes as high as 1-1.5 tons, per lineal metre of membrane, usually measured at the perimeter is required to provide the out of plane stiffness to prevent buckling or wrinkling and is an intrinsic part of the actual membrane design. 

The resulting figures are taken by the engineer performing the analysis and are compared to 'rule of thumb' estimates and results from previous similar successful structures as a rough check to determine that these precise numbers are accurate. Once the maximum displacement has been checked of the membrane; it's maximum shape change, it is often a good idea to re-run the shape finding software, with the nodes in that position to determine whether the pre-determined form matches the maximum shape deformation or whether local high stress points or even by generating high stress points in one area, relaxation of the membrane occurs in another area. All of these must be allowed for and the best and most complex of software achieves all of these in an interactive package that combines all the functions described and in a form of dynamic loop of shape finding, applying pressure, measuring the dynamic response, checking the maximum displacement and checking the patterned shape against that maximum displacement and in the pretension state, to give a software package that is truly rounded. Various offices have forms of this, and usually the engineers prices reflect the sophistication of the software, rather than the actual skill of the engineer although it is usually only the most skilled and experienced engineers that use the top end software. 
This process of the design of fabri membranes is further complicated by the addition of stiffening members or webbing's or rigid members within the membrane, particularly when the stretch characteristics of the stiffening members may be different from the membrane itself, for example; the membrane will have one stretch characteristic of co-efficient, and a webbing sewn to a fabric strip and then welded to the membrane will have considerably different stretch characteristics, therefore both must be tested and the stretch correction factors allowed for in the dimensions and when the webbing is welded to the fabric membrane each must be stretched to the correct tensions prior to welding tone to the other. This will result in the webbing puckering the fabric membrane that it is attached to and when loose in the workshop and will only pull out flat when have been tensioned to the correct amount in their service conditions. 

THE DESIGN PROCESS FOR MEMBRANES 

The Design process for any membrane begins with establishing the control points/ registration points/ system points; whatever terminology you use to describe the method of establishing the boundary geometry of the structure. This is usually achieved by modelling the structure in 3D on a graphics computer. The surface is usually represented as a mesh modelled on the computer in 3D which is then assigned to specific properties, for example; catenary arches must be defined as so and given a value or tension. Straight edges, or rigid members must be defined as straight edges. Fixed control points must be defined as fixed control points and there can be one further type of entity or node which is the mirror node. This is an edged node which acts mathematically as if it were not an edge, but as if the membrane had continued around past its own point, i.e., whatever values acted upon it one side, are also specified or stated to act as its equal and opposite side even though they are not there. This is purely to allow you to model one quarter of a structure that is uniform instead of the whole structure and obviously is quicker and simpler, and obviously only works on structures that have a regular shape that can be broken down to equal or mirrored sections. The other nodes of the surface mesh apart from all the described edge nodes have a floating value and it is this part of the mesh that is allowed to be balanced. 

The links between the floating nodes are weighted against each other and all surrounding nodes and the 3D spacial positions of the node are compared against all the other nodes that surround it starting at 0,0,0 (The datum point). This balancing is calculated for each node right the way across the membrane. Having once changed the nose positions, and moved onto the next one, the previous node is then no longer balanced against the next one and must therefore be re-calculated a number of times (or iterated) to a level that is acceptable. 

The links for logical lines across or diagonal to the mesh, as can be seen in illustrations xxx, xxx and xxx, are highlighted links which can be made into geodesics which will represent the edges of the fabric panels as they follow up or across the shape of the surface. These links (or quasi panels) are measured by their 3 dimensional spacial co-ordinates and redrawn in a flat plane as a series of triangular polygons and rolled out along the common side of the triangles to provide the flat 2 dimensional patterns needed for the creation of 3 dimensional shapes, and these two dimensional panels can be exported into CAD packages, dimensioned, or imported into plotters for cutting. However once these panels are rolled flat, the longest dimension is measured, and a perpendicular line through that longest dimension is measured and compared with a maximum width that corresponds to the fabric role width. This is user-definable in software, for example, 1500 mm, 2050mm or 2500mm, all standard role widths. The membrane can then show whether the results of flat panels would be within that width if laid flat. This software is a very powerful tool for the conceptual design and the production finishing of membranes. From this description of membranes, I have only omitted the analysis section, i.e.. the loading and determining of stress levels within the membrane. This will be detailed separately. 

From the previous description it is possible to understand that by repositioning the control points, or joining sections (mirror nodes) to other fabric sections, which would usually be where it would be laced or joined, it is possible to assemble large sections with disparate shapes. These control points can be fixed boundaries such as solid framework to fasten the framework edges to, or system points at the top of perimeter poles or the tops of the membrane cones at the top of the lifting rings. 

The whole process to design a simple membrane can take as little as two to three hours, to arrive at the level where conceptual drawings are good enough to show the client. The analysis part is much more complex and would require much explanation at a highly technical level by other members of our design team who are involved with the writing of analysis software and of structural engineering generally. The basics of analysis are: the pre-determined shape is given a load equal to that envisaged by the structural engineer. This is determined from; 

1) code provisions from national research bodies 

2) assessment of the conditions, ground terrain factors and likely exposure to wind etc. by the engineer 

3) from fixed formulae laid down in building codes 

4) from the experience of the engineer on previous structures 

DYNAMIC LOADING 

Once these pressure coefficients have been determined they are applied to the surface in the form of a load with factors equalling the varying loads at the varying points on the surface, either positive or negative. These loads are applied as a force to each node, an accelerative force, either perpendicular, or vectored away from the direction of the force. This force depending upon the plastic properties of the membrane, (plastic in engineering terms not in materials terms), allows the material to give somewhat, (this even includes solid sheet products such as steel), and as fabric membranes tend to displace more than such solid products, this accelerated force away from the node is damped by the increased tension in the membrane, which then snaps back in a dynamic response to the applied load. The speed and the force of this response forms a dynamic oscillation which can be measured by the analysis package. 
From these measurements these structural conclusions can be drawn; i.e. will the membrane withstand the projected loads (wind and even snow in the case of permanently enclosed structures). This analysis, much like the shape finding previously is conducted on a node by node basis starting at one point on the membrane and working node by node on every point on the membrane and the whole process iterated many times until precise figures from the whole surface are recorded. Certain packages are also able to determine the maximum deflection of the membrane under its maximum load, or on an over-maximum load to allow for factor of safety. Both of these are not required to answer the basic question; Is this membrane strong enough for the envisaged loads, if a rough rule of thumb is applied. There are other luxuries which can be added to the analysis package such as providing a pre-determined figure for maximum tear strength, usually measured in kilograms per lineal metre and showing whether certain areas of the membrane exceed these values or not. These individual polygons can then be shaded according to the maximum stress measured in that area. The resultant colour-graded stress graph is known as a Von Mises graph. 

The resulting figures are taken by the engineer performing the analysis and are compared to 'rule of thumb' estimates and results from previous similar successful structures as a rough check to determine that these precise numbers are accurate. Mistakes can always occur, which is why a scientific approach is the norm. Once the maximum displacement has been checked of the membrane, (it's maximum shape change), it is often a practice to re-run the shape finding software, with the nodes in that loaded position to determine whether the pre-determined (prestress) form matches the maximum shape deformation, (loaded state). This checks whether local high stress points, (for example, the generation of high stress points in one area such as near a stiffening belt), causes the relaxation of the membrane in another area. Therefore, during the membrane analysis; it is necessary to allow for a given pre-tension in the erected structure as a value during the initial form finding. This pretension, sometimes as high as 1-1.5 tonnes per lineal metre of membrane, (in the installed state), usually measured at the perimeter, is required to provide the out of plane stiffness to prevent buckling or wrinkling and is an intrinsic part of the actual membrane design. 

All of these must be allowed for and the best and most complex of software achieves all of these in an interactive package that combines all the functions described and in a form of dynamic loop of : 
 

Shape finding, applying simulated loads, measuring the dynamic response, checking the maximum displacement, and checking the patterned shape against that maximum displacement and in the pretension state to give a software package that is truly rounded. Different vendors have various forms of this, and usually the engineers prices reflect the sophistication of the software, rather than the actual skill of the engineer although it is usually only the most skilled and experienced engineers that use the top end software.