Post-Tensioned Modular Inflated Structures Romuald Tarczewskil Wroclaw University of Technology romuald.tarczewskiOpwr.wroc.pl Pneumatic structures are usually considered as inalterable,with predeter- mined features,e.g.shape etc.According to this approach,they cannot be easily rebuilt or modified.Application of techniques current in other sectors of construction industry leads to the structures that are much more flexible and adaptable. 1 Introduction The prestressing technique was applied to concrete and steel constructions in first decades of 20th century.It appeared after a period of development of these constructions,and its usage is obvious and common at present.Yet in reference to pneumatic constructions,the conception of prestressing ap- peared at the beginning of their development.The first known documentary evidence of the conception to use structural pneumatic elements comes from engineer Joachim A.Sumovski.He obtained,in 1893,an American patent on air-inflated structures [1].One of the drawings included in patent specification presents the structure that obtains its shape and loading capacity as a result of prestressing,Fig.1. Fig.1.An example of air-inflated structure invented by J.A.Sumovski 221 E.Onate and B.Kroplin (eds.).Textile Composites and Inflatable Structures,221-239. C 2005 Springer.Printed in the Netherlands
Post-Tensioned Modular Inflated Structures Romuald Tarczewski 1 1Wroclaw University of Technology romuald.tarczewski@pwr.wroc.pl Pneumatic structures are usually considered as inalterable, with predetermined features, e.g. shape etc. According to this approach, they cannot be easily rebuilt or modified. Application of techniques current in other sectors of construction industry leads to the structures that are much more flexible and adaptable. 1 Introduction The prestressing technique was applied to concrete and steel constructions in first decades of 20th century. It appeared after a period of development of these constructions, and its usage is obvious and common at present. Yet in reference to pneumatic constructions, the conception of prestressing appeared at the beginning of their development. The first known documentary evidence of the conception to use structural pneumatic elements comes from engineer Joachim A. Sumovski. He obtained, in 1893, an American patent on air-inflated structures [1]. One of the drawings included in patent specification presents the structure that obtains its shape and loading capacity as a result of prestressing, Fig. 1. Fig. 1. An example of air-inflated structure invented by J.A. Sumovski 221 E. Oñate and B. Kröplin (eds.), Textile Composites and Inflatable Structures, 221–239. © 2005 Springer. Printed in the Netherlands
222 Romuald Tarczewski However in air-supported structures,particularly of large span,strength- ening cables are nowadays often applied [2]-prestressing is not yet obvious in air-inflated structures. Another,well-known structural concept,which provides with many ad- vantages in terms of creating structures -is the use of repeatable,modular units,that can be assembled in a larger,complex structure.The spectacular example of application of repeatable air-inflated units for constructing a large structure-was the pavilion of Fuji Group,at Expo'70 exposition in Osaka 3. The advantages of modular structures are especially exposed,when units of relatively small dimensions are used.This allows constructing structures of various shapes,while limited quantity of different units are applied.The units can be used repeatedly many times.Shape of the structures created in this way is limited only by topological restrictions of division of considered surface.This applies in particular to the shell structures. Post-tensioning is a way of splicing small elements but also a way of shap- ing the structure.Coupling of these operations raises the efficiency of solution. Because of specific properties of pneumatic structures,suitable technical so- lutions are required,especially concerning supplying the elements with air, stabilization of their shape as well as method of connection. 2 Modular Air-Inflated Elements Applied to Shell Structures 2.1 Principles of Composition Depicted structures present a class of spatially curved surface girders.Their rigidity and loading ability are strongly related with the shape.Spatial cur- vature itself,is not a permanent,generic feature of the structure (as it is in concrete shells for example),but is achieved and maintained by means of post-tensioning,causing very large initial deformation.Thus,the final shape and properties of the structure are function of initial configuration and the course of post-tensioning process. Internal structure of modular air-inflated shells distinguishes them from other air-inflated structures and from other shell structures.They consist of the following basic elements: air cushions (main modular elements) tension cables cross-braces (optional) Air cushions and cables appear in shells of all types,while cross-braces only in the shells with increased structural height [4.After assembling,structure forms complete roofing and does not require any additional membranes to cover space.General view and components of an exemplary structure is shown on Fig.2
222 Romuald Tarczewski However in air-supported structures, particularly of large span, strengthening cables are nowadays often applied [2] – prestressing is not yet obvious in air-inflated structures. Another, well-known structural concept, which provides with many advantages in terms of creating structures – is the use of repeatable, modular units, that can be assembled in a larger, complex structure. The spectacular example of application of repeatable air-inflated units for constructing a large structure – was the pavilion of Fuji Group, at Expo ’70 exposition in Osaka [3]. The advantages of modular structures are especially exposed, when units of relatively small dimensions are used. This allows constructing structures of various shapes, while limited quantity of different units are applied. The units can be used repeatedly many times. Shape of the structures created in this way is limited only by topological restrictions of division of considered surface. This applies in particular to the shell structures. Post-tensioning is a way of splicing small elements but also a way of shaping the structure. Coupling of these operations raises the efficiency of solution. Because of specific properties of pneumatic structures, suitable technical solutions are required, especially concerning supplying the elements with air, stabilization of their shape as well as method of connection. 2 Modular Air-Inflated Elements Applied to Shell Structures 2.1 Principles of Composition Depicted structures present a class of spatially curved surface girders. Their rigidity and loading ability are strongly related with the shape. Spatial curvature itself, is not a permanent, generic feature of the structure (as it is in concrete shells for example), but is achieved and maintained by means of post-tensioning, causing very large initial deformation. Thus, the final shape and properties of the structure are function of initial configuration and the course of post-tensioning process. Internal structure of modular air-inflated shells distinguishes them from other air-inflated structures and from other shell structures. They consist of the following basic elements: – air cushions (main modular elements) – tension cables – cross-braces (optional) Air cushions and cables appear in shells of all types, while cross-braces only in the shells with increased structural height [4]. After assembling, structure forms complete roofing and does not require any additional membranes to cover space. General view and components of an exemplary structure is shown on Fig. 2
Post-Tensioned Modular Inflated Structures 223 air-inflated cushions tension cables cross-braces (optional) Fig.2.Composition of modular air-inflated shell 2.2 Structural Components Air cushions Pneumatic modular elements have a form of cushions shaped in order to fit geometrical constrains of the prospective surface.Basic shapes are:rectangle, square,rhomb,hexagon and triangle.Following conditions must be fulfilled in order to enable effective application of modular system: shape of the cushions must correspond with final shape of the structure;it is obvious that the usage of as few varying shapes as possible is profitable elements must be small enough in relation to the final structure,to form a smooth,easily deformable surface(at least ten times smaller);additional criteria can be also applied,such as easiness of in-site manipulation e.g. one workers should be able to carry the cushion the connections between the elements have to assure their suitable inte- gration as well as continuity of transmission of internal forces the cushions should be suitably equipped with guides allowing the usage of post-tensioning cables Other components Bar members (i.e.cross-braces)are optional-they appear only in some types of shells.These additional bars are used in order to increase the structural height.They can be made of any lightweight material capable of carrying com- pression,like steel,aluminum,wood or composite.Naturally,closed sections (tubular)are better than the others,for this purpose.Connection of bars and cushions must prevent damages (e.g.by means of strengthened pockets)
Post-Tensioned Modular Inflated Structures 223 Fig. 2. Composition of modular air-inflated shell 2.2 Structural Components Air cushions Pneumatic modular elements have a form of cushions shaped in order to fit geometrical constrains of the prospective surface. Basic shapes are: rectangle, square, rhomb, hexagon and triangle. Following conditions must be fulfilled in order to enable effective application of modular system: – shape of the cushions must correspond with final shape of the structure; it is obvious that the usage of as few varying shapes as possible is profitable – elements must be small enough in relation to the final structure, to form a smooth, easily deformable surface (at least ten times smaller); additional criteria can be also applied, such as easiness of in-site manipulation e.g. one workers should be able to carry the cushion – the connections between the elements have to assure their suitable integration as well as continuity of transmission of internal forces – the cushions should be suitably equipped with guides allowing the usage of post-tensioning cables Other components Bar members (i.e. cross-braces) are optional – they appear only in some types of shells. These additional bars are used in order to increase the structural height. They can be made of any lightweight material capable of carrying compression, like steel, aluminum, wood or composite. Naturally, closed sections (tubular) are better than the others, for this purpose. Connection of bars and cushions must prevent damages (e.g. by means of strengthened pockets)
224 Romuald Tarczewski Post-tensioning cables are always placed at the internal side of curved shell.In case of anticlastic shells,cables are placed in two layers -at the opposite sides of the shell.Direction of cables in each layer corresponds with the curvature of the shell,Fig.6.The cables can be placed directly below the cushions or below cross-braces.In both cases the cable should be able to slide freely through the nodes.Both,fiber ropes (made of natural or man-made fibers)and wire ropes can be used as post-tensioning cables.It is significant that the cushion was protected from damages caused by ropes,e.g.by means of protective jackets. 2.3 Transmission of Forces After completion,modular elements must transmit internal forces induced in the structure.It is possible due to the compression of cushions'sides(touching each other)and tension of their external cover and post-tensioning cables, Fig.3.Thus,the way of assembling the cushions must ensure a full contact of side surfaces and continuity of external cover. These basic principles allow setting a geometrical configuration of the shells of various size and shape,designed for various purposes. tension of external cover compression of side surfaces air-inflated cushion post-tensioning tension of cable bottom cable cross-braces Fig.3.Transmission of forces in modular air-inflated shells
224 Romuald Tarczewski Post-tensioning cables are always placed at the internal side of curved shell. In case of anticlastic shells, cables are placed in two layers – at the opposite sides of the shell. Direction of cables in each layer corresponds with the curvature of the shell, Fig. 6. The cables can be placed directly below the cushions or below cross-braces. In both cases the cable should be able to slide freely through the nodes. Both, fiber ropes (made of natural or man-made fibers) and wire ropes can be used as post-tensioning cables. It is significant that the cushion was protected from damages caused by ropes, e.g. by means of protective jackets. 2.3 Transmission of Forces After completion, modular elements must transmit internal forces induced in the structure. It is possible due to the compression of cushions’ sides (touching each other) and tension of their external cover and post-tensioning cables, Fig. 3. Thus, the way of assembling the cushions must ensure a full contact of side surfaces and continuity of external cover. These basic principles allow setting a geometrical configuration of the shells of various size and shape, designed for various purposes. Fig. 3. Transmission of forces in modular air-inflated shells
Post-Tensioned Modular Inflated Structures 225 3 Application of Post-Tensioning and Self-Erection The structure is stabilized by means of post-tensioning.This process induces internal forces that are shown on Fig.3.Distribution of these forces is invari- able during exploitation,though their values can change.Alteration of forces' direction effects in destruction of the structure -in consequence of opening of the gaps between cushions or "compression"of their external cover,Fig.4. tension of external cover and compression of side surfaces disappears gap between chusions starts to open Fig.4.Failure mode of the shell There are two ways of realizing the post-tensioning procedure: structure is post-tensioned and erected simultaneously (self-erection) post-tensioning is applied to previously erected structure 3.1 Self-Erection Procedure In that case,the flat structure is assembled at ground level as a near mecha- nism.It is stabilized and finally shaped by means of self-erection.This process unifies operations of post-tensioning,erection (i.e.construction)and spatial curving of the structure.The essence of the process is the introducing into the structure forces that cause its large deformation [5].In practice,the process starts simply with a shortening of the bottom cables.The cables are attached to the fixed supporting points while going through all the other joints to the opposite,mobile,supporting points. As a result-supporting points are brought closer to each other.Thus the deformation is introduced to the structure and it starts to erect.The process is continued till required position is obtained.Then the cables are fixed in the mobile supporting points.Fig.5 presents successive stages of self-erection process. Air-inflated shell can be post-tensioned either in one direction or in two directions.Unidirectional post-tensioning is applied in order to get structures with zero Gausian curvature (cylindrical),while bidirectional-when struc- tures with negative Gausian curvature (anticlastic)are required,e.g.hypar surfaces,Fig.6. Bidirectional post-tensioning is performed successively.At the beginning, cables of the first direction are tensioned to 50-60 of assumed value.Then
Post-Tensioned Modular Inflated Structures 225 3 Application of Post-Tensioning and Self-Erection The structure is stabilized by means of post-tensioning. This process induces internal forces that are shown on Fig. 3. Distribution of these forces is invariable during exploitation, though their values can change. Alteration of forces’ direction effects in destruction of the structure – in consequence of opening of the gaps between cushions or “compression”of their external cover, Fig. 4. Fig. 4. Failure mode of the shell There are two ways of realizing the post-tensioning procedure: – structure is post-tensioned and erected simultaneously (self-erection) – post-tensioning is applied to previously erected structure 3.1 Self-Erection Procedure In that case, the flat structure is assembled at ground level as a near mechanism. It is stabilized and finally shaped by means of self-erection. This process unifies operations of post-tensioning, erection (i.e. construction) and spatial curving of the structure. The essence of the process is the introducing into the structure forces that cause its large deformation [5]. In practice, the process starts simply with a shortening of the bottom cables. The cables are attached to the fixed supporting points while going through all the other joints to the opposite, mobile, supporting points. As a result – supporting points are brought closer to each other. Thus the deformation is introduced to the structure and it starts to erect. The process is continued till required position is obtained. Then the cables are fixed in the mobile supporting points. Fig. 5 presents successive stages of self-erection process. Air-inflated shell can be post-tensioned either in one direction or in two directions. Unidirectional post-tensioning is applied in order to get structures with zero Gausian curvature (cylindrical), while bidirectional - when structures with negative Gausian curvature (anticlastic) are required, e.g. hypar surfaces, Fig. 6. Bidirectional post-tensioning is performed successively. At the beginning, cables of the first direction are tensioned to 50–60 % of assumed value. Then