21Бетонные оболочки: проектирование и конструкция
Нджороге Деннис Мбутиа,
аспирант, Департамент строительства и построенной среды, Российский университет дружбы народов, dennohmbuthia@gmail.com,
Чонго Питер,
аспирант, Департамент строительства и построенной среды, Российский университет дружбы народов, pchongo.pc@gmail.com,
Тембо Оливер,
аспирант, Департамент строительства и построенной среды, Российский университет дружбы народов, tembokoliver,@gmail.com,
Гебрегзиабхер Арегави Гебремескел,
аспирант, Департамент строительства и построенной среды, Российский университет дружбы народов, rigbeareg@gmail.com,
Наджи Абдулла Абдулрахман Саид,
аспирант, Департамент строительства и построенной среды, Российский университет дружбы народов, naji2021@mail.ru
Архитекторы и инженеры должны признать, что техника опалубки оказывает большее влияние на форму современных бетонных конструкций, чем свойства конструкционного материала. Мастерство изготовления бетонных оболочек быстро исчезает. Поэтому очень важно следить за развитием пневматических опалубочных систем, которые обеспечивают экономически эффективный способ возведения бетонных оболочек меньшей толщины. Использование бетонных оболочек в строительстве может быть возрождено. Нельзя отрицать, что методы пневматической опалубки могут помочь «оживить» строительство конструкций из бетонных оболочек. Также очевидно, что при использовании этих методов бетонная конструкция приобретет большую эстетику. В строительной отрасли должны принять соответствующие методологии, подтвержденные научными исследованиями за последние десять лет. Метод пневматически стабилизированной опалубки не только позволяет реализовать большепролетные конструкции в рамках экономических ограничений, но и позволяет согласовать подходящую форму конструкции с соответствующими свойствами материала.
Ключевые слова: бетон, оболочка, оболочечные конструкции, оболочечный каркас
Introduction
Concrete is an outstanding material used for structural works, the shape of which has been designed in accordance with their internal flow of forces: Concrete offers many advantages [1], including:
• easy processing.
• high compression strength.
• high durability.
• low price.
Another interesting aspect of this material is its ability to be formed into any shape, on the construction site [2].
However, concrete is preferably used today in rectangular shapes. This preference can largely be attributed to the clients design to reduce the costs of the formwork, complex shapes often attract increased cost. Architects and engineers, therefore, must face the fact
that formwork techniques have greater influence on the shape of today's concrete structures than the characteristics of the structural material itself, or the flow of forces within the structural elements.
Concrete structures which are modelled using irregular shapes can only be designed and constructed with increased technical difficulties on site. Consequently, the art of constructing concrete shells is fast becoming extinct.
Shells are thin-walled structures which combine the function of loadbearing and space enclosure. Their high effectiveness is quite well known from natural shells such as mussels, diatoms, plant structures and the eggshell. Shells have technical applications such as steam-boilers, cooling towers, wings or large-span roofs are impressive examples of the conceivable applications of this type of structure. Shells are principally subjected to biaxial stresses. Since load transfer by bending action is, or should be of lesser importance, the shell shape and the load bearing behaviour are interdependent [3,4]. In concrete shell structures the shear and bending stresses can be minimized if the geometry is optimized, and dead weight and other permanent loads can be carried mostly by in-plane membrane forces. In most situations, the consequence of such optimization is a double-curved geometry that necessitates the use of sophisticated falsework and formwork in order to be constructed [14].
Form finding
Shell is complex hence it cannot be designed by hand drawing, not only because of their spatially curved surface but also because the structure should show, if possible, uniform states of stress, under different load cases. The shapes of shell structures are created today based on different form finding techniques. The entire design procedure is called a 'Form finding process'. Within such a form finding process, a structural shape with defined characteristics under a form-defining load case is developed either by experimental or computer-based methods.
Fig 1. Realizable pneumatic stabilized membranes shapes
Fig 2. Pneumatic structure types [5]
a. Air supported pneumatic structures
b. Air inflated pneumatic structures
The Pneumatic structure works on the principle of using thin walled membrane that is sustained by a pressure differential [13] (see Fig. 1). The internal air pressure is increased to balance the dead weight of the space available in the envelope [11]. The thin membrane becomes stressed to the point where the asymmetrical loading cannot indent it. Pneumatic structures can be divided into two categories (see Fig. 2).
• Air supported pneumatic structures
• Air inflated pneumatic structures
Experimental form finding methods, such as pneumatically created shapes or suspension structures, are easily understood because of their visual effect. This form offer striking visual rendering, hence they are easily understood, they are usually used for the first stage of the design process. After determining the essential boundary conditions and the structural principles, the subsequent step is computer based, mathematical form finding methods.
The most important experimental methods are:
• suspension structures.
• shapes created by plastification of thin sheets.
• pneumatically created shapes.
The computer-based methods may be split into two groups: direct and indirect methods [6].
The direct methods are:
• the solution of the set of (differential) equations which describes the membrane shell [3].
• indirect methods in combination with optimization procedures.
The indirect methods are:
• the geometric non-linear finite element method.
• the force density method.
• methods based on vector analysis.
• algorithms limited to certain geometric conditions.
The direct methods facilitates the computation of the shape of a structure which shows a prescribed state of stress under the so-called form-defining load case for a given set of geometric and static boundary conditions.
It is important to note that the direct methods may not always yield a result, because the prescribed state of stress and the associated load case exclude any solution. The indirect methods has several advantages one of which is that they always have a result. However, the state of stress within the shell, obtained at the end of such a computation, may vary from the required level.
Construction methods
The curved geometry of a shell does not only add a layer of complexity to the design process, but they are often labour-intensive, expensive, or material wasting and complicated [10] Concrete requires a formwork, the shape of which is also the shape of the shell [7]. In addition, this formwork must carry the heavy dead weight of the fresh concrete.
Conventional formwork systems, such as shuttering with boards, are too expensive to be used for double curved shells. There are, however, only very few cost effective methods are available, this challenge has negatively affected the development, economic feasibility and prospects of new shell structures. There are alternative construction methods, some of the most important are:
• free cantilevering construction with cast-in-place concrete or precast elements.
• shotcreting onto a fine wire mesh net.
• earth embankments as formwork.
• use of pneumatic (air-supported) formwork systems.
The current level of knowledge indicates that only the pneumatic formwork method fulfils the below requirements:
• high level of prefabrication.
• quick erection and dismantling.
• almost unlimited spatial curvatures.
• large spans.
• multiple use.
Because of these superior features, discussions in this paper will be restricted to this type of formwork (fig. 1 and 3).
Fig 3. The different principles of pneumatic stabilisation of a fabric membrane: A. air-supported structure. B. air-inflated bag partially water-filled.
C. internal pressure below atmospheric pressure. D. a series of cushions which are prestressed by reduced internal pressure. E. air-inflated cushion. F. an air-supported membrane, the shape of which has been structured by cables
Pneumatic formwork systems for concrete shells
The history of pneumatic formwork systems goes back to 1936. Since that time, several different systems and a series of different erection-procedures have been developed.
The most important are:
• high internal pressure formwork systems.
• concreting in single layers, appropriate when using shotcreting techniques.
• concreting in sections with hardening intervals; - stabilizing the formwork with additional cables. also, in combination with the reinforcement.
• stabilizing the formwork with plastic foams.
• finish concreting before the material starts hardening.
The individual measures can also be combined. All the methods mentioned above are characterized by the intention to reduce deformation in the formwork. This limitation and the control of formwork deformations are of importance because the formwork can change shape remarkably, under the load of the concrete. In addition, the concrete usually starts hardening while the concreting is still in progress. While it is hardening, the initially large deformability of concrete decreases appreciably. When it reaches minimum ultimate strain, the concrete is still very weak. In this phase, formwork deformations can lead to permanent damage of the concrete [3].
The simplest way of stiffening the formwork is to increase the internal pressure. However, this is only possible within narrow limits: on the one hand commercially available membranes and their joints, have limited mechanical strength; on the other hand, the uplifting forces rapidly become so great, that due to the measures necessary to anchor them, it is questionable whether the construction method is still economical. Therefore, a high internal pressure is only suitable for closed systems with small radii of curvature. This is applicable in the case of tubular formwork, used in Italy as early as 1938, to construct water lines (see Fig 4).
Fig 4. Tubular inflated formwork for the construction of water lines [8]
A system developed by Haim Heifetz, with which numerous smaller shells have been constructed since 1960 in Israel, can also be described as a high-pressure formwork system. With this system, the membranes are connected to a rigid, easily transportable base construction. The forces are thus 'short-circuited' within the system itself, so that nothing need be done to anchor the formwork on the actual structure. Since the membranes are tightly curved, internal pressures of up to 10 kN/m2 are possible. PVC-coated fabrics were used as membranes (fig. 6).
Fig 6. A water and air-filled fonnwork for concrete water-tanks
Partial or total filling with fluids, e.g., water, also increases the stiffness of the formwork. In addition, fluid and air filling allows an enlarged range of pneumatically formable shapes. Whereas the application of high-pressure systems is limited, a wide range of structures can be built by concreting in single layers. This method was developed as early as 1948 by Walace Neff; one of the pioneers of pneumatic formwork construction. Harrington used the
same principle today. He laid a system of radially arranged cables over a dome shaped formwork. The formwork is additionally stabilized by the cables and by the reinforcement fixed to them Guniting is then carried out in several layers.
Besides concreting in individual layers, step-by-step stiffening of the membrane can also be accomplished by concreting in individual sections. The parts of the shell already concreted and hardened then limit deformations of the formwork under the load of the fresh concrete. The size of the sections of the shell to be freshly concreted must be decided on in such a way, that the concreting work is completed before the ultimate strains of the young concrete attain the same magnitude as the actual deformations of the formwork.
A pre-stiffening of the membrane can be achieved by spraying polyurethane foams onto the membrane. The foams, which harden within seconds, can be sprayed onto the interior or the exterior of the air-supported membrane. Total foam thickness is usually in the range of 80-150 mm, depending on insulation requirements. The foam is applied in single layers, each of them with a thickness of about 20-40 mm. Special fixation elements are pinned to the foam-shell before the last PU-layer is foamed.
Finally, some construction methods employing unstiffened formwork deserve mention, since they may be regarded as special cases. With the first, the Bini method hardening of the concrete is delayed until concreting is finished: the reinforcement is laid on the membrane while it is slack. The concrete is poured on and covered with a second membrane. Only then is the formwork inflated. During the inflation, the reinforcement must undergo the same deformations as the membrane. For this reason, the Bini method requires a special type of reinforcement.
The second method is the use of precast concrete elements laid on the membrane. Only small quantities of fresh concrete are required, to grout the joints. As a result, the formwork is hardly deformed at all while the final concreting is in progress.
Thirdly, the textile reinforced cement (TRC) is made up of continuous fiber systems, such as textiles, that have been impregnated with cement or fine-grained mortar. At room temperature, they harden. Because TRC composites are flexible in the wet phase, curved shapes are simple to achieve. They are rigid and strong in both tension and compression when they have hardened. TRC formwork can be moulded into any (reusable) mould, such as foam molds, flexible formwork moulds, pneumatic formwork, and prestressed membranes, to achieve a curved TRC surface. The TRC layer has low weight, when compared to the concrete that is typically poured on these molds, is a significant benefit. [10] .
Aspects concerning the shape of the formwork
There is an almost unlimited variety of shapes which can be realized with pneumatic formwork systems. These shapes are said to be 'pneumatically possible'. A pressure load vector normally acts at each point of the formwork's surface. It is an external force which must be counterbalanced by the internal forces within the form work membrane [9]. This relation is represented by the equations of equilibrium.
A formwork membrane may be subjected to tensile stresses exclusively. The principal stresses within the formwork membrane are restricted to the non-negative. These inequations also must be fulfilled at each point of the formwork.
The question whether a given shape can be realized with a pneumatic formwork or not must be answered based on this characteristic set of equations and inequations. The curvature of a structure is no criterion as to whether it is pneumatically possible or not.
The challenge associated with identifying whether or not a given shape is pneumatically possible can be circumvented if, in the form-finding process, one designs not the form of the concrete shell, but the shape of the formwork loaded by internal pressure. The formwork is then, itself, pneumatically possible.
The question whether the concrete shell with such a shape can provide advantageous load bearing behaviour can be answered mostly in the affirmative: If one assumes that in shallow shapes the lines of action of the internal pressure and the deadweight almost coincide, then concrete shells of this shape will be under uniform biaxial compressive stress at all points, when subjected to the dead weight load, while the associated formwork membrane is only tensioned by the internal pressure load.
However, the described state of stress does not occur with all concrete shells with the shape of a pneumatically spanned membrane, because of effects caused by the boundary - or support - conditions [3]. The designing engineer must discern these exceptions, and take the appropriate measures accordingly.
Conclusion
It is undeniable that pneumatic formwork methods can help reinvigorate the building of concrete shells structures. It is also obvious that the concrete construction will achieve greater aesthetic if these methods are used. As a result, stakeholders in the construction industry should adopt these methodologies developed by a few engineers over the last fifty years and validated by scientific research in the last ten years. The method of the pneumatically stabilized formwork not only allows the realization of large-span structures within economic bounds - it also allows for suitable structural shape to be matched with appropriate material properties.
References
1. Won-Kee Hong, Hybrid Composite Precast Systems Numerical Investigation to Construction Woodhead Publishing Series in Civil and Structural Engineering, 2020, Pages 1-14. https://doi.org/10.1016/B978-0-08-102721-9.00001-7
2. The many shapes of concrete. PUBLICATION #C800015
3. Sobek, W., Auf pneumatisch gestutzten Schalungen hergestellte Betonschalen. Stuttgart, 1987.
4. Schlaich, J., Sobek, W., Suitable Shell Shapes. Concrete Internationa 8, Heft 1, 1986.
5. Pneumatic Structures. https://civiljungle.com/pneumatic-structures/#Principle_of_Pneumatic_Structures
6. Sobek, W., Betonschalen und pneumatisch vorgespannte Membranen. Deutsche Bauzeitung 124, Heft 7, 1990.
7. Peter Wehrmann. Formwork Making - Course: Timberwork techniques. Trainees' handbook of lessons. Institut für Berufliche Entwicklung.
8. Pneumatic Tubular Forms https://www.pcne.eu/uploads/tx_etim/STW_013_TUB_FORMS.pdf
9. Sobek, W., Concrete Shells Constructed on Pneunmatic Formwork. Proceedings of the lASS Symposium on Membrane Structures and Space Frames, Osaka (Japan), Amsterdam, 1986.
10.Verwimp, Evy. "Flexible Formwork and Reinforcement for Concrete Shells — Vrije Universiteit Brussel." Vrije Universiteit Brussel. researchportal.vub.be, January 1, 2013. https://researchportal.vub.be/en/publications/flexible-formwork-and-reinforcement-for-concrete-shells.
11. Meneghetti, Leila C, Wesley, Nyema, Pauletti, Ruy M.O, Adriaenssens, Sigrid. Pneumatic formwork systems to build thin concrete shells. Proceedings of IASS Annual Symposia, IASS 2018 Boston Symposium: Construction-aware structural design, pp. 1-8(8). 2018.
12. Benjamin Kromoser, Johann Kollegger. Efficient construction of concrete shells by Pneumatic Forming of Hardened Concrete: Construction of a concrete shell bridge in Austria by inflation. 2019. https://doi.org/10.1002/suco.201900169
13. Kromoser, Benjamin and Johann Kollegger. "Pneumatic forming of hardened concrete - building shells in the 21st century." Structural Concrete 16 (2015)
14. Lusis, V. Production Technology for Concrete Shells Using Pneumatic Formwork with Variable Elevation . Construction Science. Vol.12, 2011, pp.35-39.
Concrete shells: the design and construction
Njoroge Dennis Mbuthia, Peter Chongo, Tembo Oliver, Gebregziabher Aregawi Gebremeskel, Naji Abdullah Abdulrahman Saeed
People's Friendship University of Russia
Architects and engineers must acknowledge that formwork techniques have a greater impact on the shape of today's concrete structures than the structural material's properties. The craftsmanship of constructing concrete shells is fast becoming extinct. As a result, it's crucial to keep an eye on the development of pneumatic formwork systems, which provide a cost-effective means of constructing concrete shells can be constructed lesser thicknesses. The use of concrete shells for construction could be revived.
Keywords: concrete, shell, shell structures, shell framework, formwork References
1. Won-Kee Hong, Hybrid Composite Precast Systems Numerical Investigation to Construction Woodhead Publishing Series in
Civil and Structural Engineering, 2020, Pages 1-14. https://doi.org/10.1016/B978-0-08-102721-9.00001-7
2. The many shapes of concrete. PUBLICATION #C800015
3. Sobek, W., Auf pneumatisch gestutzten Schalungen hergestellte Betonschalen. Stuttgart, 1987.
4. Schlaich, J., Sobek, W., Suitable Shell Shapes. Concrete Internationa 8, Heft 1, 1986.
5. Pneumatic structures. https://civiljungle.com/pneumatic-structures/#Principle_of_Pneumatic_Structures
6. Sobek, W., Betonschalen und pneumatisch vorgespannte Membranen. Deutsche Bauzeitung 124, Heft 7, 1990.
7. Peter Wehrmann. Formwork Making - Course: Timberwork techniques. Trainees' handbook of lessons. Institut für Berufliche
Entwicklung.
8. Pneumatic Tubular Forms https://www.pcne.eu/uploads/tx_etim/STW_013_TUB_F0RMS.pdf
9. Sobek, W., Concrete Shells Constructed on Pneunmatic Formwork. Proceedings of the lASS Symposium on Membrane
Structures and Space Frames, Osaka (Japan), Amsterdam, 1986.
10. Verwimp, Evy. "Flexible Formwork and Reinforcement for Concrete Shells — Vrije Universiteit Brussel." Vrije Universiteit
Brussel. researchportal.vub.be, January 1, 2013. https://researchportal.vub.be/en/publications/flexible-formwork-and-reinforcement-for-concrete-shells. 11 Meneghetti, Leila C, Wesley, Nyema, Pauletti, Ruy M.O, Adriaenssens, Sigrid. Pneumatic formwork systems to build thin concrete shells. Proceedings of IASS Annual Symposia, IASS 2018 Boston Symposium: Construction-aware structural design, pp. 1-8(8). 2018.
12. Benjamin Kromoser, Johann Kollegger. Efficient construction of concrete shells by Pneumatic Forming of Hardened Concrete: Construction of a concrete shell bridge in Austria by inflation. 2019. https://doi.org/10.1002/suco.201900169
13. Kromoser, Benjamin and Johann Kollegger. "Pneumatic forming of hardened concrete - building shells in the 21st century." Structural Concrete 16 (2015)
14. LQsis, V. Production Technology for Concrete Shells Using Pneumatic Formwork with Variable Elevation. construction science. Vol.12, 2011, pp.35-39.
