The case study provided some important conclusions, and revealed common misun- derstandings about pneumatic formwork:
• Internal pressure>load sprayed concrete.
• Deformations formwork under concrete load=0.
• Vertical parts cause problems.
P.C. van Hennik and R. Houtman
• Steel fibres partly improvement.
The two most important ones are shortly explained:
Internal Pressure=Dead Load
One of the conclusions from this parameter study is that an internal pressure of ap- proximately the same value as the dead load is not enough to support the pneumatic formwork. Low pressures are enough to support almost flat pneumatic formworks, however, as soon as the formworks become higher, the slanting or vertical parts supply a downwards force resultant, which can only be counterbalanced by higher pressures.
Deformation Formwork Under Concrete Load=0
The different causes for deformations of the pneumatic formwork after spraying were studied, because they are harmful for the curing concrete. Of importance are the shape of the formwork – a low structure with large radii will sag more under ver- tical load than a higher structure – temperature changes, and changes of atmospheric pressure. In combination with the results of part of the research can be concluded that steel fibre reinforced concrete is advantageous for this building method, because of its high initial strength.
References
1. van Hennik PC (2005) Pneumatic formwork for irregular curved thin shells; shape vs force, shell vs pneumatic structure. Delft University of Technology.
2. Frutiger International (1979) Swiss dome house, product information. Frutiger Interna- tional, Thun (CH).
3. Sigler V (2004) Dome of a home, vacation rental home on Pensecola beach, Florida (On- line). Available from: www.domeofahome.com (accessed February 2004).
4. Monolithic Dome Institute (Online), Monolithic Dome Institute. Available from www.monolithic.com (accessed 7 November 2003).
5. Sobek W (1987) Auf pneumatisch gestutzen Schalungen hergestellte Betonschalen, Sobek, Stuttgart.
6. PIRS SA, ZI St Hermentaire 309, Avenue de l’Europe, 83300 Draguignan, France, www.domepirs.com; E-mail: pirs@domepirs.com.
7. Otto F (1962) Zugbeanspruchte Konstruktionen, Band 1, Ullstein Fachverlag, Frank- furt/Berlin.
8. Pronk ADC, (2003)Kunst-expopaviljoen Technische Universiteit Eindhoven – Ontwerpen met vrije vormen en nieuwe materialen, Guidebook Student Project, Technical University Eindhoven.
9. Austin S, Robins P (eds) (1995)Sprayed Concrete, Properties, Design and Application.
McGraw-Hill, New York (first published in UK).
10. Herzog T (1976)Pneumatische Konstruktionen, Bauten aus Membranen und Luft. Verlag Gerd Hatje, Stuttgart.
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R.M.O. Pauletti
Department of Structural and Geotechnical Engineering, Polytechnic School, University of São Paulo, P.O Box 61548, 05424-970 São Paulo, Brazil; E-mail: pauletti@usp.br
Abstract. The article presents a general framework for the nonlinear equilibrium analysis of taut structures, such as cables and membranes. Distinction is done between geometric and constitutive stiffness, and all the relevant matrices for truss and membrane finite element static analyses are derived, including the effects of sliding cables and following forces (such as wind pressures). The peculiarities of the design of taut structures are briefly discussed, considering the design of an existent membrane structure as a benchmark.
Key words: taut structures, tension structures, cables and membranes, nonlinear structural analysis and design.
1 Introduction
A taut string is frequently suggested to explain the behavior of more complex struc- tures, such as cable nets or membranes. Indeed, all these structures have essentially two states: either they aretaut(in proper behavior) or they areslack, and they rely es- sentially on the existence of a tension field to behave properly. I would like to refer to these structures as ‘taut structures’, instead of ‘tension’ or ‘tensile structures’, terms used as well.
Taut structures are characterized by profusion of solutions, and it is difficult to define their geometric shapea priori. Since cables and membranes do not withstand bending – and thus, neither compression – shape cannot in general be imposed, but has to interact with external loads and internal stress field, to satisfy equilibrium.
The design of a taut structure thus involves the determination of an initial orvi- able configuration, encompassing the structure’s shape and the corresponding stress field. Besides, the viable configuration has to accommodate both architectonic re- quirements (form and function) and – minding materials – structural requirements (resistance and stability).
©2008Springer. Printed in the Netherlands.
E. Oủate and B. Krửplin (eds.), Textile Composites and Inflatable Structures II,117–139.
R.M.O. Pauletti
The geometric nonlinear behavior presented by taut structures usually overrules the use of analytical solutions, letting numerical analysis as the only general ap- proach to their design. The most systematic way to pose the overall design process of taut structures is via matrix structural analysis, and, within that scope, the finite element method (FEM), using Newton’s, dynamic relaxation or conjugate gradient procedures to solve the resulting nonlinear equilibrium equations.
One advantage of the FEM is that it provides, besides a viable shape, also a map of the stresses to which the structure is subjected. It is also adequate to determine the behavior of the structure under design loads, as well as to easily transferring data to the patterning routines, also these conveniently performed via structural analysis.
On the other hand, procedures based on the FEM or in other forms of structural analysis result, as a rule, in nonlinear analysis, and require specification of an ini- tial geometry, loads and boundary conditions, not always with well-defined physical meanings.
In brief, design of taut structures is necessarily integrated to analysis, in a process that encompasses procedures for shape finding, patterningand load analysis. An example encompassing these procedures is given later in this text. Some references on the subject are Haber and Abel (1982a, 1982b), Knudson (1991), Moncrief and Topping (1993) and Barnes (1994).