IMPLEMENTATION OF NON-METALLIC MEMBRANES INTO STEEL SUPPORTING STRUCTURES

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1 Proceedings of the 6th International Conference on Mechanics and Materials in Design, Editors: J.F. Silva Gomes & S.A. Meguid, P.Delgada/Azores, July 2015 PAPER REF: 5592 IMPLEMENTATION OF NON-METALLIC MEMBRANES INTO STEEL SUPPORTING STRUCTURES David Jermoljev 1, Josef Machacek 2(*) 1 EXCON corp., Prague, Czech Republic 2 Faculty of Civil Engineering, Czech Technical University in Prague, Czech Republic (*) machacek@fsv.cvut.cz ABSTRACT The paper deals with analysis of textile/foil membranes supported by peripheral non-rigid steel structures. Approaches to global analysis of light membrane structures which are presently required for both temporary and permanent structures are discussed. The investigation relates to geometrically non-linear analysis (GNA) of structures composed of prestressed membranes located between steel arch beams. Extensive parametric study concerning possibility of separate analyses of the membranes and supporting steel structures is presented, giving limiting parameters for such approach. Influence of construction procedures (introduction of prestressing) is also analysed. Keywords: prestressing, structural analysis, steelwork, textile membranes. INTRODUCTION Textile membranes are becoming routine components to cover not only common shelters but also sophisticated outward load bearing structures ( The visual expression of structures is becoming more and more crucial, based on availability of novel structural elements. Extraordinary tensile surface structures are required by architects, designers and developers and corresponding new forms are being developed, as tensegrity and tensairity structures (see e.g. Lewis 2003, Pauletti and Brasil 2003, 2005, Seidel, 2009). Specialized companies (e.g. Base Structures Ltd., Tension structures.com, Mehler Ltd., TechArchitects sro., and others) have realized many unique tensile structures using fabric/foil membranes in the last few decades. Fabric/foil membranes were traditionally used for temporary structures and in warm countries. For common modest use the PVC coated polyester seems to be appropriate as inexpensive variant, giving up to 20 years lifetime (e.g. Précontraint FERRARI ), joined by welding or sewing. More expensive but longer lifetime provides glass fabric coated by PTFE (Teflon), possibly by silicon rubber or titanium dioxide, joined by bonding. Rather expensive but excellent material is expanded PTFE coated 2 sides by fluoropolymer film (TENARA ), joined by welding. The membranes may also be thermally insulated using Nanogel Aerogel and 2 sides coated with PTFE (in result translucent, with total thickness 9 mm, CABOT Cor.). High density polyethylene fabrics (HDPE, coated with LDPE) joined by sewing may also be used however, with short lifespan up to 10 years. Thin foils ( µm) are used mainly as inflatable cushions, nowadays predominantly from ETFE (TEXLON ) or THV materials. However, complex analysis of membrane structures in interaction with steel structure (carbon/stainless steel perimeter elements) is still rather demanding

2 Symposium_29 Safety in Wood Materials Design of membrane structures follows the general concept (Lewis, 2003): i) Pre-design of a form ensuring tension within all membrane area during assembly and loading, requiring sufficient prestressing: basic shapes are hypar, cone and barrel (Seidel, 2009). ii) Deciding on boundary conditions and elements (point/continuous, rigid/elastic, cables/frames/anchor points). iii) Form-finding process: physical model or numerical modeling based on forcedensity method (Linkwitz, 1999, Gründig, 2000). iv) Structural analysis of the membrane with supporting structure under prestressing, dead and live loading: snow, wind, facility (Foster and Mollaert, 2004, Wakefield, 1999). Prestressing procedure often determines the design and final geometry. In the last decade an intensive effort of Roithmayr and Gründig resulted in formfinding software (Formfinder Software GmbH, ), which enables intuitive manipulation with membrane shapes under required stress level in interactive way and export/import to other programs through DXF/DWG files. Constantly improved versions upgrade the software for designing of supporting elements. In general the material of textile membranes is due to its structure non-homogeneous, orthotropic (different in warp and fill directions) and non-linear. In accord with recommendation by Tensinet Analysis & Materials working Group (Gosling, 2007) a simplified elastic approach may be employed using the simple plane stress theory. More recently the well-developed non-linear material model for textile membranes based on experimental results was proposed (Galliot and Luchsinger, 2009). Supporting steel structures as anchor, perimeter, valley and ridge ropes or stiff load-bearing structure form an integral part of the resulting structure. Interaction of membranes with the steel elements requires sophisticated analysis using specialized software (e.g. EASY, FORTEN, SOFiSTiK, Rhino Membrane, NDN, etc. - with respective web site references). In general geometrically and materially non-linear analysis considering imperfections (GMNIA) is required for the proper analysis. Separate analysis of membranes alone and supporting steel structure is rather questionable. Prestressing and individual assembly phases (Seidel, 2009) ensuring the full functionality of the resulting structure must carefully be taken into account. This paper is, therefore, concentrated on the simplest forms of membrane structures (barrels and hypars) to assess the following questions: i) Is the simplified separate analysis of a membrane stretched between non-rigid steel arches as a membrane alone (with rigid supports) and the steel arches (i.e. arches loaded by the relevant membrane response), Fig 1 (left), reasonable? ii) How important is the method of assembly and prestressing for hypars acc. to Fig.1 (right)? B L H Fig. 1 - Membrane between non-rigid steel arch beams (left), hypar membrane (right)

3 Proceedings of the 6th International Conference on Mechanics and Materials in Design, Editors: J.F. Silva Gomes & S.A. Meguid, P.Delgada/Azores, July 2015 MEMBRANES BETWEEN ARCHES In practice, separate modeling of a membrane and steel framework is common. The membrane is designed by a specialized office and boundary data are given to the steel designer. However, the significance of interaction between membrane and steelwork is obvious. Separate modeling may only be successful provided the design of the membrane considers geometry and rigidity of the supporting framework. In case the support is not fully rigid, the introduction of real rigidities is necessary, otherwise resultant membrane stresses and deflections are distorted and data provided to the designer of steel structure are wrong. The situation is demonstrated with a typical membrane spanning between arch edges, Fig. 2. The simplified membrane characteristics were taken as E = 1000 MPa, ν =0.25, t = 1 mm (modulus of elasticity, Poisson s ratio, membrane thickness). Two models were investigated: i) The membrane supported by steel tube arches built-in at supports both in and out of plane, named membrane with arches (the tubes designed for expected loading with cross section 324x25 [mm]). ii) The membrane supported by fully rigid supports along the all arch lines (denominated as membrane alone ). Fig. 2 - Geometry of the analyzed membrane The GNA was performed using common SCIA Engineer structural frame software, with the membrane modeled by quadrilateral elements. Sensitivity of the finite element size was assessed through three mesh divisions, with basic lengths 50 mm, 150 mm, 250 mm, Fig. 3. size 50 mm size 150 mm size 250 mm Fig. 3 - Membrane: Element divisions

4 Symposium_29 Safety in Wood Materials After decreasing size from 150 mm to 50 mm the deflections remained nearly unaffected (see Fig. 4), stresses increased by 5.1 %. After increasing the size from 150 mm to 250 mm the deflections decreased by 0.1 % and stresses decreased by 2.6 %. The finest mesh gives more appropriate results for detailed stresses in corners/edges. In the following the medium mesh (150 mm) was used and considered adequate for the parametric studies. mesh size 50 mm mesh size 150 mm mesh size 250 mm Fig. 4 - Vertical deflections The planar prestressing through deformation ε was introduced in numerical analysis. In the membrane alone ε = (i.e. 4 N/mm), for the membrane with arches the value ε = resulted from condition of identical horizontal reaction along arch lines to ensure the same prestressing due to horizontal deflection of arches. Vertical loading 1 kn/m 2 only was considered in the study, representing snow loading. Considering the above prestressing and vertical loading the maximal transverse unit force for the membrane alone (i.e. membrane with fully rigid supports) is 11 % higher in comparison with the membrane with arches (i.e. membrane acting together with non-rigid steel arches) and the maximal membrane deflection attains just 78 % of the latter, Fig. 5 (the right pictures always concerns membrane alone ). Fig. 5 - Comparison of results for membrane with arches and membrane alone. Transverse membrane forces n x [N/mm] (left) and vertical deflections u z [mm] (right) The transverse forces due to prestressing in this study are nearly identical. However, introduction of prestressing values from a separate analysis to the actual structure would lead to incorrect, much greater deflection of the actual membrane (roughly to 129 % of the

5 Proceedings of the 6th International Conference on Mechanics and Materials in Design, Editors: J.F. Silva Gomes & S.A. Meguid, P.Delgada/Azores, July 2015 expected one). Therefore, an attempt was taken to simulate the flexibility of arches. Nevertheless, it is not easy to simulate flexible arch tubes by simplified elastic linear supports because the actual value of rigidity along the arches is changing (e.g. in arch supports is approaching the infinity). Various rigidities with uniform distribution along arch lines were tested. Finally, results for uniform rigidity of 1950 N/mm are shown in Fig. 6. The rigidity resulted from an iterative procedure, requires prestressing 148 % of the prestressing corresponding to the membrane alone and provides both the same total horizontal reaction and maximal horizontal deflection from prestressing as in the membrane with arches. Nevertheless, the maximal transverse forces are still 11 % higher and the deflections attain only 85 % of the membrane with arches. Clearly the separate analysis of the membrane and the supporting arches may give incorrect results. Fig. 6 - Comparison of results for membrane with arches and membrane with elastic supports (1950 N/mm). Transverse membrane forces n x [N/mm] (left) and vertical deflections u z [mm] (right) PARAMETRIC STUDIES The study covers 27 membrane structures with support conditions acc. to Fig. 7, with dimensions given in Table Fig. 7 - Support conditions of the membrane with arches (left) and membrane alone (right)

6 Symposium_29 Safety in Wood Materials The loading was introduced as in the previous study (i.e. in the membrane alone by the directionless prestressing ε = and by the respective value of ε in the membrane with arches, resulting from condition of identical horizontal reaction along arch lines to ensure the same prestressing as in the former, and vertical uniform loading 1 kn/m 2 ). No. span L [m] Table 1 - Dimensions of structures according to Fig. 7 width B [m] rise H [m] tube D x t [mm] slenderness L ) /r x x x x x x x x x x x x x x x x x x x x x x x x x x x The FEM nonlinear study (GNA) was performed with a fictitious membrane (modulus of elasticity E = 1000 MPa, Poisson s ratio ν = 0.25, thickness t = 1 mm). From the results is obvious (Table 2), that for arch span up to 9 m the interaction of arches with membrane may be neglected (i.e. analysis of the membranes with rigid supports and arches with resulting

7 Proceedings of the 6th International Conference on Mechanics and Materials in Design, Editors: J.F. Silva Gomes & S.A. Meguid, P.Delgada/Azores, July 2015 reactions gives reasonable results). Separated analysis for span above 10 m however, markedly underestimates both vertical membrane and horizontal arch deflections, which negatively influence cutting and prestressing process of membranes. Faulty results give separate analyses for majority of spans above 16 m, where the necessary prestressing for membrane with arches in comparison with membrane alone should be much higher and in spite of such prestressing an enormous increase of membrane deflection must be expected. The results may also be related to the arch slenderness (arch length to appropriate tube radius of gyration). For slenderness values under 100 the ratios for prestressing ensuring the same total transverse force (resulting from analyses of the membrane with arches to membrane with rigid supports) are in range % and ratios for the membrane vertical deflection between %. Slenderness above 100 give the ratios in range % for prestressing and % for deflections. Table 2 - Resulting prestressing and maximal deflections for membranes with arches and membranes alone No membrane with arches/membrane alone [%] prestressing max. deflections

8 Symposium_29 Safety in Wood Materials ASSEMBLY AND PRESTRESSING FOR HYPARS Construction procedure, i.e. activation of the prestressing was analyzed for hyperbolic paraboloid in acc. with Fig. 8. The actual investigated HP is not fully symmetrical due to site conditions and therefore the results are shown to demonstrate the importance of assembly procedure only. The needed prestressing may be achieved either by stretching out of the anchoring cables (Fig. 9) or by tensioning of peripheral cables (Fig. 10). Fig. 8 - Hyperbolic paraboloid shelter ( hypar ) Z Y X Z Y X Fig. 9 - Prestressing by stretching out of the anchoring cables: axial forces in pylons and cables (left), deflections of the pylon tops (right) Z Y X Z Y X Fig Prestressing by stretching out of peripheral cables: axial forces in pylons and cables (left), deflections of the pylon tops (right) While the axial forces in the steelwork and stresses in the membrane remain nearly identical, in the first case the pylons are tilted outward, in the second case inward. Way of the prestressing therefore influences the final membrane structure geometry, position and placing of rectification elements, cutting and local corner stresses of the membrane

9 Proceedings of the 6th International Conference on Mechanics and Materials in Design, Editors: J.F. Silva Gomes & S.A. Meguid, P.Delgada/Azores, July 2015 CONCLUSIONS The proper design of textile membranes embedded into a steel structure is the demanding task. The correct analysis evidently requires geometrically and materially nonlinear analysis with imperfections (GMNIA), available with specialized software. Regardless of difficulties with relevant input data concerning inherent membrane structural properties the use of common structural frame software is often the choice of designers in rather simple membrane structures supported by a steelwork. Using simplified material properties the structures with membranes between arches according to Fig. 1 may be designed with common structural frame software neglecting joint behavior (i.e. design of the membrane alone as an isolated element), provided: - geometrically nonlinear analysis (GNA) is used, - prestressing must be used as the basic entry data, - the arch span or arch slenderness are limited (approx. to 9 m of the former or to 100 of the latter), - introduction of a suitable elastic support provided by the arches may improve the results but is rather demanding task. The joint modeling (especially using specialized software) of the membrane with actual supporting steelwork is however always preferred. More complicated structures require analysis with imperfections (GNIA), covering slacks of cables/rods due to their own weight. Design of hypars and other membrane structures requires elaborated process of assembly as shown on the practical example. The methods of erection substantially affect the resulting geometry and state of stress of the membranes, necessary rectification and membrane cutting. ACKNOWLEDGMENTS Support of the Czech Grant Agency GACR No. 105/13/25781S is gratefully acknowledged. REFERENCES [1]-Formfinder Software GmbH, Wien, Foster B, Mollaert M. European Design Guide for Tensile Surface Structures, 2004, TensiNet. [2]-Gosling, P. Basic Philosophy and calling notice. Tensinet analysis & Material working group, Tensinews No. 13 ( 2007, pp [3]-Galliot,C, Luchsinger RH. A simple model describing the non/linear biaxial tensile behaviour of PVC/coated polyester fabrics for use in finite element analysis, Composite Structures, 2009, 90, 4, p [4]-Gründig L, Moncrieff E, Singer P, Ströbel D. A History of the Principal Developments and Application of the Force Density Method in Germany. In: Proc. IASS-IACM, Greece, 2000, 13 p. [5]-Lewis WJ. Tension Structures Form and Behaviour. Thomas Telford Publishing, 2003, 256 p. [6]-Linkwitz K. About Formfinding of Double-Curved Structures. Engineering Structures, 1999, 21, p

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