 Advances in Technology Innovation , vol. 1, no. 2, 2016, pp. 50 - 52 50 Copyright © TAETI Tubular Steel Arch Stabilized by Textile Membranes Ondrej Svoboda, Josef Machacek * Czech Technical University in Prague, Faculty of Civil Engineering, Prague, Czech Republic. Received 17 February 2016; received in revised form 01 April 2016; accept ed 06 April 2016 Abstract Tubular steel arch supporting textile me mbrane roofing is investigated experimentally and numerically. The stabilizat ion effects of the text ile me mbrane on in-p lane and out-of-plane behavior of the arch is of prima ry interest. First a model of a large me mbrane structure tested in laboratory is described. Prestressed me mbranes of PVC coated polyester fabric Fe rrari ® Précontraint 702S were used as a currently standard and excellent material. The test arrangement, loading and resulting load/deflection values are presented. The supporting structure consisted of two steel a rch tubes, outer at edge of the me mbrane and inner supporting interior of the me mb rane roofing. The stability and strengt h behavior of the inner tube under both symmetrica l and asymmetrica l loading was monitored and is shown in some details. Second the SOFiST iK software was employed to analyze the structural behavior in 3D, using geometrica lly nonlinear analysis with imperfections (GNIA). The nu me rica l ana lysis , FE mesh sensitivity, the me mb rane prestressing and common boundary conditions are validated by test results. Finally a para metrica l study concerning stability of mid a rch with various geometries in a me mb rane structure with several supporting arches is presented, with recommendations for a practical design. Ke ywor ds : te xt ile me mbranes, prestressing, steel arch, arch stabilizat ion, GNIA, tests 1. Introduction Design of steel structures cooperating with TSF (Tensioned Fabric Structures) requires geometrica lly and materia lly non -linear analysis with imperfect ions (GMNIA). The essential in such analysis is an appropriate input of the me mb rane materia l behavior; see [1], [2], [3], [4], etc. While me mb rane surface is e xc lusively tensioned, supporting steelwork is most often e xposed to a compression and/or bending. This type of loading, in co mbination with slender steel ele ments, results into stability proble ms . Usually the me mb rane represents a spring support for the steel structure and the co mple x structure need to be designed using proper software package allowing integrated modelling, e.g. EASY [5], SOFiSTiK [6], etc., wh ile a separated modelling of the me mb rane and steelwork is rather limited [7]. Th is paper demonstrates significant stabilizing effects of me mb ranes to the respective supporting steelwork, based on numerical para metrica l studies validated by tests. 2. Validation by Tests The tested me mbrane structure supported by two steel tube arches is shown in Fig. 1. The me mb rane is PVC coated polyester fabric Ferra ri ® Précontraint 702S (with bra king loadings in both warp and fill direct ions Sult ≈ 56 kN/ m, wo rking loading Smax = Sult/5 ≈ 11.2 kN/ m and suitable prestressing up to Pmax = Smax/5 ≈ 2.24 kN/ m). Princ ipal dimensions of the vertical inner tubular arch of ø 26.9x3.2 [mm] are LxH = 4500x1200 [mm], while outer tubular arch has inclination of 60° in respect to horizontal. Fig. 1 The layout of the tested model * Corresponding aut hor, Email: machacek@cvut .fsv.cz Advances in Technology Innovation , vol. 1, no. 2, 2016, pp. 50 - 52 51 Copyright © TAETI The shape and cut of the me mbranes resulted fro m formfinder software [ 8] and the me mb ranes were prestressed roughly with P ≈ 0.2 kN/ m. The investigation concerned e xclusively the inner steel a rch to find stabilizing effect of the me mbrane to its nonlinear behavior. First the inner arch alone (without fastening the me mbrane) was loaded and second, after the me mbrane assembly, the complete me mb rane structure. For loading calibrated pouches with steel pellets we re used and suspended from seven points of the arch (for the symmetrica l loading see Fig. 2) or fro m four points in case of asymmetrical loading. Fig. 2 Sy mmetrical loading of the tested model During the tests the deflections and stresses were carefu lly monitored in 9 locations (with No. 4 at midspan). In this paper the symmetrica l test and deflections only are described due to a space limit . The deflections (vertical in Fig. 3 and transverse in Fig. 4) de monstrate that t he arch without me mbrane buckled out-of-plane at total loading of F0 = 5.5 kN, with vertica l deflection along all span down, while the test of the arch stabilized by the me mbrane was terminated under total load of FM = 8.3 kN, showing the enormous stabilizing effect of the membrane. Fig. 3 Symmetrical loading - vertical deflections Fig. 4 Symmetrical loading – transverse deflections SOFiSTiK software [6] was used to perform GNIA (using N-R iteration) both for the inner arch alone and the complete me mbrane structure, emp loying orthotropic model with 5 para meters according to [3]. Various meshing of the me mb rane was analysed (square sizes of 25, 50, 100 and 200 [mm]) with diffe rences ≤ 0.2 % and optimu m size o f 50 mm was used in the ana lysis. The equilibriu m state and final unloaded shape of the me mbrane structure was found under initia l SOFiSTiK software ca lculations. Both arch alone analysis and membrane with the two arches were performed and results compared with tests showing e xcellent agree ment. The results of GNIA for the symmet rica l loading under various prestress of the me mbrane P [kN/ m] are shown in Fig. 8 and with the prestress of 0.2 kN/ m (corresponding to test) justify use of the model for fo llo wing para metric studies. Fig. 5 Comparison of the test and GNIA vertical deflections under various prestressing 3. Parametrical Studies In-plane and out-of-p lane stability of 132 central arches in the 5 arches assembly (see Fig. 5), where the edge a rches were continuously transversely supported, have been studied under various geometries, loadings and me mbrane prestressing. More details and results are ready for publication, but due to limited space not shown here. Advances in Technology Innovation , vol. 1, no. 2, 2016, pp. 50 - 52 52 Copyright © TAETI Fig. 5 Mid-arch with out-of-plane buckling 4. Conclusions (1) The effect of te xt ile me mb ranes on both in-plane and out-of-plane supporting arch stability and strength is enormous. (2) GNIA (by SOFiSTiK) proved to be adequate, provided the right value of the me mb rane prestressing is used. (3) Large parametric studies of barrel me mb rane structures supported by a row of steel a rches show enormous increase of both in -plane and particularly out-of-plane buckling loads in comparison to the ones of an arch alone. Provided the outer arches are transversely supported, the out-of plane buckling of the mid arches due to me mbrane support may always be neglected. Acknowledgement This work was supported by the Czech Grant Agency; grant GACR No. 105/13/25781S. References [1] S. Kato, T. Yoshino, and H. M ina mi, “Formulat ion of constitutive equatio ns for fabric me mb ranes based on concept of fabric lattice model,” Engineering Structures, vol. 21, pp. 691-708, 1999. [2] P. Gosling, “ Basic philosophy and calling notice,” Tensinet analysis & Materia l working group, Tensinews, vol. 13, pp. 12-15, 2007. [3] C. Ga lliot and R. H. Luchsinger, “A simp le model describing the non -linear b ia xia l tensile behaviour of PVC/coated polyester fabrics for use in finite e le ment analysis,” Co mp. Structures, vol. 90, pp. 438-447, 2009. [4] J. B. Pargana and W. M . A. Le itao, “A simp lified stress -strain model for coated plain-weave fabrics used in tensioned fabric structures,” Engineering Structures, vol. 84, pp. 439-450, 2015. [5] “Technet gmbh Berlin-Stuttgart,” http://www.technet-gmbh.com, 2016. [6] “SOFiSTiK 2014,” http://www.sofistik.de/, 2015. [7] D. Jermo ljev and J. Macháček, “ Imp le ment- ation of non-meta llic me mbranes into steel supporting structures ,” Proc. Recent Advances in Mechanics and Materials in Design, Ponta Delgada, pp. 907-908, July 2015. [8] “Formfinder software Gmb H, wien,” http://www.formfinder.at/ ma in/software/, 2015.