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DESIGNING AND DETAILING OF BUILDING SYSTEMS. MECHANICS IN CIVIL ENGINEERING

Experimental and theoretical studies into the stress-strain state of the purlin supported by sandwich panels

Vestnik MGSU 11/2014
  • Danilov Aleksandr Ivanovich - Moscow State University of Civil Engineering (MGSU) Candidate of Technical Sciences, Associate Professor, Department of Metal Structures, Moscow State University of Civil Engineering (MGSU), 26 Yaroslavskoe shosse, Moscow, 129337, Russian Federation; This e-mail address is being protected from spambots. You need JavaScript enabled to view it .
  • Tusnina Ol’ga Aleksandrovna - Moscow State University of Civil Engineering (MGSU) postgraduate student, Department of Metal Structures, Moscow State University of Civil Engineering (MGSU), 26 Yaroslavskoe shosse, Moscow, 129337, Russian Federation; This e-mail address is being protected from spambots. You need JavaScript enabled to view it .

Pages 26-36

In the article, the co-authors analyze the findings of the experimental and theoretical studies into the real behaviour of a thin-walled cold-formed purlin as part of the roof structure made of sandwich panels. The roof structure fragment was tested; displacements and stresses, that the purlin was exposed to, were identified in respect of each loading increment. NASTRAN software was employed to perform the numerical analysis of the roof structure, pre-exposed to experimental tests, in the geometrically and physically non-linear setting. The finite element model, generated as a result (the numerical analysis pattern), is sufficiently well-set, given the proposed grid of elements, and it ensures reasonably trustworthy results. The diagrams describing the stress/displacement to the load ratio and obtained numerically are consistent with those generated experimentally. The gap between the critical loading values reaches 4%. Analytical and experimental findings demonstrate their close conformity, and this fact may justify the application of the numerical model, generated within the framework of this research project, in the course of any further research actions. The co-authors have identified that the exhaustion of the bearing capacity occurs due to the loss of the buckling resistance as a result of the lateral torsional buckling.

DOI: 10.22227/1997-0935.2014.11.26-36

References
  1. Georgescu M. Distortional Behavior of Z Purlins Continuously Connected to Sandwich Panel Roofs. Proceedings of International Conference “Steel — a New and Traditional Material For Building”. Brasov, 2006, 143—148 p.
  2. Joo A.L. Analysis and Design of Cold-Formed Thin-Walled Roof Systems. PhD Dissertation, Budapest, 2009, 107 p.
  3. Ayrumyan E.L. Osobennosti rascheta stal’nykh konstruktsiy iz tonkostennykh gnutykh profiley [Features of Calculating Steel Structures of Thin-Walled Formed Sections]. Montazhnye i spetsial’nye raboty v stroitel’stve [Erection and Special Works in Construction]. 2008, no. 3, pp. 2—7. (In Russian).
  4. Ayrumyan E.L. Rekomendatsii po raschetu stal’nykh konstruktsiy iz tonkostennykh gnutykh profiley [Recommendations on Calculating Steel Structures of Thin-Walled Formed Sections]. StroyPROFIl’ [Construction Profile]. 2009, no. 8 (78), pp. 12—14. (In Russian).
  5. Ayrumyan E.L., Galstyan V.G. Issledovanie deystvitel’noy raboty tonkostennykh kholodnognutykh progonov iz otsinkovannoy stali [Investigation of the Actual Work of Thin-Walled Cold-Formed Beams of Galvanised Steel]. Promyshlennoe i grazhdanskoe stroitel’stvo [Industrial and Civil Engineering]. 2002, no. 6, pp. 31—34. (In Russian).
  6. Luza G., Robra J. Design of Z-purlins: Part 1. Basics and Cross-section Values According to EN 1993-1-3. Proceedings of the 5th European Conference on Steel and Composite Structures EUROSTEEL. Graz, Austria, 2008, vol. A, pp. 129—134.
  7. Luza G., Robra J. Design of Z-purlins: Part 2. Design Methods Given in Eurocode EN 1993-1-3. Proceedings of the 5th European Conference on Steel and Composite Structures EUROSTEEL. Graz, Austria, 2008, vol. A, pp. 135—140.
  8. EN 1993-1-1:2009 Eurocode 3: Design of Steel Structures — Part 1-1: General Rules and Rules for Buildings. Available at: http://www.eurocodes.fi/1993/1993-1-1/SFS-EN1993-1-1-AC.pdf/. Date of access: 27.07.2014.
  9. Gardner L., Neterkot D.A. Rukovodstvo dlya proektirovshchikov k evrokodu 3: proektirovanie stal’nykh konstruktsiy EN 1993-1-1,1993-1-3, 1993-1-8 [Guidance for Designers to Eurocode 3: Design of Steel Structures EN 1993-1-1,1993-1-3, 1993-1-8]. Moscow, MISIMGSU Publ., 2013, 224 p. (In Russian).
  10. Young-Lin P., Put B.M., Trahair N.S. Lateral Buckling Strength of Cold-Formed Steel Z-Section Beams. Thin-Walled Structures. 1999, vol. 34, no. 1, pp. 65—93.
  11. Chu X., Rickard J., Li L. Influence of Lateral Restraint on Lateral-torsional Buckling of Cold-formed Steel Purlins. Thin-Walled Structures. 2005, vol. 43, no. 5, pp. 800—810. DOI: http://dx.doi.org/10.1016/j.tws.2004.10.012.
  12. Chu X., Ye Z., Kettle R., Li L. Buckling Behavior of Cold-formed Channel Sections under Uniformly Distributed Loads. Thin-Walled Structures. 2005, vol. 43, no. 4, pp. 531—542. DOI: http://dx.doi.org/10.1016/j.tws.2004.10.002.
  13. Duerr M., Misiek T., Saal H. The Torsional Restraint of Sandwich-panels to Resist the Lateral Torsional Buckling of Beams. Steel Construction. 2011, vol. 4, no. 4, pp. 251—258. DOI: http://dx.doi.org/10.1002/stco.201110033.
  14. Li L.Y. Lateral-torsional Buckling of Cold-formed Zed-purlins Partial-laterally Restrained by Metal Sheeting. Thin-Walled Structures. 2004, vol. 42, no. 7, pp. 995—1011.
  15. Seek M.W., Murray T.M. Mechanics of Lateral Brace Forces in Z-purlin Roof Systems. Conference Proceedings, Structural Stability Research Council Annual Stability Research Council. Rolla, Missouri, 2005, pp. 56—76.
  16. Albermani F.G.A., Kitipornchai S. Cold-formed purlin-sheeting systems. Proceedings of the Third International Conference on Advances in Steel Structures. Hong Kong, China, 2002, pp. 429—435.
  17. Lucas R.M., Albermani F.G.A., Kitiporchai S. Modelling of Cold-Formed Purlin-Sheeting Systems — Part 1: Full Model. Thin-Walled Structures. 1997, vol. 27, no. 4, pp. 223—243. DOI: http://dx.doi.org/10.1016/S0263-8231(96)00038-9.
  18. Rzeszut K., Czajkowski A. Laterally Braced Thin-walled Purlins in Stability Problems. Proceedings of the Conference Computer Methods in Mechanics. 2011. Available at: http://www.cmm.il.pw.edu.pl/cd/pdf/202.pdf/. Date of access: 27.07.2014.
  19. Vrany T., Braham M., Belica A. Restraint of Purlins for Various Roof Systems. 11th Nordic Steel Construction Conference NSCC. 2009, pp. 422—429.
  20. Kujawa M., Werochowski W., Urba?ska-Galewska E. Restraining of the Cold-formed Z-purlins with Sandwich Panels. Final Report. Gdansk, Poland, 2008, 126 p.
  21. Shimkovich D.G. Raschet konstruktsiy v MSC/NASTRAN for Windows [Calculation of Structures in MSC/NASTRAN for Windows]. Moscow, DMK Press, 2001, 448 p. (In Russian).

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The features of behaviour of a thin-walled cold-formed C-purlin

Vestnik MGSU 10/2014
  • Tusnina Ol’ga Aleksandrovna - Moscow State University of Civil Engineering (MGSU) postgraduate student, Department of Metal Structures, Moscow State University of Civil Engineering (MGSU), 26 Yaroslavskoe shosse, Moscow, 129337, Russian Federation; This e-mail address is being protected from spambots. You need JavaScript enabled to view it .

Pages 64-74

Nowadays thin-walled cold-formed profiles are widely used as bearing structures of buildings. The features of these profiles are little thickness and complicated cross-section shape. These features influence the behaviour of the structures made of cold-formed profiles. It is an often situation that we can not apply load directly on the element in the shear center due to its complicated shape and boundary conditions, such as support fixation. Thus, the purlin experiences a combined action of bending and restraint torsion. Besides, the distortion of purlin occurs and in this case the Vlasov’s theory of thin-walled elastic beams is not applicable. In this paper the analysis of cold-formed C-purlin is considered. The results of physically and geometrically nonlinear analysis are represented. The components of the stress state of purlin are determined. An estimation of the influence of cross-section distortion on the angles of rotation about longitudinal axis of purlin is done. The buckling analysis according to Russian standards SNiP was done.

DOI: 10.22227/1997-0935.2014.10.64-74

References
  1. Mezentseva E.A., Lushnikov S.D. Bystrovozvodimye zdaniya iz legkikh stalnykh konstruktsiy [Prefabricated Buildings of Light Steel Structures]. Vestnik MGSU [Proceedings of Moscow State University of Civil Engineering]. 2009, Special issue, no. 1, pp. 62—64. (in Russian)
  2. Vatin N.I., Sinel’nikov A.S. Bolsheproletnye nadzemnye peshekhodnye perekhody iz legkogo kholodnognutogo stal’nogo profilya [Long Span Footway Bridges: Cold-Formed Steel Cross-Section]. Stroitel’stvo unikal’nykh zdaniy i sooruzheniy [Construction of Unique Buildings and Structures]. 2012, no. 1, pp. 47—53. (in Russian)
  3. Ayrumyan E.L. Osobennosti rascheta stal’nykh konstruktsiy iz tonkostennykh gnutykh profiley [The Features of the Analysis of Thin-Walled Cold-Formed Steel Structures]. Montazhnye i spetsial’nye raboty v stroitel’ste [Erecting and Special Works in Construction]. 2008, no. 3, pp. 2—7. (in Russian)
  4. Ayrumyan E.L., Belyy G.I. Issledovanie raboty stal’noy fermy iz kholodnognutykh profiley s uchetom ikh mestnoy i obshchey ustoychivosti [A Study of Steel Cold-Formed Profiles of Trusses with Regard to Their Local and General Stability]. Promyshlennoe i grazhdanskoe stroitel’stvo [Industrial and Civil Engineering]. 2010, no. 5, pp. 41—44. (in Russian)
  5. Yu C., Schafer B.W. Distortional Buckling Tests on Cold-Formed Steel Beams. Journal of Structural Engineering. 2006, vol. 132, no. 4, pp. 515—528.
  6. Tusnin A.R., Tusnina O.A. Vychislitel’naya sistema «STAL’KON» dlya rascheta i proektirovaniya sterzhnevykh konstruktsiy iz tonkostennykh sterzhney otkrytogo profilya [Computing System "STALKON" for Analysis and Design of Lattice Structures of Thin-walled Rods of Open Profile]. Promyshlennoe i grazhdanskoe stroitel’stvo [Industrial and Civil Engineering]. 2012, no. 8, pp. 62—65. (in Russian)
  7. Vatin N.I., Rybakov V.A. Raschet metallokonstruktsiy — sed’maya stepen’ svobody [An Analysis of Metal Structures — the Seventh Degree of Freedom]. StroyPROFIl" [Construction Profile]. 2007, no. 2 (56), pp. 60—63. (in Russian)
  8. Heinisuo M., Liukkonen V.-P., Tuomala M. New Beam Element Including Distortion. Nordic Steel Construction Conference 95, Malmö, Sweden, June 19—21. Swedish Institute of Steel Construction, 1995, Publication 150, vol. I, pp. 65—72.
  9. Gordeeva A.O., Vatin N.I. Raschetnaya konechno-elementnaya model’ kholodnognutogo perforirovannogo tonkostennogo sterzhnya v programmno-vychislitel’nom kom-plekse SCAD Office [Finite Element Calculation Model of Thin-Walled Cold-Formed Profile in Software Package SCAD Office]. Inzhenerno-stroitel’nyy zhurnal [Engineering and Construction Journal]. 2011, no. 3 (21), pp. 36—46. (in Russian)
  10. Lalin V.V., Rybakov V.A., Morozov S.A. Issledovanie konechnykh elementov dlya rascheta tonkostennykh sterzhnevykh sistem [The Finite Element Research for Calculation of Thin-Walled Bar Systems]. Inzhenerno-stroitel’nyy zhurnal [Engineering and Construction Journal]. 2012, no. 1 (27), pp. 53—73. (in Russian)
  11. Lalin V.V., Rybakov V.A. Konechnye elementy dlya rascheta ograzhdayushchikh konstruktsiy iz tonkostennykh profiley [Creating the Finite Elements of Thin-Walled Beams for Design of Light Steel Constructions]. Inzhenerno-stroitel’nyy zhurnal [Engineering and Construction Journal]. 2011, no. 8 (26), pp. 69—80. (in Russian)
  12. Selyantsev I., Tusnin A. The Influence of Cross-Section Shape Changing on Work of Thin-Walled Cold-Formed Steel Beam. Proceedings of the METNET Seminar 2011 in Aarhus. HAMK University of Applied Science, Einland, 2011, pp. 143—148.
  13. Yu C., Schafer B.W. Distortional Buckling of Cold-Formed Steel Members in Bending. Final report. AISI. Baltimore, January 2005, 386 p.
  14. Chu X.T., Ye Z.M., Li L.Y., Kettle R. Local and Distortional Buckling of Cold-Formed Zed-Sections Beams under Uniformly Distributed Transverse Loads. International Journal of Mechanical Sciences. 2006, vol. 48, pp. 378—388. DOI: http://dx.doi.org/10.1016/j.ijmecsci.2005.11.005.
  15. Chu X.T., Ye Z.M., Li L.Y., Kettle R. Buckling Behaviour of Cold-Formed Channel Sections under Uniformly Distributed Loads. Thin-Walled Structures. 2005, vol. 43, no. 4, pp. 531—542.
  16. Pavazza R., Blagojevic B. On the Cross-Section Distortion of Thin-Walled Beams with Multi-Cell Cross-Sections Subjected to Bending. International Journal of Solids and Structures. 2005, vol. 42, no. 3—4, pp. 901—925. DOI: http://dx.doi.org/10.1016/j.ijsolstr.2004.06.036.
  17. Silvestre N., Camotim D. Distortional Buckling Formulae for Cold-Formed Steel C- and Z-Section Members: Part I — Derivation. Thin-Walled Structures. 2004, vol. 42, no. 11, pp. 1567—1597.
  18. Silvestre N., Camotim D. Distortional Buckling Formulae for Cold-Formed Steel C- and Z-Section Members: Part II — Validation and Application. Thin-walled Structures. 2004, vol. 42, no. 11, pp. 1599—1629.
  19. Silvestre N., Camotim D. On the Mechanics of Distortion in Thin-Walled Open Sections. Thin-walled Structures. 2010, vol. 48, no. 7, pp. 469—481. DOI: http://dx.doi.org/10.1016/j.tws.2010.02.001.
  20. Vieira L.C.M., Malite M., Schafer B.W. Simplified Models for Cross-Section Stress Demands on C-Section Purlins in Uplift. Thin-walled Structures. 2010, vol. 48, no. 1, pp. 33—41. DOI: http://dx.doi.org/10.1016/j.tws.2009.07.009.
  21. Wang X.P., Lam S.S.E., Chung K.F. Cross-section Distortion due to Cutting of Cold-Formed Steel Lipped C-Section. Thin-walled Structures. 2006, vol. 44, no. 3, pp. 271—280. DOI: http://dx.doi.org/10.1016/j.tws.2006.03.007
  22. Vlasov V.Z. Tonkostennye uprugie sterzhni [Thin-walled Elastic Beams]. Moscow, Fizmatgiz Publ., 1959, 574 p. (in Russian)

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Study of parametric oscillations of viscoelastic cylindrical panel of variable thickness

Vestnik MGSU 11/2018 Volume 13
  • Abdikarimov Rustamkhan A. - Tashkent Institute of Finance Doctor of Physical and Mathematical Sciences, Associate Professor, Tashkent Institute of Finance, 60A A. Temur st., Tashkent, 100000, Uzbekistan.
  • Khodzhaev Dadakhan A. - Tashkent Institute of Irrigation and Agricultural Mechanization Engineers (TIIAME) Candidate of Physical and Mathematical Sciences, Associate Professor, Tashkent Institute of Irrigation and Agricultural Mechanization Engineers (TIIAME), 39 Kary-Niyazov st., Tashkent, 100000, Uzbekistan.
  • Normuminov Bakhodir A. - Tashkent Institute of Irrigation and Agricultural Mechanization Engineers (TIIAME) Senior Lecture, Tashkent Institute of Irrigation and Agricultural Mechanization Engineers (TIIAME), 39 Kary-Niyazov st., Tashkent, 100000, Uzbekistan.
  • Mirsaidov Mirziyod M. - Tashkent Institute of Irrigation and Agricultural Mechanization Engineers (TIIAME) Academician of Academy of Sciences of Uzbekistan, Doctor of Technical Sciences, Professor, Tashkent Institute of Irrigation and Agricultural Mechanization Engineers (TIIAME), 39 Kary-Niyazov st., Tashkent, 100000, Uzbekistan.

Pages 1315-1325

ABSTRACT Introduction. Isotropic viscoelastic cylindrical panels of variable thickness under the effect of a uniformly distributed vibration load applied along one of the parallel sides, resulting in parametric resonance (with certain combinations of eigenfrequencies of vibration and excitation forces) are considered. Materials and methods. It is believed that under the effect of this load, the cylindrical panels undergo the displacements (in particular, deflections) commensurate with their thickness. Based on the classical Kirchhoff-Love hypothesis, a mathematical model of the problem of parametric oscillations of a viscoelastic isotropic cylindrical panel of variable thickness in a geometrically non-linear formulation is constructed. Corresponding nonlinear equations of vibration motion of panels under consideration are derived (in displacements). The technique of the nonlinear problem solution by applying the Bubnov-Galerkin method at polynomial approximation of displacements (and deflection) and a numerical method that uses quadrature formula are proposed. The Koltunov-Rzhanitsyn kernel with three different rheological parameters is chosen as a weakly singular kernel. Results. Parametric oscillations of viscoelastic cylindrical panels of variable thickness under the effect of an external load are investigated. The effect on the domain of dynamic instability of geometric nonlinearity, viscoelastic properties of material, as well as other physical-mechanical and geometric parameters and factors (initial imperfections of the shape, aspect ratios, thickness, boundary conditions, excitation coefficient, rheological parameters) are taken into account. Conclusions. A mathematical model and method have been developed for estimating parametric oscillations of a viscoelastic cylindrical panel of variable thickness, taking into account geometric nonlinearity under the action of periodic loads. The results obtained are in good agreement with the results and data of other authors. The convergence of the Bubnov-Galerkin method is verified.

DOI: 10.22227/1997-0935.2018.11.1315-1325

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