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DESIGNING AND DETAILING OF BUILDING SYSTEMS. MECHANICS IN CIVIL ENGINEERING

The resistance problem of compressed-bent shanks with step inflexibility change

Vestnik MGSU 2/2015
  • Galkin Aleksandr Vasil’evich - Lipetsk State Technical University (LGTU) Candidate of Technical Sciences, Associate Professor, chair, Department of Applied Mathematics, Lipetsk State Technical University (LGTU), 30 Moskovskaya str., Lipetsk, 398600, Russian Federation; +7 (4742) 32-80-50; This e-mail address is being protected from spambots. You need JavaScript enabled to view it .
  • Sysoev Anton Sergeevich - Lipetsk State Technical University (LGTU) Candidate of Technical Sciences, Assistant Lecturer, Department of Applied Mathematics, Lipetsk State Technical University (LGTU), 30 Moskovskaya str., Lipetsk, 398600, Russian Federation; +7 (4742) 32-80-51; This e-mail address is being protected from spambots. You need JavaScript enabled to view it .
  • Sotnikova Irina Vladimirovna - Lipetsk State Technical University (LGTU) postgraduate student, Department of Metal Structures, Lipetsk State Technical University (LGTU), 30 Moskovskaya str., Lipetsk, 398600, Russian Federation, +7 (4742) 32-80-79; This e-mail address is being protected from spambots. You need JavaScript enabled to view it .

Pages 38-44

The main tasks of optimizing metal structures is reducing their materials consumption, time of production and erection. This is achieved by using thin-walled frame structures. Cold-formed profiles are some of them. The volume of such structures application in modern construction is constantly growing. At the same time it is necessary to note, that in Russia there is no regulatory base for design of structures made of cold formed profiles, because the actual operation of such constructions differs from the operation of constructions made of hot-rolled profiles. Buckling greatly influences the operation of frame structures made of cold-formed profiles. The problem connected with the resistance of compressed-bent shanks with variable inflexibility hinge-supported at the ends is under consideration. The way to calculate the critical load at which buckling of a shank happens was found out. This task solution will help to develop the normative base for designing made of cold-formed profiles.

DOI: 10.22227/1997-0935.2015.2.38-44

References
  1. Ayrumyan E.L., Kamenshchikov N.I., Liplenko M.A. Perspektivy LSTK v Rossii [Future of Steel Frames in Russia]. StroyPROFI. 2013, no. 10, pp. 12—17. (In Russian)
  2. Zverev V.V., Zhidkov K.E., Semenov A.S., Sotnikova I.V. Eksperimental’nye issledovaniya ramnykh konstruktsiy iz kholodnognutykh profiley povyshennoy zhestkosti [Experimental Researches of Frame Constructions Produced of Increased Rigidity Profiles]. Nauchnyy vestnik Voronezhskogo gosudarstvennogo arkhitekturno-stroitel'nogo universiteta. Stroitel'stvo i arkhitektura [Bulletin of Voronezh State University of Architecture and Civil Engineering]. 2011, no. 4 (24), pp. 20—24. (In Russian)
  3. Ayrumyan E.L. Rekomendatsii po raschetu stal’nykh konstruktsiy iz tonkostennykh gnutykh profiley [Recommendations for Calculating Steel Constructions Produced with Thin-Walled Roll-Formed Shapes]. StroyPROFI. 2009, no. 8 (78), pp. 12—14. (In Russian)
  4. Ayrumyan E.L. Osobennosti rascheta stal’nykh konstruktsiy iz tonkostennykh gnutykh profiley [Calculation Peculiarities of Steel Thin-Walled Roll-Formed Shapes]. Montazhnye i spetsial’nye raboty v stroitel’stve stroitelstve [Installation and Special Works in Construction]. 2008, no. 3, pp. 2—7. (In Russian)
  5. 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.
  6. 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.
  7. Smaznov D.N. Ustoychivost’ pri szhatii sostavnykh kolonn, vypolnennykh iz profiley iz vysokoprochnoy stali [Buckling Resistance of Composite Columns Made of High-Strength Steel Shapes]. Inzhenerno-stroitel’nyy zhurnal [Magazine of Civil Engineering]. 2009, no. 3 (5), pp. 42—49. (In Russian)
  8. Yu W-W., LaBoube R.A. Cold-Formed Steel Design. 4 ed. Wiley, 2010, 512 p.
  9. Timoshenko S.P. Ustoychivost' sterzhney, plastin i obolochek [Resistance of Shanks, Plates and Shells]. Under editorshop of E.I. Grigolyuk. Moscow, Nauka Publ., 1971, 807 p. (In Russian)
  10. Vol’mir A.S. Ustoychivost’ uprugikh system [Resistance of Flexible Systems]. Moscow, Fizmatgiz Publ., 1963, 879 p. (In Russian)
  11. Gorbachev V.I., Moskalenko O.B. Ustoychivost’ sterzhney s peremennoy zhestkost’yu pri szhatii raspredelennoy nagruzkoy [Resistance of Shanks with Variable Inflexibility while Pressing with Distributed Load]. Vestnik Moskovskogo gosudarstvennogo universiteta. Seriya 1. Matematika. Mekhanika [Proceedings of Moscow State University. Series 1. Mathematics. Mechanics]. 2012, no. 1, pp. 41—47. (In Russian)
  12. Temis Yu.M., Fedorov I.M. Sravnenie metodov analiza ustoychivosti sterzhney peremennogo secheniya pri nekonservativnom nagruzhenii [Comparing Analysis Methods of the Resistance of Shanks with Variable Cross Section at Neoconservative Loading]. Problemy prochnosti i plastichnosti [Problems of Stability and Plasticity]. 2006, no. 68, pp. 95—106. (In Russian)
  13. Lalin V.V., Rozin L.A., Kushova D.A. Variatsionnaya postanovka ploskoy zadachi geometricheski nelineynogo deformirovaniya i ustoychivosti uprugikh sterzhney [Variance Definition of Plane Problem of Nonlinear Deformation and Resistance of Flexible Shanks]. Inzhenerno-stroitel’nyy zhurnal [Magazine of Civil Engineering]. 2013, no. 1 (36), pp. 87—96. (In Russian)
  14. Kagan-Rozentsveyg L.M. O raschete uprugikh ram na ustoychivost’ [On Resistance Calculating of Flexible Frames]. Inzhenerno-stroitel’nyy zhurnal [Magazine of Civil Engineering]. 2012, no. 1 (27), pp. 74—78. (In Russian)
  15. Gukova M.I., Simon N.Yu., Svyashenko A.E. Vychislenie raschetnykh dlin szhatykh sterzhney s uchetom ikh sovmestnoy raboty [Calculation of the Designed lengths of Compression Bars with Account for TheirComposite Action ]. Stroitel'naya mekhanika i raschet sooruzheniy [Structural Mechanics and Calculation of Structures]. 2012, no. 3, pp. 43—48. (In Russian)
  16. Soldatov A.Yu., Lebedev V.L., Semenov V.A. Analiz ustoychivosti stal’nykh sterzhnevykh sistem s uchetom nelineynoy diagrammy deformirovaniya materiala [Flexibility Analysis of Steel Shank Systems Taking into Account Non-Linear Diagram of Deformation of Material]. Stroitel’naya mekhanika i raschet sooruzheniy [Structural Mechanics and Calculation of Structures]. 2012, no. 2, pp. 48—53. (In Russian)
  17. Soldatov A.Yu., Lebedev V.L., Semenov V.A. Analiz ustoychivosti stroitel’nykh konstruktsiy s uchetom fizicheskoy nelineynosti metodom konechnykh elementov [Flexibility Analysis of Construction Systems Taking into Account Physical Non-Linearity Using Finite Elements Method]. Stroitel’naya mekhanika i raschet sooruzheniy [Structural Mechanics and Calculation of Structures]. 2011, no. 6, pp. 60—66. (In Russian)
  18. Krutiy Yu.S. Zadacha Eylera v sluchae nepreryvnoy poperechnoy zhestkosti (prodolzhenie) [Euler Problem in Case of Constant Transverse Inflexibility (Continuance)]. Stroitel'naya mekhanika i raschet sooruzheniy [Structural Mechanics and Calculation of Structures]. 2011, no. 2, pp. 27—33. (In Russian)
  19. Slivker V.I. Ustoychivost’ sterzhnya pod deystviem szhimayushchey sily s fiksirovannoy liniey deystviya [Resistance of Shanks under the Influence of Comprehensive Load with Fixed Force Line]. Stroitel’naya mekhanika i raschet sooruzheniy [Structural Mechanics and Calculation of Structures]. 2011, no. 2, pp. 34—37. (In Russian)
  20. Nasonkin V.D. Predel’naya nagruzka dlya szhatykh sterzhney, deformiruemykh za predelom uprugosti [Ultimate Load for Compression Bars Deformable outside Limit of Elasticity]. Stroitel’naya mekhanika i raschet sooruzheniy [Structural Mechanics and Calculation of Structures]. 2007, no. 2, pp. 24—28. (In Russian)
  21. Potapov A.V. Ustoychivost’ stal’nykh sterzhney otkrytogo profilya s uchetom real’noy raboty materiala [Resistance of Steel Shanks with Open Profile Taking into Account Real Operation of the Material]. Izvestiya Kazanskogo gosudarstvennogo arkhitekturno-stroitel'nogo universiteta [Bulletin of Kazan State University of Architecture and Engineering]. 2009, no. 1, pp. 112—115. (In Russian)

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Solving the stability problem of compressed-bendablepinned rigid rods of variable rigidity

Vestnik MGSU 5/2015
  • Blyumin Semen L'vovich - Lipetsk State Technical University (LGTU) Doctor of Physical and Math- ematical Sciences, Professor, Department of Applied Mathematics, Lipetsk State Technical University (LGTU), 30 Moskovskaya str., Lipetsk, 398600, Russian Federation; This e-mail address is being protected from spambots. You need JavaScript enabled to view it .
  • Zverev Vitaliy Valentinovich - Lipetsk State Technical University (LGTU) Doctor of Technical Sciences, Professor, chair, De- partment of Metal Structures, Lipetsk State Technical University (LGTU), 30 Moskovskaya str., Lipetsk, 398600, Russian Federation; This e-mail address is being protected from spambots. You need JavaScript enabled to view it .
  • Sotnikova Irina Vladimirovna - Lipetsk State Technical University (LGTU) postgraduate student, Department of Metal Structures, Lipetsk State Technical University (LGTU), 30 Moskovskaya str., Lipetsk, 398600, Russian Federation; This e-mail address is being protected from spambots. You need JavaScript enabled to view it .
  • Sysoev Anton Sergeevich - Lipetsk State Technical University (LGTU) Candidate of Technical Sciences, Assistant Lecturer, Department of Applied Mathematics, Lipetsk State Technical University (LGTU), 30 Moskovskaya str., Lipetsk, 398600, Russian Federation; +7 (4742) 32-80-51; This e-mail address is being protected from spambots. You need JavaScript enabled to view it .

Pages 18-27

The problem connected with the stability of compressed-bendable rigid rods of variable rigidity (with the reduced rigidity in the centre) is formulated and solved. The system of transcendent equations with roots for critical load for a rod is founded out.

DOI: 10.22227/1997-0935.2015.5.18-27

References
  1. Ayrumyan E.L., Kamenshchikov N.I., Liplenko M.A. Perspektivy LSTK v Rossii [Prospects of Steel Frames in Russia]. StroyPROFI [Construction Prof]. 2013, no. 10, pp. 12—17. (In Russian)
  2. Zverev V.V., Zhidkov K.E., Semenov A.S., Sotnikova I.V. Eksperimental'nye issledovaniya ramnykh konstruktsiy iz kholodnognutykh profiley povyshennoy zhestkosti [Experimental Studies of Frame Constructions Produced of Cold-Formed Profiles of Increased Rigidity]. Nauchnyy vestnik Voronezhskogo gosudarstvennogo arkhitekturno-stroitel'nogo universiteta. Stroitel'stvo i arkhitektura [Bulletin of Voronezh State University of Architecture and Civil Engineering. Construction and Architecture]. 2011, no. 4 (24), pp. 20—25. (In Russian)
  3. Ayrumyan E.L. Rekomendatsii po raschetu stal'nykh konstruktsiy iz tonkostennykh gnutykh profiley [Recommendations for Calculating Steel Constructions Produced of Thin-Walled Roll-Formed Profiles]. StroyPROFIl' [Construction Profile]. 2009, no. 8 (78), pp. 12—14. (In Russian)
  4. Ayrumyan E.L. Osobennosti rascheta stal'nykh konstruktsiy iz tonkostennykh gnutykh profiley [Features of Calculation for Steel Thin-Walled Roll-Formed Shapes]. Montazhnye i spetsial'nye raboty v stroitel'stve [Installation and Special Works in Construction]. 2008, no. 3, pp. 2—7. (In Russian)
  5. Luza G., Robra J. Design of Z-purlins: Part 1. Basics and Cross-Section Values Ac-сording 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.
  6. 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.
  7. Smaznov D.N. Ustoychivost' pri szhatii sostavnykh kolonn, vypolnennykh iz profiley iz vysokoprochnoy stali [Stability in Compression of Composite Columns Made of High-Strength Steel Profiles]. Inzhenerno-stroitel'nyy zhurnal [Magazine of Civil Engineering]. 2009, no. 3, pp. 42—49. (In Russian)
  8. Yu W.-W., LaBoube R.A. Cold-Formed Steel Design. 4th Edition, John Wiley & Sons, 2010, 512 p.
  9. Timoshenko S.P., Grigolyuk E.I. Ustoychivost' sterzhney, plastin i obolochek [Stability of Rods, Plates and Shells]. Moscow, Nauka Publ., 1971, 807 p. (In Russian)
  10. Vol'mir A.S. Ustoychivost' uprugikh system [Stability of Elastic Systems]. Moscow, Fizmatlit Publ., 1972, 879 p. (In Russian)
  11. Galkin A.V., Sysoev A.S., Sotniko-va I.V. Zadacha ustoychivosti szhato-izgibaemykh sterzhney so stupenchatym izmeneniem zhestkosti [The Resistance Problem of Compressed-Bent Shanks with Step Inflexibility Change]. Vestnik MGSU [Proceedings of Moscow State University of Civil Engineering]. 2015, no. 2, pp. 38—44. (In Russian)
  12. Gorbachev V.I., Moskalenko O.B. Ustoychivost' sterzhney s peremennoy zhestkost'yu pri szhatii raspredelennoy nagruzkoy [Stability of the Rods with Variable Inflexibility While Pressing with Distributed Load]. Vestnik Moskovskogo universitetata. Seriya 1, Matematika. Mekhanika [Bulletin of the Moscow State University. Series 1. Mathematics, Mechanics]. 2012, no. 1, pp. 41—47. (In Russian)
  13. Temis Yu.M., Fedorov I.M. Sravnenie metodov analiza ustoychivosti sterzhney peremennogo secheniya pri nekonservativnom nagruzhenii [Comparing the Analysis Methods of the Stability of Rods with Variable Cut Set at Nonconservative Loading]. Problemy prochnosti i plastichnosti [Problems of Strength and Plasticity]. 2006, no. 68, pp. 95—106. (In Russian)
  14. Gukova M.I., Simon N.Yu., Svyatoshenko A.E. Vychislenie raschetnykh dlin szhatykh sterzhney s uchetom ikh sovmestnoy raboty [Calculation of the Lengths of Compressed Rods with Account for their Joint Action]. Stroitel'naya mekhanika i raschet sooruzheniy [Construction Mechanics and Calculation of Structures]. 2012, no. 3, pp. 43—47. (In Russian)
  15. Soldatov A.Yu., Lebedev V.L., Semenov V.A. Analiz ustoychivosti stal'nykh sterzhnevykh sistem s uchetom nelineynoy diagrammy deformirovaniya materiala [Stability Analysis of Steel Rod Systems Taking into Account the Non-Linear Diagram of Material Deformation]. Stroitel'naya mekhanika i raschet sooruzheniy [Construction Mechanics and Calculation of Structures]. 2012, no. 2, pp. 48—52. (In Russian)
  16. Soldatov A.Yu., Lebedev V.L., Semenov V.A. Analiz ustoychivosti stroitel'nykh konstruktsiy s uchetom fizicheskoy nelineynosti metodom konechnykh elementov [Stability Analysis of Building Structures Taking into Account the Physical Non-Linearity Using Finite Element Method]. Stroitel'naya mekhanika i raschet sooruzheniy [Construction Mechanics and Calculation of Structures]. 2011, no. 6, pp. 60—65. (In Russian)
  17. Krutiy Yu.S. Zadacha Eylera v sluchae nepreryvnoy poperechnoy zhestkosti (prodolzhenie) [Euler Problem in Case of Constant Transverse Inflexibility (Continuation)]. Stroitel'naya mekhanika i raschet sooruzheniy [Construction Mechanics and Calculation of Structures]. 2011, no. 2, pp. 27—33. (In Russian)
  18. Slivker V.I. Ustoychivost' sterzhnya pod deystviem szhimayushchey sily s fiksirovannoy liniey deystviya [Stability of a Rod under the Influence of Comprehensive Load with Fixed Force Line]. Stroitel'naya mekhanika i raschet sooruzheniy [Construction Mechanics and Calculation of Structures]. 2011, no. 2, pp. 34—36. (In Russian)
  19. Nasonkin V.D. Predel'naya nagruzka dlya szhatykh sterzhney, deformiruemykh za predelom uprugosti [Ultimate Load for Compressed Rods Deformable outside the Limit of Elasticity]. Stroitel'naya mekhanika i raschet sooruzheniy [Construction Mechanics and Calculation of Structures]. 2007, no. 2, pp. 24—28. (In Russian)
  20. Potapov A.V. Ustoychivost' stal'nykh sterzhney otkrytogo profilya s uchetom real'noy raboty materiala [Stability of Steel Rods with Open Profile Taking into Account the Real Operation of the Material]. Izvestiya Kazanskogo gosudarstvennogo arkhitekturno-stroitel'nogo universiteta [Bulletin of Kazan State University of Architecture and Engineering]. 2009, no. 1 (11), pp. 112—115. (In Russian)

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