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Foundation calculation for buildings and structures with two elastic characteristics of the foundation using features of Fourier transformsfor finite functions

Vestnik MGSU 1/2014
  • Kurbatskiy Evgeniy Nikolaevich - Moscow State University of Railway Engineering (MIIT) Doctor of Technical Sci- ences, Professor, head, Department of Underground Structures, Moscow State University of Railway Engineering (MIIT), 9-9 Obraztsova st., Moscow, 127994, Russian Federation; This e-mail address is being protected from spambots. You need JavaScript enabled to view it .
  • Mai Duc Minh. - Moscow State University of Railway Engineering (MIIT) postgraduate student, Department of Underground Structures, Moscow State University of Railway Engineering (MIIT), 9-9 Obraztsova st., Moscow, 127994, Russian Federation; This e-mail address is being protected from spambots. You need JavaScript enabled to view it .

Pages 41-51

The problem of a beam resting on elastic foundation often occurs in the analysis of building, geotechnical, highway, and railroad structures. Its solution demands modeling of the mechanical behavior of the beam, the mechanical behavior of the soil as elastic subgrade and the form of interaction between the beam and the soil. The oldest, most fa- mous and most frequently used mechanical model is the one devised by Winkler (1867), in which the beam-supporting soil is modeled as a series of closely spaced, mutually independent, linear elastic vertical springs, which, evidently, provide resistance in direct proportion to the deflection of the beam.The solution is presented for the problem of an Euler–Bernoulli beam supported by an infinite two-parameter Pasternak foundation. The beam is subjected to arbitrarily distributed or concentrated vertical loading along its length. Static response of a beam on an elastic foundation characterized by two parameters is investigated assuming, that the beam is subjected to external loads and two concentrated edge load. The governing equations of the problem are obtained and solved by pointing out that there is a concentrated edge foundation reaction in addition to a continuous foundation reaction along the beam axis in the case of complete contact in the foundation reactions of the two-parameter foundation model. The proposed method is based on the properties of Fourier transforms of the finite functions. Particular attention is paid to the problem, taking into account the deformation of soil areas outside the beam. The beam model with two foundation coefficients more realistically describes the behavior of strip footings under loading.

DOI: 10.22227/1997-0935.2014.1.41-51

References
  1. Korenev B.G. Voprosy rascheta balok i plit na uprugom osnovanii [Problems of Calculating Beams and Slabs on Elastic Foundation]. Moscow, Gosstroyizdat Publ., 1954, 231 p.
  2. Gorbunov-Posadov M.I, Malikova T.A. Raschet konstruktsiy na uprugom osnovanii [Calculation of Structures on Elastic Foundation]. 2-nd edition. Moscow, Stroyizdat Publ., 1973, 627 p.
  3. Pasternak P.L. Osnovy novogo metoda rascheta fundamentov na uprugom osnovanii pri pomoshchi dvukh koeffitsientov posteli [Fundamentals of a New Method of Elastic Foundation Analysis by Means of Two-constants]. Moscow, 1954, 55 p.
  4. Celep Z., Demir F. Symmetrically Loaded Beam on a Two-parameter Tensionless Foundation. Structural Engineering and Mechanics. 2007, vol. 27, no. 5, pp. 555—574.
  5. Eisenberger M., Bielak J. Finite Beams on Infinite Two-parameter Elastic Foundations. Computers & Structures. 1992, vol. 42, no. 4, pp. 661—664.
  6. Sapountzakis E.J., Kampitsis A.E. Inelastic Analysis of Beams on Two Parameter Tensionless Elastoplastic Foundation. Engineering Structures. 2013, no. 48, pp. 389—401.
  7. Ma X., Butterworth J.W., Clifton G.C. Static Analysis of an Infinite Beam Resting on a Tensionless Pasternak Foundation. European Journal of Mechanics — A/Solids. 2009, vol. 28, no. 4, ðð. 697—703.
  8. Razaqpur A., Shah K. Exact Analysis of Beams on Two-parameter Elastic Foundations. International Journal of Solids and Structures. 1991, vol. 27, no. 4, pp. 435—454.
  9. Morfidis K., Avramidis I.E. Formulation of a Generalized Beam Element on a Twoparameter Elastic Foundation with Semi-rigid Connections and Rigid Offsets. Computers & Structures. 2002, vol. 80, no. 25, ðð. 1919—1934.
  10. Kurbatskiy E.N. Metod resheniya zadach stroitel'noy mekhaniki i teorii uprugosti, osnovannyy na svoystvakh izobrazheniy Fur'e finitnykh funktsiy [Solution Method for the Tasks of Construction Mechanics and the Elasticity Theory Based on the Properties of Fourier Transform for Finite Functions]. Dissertatsiya na soiskanie uchenoy stepeni doktora tekhnicheskikh nauk [Doctoral Thesis in Engineering Sciences]. Moscow, MIIT Publ., 1995, 205 p.
  11. Mai Duc Minh. Raschet tonneley, raspolozhennykh v uprugoplasticheskikh gruntakh, peresekayushchikh zony razloma, na seysmicheskie vozdeystviya [Seismic Design for the Tunnels Located on Elasto-plastic Soils Across Fault Zones]. Stroitel'stvo i rekonstruktsiya [Construction and Reconstruction]. 2013, no. 1 (45), pp.19—25.
  12. Klepikov S.N. Raschet konstruktsiy na uprugom osnovanii [Calculation of Structures on Elastic Foundation]. Moscow, Kiev Publ., 1967, 185 p.

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Influence of location and parameters of stiffeners on the stability of a square plate under shear

Vestnik MGSU 12/2014
  • Pritykin Aleksey Igorevich - Immanuel Kant Baltic Federal University (IKBFU) Doctor of Technical Sciences, Associate Professor, Department of Urban Development, Land Planning and Design, Immanuel Kant Baltic Federal University (IKBFU), 14 Aleksandra Nevskogo str., Kaliningrad, 236041; This e-mail address is being protected from spambots. You need JavaScript enabled to view it .
  • Kirillov Il’ya Evgen’evich - Kaliningrad State Technical University (KSTU) postgraduate student, Department of Industrial and Civil Engineering, Kaliningrad State Technical University (KSTU), 1 Sovetskiy Prospect, Kaliningrad, 236022, Russian Federation; This e-mail address is being protected from spambots. You need JavaScript enabled to view it .

Pages 77-87

Application of flexible-walled beams is rather effective because the reducing of wall thickness compared to ordinary welded beams leads to substantial reduction of metal expenditure for the walls and its more rational use. The operation experience of such beams shows that the loss of local stability of a wall takes place near bearing cross section with characteristic diagonal type of half waves, indicating, that the reason for the stability loss is in shear deformation. In plate girder with slender web big transverse forces appear, which leads to its buckling as a result of shear. One of the ways to increase stability of the parts of web near supports is to install stiffeners. In the given work the task of finding critical stresses of fixed square plate with installed inclined stiffener is considered. Investigations were performed with the help of finite element method and were experimentally checked. Recommendations were given on the choice of optimal size of the stiffener.

DOI: 10.22227/1997-0935.2014.12.77-87

References
  1. Chen W.F., Lui E.M. Handbook of Structural Engineering, 2nd ed. CRC Press, 2005, 1768 p.
  2. Duggal S.K. Design of Steel Structures. Tata McGraw-Hill Education, 2000, 663 p.
  3. Darko Beg. Plate and Box Girder Stiffener Design in View of Eurocode 3: Part 1.5. 6th National Conference on Metal Structures. 2008, vol. 1, pp. 286—303.
  4. Hendy C.R., Presta F. Transverse Web Stiffeners and Shear Moment Interaction for Steel Plate Girder Bridges. Proceedings of the 7th International Symposium on Steel Bridges. Guimaracs. Portugal. 2008. ECCS, p. 8.
  5. Evans H.R. Longitudinally and Transversely Reinforced Plate Girders. Chapter 1. Plated Structures, Stability&Strength. Ed R. Narayanan. Elsevier Applied Science Publishers, London, 1983, pp. 1—73.
  6. Ravi S. Bellur. Optimal Design of Stiffened Plates. M. Sc. Thesis, University of Toronto, Graduate Department of Aerospace Science and Engineering, 1999, 100 p.
  7. Mohammed M. Hasan. Optimum Design of Stiffened Square Plates for Longitudinal and Square Ribs. Al-khwarizmi Engineering Journal. 2007, vol. 3, no. 3, pp. 13—30.
  8. Leitch S.D. Steel Plate Girder Webs with Slender Intermediate Transverse Stiffeners. Ottawa: National Library of Canada. Biblioth? que national edu Canada, 1999.
  9. Virag Z. Optimum Design of Stiffened Plates for Different Load and Shapes of Ribs. Journal of Computational and Applied Mechanics. 2004, vol. 5, no. 1, pp. 165—179.
  10. Kubiak T. Static and Dynamic Buckling of Thin-Walled Plate Structures. Cham, Springer, 2013, 250 p. DOI: http://dx.doi.org/10.1007/978-3-319-00654-3.
  11. ?kesson B. Plate Buckling in Bridges and Other Structures. London, Taylor & Francis, 2007, 282 p.
  12. Gaby Issa-El-Khoury, Daniel G Linzell, Louis F. Geschwindner. Computational Studies of Horizontally Curved, Longitudinally Stiffened, Plate Girder Webs in Flexure. Journal of Constructional Steel Research. February 2014, vol. 93, pp. 97—106. DOI: http://dx.doi.org/10.1016/j.jcsr.2013.10.018.
  13. Aleksi? S., Roga? M., Lu?i? D. Analysis of Locally Loaded Steel Plate Girders: Model for Patch Load Resistance. Journal of Constructional Steel Research. October 2013, vol. 89, pp. 153—164. DOI: http://dx.doi.org/10.1016/j.jcsr.2013.07.005.
  14. Saliba N., Real E., Gardner L. Shear Design Recommendations for Stainless Steel Plate Girders. Engineering Structures. February 2014, vol. 59, pp. 220—228. DOI: http://dx.doi.org/10.1016/j.engstruct.2013.10.016.
  15. Real E., Mirambell E., Estrada I. Shear Response of Stainless Steel Plate Girders. Engineering Structures. July 2007, vol. 29, no. 7, pp. 1626—1640. DOI: http://dx.doi.org/10.1016/j.engstruct.2006.08.023.
  16. Chac?n R., Mirambell E., Real E. Transversally stiffened plate girders subjected to patch loading. Part 1. Preliminary study. Journal of Constructional Steel Research. January 2013, vol. 80, pp. 483—491. : http://dx.doi.org/10.1016/j.jcsr.2012.06.008.
  17. Tang K.H., Evans H.R. Transverse Stiffeners for Plate Girder Webs—an Experimental Study. Journal of Constructional Steel Research. 1984, vol. 4, no. 4, pp. 253—280. DOI: http://dx.doi.org/10.1016/0143-974X(84)90002-6.
  18. Birger I.A., Panovko Ya.G., editors. Prochnost’, ustoychivost’, kolebaniya. Spravochnik v trekh tomakh [Strength, Stability, Fluctuations. Reference Book]. Vol. 3, Moscow, Mashinostroenie Publ., 1968, 567 p. (In Russian)
  19. SP 16.13330.2011. Stal’nye konstruktsii. Aktualizirovannaya redaktsiya SNiP II-23—81* [Construction Requirements SP 16.13330.2011. Steel Structures. Revised edition of SN&R II-23—81*]. Minregion Rossii [Ministry of Regional Development of Russia]. Moscow, OAO «TsPP» Publ., 2011, 172 p. (In Russian)
  20. Pritykin A.I. Mestnaya ustoychivost’ balok-stenok s shestiugol’nymi vyrezami [Local Stability of Wall Beams with Hexagonal Gains]. Stroitel’naya mekhanika i raschet sooruzheniy [Structural Mechanics and Calculation of Structures]. 2011, no. 1, pp. 2—6. (In Russian)

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THE STRENGTH OF REINFORCED CONCRETE BEAM ELEMENTS UNDER CYCLIC ALTERNATING LOADING AND LOW CYCLE LOAD OF CONSTANT SIGN

Vestnik MGSU 9/2015
  • Semina Yuliya Anatol'evna - Odessa State Academy of Civil Engineering and Architecture (OGASA) postgraduate student, Department of Strength of Materials, Odessa State Academy of Civil Engineering and Architecture (OGASA), 4 Didrikhsona Str., Odessa, 65045, Ukraine; This e-mail address is being protected from spambots. You need JavaScript enabled to view it .

Pages 36-50

The behavior of reinforced concrete elements under some types of cyclic loads is described in the paper. The main aim of the investigations is research of the stress-strain state and strength of the inclined sections of reinforced concrete beam elements in conditions of systemic impact of constructive factors and the factor of external influence. To spotlight the problem of cyclic loadings three series of tests were conducted by the author. Firstly, the analysis of the tests showed that especially cyclic alternating loading reduces the bearing capacity of reinforced concrete beams and their crack resistance by 20 % due to the fatigue of concrete and reinforcement. Thus the change of load sign creates serious changes of stress-strain state of reinforced concrete beam elements. Low cycle loads of constant sign effect the behavior of the constructions not so adversely. Secondly, based on the experimental data mathematical models of elements’ strength were obtained. These models allow evaluating the impact of each factor on the output parameter not only separately, but also in interaction with each other. Furthermore, the material spotlighted by the author describes stress-strain state of the investigated elements, cracking mechanism, changes of deflection values, the influence of mode cyclic loading during the tests. Since the data on the subject are useful and important to building practice, the ultimate aim of the tests will be working out for improvement of nonlinear calculation models of span reinforced concrete constructions taking into account the impact of these loads, and also there will be the development of engineering calculation techniques of their strength, crack resistance and deformability.

DOI: 10.22227/1997-0935.2015.9.36-50

References
  1. Babich E.M. Vliyanie dlitel'nykh i malotsiklovykh nagruzok na mekhanicheskie svoystva betonov i rabotu zhelezobetonnykh elementov [Influence of Long-Term and Low-Cycle Loads on the Mechanical Properties of Concrete and on the Work of Reinforced Concrete Elements]. Rovno, 1995, 386 p. (In Ukrainian)
  2. Albu E.I., Kitsak A.K., Semina Yu.A., Gaydarzhi A.P., Grebenyuk A.V., Sashin V.O., Karpyuk V.M. Metodika eksperimental'nykh issledovaniy napryazhenno-deformirovannogo sostoyaniya priopornykh uchastkov zhelezobetonnykh balok pri malotsiklovom nagruzhenii [Technique of Experimental Studies of Stress-Strain State of Reinforced Concrete Beams under Low-Cycle Loading in the Supporting Areas]. Stroitel'stvo — kak faktor formirovaniya komfortnoy sredy zhiznedeyatel'nosti: sbornik materialov V Respublikanskoy nauchno-tekhnicheskoy konferentsii (28 noyabrya 2013 g.) [Construction as a Factor of Comfortable Living Environment Formation: Collection of the Materials of the 5th Republican Scientific and Technical Conference]. Bendery, 2014. Рр. 3—10. (In Russian)
  3. Zalesov A.S., Klimov Yu.A. Prochnost' zhelezobetonnykh konstruktsiy pri deystvii poperechnykh sil [The Strength of Reinforced Concrete Structures under the Action of Shear Forces]. Kiev, Budіvel'nik Publ., 1989, 104 p. (In Russian)
  4. Korneychuk A.I., Masyuk G.Kh. Eksperimental'nye issledovaniya nesushchey sposobnosti naklonnykh secheniy izgibaemykh zhelezobetonnykh elementov pri deystvii malotsiklovykh znakoperemennykh nagruzok [Experimental Study of the Bearing Capacity of Inclined Cross Sections of Bending Reinforced Concrete Elements under the Action of Low-Cycle Alternating Loads]. Resursoekonomnye materialy, konstruktsii zdaniya i sooruzheniya : sbornik nauchnykh trudov [Resource Saving Materials, Buildings Constructions and Structures: Collection of Scientific Papers]. Rovno, 2008, no. 16, part 2, pp. 217—222. (In Ukrainian)
  5. Dorofeev V.S., Karpyuk V.M., Yaroshevich N.M. Prochnost' i treshchinostoykost' izgibaemykh zhelezobetonnykh elementov [Strength and Crack Resistance of Bending Reinforced Concrete Elements]. Vestnik OGASA [Bulletin of the Odessa State Academy of Building and Architecture]. 2008, no. 28, pp. 149—158. (In Russian)
  6. Karpyuk V.M. Raschetnye modeli silovogo soprotivleniya progonnykh zhelezobetonnykh konstruktsiy v obshchem sluchae napryazhennogo sostoyaniya [Calculation Models of Power Resistance of Girder Reinforced Concrete Constructions in General Case of Stress State]. Odessa, OGASA Publ., 2014, 352 p. (In Ukrainian)
  7. Gomon P.S. Rabota zhelezobetonnykh balok tavrovogo secheniya pri deystvii povtornogo nagruzheniya [Work of T-section Reinforced Concrete Beams under Repeated Loading]. Novye materialy, oborudovanie i tekhnologii v promyshlennosti : materialy Mezhdunarodnoy konferentsii molodykh uchenykh [New Materials, Equipment and Technologies in the Industry: Proceedings of the International Conference of Young Scientists]. Mogilev, 2009, p. 90. (In Ukrainian)
  8. Zarechanskiy O.O. Issledovanie szhato-izognutykh elementov pri povtornom deystvii poperechnoy sily vysokikh urovney [Research of Compressed-Bent Elements by Repeated Transverse Force of High Levels]. Resursoekonomnye materialy, konstruktsii zdaniya i sooruzheniya : sbornik nauchnykh trudov [Resource Saving Materials, Buildings Constructions and Structures: Collection of Scientific Papers]. Rovno, 2005, no. 13, pp. 129—135. (In Ukrainian)
  9. Zinchuk N.S. Eksperimental'nye issledovaniya napryazhenno-deformirovannogo sostoyaniya zhelezobetonnykh izgibaemykh elementov pri odnokratnom i malotsiklovom nagruzheniyakh v usloviyakh povyshennykh temperatur [Experimental Study of Stress-Strain State of Reinforced Concrete Bent Elements under the Single and Low-Cycle Loading at Elevated Temperatures]. Resursoekonomnye materialy, konstruktsii zdaniya i sooruzheniya : sbornik nauchnykh trudov [Resource Saving Materials, Buildings Constructions and Structures: Collection of Scientific Papers]. Rovno, 2004, no. 11, pp. 164—166. (In Ukrainian)
  10. Karavan V.V., Masyuk G.Kh. Rezul'taty eksperimental'nykh issledovaniy treshchinostoykosti i deformativnosti izgibaemykh zhelezobetonnykh elementov pri vozdeystvii malotsiklovykh znakoperemennykh nagruzok [The Experimental Results of Crack Resistance and Deformability Bending Reinforced Concrete Elements When Exposed to Low-Cycle Alternating Loads]. Stalezhelezobetonnye konstruktsii. Issledovanie, proektirovanie, stroitel'stvo, ekspluatatsiya : sbornik nauchnykh statey [Composite Structures. Research, Design, Construction, Operation: Collection of Scientific Papers]. Krivoy Rog, 2002, no. 5, pp. 168—172. (In Ukrainian)
  11. Grigorchuk A.B., Masyuk G.Kh. Prochnost' i deformativnost' zhelezobetonnykh elementov, kotorye podvergayutsya vozdeystviyu znakoperemennogo nagruzheniya [Strength and Deformability of Reinforced Concrete Elements That are Exposed to Action of Alternating Loading]. Sbornik materialov konferentsii Ch. 1. Stroitel'stvo [Collection of Conference Materials. Part 1 Building]. L'vov, 2001, pp. 29—34. (In Ukrainian)
  12. Karpenko N.I., Karpenko S.N. O postroenii bolee sovershennoy modeli deformirovaniya zhelezobetona s treshchinami pri ploskom napryazhennom sostoyanii [On Construction of a More Perfect Model of Deformation of Cracked Reinforced Concrete under Plane Stress State]. Beton i zhelezobeton — puti razvitiya : materialy ІІ Vserossiyskoy Mezhdunarodnoy konferentsii po betonu i zhelezobetonu (05.09—09.09.2002) [Concrete and Reinforced Concrete — Ways of Development: Materials of the 2nd All-Russian International Conference on Concrete and Reinforced Concrete]. Moscow, 2005, pp. 431—444. (In Russian)
  13. Zalesov A.S., Mukhamediev T.A., Chistyakov E.A. Raschet prochnosti zhelezobetonnykh konstruktsiy pri razlichnykh silovykh vozdeystviyakh po novym normativnym dokumentam [Calculation of the Strength of Concrete Structures under Different Force Actions on New Regulations]. Beton i zhelezobeton [Concrete and Reinforced Concrete]. 2002, no. 3, pp. 10—13. (In Russian)
  14. Babich E.M., Gomon P.S., Filipchuk S.V. Rabota i raschet nesushchey sposobnosti izgibaemykh zhelezobetonnykh elementov tavrovogo profilya pri vozdeystvii povtornykh nagruzok [Work and Calculation of the Bearing Capacity of Bending T-Sections Reinforced Concrete Elements under the Influence of Repeated Loads]. Rovno, NUVGP Publ., 2012, 108 p. (In Ukrainian)
  15. Masyuk G.Kh., Korneychuk A.I. Napryazhenno-deformirovannoe sostoyanie naklonnykh secheniy izgibaemykh zhelezobetonnykh elementov, kotorye podvergayutsya vozdeystviyu malotsiklovykh znakoperemennykh nagruzok [Stress-strain State of Incline Sections of Bending Concrete Elements That are Exposed to the Action of Low-Cycle Alternating Loads]. Resursoekonomnye materialy, konstruktsii zdaniya i sooruzheniya : sbornik nauchnykh trudov [Resource Saving Materials, Buildings Constructions and Structures: Collection of Scientific Papers]. Rovno, NUVGP Publ., 2008, no. 17, pp. 204—211. (In Ukrainian)
  16. Mel'nik S.V., Borisyuk O.P., Kononchuk O.P., Petrishin V.M. Issledovanie raboty usilennykh zhelezobetonnykh balok pri deystvii malotsiklovykh nagruzheniy [Research of Reinforced Concrete Beams Work under the Action of Low-Cycle Loading]. Resursoekonomnye materialy, konstruktsii zdaniya i sooruzheniya : sbornik nauchnykh trudov [Resource Saving Materials, Buildings Constructions and Structures: Collection of Scientific Papers]. Rovno, 2008, no. 17, pp. 404—410. (In Ukrainian)
  17. Koval'chik Ya.I., Koval' P.M. Issledovanie treshchinostoykosti predvaritel'no napryazhennykh zhelezobetonnykh balok pri vozdeystvii malotsiklovykh nagruzheniy [Investigation of Crack Resistance of Prestressed Concrete Beams under the Influence of Low-Cycle Loading]. Nauchno-prikladnye aspekty avtomobil'noy i transportno-dorozhnoy otrasley : Nauchnye zametki [Scientific and Practical Aspects of the Automobile and Transport Industries: Scientific Notes]. Lutsk, 2014, no. 45, pp. 282—287. (In Ukrainian)
  18. Dovbenko V.S. Issledovanie raboty zhelezobetonnykh balok, usilennykh polimernoy kompozitsiey pri vozdeystvii malotsiklovykh nagruzok [Research of Reinforced Concrete Beams Work Reinforced with Polymer Composition When Exposed to Low-Cycle Loads]. Resursoekonomnye materialy, konstruktsii zdaniya i sooruzheniya : sbornik nauchnykh trudov [Resource Saving Materials, Buildings Constructions and Structures: Collection of Scientific Papers]. Rovno, 2011, no. 22, pp. 787—794. (In Ukrainian)
  19. Babich V.E. Osobennosti raboty nerazreznykh zhelezobetonnykh balok pri povtornykh nagruzkakh [Features of Continuous Reinforced Concrete Beams Work under the Repeated Loads]. Stroitel'nye konstruktsii : sbornik nauchnykh trudov [Building Structures: Collection of Scientific Works]. Kiev, 2003, no. 58, pp. 8—13. (In Ukrainian)
  20. Drobyshinets S.Ya., Babich E.M. Rabota stalefibrobetonnykh i stalefibrozhelezobetonnykh balok pri odnokratnom i povtornom nagruzheniyakh [Work of Fiber Concrete and Fiber Reinforced Concrete Beams under the Action of Single and Repeated Loadings]. Stalezhelezobetonnye konstruktsii. Issledovanie, proektirovanie, stroitel'stvo, ekspluatatsiya : sbornik nauchnykh statey [Composite Structures. Research, Design, Construction, Operation: Collection of Scientific Papers]. Krivoy Rog, 2004, no. 6, pp. 65—71. (In Ukrainian)
  21. Valovoy M.A. Prochnost', deformativnost' i treshchinostoykost' zhelezobetonnykh balok pri vozdeystvii povtornykh nagruzok [The Strength, Crack Resistance and Deformability of Concrete Beams under the Influence of Repeated Loads]. Stalezhelezobetonnye konstruktsii. Issledovanie, proektirovanie, stroitel'stvo, ekspluatatsiya : sbornik nauchnykh statey [Composite Structures. Research, Design, Construction, Operation: Collection of Scientific Papers]. Krivoy Rog, 2008, no. 8, pp. 45—48. (In Ukrainian)

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