Resistance of i-beams in warping torsion with account for the development of plasticdeformations

Vestnik MGSU 1/2014
  • Tusnin Aleksandr Romanovich - Moscow State University of Civil Engineering (MGSU) Doctor of Technical Sciences, Professor, Chair, Department of Metal Structures, Moscow State University of Civil Engineering (MGSU), 26 Yaroslavskoe shosse, Moscow, 129337, Russian Federation.
  • Prokic Milan - 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 75-82

Torsion of thin-walled open-section beams due to restrained warping displacements of cross-section is causing additional stresses, which make a significant contribution to the total stress. Due to plastic deformation there are certain reserves of bearing capacity, identification of which is of significant practical interest. The existing normative documents for the design of steel structures in Russia do not include design factor taking into account the development of plastic deformation during warping torsion. The analysis of thin-walled open-section members with plastic deformation will more accurately determine their load-bearing capacity and requires further research. Reserves of the beams bearing capacity due to the development of plastic deformations are revealed when beams are influenced by bending, as well as tension and compression. The existing methodology of determining these reserves and the plastic shape factor in bending was reviewed. This has allowed understanding how it was possible to solve this problem for warping torsion members and outline possible ways of theoretical studies of the bearing capacity in warping torsion. The authors used theoretical approach in determining this factor for the symmetric I-section beam under the action of bimoment and gave recommendations for the design of torsion members including improved value of plastic shape factor.

DOI: 10.22227/1997-0935.2014.1.75-82

References
  1. Vlasov V.Z. Tonkostennye uprugie sterzhni [Thin-walled Elastic Beams]. Moscow, Fizmatgiz Publ., 1959, 568 p.
  2. Timoshenko S.P., Gere J.M. Theory of Elastic Stability. 2nd Ed. McGraw-Hill, New York, 1961, 541 p.
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  4. Dinno K.S., Merchant W. A Procedure for Calculating the Plastic Collapse of I-sections under Bending and Torsion. The Structural Engineer. 1965, vol. 43(7), pp. 219—221.
  5. Pi Y.L., Trahair N.S. Inelastic Torsion of Steel I-beams. Research Report no. R679. The University of Sydney, 1993.
  6. Trahair N.S. Plastic Torsion Analysis of Monosymmetric and Point-symmetric Beams. Journal of Structural Engineering, ASCE. 1999, vol. 125, no. 2, pp. 175—182.
  7. Trahair N.S., Bradford M.A., Nethercot D.A., Gardner L. The Behaviour and Design of Steel Structure to EC3. 4th Ed. Taylor & Francis, New York, 2008, 490 p.
  8. Sokolovskiy V.V. Teoriya plastichnosti [Theory of Plasticity]. Moscow, Vysshaya Shkola Publ., 1969, 608 p.
  9. Belenya E.I. Metallicheskie konstruktsii [Metal Structures]. Moscow, Stroyizdat Publ., 1986, 560 p.
  10. Bychkov D.V. Stroitel'naya mekhanika sterzhnevykh tonkostennykh konstruktsiy [Structural Mechanics of Bar Thin-walled Systems]. Moscow, Gosstroyizdat Publ., 1962, 475 p.

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Derivative criteria of plasticity anddurability of metal materials

Vestnik MGSU 9/2014
  • Gustov Yuriy Ivanovich - Moscow State University of Civil Engineering (MGSU) Doctor of Technical Sciences, Professor, Department of Machinery, Machine Elements and Process Metallurgy, Moscow State University of Civil Engineering (MGSU), 26 Yaroslavskoe shosse, Moscow, 129337, Russian Federation; +7 (499) 183-94-95; This e-mail address is being protected from spambots. You need JavaScript enabled to view it .
  • Gustov Dmitriy Yur’evich - Moscow State University of Civil Engineering (MGSU) Candidate of Technical Sciences, Professor, Department of Building and Hoisting Machinery, Moscow State University of Civil Engineering (MGSU), 26 Yaroslavskoe shosse, Moscow, 129337, Russian Federation; +7 (499) 183-53-83; This e-mail address is being protected from spambots. You need JavaScript enabled to view it .
  • Voronina Irina Vladimirovna - Moscow State University of Civil Engineering (MGSU) Senior Lecturer, Department of Building and Hoisting Machinery, Moscow State University of Civil Engineering (MGSU), 26 Yaroslavskoe shosse, Moscow, 129337, Russian Federation; +7 (499) 182-16-87; This e-mail address is being protected from spambots. You need JavaScript enabled to view it .

Pages 39-47

Criteria of plasticity and durability derivative of standard indicators of plasticity (δ, ψ) and durability (σ
0,2, σ
B) are offered. Criteria К
δψ and К
s follow from the equation of relative indicators of durability and plasticity. The purpose of the researches is the establishment of interrelation of derivative criteria with the Page indicator. The values of derivative criteria were defined for steels 50X and 50XH after processing by cold, and also for steels 50G2 and 38HGN after sorbitizing. It was established that the sum of the offered derivative criteria of plasticity and durability С
к considered for the steels is almost equal to unit and corresponds to a square root of relative durability and plasticity criterion C
0,5. Both criteria testify to two-unity opposite processes of deformation and resistance to deformation. By means of the equations for S
к and С it is possible to calculate an indicator of uniform plastic deformation of σ
р and through it to estimate synergetic criteria - true tension and specific energy of deformation and destruction of metal materials. On the basis of the received results the expressions for assessing the uniform and concentrated components of plastic deformation are established. The preference of the dependence of uniform relative lengthening from a cubic root of criterion К
δψ, and also to work of the criteria of relative lengthening and relative durability is given. The advantage of the formulas consists in simplicity and efficiency of calculation, in ensuring necessary accuracy of calculation of the size δ
р for the subsequent calculation of structural and power (synergetic) criteria of reliability of metals.

DOI: 10.22227/1997-0935.2014.9.39-47

References
  1. Gustov Yu.I., Allattuf Kh. Issledovanie vzaimosvyazi koeffitsientov plastichnosti i predela tekuchesti staley standartnykh kategoriy prochnosti [Study of Interdependence between Ductility Factors and Yield Limits for Steels of Standard Strength Grades]. Vestnik MGSU [Proceedings of Moscow State University of Civil Engineering]. 2013, no. 7, pp. 22—26.
  2. Gustov Yu.I., Gustov D.Yu. K razvitiyu nauchnykh osnov stroitel’nogo metallovedeniya [To Development of Scientific Fundamentals of Construction Metallurgical Science]. Doklady X rossiysko-pol’skogo seminara «Teoreticheskie osnovy stroitel’stva». Varshava [Reports of the 10th Russian-Polish Seminar "Theoretical Foundations of Construction"]. Warsaw, Moscow, ASV Publ., 2001, pp. 307—314.
  3. Ivanova V.S., Balankin A.S., Bunin I.Zh., Oksogoev A.A. Sinergetika i fraktaly v materialovedenii [Synergetrics and Fractals in Materials Science]. Moscow, Nauka Publ., 1994, 383 p.
  4. Skudnov V.A. Novye kompleksy razrusheniya sinergetiki dlya otsenki sostoyaniya splavov [New Synergetrics Collapse Complexes for an Assessment of Alloys Condition]. Metalovedenie i metallurgiya. Trudy NGTU imeni R.E. Alekseeva [Metal Science and Metallurgy. Works of Nizhny Novgorod State Technical University n.a. R.E. Alekseev]. N. Novgorod, 2003, vol. 38, pp. 155—159.
  5. Gustov Yu.I., Gustov D.Yu., Voronina I.V. Sinergeticheskie kriterii metallicheskikh materialov [Synergetic Criteria of Metal Materials]. Sbornik dokladov XV Rossiysko-slovatsko-pol’skogo seminara «Teoreticheskie osnovy stroitel›stva». Varshava [Reports of the 15th Russian-Polish Seminar "Theoretical Foundations of Construction"]. Warsaw, Moscow, MGSU Publ., 2006, pp. 179—184.
  6. Il’in L.N. Osnovy ucheniya o plasticheskoy deformatsii [Doctrine Bases on Plastic Deformation]. Moscow, Mashinostroenie Publ.,1980, 150 p.
  7. Fridman Ya.B. Mekhanicheskie svoystva metallov. Ch. 2 Mekhanicheskie ispytaniya. Konstruktsionnaya prochnost’ [Mechanical Properties of Metals. Part 2. Mechanical Tests. Constructional Strength]. Moscow, Mashinostroenie Publ., 1974, 368 p.
  8. Goritskiy V.M., Terent’ev V.F. Struktura i ustalostnoe razrushenie metallov [Structure and Fatigue Failure of Metals]. Moscow, Metallurgiya Publ., 1980, 208 p.
  9. Arzamasov B.N., Solov’eva T.V., Gerasimov S.A., Mukhin G.G., Khovava O.M. Spravochnik po konstruktsionnym materialam [Reference Book on Construction Materials]. Moscow, Izd-vo MGTU im. N.E. Baumana Publ., 2005, 640 p.
  10. Larsen B. Formality of Sheet Metal. Sheck Metal Ind. 1977, vol. 54, no. 10, pp. 971—977.
  11. Abramov V.V., Djagouri L.V., Rakunov Yu.P. Kinetics and Mechanism of Contact Interaction with the Deformation and Thermal Deformation Effects on Crystalline Inorganic Materials. Materials of the 1st International Scientific Conference "Global Science and Innovation" (Chicago, USA, December 17—18th, 2013). Chicago, USA, 2013, vol. 2, pp. 360—371.
  12. Abramov V.V., Djagouri L.V., Rakunov Yu.P. Growth Kinetics of Strength (Setting) between Dissimilar Crystalline Materials with Dramatically Different Resistances to Plastic Deformation and Natures of Chemical Bonds. Materials of the 1st International Scientific Ñonference «Global Science and Innovation» (Chicago, USA, December 17—18th, 2013). Chicago, USA, 2013, vol. 2, pp. 372—380.
  13. Callister W.D., Rethwisch D.G. Fundamentals of Materials Science and Engineering. An Integrated Approach. John Wiley Sons, Ins., 2008, 896 p.
  14. Sansalone M., Jaeger B. Applications of the Impact-Echo Method for Detecting Flaws in Highway Bridges. Structural Materials Technology. An NTD Conference, San Diego, California, 1996, pp. 204—210.
  15. Tylkin M.A. Prochnost’ i iznosostoykost’ detaley metallurgicheskogo oborudovaniya [Strength and Wear Resistance of Details of the Metallurgical Equipment]. Moscow, Metallurgiya Publ., 1965, 347 p.

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Research into interrelations between plasticity and hardness of standardstrength steel grades

Vestnik MGSU 3/2013
  • Gustov Yuriy Ivanovich - Moscow State University of Civil Engineering (MGSU) Doctor of Technical Sciences, Profes- sor, Department of Machinery, Machine Elements and Process Metallurgy; +7 (499) 183-94-95, Moscow State University of Civil Engineering (MGSU), 26 Yaroslavskoe shosse, Moscow, 129337, Rus- sian Federation; This e-mail address is being protected from spambots. You need JavaScript enabled to view it .
  • Voronina Irina Vladimirovna - Moscow State University of Civil Engineering (MGSU) Senior Lecturer, Department of Building and Hoisting Machinery, Moscow State University of Civil Engineering (MGSU), 26 Yaroslavskoe shosse, Moscow, 129337, Russian Federation; +7 (499) 182-16-87; This e-mail address is being protected from spambots. You need JavaScript enabled to view it .
  • Allattouf Hassan Latuf - Moscow State University of Civil Engineering (MGSU) postgraduate student, Department of Machinery, Machine Elements and Process Metallurgy, Moscow State University of Civil Engineering (MGSU), 26 Yaroslavskoe shosse, Moscow, 129337, Rus- sian Federation; This e-mail address is being protected from spambots. You need JavaScript enabled to view it .

Pages 46-52

The objective of the study is research into interrelation between values of plasticity(d, y) and hardness (HB).Numerical values of hardness are insufficient to make accurate assessments of plasticity values. Meanwhile, hardness is the property identified using small-sized samples extracted from the metalwork of restored and reconstructed buildings. The most suitable method is the Rockwell one used to obtain HRB or HRC hardness values. However, these values maintain an analytical relationship neither with durability, nor with plasticity values. The difference between metal testing methods consists in their relation to dimensions: HRB and HRC values are dimensionless, while HB values are size dependent (kgf/mm2, or MPa). Therefore, the approach employed in this article can be used to generate supplementary information about the properties of metals using HRB or HRC hardness measurements.It is noteworthy that the proposed technique of coordination of HRB hardness val-ues with HB hardness values may be employed to, first, analyze σ and σ sizes using HBт вvalues, and second, to identify the nature of relationship between HRB, on the one hand,and d and y values, on the other hand, to compose the equation of relative strength and plasticity values and to assess the most important factor of reliability of metals.

DOI: 10.22227/1997-0935.2013.3.46-52

References
  1. Tylkin M.A. Spravochnik termista remontnoy sluzhby [Reference Book for a Heat Treater of the Repair Service]. Moscow, Metallurgiya Publ., 1981, 647 p.
  2. Mozberg R.K. Materialovedenie [Material Engineering]. Valgus Publ., Tallinn, 1976, p. 554.
  3. Gulyaev A.P. Metallovedenie [Metal Engineering]. Moscow, Metallurgiya Publ., 1986, 541 p.
  4. Arzamasov B.N., Makarova V.I., Mukhin G.G. Materialovedenie [Material Engineering]. Moscow, MGTU im. N.E. Baumana publ., 2008, 648 p.
  5. GOST 8479—70. Kategorii prochnosti, normy mekhanicheskikh svoystv, opredelennye pri ispytanii na prodol’nykh obraztsakh, i normy tverdosti [All-Russian State Standard 8479—70. Strength Categories, Standards of Mechanical Properties Identified in the Course of Testing of Longitudinal Samples, and Standards of Hardness].
  6. Gustov Yu.I., Gustov D.Yu., Bol’shakov V.I. Prochnostno-plasticheskaya indeksatsiya metallicheskikh materialov [Strength and Plasticity Indexing of Metal Materials]. Metallurgiya i gornorudnaya promyshlennost’ [Metallurgy and Mining Industry]. 1996, no. 3-4, pp. 31—33.
  7. Gustov Yu.I., Gustov D.Yu. Issledovanie vzaimosvyazi mekhanicheskikh svoystv metallicheskikh materialov. Teoreticheskie osnovy stroitel’stva. Doklady VII Pol’sko-rossiyskogo seminara [Research into Interrelations between Mechanical Properties of Metal Materials. Theoretical Fundamentals of Civil Engineering. Collected works of the 7th Russian-Slovak-Polish Seminar]. Moscow, ASV Publ., 1998, pp. 225—228.
  8. Gustov Yu.I., Gustov D.Yu., Voronina I.V. Opredelenie tverdosti staley po khimicheskomu sostavu i uglerodnomu ekvivalentu. Teoreticheskie osnovy stroitel’stva. Doklady XVII Pol’sko-rossiysko-slovatskogo seminara [Analysis of Steel Hardness on the Basis of the Chemical Composition and Carbon Equivalent. Theoretical Fundamentals of Civil Engineering. Collected works of the 7th Polish-Russian-Slovak Seminar]. Part 2. Zilina, 2008, pp. 237—244.
  9. Gustov Yu.I., Gustov D.Yu., Voronina I.V. Sinergeticheskie kriterii metallicheskikh materialov. Teoreticheskie osnovy stroitel’stva. Doklady XV Rossiysko-slovatsko-pol’skogo seminara [Synergetic Criteria of Metal Materials. Theoretical Fundamentals of Civil Engineering. Collected works of the 15th Russian-Slovak-Polish Seminar]. Warsaw, 2006, pp. 179—184.
  10. Skudnov V.A. Primenenie kompleksov razrusheniya sinergetiki dlya otsenki sostoyaniya i povedeniya (rabotosposobnosti) metallov. Fraktaly i prikladnaya sinergetika «FiPS-2005». Trudy IV mezhdunar. mezhdistsiplinarnogo simpoziuma. [Application of Synergy Destruction Sets in Assessment of Condition and Behaviour (Serviceability) of Metals. Fractals and Applied Synergy «FiPS-2005». Works of the 4th International Inter-disciplinary Symposium]. Moscow, Interkontakt Nauka Publ., 2005, pp. 221—226.
  11. Sorokin V.G., Volosnikova A.V., Vyatkin S.A. Marochnik staley i splavov [Reference Book of Steel and Alloy Grades]. Moscow, Mashinostroenie Publ., 1989, 640 p.

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Application of the homogenization method to the elastoplastic bending of a plate

Vestnik MGSU 9/2012
  • Savenkova Margarita Ivanovna - Lomonosov Moscow State University postraduate student, Department of Composite Mechanics, Faculty of Mechanics and Mathematics, Lomonosov Moscow State University, MSU Main Building, Vorobevy gory, Moscow, 119991, Russian Federation; This e-mail address is being protected from spambots. You need JavaScript enabled to view it .
  • Sheshenin Sergey Vladimirovich - Lomonosov Moscow State University (MGU) Doctor of Physical and Mathematical Sciences, Professor, Department of Composite Mechanics, Faculty of Mechanics and Mathematics, Lomonosov Moscow State University (MGU), ; Leninskie Gory, Moscow, 119991, Russian Federation; This e-mail address is being protected from spambots. You need JavaScript enabled to view it .
  • Zakalyukina Irina Mikhaylovna - Moscow State University of Civil Engineering (MGSU) Candidate of Physical and Mathematical Sciences, Assosiate Professor, Department of Theoretical Mechanics and Aerodynamics, Moscow State University of Civil Engineering (MGSU), 26 Yaroslavskoe shosse, Moscow, 129337, Russian Federation; +7 (499) 183-24-01; This e-mail address is being protected from spambots. You need JavaScript enabled to view it .

Pages 156 - 164

The authors present a method of homogenization used to solve nonlinear equilibrium problems
of laminated plates exposed to transversal loads.
The homogenization technique is a general and mathematically rigorous solution to elasticity
problems. It describes the processes of deformation of composite structural elements. It was originally
developed for linear problems. This method encompasses the calculation of all characteristics
related to deflection by combining solutions to local and global homogenization problems. Thus, it
implements the general idea of the domain decomposition into subdomains.
The homogenization method has been most widely used in cases of periodical heterogeneity
because of significant simplification that happens due to periodicity. This simplification implies that
any cell of periodicity appears to be the material representative volume element (RVE). Therefore,
it is sufficient to solve local problems within a single periodicity cell. Hence, with reference to local
problems, conditions of periodicity are a mere consequence of the periodicity of the material
structure. Decomposition of the domain causes decomposition of the solution. The latter means that
displacements, stresses and strains are represented by functions that depend on both global and local
coordinates. Global coordinates are associated with the whole body scale and local coordinates
vary in the periodicity cell, i.e. in RVE only.
If the material structure is not periodic, but its properties do not depend on global coordinates,
material effective properties can be determined by solving local problems in any RVE. That is not the ase of nonlinear materials. Now local problems have to be solved in every RVE because of the homogenized
properties dependence on global coordinates. Another complication arises due to nonlinearity.
Indeed, the homogenization method employs the superposition principle to represent the solution to the
elasticity problem as summarized solutions to global and local problems. This principle doesn't work in
the case of nonlinearity. We suggest combining the standard homogenization technique with linearization
by using the loading history to solve the nonlinear problem. On the contrary, local linear problems
have to be solved in every RVE. Certainly, this method involves numerous calculations.
As for the problem considered in the paper, its nonlinearity is caused by material plastic properties.
Most plasticity-related principles are formulated as tensorial linear relationships between the
stress and strain rates. Hence, here we identify a perfect opportunity to employ the homogenization
method combined with linearization with regard to the load parameter. This combined technique is
implemented to resolve the heterogeneous plate bending problem. Heterogeneous materials are of
the two types: laminates and functionally graded materials (FGM).
The computer code is developed for the purpose of numerical plate bending simulation. It employs
the parallel programming MPI technique and the Euler type explicit and implicit methods. For
example, laminated plate bending due to the distributed transversal load was the subject of research.
Each layer of the plate was composed of FGM or a homogeneous material. The authors have discovered
that FGM plates have a higher yield stress then the plates composed of homogeneous layers.

DOI: 10.22227/1997-0935.2012.9.156 - 164

References
  1. Hui-Shen Shen. Functionally Graded Materials: Nonlinear Analysis of Plates and Shells. Boca Raton: CRC Press, 2009.
  2. Pobedrya B.E. Mekhanika kompozitsionnykh materialov [Mechanics of Composite Materials]. Moscow, Nauka Publ., 1984.
  3. Bakhvalov N.S., Panasenko G.P. Osrednenie protsessov v periodicheskikh sredakh. [Averaging Methods for Processes in Periodic Media]. Moscow, Nauka Publ., 1984.
  4. Bardzokas D.I., Zobnin A.I. Matematicheskoe modelirovanie fizicheskikh protsessov v kompozitsionnykh materialakh periodicheskoy struktury [Mathematical Modeling of Physical Processes in Composite Materials of Periodic Structure]. Moscow, Editorial URSS Publ., 2003.
  5. Sheshenin S.V., Fu M., Ivleva E.A. Ob osrednenii periodicheskikh v plane plastin [Averaging Methods for Plates Periodic in the Plane]. Proceedings of International Conference “Theory and Practice of Buildings, Structures, and the Element Analysis. Analytical and Numerical Methods”. Moscow, MSUCE, 2008, pp.148-158.
  6. Antonov A.S. Parallel’noe programmirovanie s ispol’zovaniem tekhnologii MPI [Parallel Programming Using the MPI Technology]. Moscow, MGU Publ., 2004.
  7. Muravleva L.V., Sheshenin S.V. Effektivnye svoystva zhelezobetonnykh plit pri uprugoplasticheskikh deformatsiyakh [Effective Properties of Reinforced-concrete Slabs Exposed to Elastopastic Strains]. Vestnik Moskovskogo universiteta. Seriya 1. Matematika i mekhanika [Bulletin of Moscow University. Series 1. Mathematics and Mechanics]. 2004, no. 3, pp. 62—65.
  8. Muravleva L.V. Effektivnye svoystva ortotropnykh kompozitov pri uprugoplasticheskikh deformatsiyakh [Effective Properties of Orthotropic Composite Materials Exposed to Elastoplastic Strains]. Elasticity and Anelasticity. Proceedings of International Scientific Symposium Covering Problems of Mechanics of Deformable Bodies, dedicated to the 95th anniversary of A.A. Ilyushin. Moscow, Editorial URSS Publ., 2006.
  9. Kristensen R. Vvedenie v mekhaniku kompozitov [Introduction into Mechanics of Composite Materials]. Moscow, Mir Publ., 1982.
  10. Jones R. Mechanics of Composite Materials. Philadelphia, Taylor & Francis, 1999.
  11. Il’yushin A.A. Plastichnost’ [Plasticity]. Moscow, OGIZ Publ., 1948, Part 1.
  12. Sheshenin S.V. Primenenie metoda osredneniya k plastinam, periodicheskim v plane [Application of the Averaging Method to Plates Periodic in the Plane]. Vestnik Moskovskogo universiteta. Seriya 1. Matematika i mekhanika [Bulletin of Moscow University. Series 1. Mathematics and Mechanics]. 2006, no. 1, pp. 47—51.

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