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Moyseychik Evgeniy Alekseevich -
Novosibirsk State Universityof Architecture and Civil Engineering (NSUACE (Sibstrin))
Candidate of Technical Sciences, Associate Professor, Doctoral Student, Department of Metal and Wooden Structures, Novosibirsk State Universityof Architecture and Civil Engineering (NSUACE (Sibstrin)), 113 Leningradskaya str., Novosibirsk, 630008, Russian Federation;
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Shafray Sergey Dmitrievich -
Novosibirsk State Academy of Architecture and Arts (NGAHA)
Doctor of Technical Sciences, Professor, Department of buildig production, Novosibirsk State Academy of Architecture and Arts (NGAHA), 38 Krasnyy prospekt, Novosibirsk, 930099, Russian Federation;;
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The article is based on the authors’ experimental research into dependence between destruction of plates made of low-carbon structural steel, if loaded along their outer edge by the shearing force, whereby the loading is accompanied by deformationinduced heat generation. The authors provide more accurate data on the influence of patterns of particular structural defects on heat generation and initiation of destruction.The experiments conducted by the authors have proven that structural defects of shifted structural elements cause localization of deformations in the zone of defects, whereas the average temperature of the steel surface in the zone of defects may go up by several dozens of degrees and predetermine initiation and development of the seat of destruction in the place exposed to shear forces.Structural defects of shifted elements of structures cause localization of deformations in the zones of defects, especially in the event of elastoplastic and plastic behaviour of steel, while the average temperature of the steel surface exposed to deformations may increase by several dozens of degrees and pre-determine the pattern for development of destructions.
DOI: 10.22227/1997-0935.2013.9.7-15
References
- Volkova V.E., Makarova A.A. Chislennoe modelirovanie napryazhenno-deformirovannogo sostoyaniya balki s gibkoy stenkoy [Numerical Modeling of the Stress-strain State of a Beam Having a Flexible Wall]. Metallicheskie konstruktsii [Metal Structures]. 2011, vol. 17, no. 4, pp. 261—269.
- Ostrikov G.M., Maksimov Yu.S. Stal'nye seysmostoykie karkasy mnogoetazhnykh zdaniy [Earthquake-resistant Steel Frames of Multi-storied Buildings]. Kazakhstan, Alma-Ata, 1985, 120 p.
- Moyseychik E.A. Issledovanie teploobrazovaniya i zarozhdeniya razrusheniya v stal'noy rastyanutoy plastine s konstruktivno-tekhnologicheskim defektom [Research into Heat Generation and Initial Destruction of a Stretched Steel Plate Having a Structural Defect]. Prikladnaya mekhanika i tekhnicheskaya fizika [Applied Mechanics and Applied Physics]. 2013, no. 1, pp. 134—142.
- Wells A.A. The Mechanics of Notch Brittle Fracture. Welding Research, 1953, vol. 7, no. 2, pp. 34—56.
- Maugin G.A. The Thermomechanics of Plasticity and Fracture. Cambridge, Cambridge University Press, 1992, 350 p.
- Pasternak H., M?ller L. Thermovision — Entwicklung eines neuen Verfahrens zur Dehnungsanalyse beanspruchter Stahlbauteile. Stahlbau, 2002, 71, no. 7, pp. 523—536.
- Pasternak H., M?ller L. Untersuchung des thermospastischen Verhaltens verschiedener Baustoffe mit Hilfe der Thermovision. Bauingenieur, 2003, 78, pp. 221—230.
- Weichert R., Schoenert K. Heat Generation at the Tip of a Moving Crack. J. Mech. Physics Solids, 1978, no. 26, pp. 151—161.
- Shafray S.D., Sergeev A.V. Sinergeticheskiy podkhod k opisaniyu kvazikhrupkogo razrusheniya stal'nykh konstruktsiy [Synergetic Approach to Description of Quasi-fragile Destruction of Steel Structures]. Izv. vuzov. Stroitel'stvo i arkhitektura [News of Institutions of Higher Education. Construction and Architecture] 1990, no. 8, pp. 11—15.
- Moyseychik E.A., Shafray S.D. O deformatsionnom teploobrazovanii v elementakh stal'nykh stroitel'nykh konstruktsiy iz nizkouglerodistoy stali [On Deformation-induced Heat Formation in Steel Structures Made of Low-carbon Steel]. Izv. vuzov. Stroitel'stvo. [News of Institutions of Higher Education. Construction] 2012, no. 7/8, pp. 101—109.
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Myasnikov Aleksey Georgievich -
Moscow State University of Civil Engineering (MGSU)
Candidate of Physical and Mathematical Sciences, Associate Professor, Department of Higher Mathematics, Moscow State University of Civil Engineering (MGSU), 26 Yaroslavskoye shosse, Moscow, 129337, Russian Federation;
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The author argues that two approaches dominate the study of amenable algebras, groups, modules, etc. They are the homological approach and the approach based on the invariance in respect of a particular group of transformations. In the latter case, an invariant mean serves as a convenient instrument. In particular, a mean is determined as a positive finitely additive measure which is identified using the algebra of all subsets of the group in question.In the first part of the article, the author introduces definitions of an inversely amenable module and an inversely amenable C* algebra. The criteria for the inverse amenability for C* algebras is formulated using virtual diagonals constructed with the help of means, which are invariant in respect of components of amenability in a certain space of limited functions. In the further part of the article, the author presents necessary and sufficient conditions of inverse amenability based on the existence of approximate diagonals. Unlike the standard approach applied to describe amenable Banach algebras, the above approach offers a set of invariant means that are more easily perceived by intuition.
DOI: 10.22227/1997-0935.2013.9.16-22
References
- Paterson A.L.T. Amenability. Providence, RI, AMS, 1988, 452 p.
- Myasnikov A.G. Amenable Banach L1(G)-modules, Invariant Means and Regularity in the Sense of Arens. Izvestiya vuzov. Matematika [News of Institutions of Higher Education. Mathematics] 1993, no. 37, pp. 69—77.
- Myasnikov A.G. Weak Amenability Components of L1(G)-modules, Amenable Groups and Ergodic Theorem. Mathematical Notes. 1999, no. 66, pp. 726—732.
- Myasnikov A.G. Amenable L1(G)-modules and amenable S*-algebras. Voprosy matematiki, mekhaniki sploshnykh sred i primeneniya matematicheskikh metodov v stroitelstve [Issues of Mathematics, Mechanics of Continuous Media and Application of Mathematical Methods in Civil Engineering]. Sb. nauchn. tr. [Collection of Research Works]. 2008, no. 11, pp. 101—119.
- Paterson A.L.T. Invariant Mean Characterizations of Amenable C*-algebras. Houston J. Math. 1991, vol.17, no. 4, pp. 551—565.
- Kaijser S., Sinclair A.M. Projective Tensor Products of C*-algebras. Math. Scand. 1984, no. 55, pp. 161—187.
- Greenleaf F.P. Invariant Means on Topological Groups and Their Applications. 1969, New York University, 113 p.
- Bodaghi A. Module Amenability of Banach Algebras. Lambert Academic Publishing, 2012, 168 p.
- Johnson B.E. Cohomology in Banach Algebras. Mem. Amer. Math. Soc. Providence, 1972, no. 127.
- Rosenberg J. Amenability of Crossed Products of C*-algebras. Commun. Math. Phys. 1977, no. 57, pp. 187—191.
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Filatov Vladimir Vladimirovich -
Moscow State University of Civil Engineering (MGSU)
Candidate of Technical Sciences, Associate Professor, Department of Structural Mechanics, Moscow State University of Civil Engineering (MGSU), 26 Yaroslavskoye shosse, Moscow, 129337, Russian Federation;
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Through beams are widely used in the construction of large-span civil and industrial buildings, bridge engineering and mechanical engineering. They include open-frame girders and castellated beams. In order to determine their stress-strain state, software systems based on the finite element method are used or approximate calculations using simplified calculation patterns of Virendel beams are performed. Recently, many projects have been completed, in which A.R. Rzhanitsyn’s theory of compound rods is applied to calculate through structures.In this model, discrete links connecting upper and lower belts of the structure are re-placed by cross ties and shift connections continuously distributed along the length of the joint. Cross links hinder the convergence or separation of belts from one another. As a rule, pliability of cross links is neglected. This assumption, which substantially facilitates the calculation, is consistent with the hypothesis that there is no lateral strain in individual rods, calculated according to the theory. Therefore, whenever a compound rod is loaded, all its layers, and in this case – belts, are deformed according to the same curve pattern. In calculations, elastically compliant shift connections are replaced by the required distribution function of shear forces distributed along the length of the beam joint. Thus, the calculation of a through-beam is reduced to the solution of three ordinary differential equations of the second order, on the basis of which the following functions should be defined: beam deflection, bending moment and shear stress in the beam joint.The author discusses development of a numerical method of calculation of through beams based on the A.R. Rzhanitsyn’s theory of compound rods. To solve the system of differential equations, difference equations of the successive approximations method are involved to take account of finite discontinuities of the desired function, its first derivative and the right-hand side of the original differential equation. They demonstrate high accuracy if compared to well-known finite difference method equations.To illustrate the algorithm, the author provides sample calculations of open-frame girders and perforated beams having openings of different shapes. The results obtained by the authors are compared with a well-known analytical solution and a numerical solution based on the finite element method.
DOI: 10.22227/1997-0935.2013.9.23-31
References
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- Kartopol'tsev V.M., Balashov E.V. K voprosu issledovaniya napryazhenno-deformirovannogo sostoyaniya sovmestnoy raboty skvoznykh balok s zhelezobetonnoy plitoy na metallicheskom poddone [Towards Research into the Stress-Strain State of Combined Behaviour of Open-frame Beams and a Reinforced-concrete Slab Resting on the Metal Tray]. Vestnik TGASU [Bulletin of Tomsk State University of Architecture and Civil Engineering]. 2004, no. 1, pp. 169—178.
- Rabinovich I.M. Spravochnik inzhenera-proektirovshchika promsooruzheniy [Reference Book for Design Engineers of Industrial Buildings]. Tom 2 Raschetno-teoreticheskiy. [Vol. 2. Analysis and Theory]. Moscow – Leningrad, Gosstroyizdat Publ., 1934, 709 p.
- Drobachev V.M., Litvinov E.V. Analiticheskoe opredelenie napryazhenno-deformirovannogo sostoyaniya stenki-peremychki perforirovannoy balki [Analytical Methods of Identification of the Stress-strain State of a Partition Wall of a Castellated Beam]. Izv. vuzov. Stroitel'stvo [News of Institutions of Higher Education. Construction.] 2003, no. 5, pp. 128—133.
- Pritykin A.I. Progiby perforirovannykh balok-stenok s pryamougol'nymi vyrezami [Deflection of Castellated Deep Beam Having Rectangular Openings]. Izv. vuzov. Stroitel'stvo. [News of Institutions of Higher Education. Construction] 2009, no. 10, pp. 110—116.
- Pritykin A.I. Primenenie teorii sostavnykh sterzhney k opredeleniyu deformatsiy perforirovannykh balok [Application of the Theory of Compound Rods to Identification of Deformations of Castellated Beams]. Vestnik MGSU [Proceedings of Moscow State University of Civil Engineering]. 2009, no. 4, pp. 177—181.
- Pimenov A.S., Kholopov I.S., Solov'ev A.V. Optimal'noe proektirovanie perforirovannykh balok [Optimal Design of Castellated Beams]. Vestnik transporta Povolzh'ya [News Bulletin of the Volga Region Transport]. 2009, no. 1, pp. 69—74.
- Bedi K.S., Pachpor P.D. Moment and Shear Analysis of Beam with Different Web Openings. International Journal of Engineering Research and Applications. November – December 2011, vol. 1, no. 4, pp. 1917—1921.
- Wakchaure M.R., Sagade A.V. Finite Element Analysis of Castellated Steel Beam. International Journal of Engineering and Innovative Technology. July 2012, vol. 2, no. 1, pp. 365—370.
- Chhapkhane N.K., Shashikant R.K. Analysis of Stress Distribution in Castellated Beam Using Element Method and Experimental Techniques. International Journal of Mechanical Engineering Applications Research. August - September 2012, vol. 3, no. 3, pp. 190—197.
- Kholoptsev V.V. Raschet sostavnykh mnogoproletnykh nerazreznykh balok [Analysis of Compound Multi-span Beams]. Stroitel'naya mekhanika i raschet sooruzheniy [Structural Mechanics and Analysis of Structures]. 1966, no. 3, pp. 26—29.
- Rzhanitsyn A.R. Sostavnye sterzhni i plastinki [Compound Rods and Plates]. Moscow, Stroyizdat Publ., 1986, 316 p.
- Gabbasov R.F., Filatov V.V. Chislennoe reshenie zadachi po raschetu sostavnykh sterzhney s peremennym koeffitsientom zhestkosti shva [Numerical Solution to the Problem of Analysis of Compound Rods Having Variable Seam Stiffness Coefficient]. ACADEMIA. Arkhitektura i stroitel'stvo [Academy. Architecture and Construction] 2007, no. 2, pp. 86—89.
- Gabbasov R.F., Gabbasov A.R., Filatov V.V. Chislennoe postroenie razryvnykh resheniy zadach stroitel'noy mekhaniki [Numerical Generation of Discontinuous Solutions to Problems of Structural Mechanics]. Moscow, ASV Publ., 2008, 280 p.
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Shirokov Vyacheslav Sergeevich -
Samara State University of Architecture and Civil Engineering (SSUACE)
postgraduate student, Department of Metal and Timber Structures, Samara State University of Architecture and Civil Engineering (SSUACE), 194 Molodogvardeyskaya st., Samara, 443001, Russian Federation;
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In this paper, the author considers the issues of design of domed space lattice frames, circular in plan and having rectangular center nets. These structures have several variables influencing their mass. Span width and dome rise are their modifiable parameters. Their fixed parameters include topology, net-to-net distance, length of top net rods, type of the transverse cross-section of rods, and the construction material. Their constraints include the tensile strength of elements, the stability of compressed elements, restrictions applied to the rigidity of a structure, and restrictions applied to the span size. The task of finding the optimal rise-to-span ratio was solved by introducing successive changes into variables. The value of the span was changed at the increments of 10 meters, while the rise was changed at the increments equal to 5 meters.As a result of a series of calculations, values of variable parameters of a convex spatial lattice frame having tubular sections and different ratios were obtained. If the value of a span is within the 30 m≤l< 60 meters range (where l is the span of a structure), the optimal rise value rests within (1/5 to 1/8)l. The optimal rise is (1/4 to 1/5)l for spans above 60 meters.
DOI: 10.22227/1997-0935.2013.9.32-40
References
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