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Savin Sergey Yur’evich -
South-West State University (SWSU)
Сandidate of Technical Sciences, Associate Professor, South-West State University (SWSU), 94 50 let Oktyabrya str., Kursk, 305040, Russian Federation.
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Ivlev Ivan Andreevich -
Orel State University named after I.S. Turgenev
Post-graduate Student, Orel State University named after I.S. Turgenev, Orel State University named after I.S. Turgenev, 95 Komsomol’skaya str., Orel, 302026, Russian Federation.
The article describes the problem of stability of elastic orthotropic rectangular plates for the case when two opposite sides are simply supported, and two other sides have boundary with either simple supports or fixed supports, which are arbitrarily combined. The plate that is simply supported all over the contour is not considered in the article since the authors described it in the earlier publication. The external load is uniformly distributed along the side and is applied to the shorter side of the plate. To solve the stability problem, the authors use an approximate analytical method - the form factor interpolation method, which is based on the functional relationship between an integral geometric parameter of the mid-plane surface (the form factor) and an integral mechanical parameter (the critical force of buckling). Subject: stability of elastic orthotropic rectangular plates for the case when two opposite sides are simply supported and two other sides have combination of simple supports and fixed supports arbitrarily combined. Materials and methods: the form factor interpolation method (FFIM) is used to solve the stability problem of elastic orthotropic rectangular plates. The solutions which were obtained by the FFIM method were compared with the results of calculations by FEM (the program SCAD Office 11.5). Results: for orthotropic rectangular plates with combined boundary conditions, we obtained analytical expressions for critical force surfaces and they depend on an integral geometric parameter - form factor and flexural stiffness ratio. To the authors’ knowledge, these expressions are obtained for the first time. The critical force surface for orthotropic rectangular plates constitutes one of the boundaries of this integral physicomechanical parameter for the entire set of orthotropic plates with arbitrary convex contour. Therefore, this surface can be used for obtaining reference solutions by the form factor interpolation method. We demonstrated how to obtain the solution of the stability problem for orthotropic rectangular plates by the form factor interpolation method using the results obtained from the aforementioned analytical expressions as the reference solutions. The solutions obtained by the form factor interpolation method are compared with the results of calculations by the finite element method and show a good accuracy. Conclusions: the analytical expressions for critical loads presented in this work can be used directly for the stability analysis of orthotropic rectangular plates loaded in one direction as well as to obtain one of the reference solutions by the form factor interpolation method for plates with arbitrary convex contour and combined boundary conditions. The proposed approach can be extended to other forms of plates, boundary conditions and loading types.
DOI: 10.22227/1997-0935.2017.12.1333-1341
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Sinel'shchikov Aleksey Vladimirovich -
Astrakhan State University of Architecture and Civil Engineering (ASUACE)
Candidate of Technical Sciences, Associate Professor, Astrakhan State University of Architecture and Civil Engineering (ASUACE), 18 Tatishcheva st., Astrakhan, 414056, Russian Federation.
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Dzhalmukhambetov Abay Ibatullaevich -
Astrakhan State University of Architecture and Civil Engineering (ASUACE)
Assistant, Department of Industrial and Civil Construction, Astrakhan State University of Architecture and Civil Engineering (ASUACE), 18 Tatishcheva st., Astrakhan, 414056, Russian Federation.
Tower cranes are one of the main tools for execution of reloading works during construction. Design of tower cranes is carried out in accordance with RD 22-166-86 “Construction of tower cranes. Rules of analysis”, according to which to ensure stability it is required not to exceed the overturning moment upper limit. The calculation of these moments is carried out with the use of empirical coefficients and quite time-consuming. Moreover, normative methodology only considers the static position of the crane and does not take into account the presence of dynamic transients due to crane functioning (lifting and swinging of the load, boom turning) and the presence of the dynamic external load (e.g. from wind for different orientations of the crane). This paper proposes a method of determining the stability coefficient of the crane based on acting reaction forces at the support points - the points of contact of wheels with the crane rail track, which allows us, at the design stage, to investigate stability of tower crane under variable external loads and operating conditions. Subject: the safety of tower cranes operation with regard to compliance with regulatory requirements of ensuring their stability both at the design stage and at the operational stage. Research objectives: increasing the safety of operation of tower cranes on the basis of improving methodology of their design to ensure static and dynamic stability. Materials and methods: analysis and synthesis of the regulatory framework and modern research works on provision of safe operation of tower cranes, the method of numerical simulation. Results: we proposed the formula for analysis of stability of tower cranes using the resulting reaction forces at the supports of the crane at the point of contact of the wheel with the rail track.
DOI: 10.22227/1997-0935.2017.12.1342-1351
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Kupavtsev Vladimir Vladimirovich -
Moscow State University of Civil Engineering (MGSU)
Candidate of Physical and Mathematical Sciences, Associated Professor, Department of Theoretical Mechanics and Aerodynamics, Moscow State University of Civil Engineering (MGSU), 26 Yaroslavskoe shosse, Мoscow, 129337, Russian Federation;
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.
The method of two-sided evaluations is extended to the problems of stability of an elastic non-uniformly compressed rod, the variation formulations of which may be presented in terms of internal bending moments with uniform integral conditions. The problems are considered, in which one rod end is fixed and the other rod end is either restraint or pivoted, or embedded into a support which may be shifted in a transversal direction.For the substantiation of the lower evaluations determination, a sequence of functionals is constructed, the minimum values of which are the lower evaluations for the minimum critical value of the loading parameter of the rod, and the calculation process is reduced to the determination of the maximum eigenvalues of modular matrices. The matrix elements are expressed in terms of integrals of basic functions depending on the type of fixation of the rod ends. The basic functions, with the accuracy up to a linear polynomial, are the same as the bending moments arising with the bifurcation of the equilibrium of a rod with a constant cross-section compressed by longitudinal forces at the rod ends. The calculation of the upper evaluation is reduced to the determination of the maximum eigenvalue of the matrix, which almost coincides with one of the elements of the modular matrices. It is noted that the obtained upper bound evaluation is not worse thanthe evaluation obtained by the Ritz method with the use of the same basic functions.
DOI: 10.22227/1997-0935.2014.2.39-46
References
- Kupavtsev V.V. Variatsionnye formulirovki zadach ustoychivosti uprugikh sterzhney cherez izgibayushchie momenty [Variational Formulations of the Problems of Elastic Rods Stability Using Bending Moments]. Vestnik MGSU [Proceedings of Moscow State University of Civil Engineering]. 2010, vol. 3, no. 4, pp. 285—289.
- Alfutov N.A. Osnovy rascheta na ustoychivost' uprugikh sistem [Fundamentals of the Stability Analysis of the Elastic Systems]. Moscow, Mashinostroenie Publ., 1991, 336 p.
- Kupavtsev V.V. Dvustoronnie otsenki v zadachakh ustoychivosti uprugikh sterzhney, vyrazhennykh cherez izgibayushchie momenty [Bilateral Estimates in Elastic Rod Stability Problems Formulated through Bending Moments]. Vestnik MGSU [Proceedings of Moscow State University of Civil Engineering]. 2013, no. 2, pp. 47—54.
- Rektoris K. Variatsionnye metody v matematicheskoy fizike i tekhnike [Variational Methods in Mathematical Physics and Engineering]. Moscow, Mir Publ., 1985, 589 p.
- Doraiswamy Srikrishna, Narayanan Krishna R., Srinivasa Arun R. Finding Minimum Energy Configurations for Constrained Beam Buckling Problems Using the Viterbi Algorithm. International Journal of Solids and Structures. 2012, vol. 49, no. 2, pp. 289—297. DOI: 10.1016/j.ijsolstr.2011.10.003.
- Panteleev S.A. Dvustoronnie otsenki v zadachakh ob ustoychivosti szhatykh uprugikh blokov [Bilateral Assessments in the Stability Problem of Compressed Elastic Blocks]. Izvestiya RAN. MTT [News of the Russian Academy of Sciences. Mechanics of Solids]. 2010, no. 1, pp. 51—63.
- Santos H.A., Gao D.Y. Canonical Dual Finite Element Method for Solving Post-buckling Problems of a Large Deformation Elastic Beam. International Journal of Non-Linear Mechanics. 2012, vol. 47, no. 2, pp. 240—247. DOI: 10.1016/j.ijnonlinmec.2011.05.012.
- Selamet Serdar, Garlock Maria E. Predicting the Maximum Compressive Beam Axial Force During Fire Considering Local Buckling. Journal of Constructional Steel Research. 2012, vol. 71, pp. 189—201. DOI: 10.1016/j.jcsr.2011.09.014.
- Tamrazyan A.G. Dinamicheskaya ustoychivost' szhatogo zhelezobetonnogo elementa kak vyazkouprugogo sterzhnya [Dynamic Stability of the Compressed Reinforced Concrete Element as Viscoelastic Bar]. Vestnik MGSU [Proceedings of Moscow State University of Civil Engineering]. 2011, vol. 2, no. 1, pp. 193—196.
- Manchenko M.M. Ustoychivost' i kinematicheskie uravneniya dvizheniya dinamicheski szhatogo sterzhnya [Dynamically Loaded Bar Stability and Kinematic Equations of Motion]. Vestnik MGSU [Proceedings of Moscow State University of Civil Engineering]. 2013, no. 6, pp. 71—76.
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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;
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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;
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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
- Chen W.F., Lui E.M. Handbook of Structural Engineering, 2nd ed. CRC Press, 2005, 1768 p.
- Duggal S.K. Design of Steel Structures. Tata McGraw-Hill Education, 2000, 663 p.
- 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.
- 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.
- 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.
- Ravi S. Bellur. Optimal Design of Stiffened Plates. M. Sc. Thesis, University of Toronto, Graduate Department of Aerospace Science and Engineering, 1999, 100 p.
- 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.
- Leitch S.D. Steel Plate Girder Webs with Slender Intermediate Transverse Stiffeners. Ottawa: National Library of Canada. Biblioth? que national edu Canada, 1999.
- 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.
- 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.
- ?kesson B. Plate Buckling in Bridges and Other Structures. London, Taylor & Francis, 2007, 282 p.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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)
- 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)
- 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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Chepurnenko Anton Sergeevich -
Don State Technical University (DGTU)
Candidate of Engineering Science, teaching assistant of the strength of materials department, Don State Technical University (DGTU), 162 Sotsialisticheskaya str., Rostov-on-Don, 344022;
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Andreev Vladimir Igorevich -
Moscow State University of Civil Engineering (National Research University) (MGSU)
Doctor of Technical Sciences, Professor, corresponding member of Russian Academy of Architecture and Construction Sciences, chair, Department of Strength of Materials, Moscow State University of Civil Engineering (National Research University) (MGSU), 26 Yaroslavskoe shosse, Moscow, 129337, Russian Federation;
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Yazyev Batyr Meretovich -
Rostov State University of Civil Engineering (RSUCE)
Doctor of Technical Sciences, Professor, Chair, Depart- ment of Strength of Materials; +7 (863) 201-91-09, Rostov State University of Civil Engineering (RSUCE), 162 Sotsialisticheskaya St., Rostov-on-Don, 344022, Russian Federation;
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The problem of stability of polymer rods with account for creeping was resolved using the energy method customized by Tymoshenko and Ritz. Possible patterns of displacements were provided in the form of trigonometric series with undetermined coefficients. The principle of the minimal total potential energy of the system was taken as the basis. According to this principle, the form in which the potential energy has a minimum value is implemented in all possible patterns of deformation occurring due to the loss of stability. The energy method makes it possible to replace the solution of complex differential equations by the solution of simple linear algebraic equations. The result was obtained numerically using MatLab software applicable to different equations describing deformations and stresses caused by the exposure to creeping. The problem was solved for low and high density polyethylene. The equation of Maxwell and Thompson was
DOI: 10.22227/1997-0935.2013.1.101-108
References
- Aleksandrov A.V. Soprotivlenie materialov. Osnovy teorii uprugosti i plastichnosti [Strength of Materials. Fundamentals of the Theory of Elasticity and Plasticity]. Moscow, Vyssh. shk. publ., 2002, 400 p.
- Klimenko E.S., Amineva E.H., Litvinov S.V., Yazyev S.B., Kulinich I.I. Ustoychivost’ szhatykh neodnorodnykh sterzhney s uchetom fi zicheskoy nelineynosti materiala [Stability of Compressed Heterogeneous Rods with Account for the Physical Nonlinearity of the Material]. Rostov-on-Don, Rostov State University of Civil Engineering Publ., 2012, 77 p.
- Alfutov N.A. Osnovy rascheta na ustoychivost’ uprugikh system [Fundamentals of Stability Analysis of Elastic Systems]. Moscow, Mashinostroenie Publ., 1991, 336 p.
- Vol’mir A.S. Ustoychivost’ deformiruemykh system [Stability of Deformable Systems]. Moscow, Nauka Publ., 1975, 984 p.
- Timoshenko S.P. Ustoychivost’ uprugikh system [Stability of Elastic Systems]. Moscow, Gostekhizdat Publ., 1946.
- Andreev V.I. Nekotorye zadachi i metody mekhaniki neodnorodnykh tel [Some Problems and Methods of Mechanics of Heterogeneous Bodies]. Moscow, ASV Pub., 2002, 288 p.
- Turusov R.A. Temperaturnye napryazheniya i relaksatsionnye yavleniya v osesimmetrichnykh zadachakh mekhaniki zhestkikh polimerov [Thermal Stresses and Relaxation Phenomena in Axisymmetric Problems of Mechanics of Rigid Polymers]. Moscow, 1970, 104 p.
- Belous P.A. Ustoychivost’ polimernogo sterzhnya pri polzuchesti s uchetom nachal’noy krivizny [Stability of a Polymer Rod Exposed to Creeping with Regard for Its Initial Curvature]. Trudy Odesskogo politekhnicheskogo instituta [Works of Odessa Polytechnic Institute]. 2001, no. 2, pp. 43—46.
- Gurevich G.I. Deformiruemost’ sred i rasprostranenie seysmicheskikh voln [Deformability of Media and Propagation of Seismic Waves]. Moscow, Nauka Publ., 1974, 482 p.
- Gol’dman A.Ya. Prochnost’ konstruktsionnykh plastmass [Structural Plastic Strength]. Leningrad, Mashinostroenie Publ., 1979, 320 p.
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Kupavtsev Vladimir Vladimirovich -
Moscow State University of Civil Engineering (MGSU)
Candidate of Physical and Mathematical Sciences, Associated Professor, Department of Theoretical Mechanics and Aerodynamics, Moscow State University of Civil Engineering (MGSU), 26 Yaroslavskoe shosse, Мoscow, 129337, Russian Federation;
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The author considers the method of two-sided evaluations in the problems of stability of a one-span elastic non-uniformly compressed rod under various conditions of fixation of its ends.The required minimum critical value of the loading parameter for the rod is the minimum value of the functional equal to the ratio of the norms of Hilbert space elements squared. Using the inequalities following from the problem of the best approximation of a Hilbert space element through the basic functions, it is possible to construct two sequences of functionals, the minimum values of which are the lower evaluations and the upper ones. The basic functions here are the orthonormal forms of the stability loss for a rod with constant cross-section, compressed by longitudinal forces at the ends, which are fixed just so like the ends of the non-uniformly compressed rod.Having used the Riesz theorem about the representation of a bounded linear functional in the Hilbert space, the author obtains the additional functions from the domain of definition of the initial functional, which correspond to the basic functions. Using these additional functions, the calculation of the lower bounds is reduced to the determination of the maximum eigenvalues of the matrices represented in the form of second order modular matrices with the elements expressed in the form of integrals of basic and additional functions. The calculation of the upper bound value is reduced to the determination of the maximum eigenvalue of the matrix, which almost coincides with one of the modular matrices. It is noted that the obtained upper bound evaluations are not worse than the evaluations obtained through the Ritz method with the use of the same basic functions.
DOI: 10.22227/1997-0935.2013.6.63-70
References
- Kupavtsev V.V. K dvustoronnim ocenkam kriticheskih nagruzok neodnorodno szhatyh uprugih sterzhnej. [On Bilateral Evaluations of Critical Loading Values in Respect of Non-uniformly Compressed Elastic Rods]. Izvestija vuzov. Stroitel’stvo I arhitektura. [News of Institutions of Higher Education. Construction and Architecture]. 1984, no. 8, pp. 24—29.
- Alfutov N.A. Osnovy rascheta na ustojchivost’ uprugih sistem. [Fundamentals of Stability Analysis of Elastic Systems]. Moscow, Mashinostroenie Publ., 1991, 336 p.
- Rektoris K. Variatsionnye metody v matematicheskoy fizike I tekhnike. [Variational Metods in Mathematical Physics and Engineering]. Moscow, Mir Publ., 1985, 589 p.
- Panteleev S.A. Dvustoronie otsenki v zadache ob ustojchivosti szhatyh uprugih blokov. [Bilateral Assessments in the Stability Problem of Compressed Elastic Blocks]. Izvestyja RAN. MTT. [News of Russian Academy of Sciences. Mechanics of Solids]. 2010, no. 1, pp. 51—63.
- Bogdanovich A.U., Kuznetsov I.L. Prodol’noe szhatie tonkostennogo sterzhnja peremennogo sechenija pri razlichnyh variantah zakreplenija torcov [Longitudinal Compression of a Thin-Walled Bar of Variable Cross Section with Different Variants of Ends Fastening (Informftion 1)]. Izvestija vuzov. Stroitel’stvo [News of Institutions of Higher Education. Construction]. 2005, no. 10, pp. 19—25.
- Bogdanovich A.U., Kuznetsov I.L. Prodol’noe szhatie tonkostennogo sterzhnja peremennogo sechenija pri razlichnyh variantah zakreplenija torcov [Longitudinal Compression of a Thin-Walled Core of Variable Cross Section with Different Variants of Ends Fastening (Informftion 2)]. Izvestija vuzov. Stroitel’stvo [News of Institutions of Higher Education. Construction]. 2005, no. 11-12, pp. 10—16.
- Nicot Francois, Challamel Noel, Lerbet Jean, Prunier Frorent, Darve Felix. Some in-sights into structure instability and the second-order work criterion. International Journal of Solids and Structures. 2012. Vol. 49, no. 1. pp. 132—142.
- Aristizabal-Ocha J. Dario. Matrix method for stability and second rigid connections. Engineering Structures. 2012. Vol. 34. pp. 289—302.
- TemisYu.M.,Fedorov I.M. Sravnenie metodov analiza ustojchivosti sterzhnej peremennogo sechenija pri nekonservativnom nagruzhenii [Comparing the Methods for Analysing the Stability of Rods of a Variable Cross-section under Non-conservative Loading]. Problems of strength and plasticity [Proceeding sof Nizhni Novgorod University]. 2006, no. 68, pp. 95—106.
- Le Grognec Philippe, Nguyen Quang-Hay, Hjiaj Mohammed. Exat buckling solution for two-layer Timoshenko beams with interlayer. International Journal of Solids and Structures. 2012. Vol. 49, ¹ 1. pp. 143—150.
- Chepurnenko A.S., Andreev V.I., Yazyev B.M. Energeticheskiy metod pri raschete na ustoychivost’ szhatykh sterzhney s uchetom polzuchesti. [Energy Method of Analysis of Stability of Compressed Rods with Regard for Creeping]. Vestnik MGSU. [Proceedings of Moscow State University of Civil Engineering]. 2013, no. 1, pp.101—108.
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Manchenko Maksim Mikhaylovich -
St.Petersburg State University of Architecture and Civil Engineering (SPbGASU)
postgraduate student, Department of Theoretical Mechanics; +7 (812) 296-20-22., St.Petersburg State University of Architecture and Civil Engineering (SPbGASU), 4 2nd Krasnoarmeyskaya st., 190005, St.Petersburg;
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Differential equations of motion for a bar are provided in this paper. The bar is exposed to the applied force that intensifies as the time progresses. The condition substantiating the trans-versal inertia force is identified using the equations. On top of the emerging inertia force, brief high-speed stress increases the yield stress of the material.The external force is accompanied by the eccentricity. Therefore, linear dimensions of the bar and its eccentricity make plastic behaviour possible both in compressed and stretched areas of the rod sections. Patterns of distribution of plastic deformations (one-sided and double-sided yield) are generated using the equations of motion for each case. Cauchy problems are supple- mented by the incoming conditions according to the principle of continuity of displacement and velocity.The criterion of stability loss is a condition when the variation of the exterior torque equals to the variation of the interior torque. At the same time, the variation of a longitudinal force must be equal to zero. Having completed a series of transformations, the author obtains the stability loss functional. It is calculated simultaneously with the motion equation. When the functional is equal to zero, the bearing capacity is exhausted.Moreover, there is a simplified method of identifying the critical force. The comparison of values with the testing findings demonstrates the efficiency of employment of the approximate method.
DOI: 10.22227/1997-0935.2013.6.71-76
References
- Timoshenko S.P., Yang D.Kh., Uiver U. Kolebaniya v inzhenernom dele [Vibrations in Engineering]. Moscow, Mashinostroenie Publ., 1985, 472 p.
- Curtze S., Kuokkala V.T. Dependence of Tensile Deformation Behaviour of TWIP Steels on Stacking Fault Energy, Temperature and Strain Rate. Acta Materialia, Elsevier. 2010, vol. 58, no. 15, pp. 5129—5141.
- Appleby-Thomas G.J., Hazell P.J. A Study on the Strength of an Armour-grade Aluminum under High Strain-rate Loading. Journal of Applied Physics, New York, American Institute of Physics. 2010, vol. 107, no. 12, p. 123508.
- Ma D., Chen D., Wu S., Wang H., Hou Y., Cai C. An Interrupted Tensile Testing at High Strain Rates for Pure Copper Bars. Journal of Applied Physics, New York, American Institute of Physics. 2010, vol. 108, no. 11, p. 114902.
- Pertsev A.K., Rukolayne A.Ya., Bolotin V.V., editor. Ustoychivost’ uprugoplasticheskikh sterzhney pri kratkovremennykh dinamicheskikh nagruzkakh [Stability of Elasto-plastic Rods Exposed to Short-term Dynamic Loads]. Problemy ustoychivosti v stroitel’noy mekhanike [Stability Problems in Structural Mechanics]. Tr. Vsesoyuzn. konf. po probl. ustoychivosti v stroit. mekhanike [Works of All-Russian Conference on Stability Problems in Structural Mechanics]. 1965, pp. 458—465.
- Nazaruk A.V. Issledovanie ustoychivosti szhatykh sterzhney, rabotayushchikh v uprugoplasticheskoy stadii pri dinamicheskikh nagruzkakh [Research into Stability of Elasto-plastic Behaviour of Compressed Rods Exposed to Dynamic Loads]. Leningrad, 1977, 23 p.
- Jones N. Structural Impact. Cambridge, Cambridge University Press. 2012, 604 p.
- Rybnov E., Sanzharovsky R., Beilin D. On the Durability of Reinforced Concrete Structures. Scientific Israel — Technological Advantages, Migdal Ha Emek. 2011, vol. 13, no. 4, pp. 111—121.
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Dudchenko Aleksandr Vladimirovich -
Moscow State University of Civil Engineering (MSUCE)
student, Moscow State University of Civil Engineering (MSUCE), 26 Yaroslavskoe shosse, Moscow, 129337, Russian Federation;
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Kupavtsev Vladimir Vladimirovich -
Moscow State University of Civil Engineering (MSUCE)
Candidate of Physical and Mathematical Sciences, Associated Professor, Department of Theoretical Mechanics and Aerodynamics,
+7 (499) 183-46-74, Moscow State University of Civil Engineering (MSUCE), 26 Yaroslavskoe shosse, Moscow, 129337, Russian Federation;
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The authors present both top and bottom limit values of loads within the two problems of stability of a rectilinear elastic cantilever bar that has a variable cross-section. In the first problem, a longitudinal compressive force applied to the bar end is transmitted through a connecting rod that has hinges on both ends, while the second problem is to be resolved in absence of any connecting rod.
The authors apply well-known expressions to identify the stability loss by a rectilinear elastic cantilever bar that has a constant cross-section compressed by a longitudinal force at its free end, with account for the inequalities generated by the best approximation problem in the Hilbert space. They constructed two series of functionals, the bottom bounds of which are the bilateral bounds of the unknown critical value of the load parameter. The calculation of the bottom bounds is reduced to determination of the biggest eigenvalues for the matrices presented in the form of second-order matrices with elements, expressed through the integrals of well-known forms of stability loss by a bar that has a constant cross-section. The calculation of the top bound is reduced to the determination of the biggest eigenvalue for the matrix which almost coincides with the one of the block matrices constructed for the determination of the bottom bound.
Bilateral bounds identified in accordance with the above method make it possible to assess the reduction of the critical load value in the first problem and to compare it to the one of the second problem.
DOI: 10.22227/1997-0935.2012.7.75 - 81
References
- Alfutov N.A. Osnovy rascheta na ustoychivost’ uprugikh sistem [Fundamentals of Stability Analysis of Elastic Systems]. Moscow, Mashinostroenie Publ., 1991, 336 p.
- Dudchenko A.V., Kupavtsev V.V. Dvustoronnie otsenki ustoychivosti uprugogo konsol’nogo sterzhnya, szhatogo polusledyashchey siloy [Bilateral Bounds of Stability of an Elastic Cantilever Bar, Compressed by the Half-Tracking Force]. Vestnik MGSU [Proceedings of Moscow State University of Civil Engineering]. 2011, no. 6, pp. 302—306.
- Klyushnikov V.D., Kupavtsev V.V. Dvustoronnie otsenki kriticheskikh nagruzok neodnorodno szhatykh sterzhney [Bilateral Evaluations of Values of the Critical Load Applicable to Non-Uniformly Compressed Elastic Rods]. Doklady akademii nauk SSSR [Reports of the Academy of Sciences of the USSR]. 1977, vol. 238, no. 3, pp. 561—564.
- Kupavtsev V.V. K dvustoronnim otsenkam kriticheskikh nagruzok neodnorodno szhatykh sterzhney [About Bilateral Assessments of Values of Critical Loads Applicable to Non-uniformly Compressed Elastic Rods]. Izvestiya VUZov. Stroitel’stvo i arkhitektura. [Proceedings of Higher Education Institutions. Construction and Architecture]. 1984, no. 8, pp. 24—29.
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Belostotskiy Aleksandr Mikhaylovich -
Moscow State University of Civil Engineering (MGSU)
Doctor of Technical Sciences, Professor, Moscow State University of Civil Engineering (MGSU), ;
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Akimov Pavel Alekseevich -
Moscow State University of Civil Engineering (MGSU)
Doctor of Technical Sciences, chair, Department of Computer Sciences and Applied Mathematics, Corresponding Member of Russian Academy of Architecture and Construction Sciences, chief research worker, Research and Educational Center of Computational Simulation of Unique Buildings, Structures and Complexes, Moscow State University of Civil Engineering (MGSU), 26 Yaroslavskoe shosse, Moscow, 129337, Russian Federation; +7 (499) 183-59-94, +7 (499) 929-50-17;
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Petryashev Nikolay Olegovich -
Moscow State University of Civil Engineering (MGSU)
engineer, Research and Educational Center of Computational Simulation of Unique Buildings, Structures and Complexes, Moscow State University of Civil Engineering (MGSU), 26 Yaroslavskoe shosse, Moscow, 129337, Russian Federation; +7 (499) 183-59-94, +7 (499) 929-50-17;
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Petryashev Sergey Olegovich -
Moscow State University of Civil Engineering (MGSU)
engineer, Research and Educational Center of Computational Simulation of Unique Buildings, Structures and Complexes, Moscow State University of Civil Engineering (MGSU), 26 Yaroslavskoe shosse, Moscow, 129337, Russian Federation; +7 (499) 183-59-94, +7 (499) 929-50-17;
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Negrozov Oleg Aleksandrovich -
Moscow State University of Civil Engineering (MGSU)
postgraduate student, Department of Computer Sciences and Applied Mathematics, engineer, Research and Educational Center of Computational Simulation of Unique Buildings, Structures and Complexes, Moscow State University of Civil Engineering (MGSU), 26 Yaroslavskoe shosse, Moscow, 129337, Russian Federation; +7 (499) 183-59-94, +7 (499) 929-50-17;
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The given paper is devoted to strength and stability analysis of load-bearing structures of a high-rise (54-storey) building with allowance for actual positions of reinforced concrete structural members (columns and walls). Finite element method (FEM) is used for structural analysis. The authors present formulations of problems, governing equations, information about basic three-dimensional finite element models (so-called “design” (ideal) model, the first “actual” model (taking into account the deviations of positions of columns from the project) and the second “actual” model (taking into account the deviations of positions of walls from the project)) of the coupled system “high-rise building - foundation” within ANSYS Mechanical software and their verification, numerical approach to structural analysis and corresponding solvers. Finite element models include mainly 4-node structural shell elements (suitable for analyzing foundation slabs, floor slabs and load-bearing walls) and three-dimensional 2-node beam elements (suitable for analyzing beams and columns), special spring-damper elements and multipoint constraint elements. Detailed finite element mesh on the bottom foundation slab is agreed with the location of piles. The advanced model of Prof. Yu.K. Zaretsky is used for approximation of soil behavior. Construction sequence and various types of nonlinearities are taken into account. The results of modal analysis, static and dynamic analysis with various load combinations (gravity load, facade load, dead (constant) loads, temporary loads, wind load, snow load, crown load etc.) are considered, the results of the regulatory assessment of the strength of structures (obtained with the use of corresponding software in accordance with design codes of the Russian Federation) are under consideration as well. The corresponding displacements, stresses, natural vibration frequencies can be used for research and development of the correct monitoring method of the foundation and load-bearing structures of a high-rise building.
DOI: 10.22227/1997-0935.2015.4.50-68
References
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- Belostotskiy A.M. Opyt raschetnogo obosnovaniya sostoyaniya unikal'nykh (vysotnykh i bol'sheproletnykh) zdaniy i sooruzheniy [Experience of Numerical Analysis of Unique (High-Rise and Long Span) Buildings and Structures]. Vysotnye zdaniya [High-Rise Buildings]. 2014, no. 2, pp. 106—109. (In Russian)
- Belostotskiy A.M. Sovremennaya metodologiya chislennogo modelirovaniya nagruzok i vozdeystviy, napryazhenno-deformirovannogo sostoyaniya i ustoychivosti vysotnykh zdaniy i kompleksov [Contemporary Approach to Numerical Simulation of Loads and Actions, Stress-Strain State and Stability of High-Rise Buildings and Complexes]. Vysotnye zdaniya [High-Rise Buildings]. 2014, no. 1, pp. 94—97. (In Russian)
- Belostotskiy A.M. Chislennoe modelirovanie staticheskogo i dinamicheskogo napryazhenno-deformirovannogo sostoyaniya prostranstvennykh sistem «sooruzhenie — osnovanie — vodokhranilishche» s uchetom nelineynykh effektov otkrytiya — zakrytiya shvov i makrotreshchin : dissertatsiya doktora tekhnicheskikh nauk [Numerical Modeling of Static and Dynamic Stress-Strain State of Three-Dimensional Systems “Construction — Foundation — Reservoir” with an Allowance for Nonlinear Effects of Open/Close Joints and Macrofractures. Doctor of Technical Sciences Thesis]. Moscow, MGUP Publ., 1998, 367 p. (In Russian)
- Belostotskiy A.M., Akimov P.A., Pavlov A.S., Kaytukov T.B., Afanas'eva I.N. O razrabotke, issledovanii i verifikatsii korrektnykh chislennykh metodov resheniya nelineynykh zadach deformirovaniya, ustoychivosti i zakriticheskogo povedeniya tonko-stennykh obolochechno-sterzhnevykh konstruktsiy [On the Development, Research and Verification of Correct Numerical Methods of Nonlinear Strength, Stability and Post-Critical Analysis of Thin-Walled Shell-Beam Structures]. Stroitel'naya mekhanika i raschet sooruzheniy [Structural Mechanics and Calculation of Structures]. 2014, no. 5 (256), pp. 7—13. (In Russian)
- Belostotskiy A.M., Sidorov V.N., Akimov P.A., Kashevarova G.G. Matematicheskoe modelirovanie tekhnogennoy bezopasnosti otvetstvennykh stroitel'nykh ob
- Belostotskiy A.M., Pen'kovoy S.B., Shcherbina S.V., Kaytukov T.B., Akimov P.A. Razrabotka i verifikatsiya metodiki chislennogo modelirovaniya NDS, prochnosti i ustoychivosti mnogoetazhnykh panel'nykh zdaniy [Development and Verification of Numerical Approach to Modeling of Stress-Strain State, Strength and Stability of Multistory Panel Buildings]. Stroitel'naya mekhanika i raschet sooruzheniy [Structural Mechanics and Calculation of Structures]. 2014, no. 6 (257), pp. 24—30. (In Russian)
- Senin N.I., Akimov P.A. Nekotorye matematicheskie osnovy rascheta prostranstvennykh nesushchikh sistem mnogoetazhnykh zdaniy v lineynoy postanovke v ramkakh diskretno-kontinual'noy modeli [Several Mathematical Foundations of Linear Analysis of Three-Dimensional Load-Bearing Systems of Multistory Buildings within Discrete-Continual Model]. Vestnik MGSU [Proceedings of Moscow State University of Civil Engineering]. 2011, no. 2, vol. 1, pp. 44—50. (In Russian)
- Akimov P.A. Correct Discrete-Continual Finite Element Method of Structural Analysis Based on Precise Analytical Solutions of Resulting Multipoint Boundary Problems for Systems of Ordinary Differential Equations. Applied Mechanics and Materials. 2012, vols. 204—208, pp. 4502—4505. DOI: http://dx.doi.org/10.4028/www.scientific.net/AMM.204-208.4502.
- Akimov P.A., Belostosky A.M., Moz-galeva M.L., Mojtaba Aslami, Negrozov O.A. Correct Multilevel Discrete-Continual Finite Element Method of Structural Analysis. Advanced Materials Research. 2014, vol. 1040, pp. 664—669.
- Akimov P.A., Mozgaleva M.L. Method of Extended Domain and General Principles of Mesh Approximation for Boundary Problems of Structural Analysis. Applied Mechanics and Materials. 2014, vols. 580—583, pp. 2898—2902. DOI: http://dx.doi.org/10.4028/www.scientific.net/AMM.580-583.2898.
- Dong J., Bathe K.J. Component Mode Synthesis with Subspace Iterations for Controlled Accuracy of Frequency and Mode Shape Solutions. Computers & Structures. 2014, vol. 139, pp. 28—32. DOI: http://dx.doi.org/10.1016/j.compstruc.2014.03.003.
- Jeon H.M., Lee Y., Lee P.S., Bathe K.J. The MITC3+ Shell Element in Geometric Nonlinear Analysis. Computers & Structures. 2015, vol. 146, pp. 91—104. DOI:http://dx.doi.org/10.1016/j.compstruc.2014.09.004.
- Kim J., Bathe K.J. Towards a Procedure to Automatically Improve Finite Element Solutions by Interpolation Covers. Computers & Structures. 2014, vol. 131, pp. 81—97. DOI: http://dx.doi.org/10.1016/j.compstruc.2013.09.007.
- Sussman T., Bathe K.J. 3D-shell Elements for Structures in Large Strains. Computers & Structures. 2013, vol. 122, pp. 2—12. DOI: http://dx.doi.org/10.1016/j.compstruc.2012.12.018.
- Afanas'eva I.N. Adaptivnaya metodika chislennogo modelirovaniya trekhmernykh dinamicheskikh zadach stroitel'noy aerogidrouprugosti : dissertatsiya kandidata tekhnicheskikh nauk [Adaptive Procedure of Numerical Modeling of Three-Dimensional Dynamic Problems of Construction Aerohydroelasticity. Candidate of Technical Sciences Thesis]. Moscow, MGSU Publ., 2014, 200 p. (In Russian)
- Kalichava D.K. Adaptivnye dinamicheskie konechnoelementnye modeli v osnove monitoringa nesushchikh konstruktsiy vysotnykh zdaniy : dissertatsiya kandidata tekhnicheskikh nauk [Adaptive Dynamic Finite Element Models as a Base for Monitoring of Load-Bearing Structures of High-rise Buildings. Candidate of Technical Sciences Thesis]. Moscow, MGSU Publ., 2012, 149 p. (In Russian)
- Kabantsev O.V., Tamrazyan A.G. Uchet izmeneniy raschetnoy skhemy pri analize raboty konstruktsiy [Structural Analysis with Allowance for Modification of Computational Scheme]. Inzhenerno-stroitel'nyy zhurnal [Magazine of Civil Engineering]. 2014, no. 5 (49), pp. 15—26. (In Russian)
- Kabantsev O.V. Verifikatsiya raschetnoy tekhnologii «Montazh» programmnogo kompleksa «SCAD» [Verification of Calculation Technology “Mounting” from Software Complex “SCAD”]. International Journal for Computational Civil and Structural Engineering. 2011, vol. 7, issue 3, pp. 103—109. (In Russian)
- Kabantsev O.V. Metod rascheta mnogoetazhnykh zdaniy s uchetom protsessa izmeneniya raschetnoy skhemy pri razlichnykh rezhimakh raboty raboty [Analysis Methods of Multi-storeyed Buildings with the Allowance for Modification of Structural Design under Various Operation Conditions]. Vestnik MGSU [Proceedings of Moscow State University of Civil Engineering]. 2013, no. 10, pp. 43—51. (In Russian)
- Kabantsev O.V., Karlin A.V. Raschet nesushchikh konstruktsiy zdaniy s uchetom istorii vozvedeniya i poetapnogo izmeneniya osnovnykh parametrov raschetnoy modeli [Analysis of Load-Bearing Structures with Allowance for Construction Sequence and Step-by-Step Modification of Basic Parameters of Computing Model]. Promyshlennoe i grazhdanskoe stroitel'stvo [Industrial and Civil Engineering]. 2012, no. 7, pp. 33—35. (In Russian)
- Kabantsev O., Perelmuter A. Modeling Transition in Design Model when Analyzing Specific Behaviors of Structures. Procedia Engineering. 2013, vol. 57, pp. 479—488.
- 2 3. Kim H.S., Shin A.K. Column Shortening Analysis with Lumped Construction Sequences. Procedia Engineering. 2011, vol. 14, pp. 1791—1798.
- Aul A.A., Belostotskiy A.M., Krakovskiy M.B. Raschet zhelezobetonnykh konstruktsiy pri sovmestnom ispol'zovanii programm ANSYS i «OM SNiP Zhelezobeton» [Analysis of Reinforced Structures with the Use of ANSYS Software and “OM Snip Zhelezobeton” Package]. Beton i zhelezobeton [Concrete and Reinforced Concrete]. 2011, no. 5, pp. 19—23. (In Russian)
- Belokopytova I.A., Kriksunov E.Z., Mikitarenko M.A., Perel'muter M.A. «Arbat» — programma dlya rascheta zhelezobetonnykh stroitel'nykh konstruktsiy [“ARBAT” — Software for Reinforced Building Structures Analysis]. CADmaster. 2001, no. 4 (9), pp. 57—61. (In Russian)
- Kukushkin I.S. SCAD Office V.21. Novyy oblik [SCAD Office V.21. New Profile]. CADmaster. 2014, no. 3—4 (76—77), pp. 100—102. (In Russian)
- Perel'muter M.A., Chertkov V.V. O komp'yuternom raschete elementov betonnykh i zhelezobetonnykh konstruktsiy [On Computational Analysis of Concrete and Reinforced Concrete Structures]. Beton i zhelezobeton [Concrete and Reinforced Concrete]. 2014, no. 3, pp. 14—16. (In Russian)
- Perel'muter M.A., Popok K.V., Skoruk L.N. Raschet shiriny raskrytiya normal'nykh treshchin po SP 63.13330.2012 [Calculation of the Normal Crack Opening Width for SP 63.13330.2012]. Beton i zhelezobeton [Concrete and Reinforced Concrete]. 2014, no. 1, pp. 21—22. (In Russian)
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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;
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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;
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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;
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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;
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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
- 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)
- 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)
- 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)
- 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)
- 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.
- 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.
- 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)
- Yu W.-W., LaBoube R.A. Cold-Formed Steel Design. 4th Edition, John Wiley & Sons, 2010, 512 p.
- 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)
- Vol'mir A.S. Ustoychivost' uprugikh system [Stability of Elastic Systems]. Moscow, Fizmatlit Publ., 1972, 879 p. (In Russian)
- 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)
- 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)
- 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)
- 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)
- 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)
- 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)
- 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)
- 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)
- 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)
- 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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Ignat'ev Oleg Vladimirovich -
Moscow State University of Civil Engineering (MGSU)
Doctor of Technical Sciences, Professor, Vice-Rector, Moscow State University of Civil Engineering (MGSU), 26 Yaroslavskoe shosse, Moscow, 129337, Russian Federation; +7 (499) 183-94-82;
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Karpov Vladimir Vasil'evich -
Saint-Petersburg State University of Architecture and Civil Engineering (SPSUACE)
Doctor of Technical Sciences, Professor, Department of Applied Mathematics and Computer Science, Saint-Petersburg State University of Architecture and Civil Engineering (SPSUACE), 190005, 4 Vtoraya Krasnoarmeyskaya str., Saint Petersburg, Russian Federation;
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Semenov Aleksey Aleksandrovich -
Saint-Petersburg State University of Architecture and Civil Engineering (SPSUACE)
postgraduate student, senior lecturer, Department of Applied Mathematics and Computer Science, Saint-Petersburg State University of Architecture and Civil Engineering (SPSUACE), 190005, 4 Vtoraya Krasnoarmeyskaya str., Saint Petersburg, Russian Federation;
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In the modern construction, shipbuilding, mechanical, aircraft engineering and other fields of industry structures in the form of shells, including orthotropic shells, gained widespread currency. In order to raise their rigidity they are strengthened by reinforcing elements (ribs). In the process of shell constructions’ design the choice of rational construction parameters is very important (rational placement of ribs, their rigidity, curvature). The volume of the shell material is usually a minimalised efficiency function. At that the limit values of stress level in the shell and its stability are the restrictions. It is proposed to use variation and parametric method for choosing the angle and reinforcements by stiffening plates so that the shell construction would not lose its stability and reliability. The applied method with change of continuation parameters gives a scheme of coordinate-wise incline, which provides relative simplicity of choosing rational construction type in case of the given loads and restrictions on its stress-strain state.
DOI: 10.22227/1997-0935.2014.10.24-33
References
- Pikul' V.V. Sovremennoe sostoyanie teorii ustoychivosti obolochek [The Current State of Shell Stability Theory]. Vestnik Dal'nevostochnogo otdeleniya Rossiyskoy akademii nauk [Proceedings of Far Eastern Branch of the Russian Academy of Sciences]. 2008, no. 3, pp. 3—9. (in Russian)
- Treshchev A.A., Shereshevskiy M.B. Issledovanie NDS pryamougol'noy v plane obolochki polozhitel'noy gaussovoy krivizny iz ortotropnykh materialov s uchetom svoystv raznosoprotivlyaemosti [Investigation of Stress-Strain State of a Rectangular-plan Shell of a Positive Gaussian Curvature Made of Orthotropic Materials with Account for Multimodulus Behavior Features]. Vestnik Volgogradskogo gosudarstvennogo arkhitekturno-stroitel'nogo universiteta. Seriya Stroitel'stvo i arkhitektura [Proceedings of Volgograd State University of Architecture and Civil Engineering. Series: Construction and Architecture]. 2013, no. 31 (50), part 2, pp. 414—421. (in Russian)
- Karpov V., Semenov A. Strength and Stability of Orthotropic Shells. World Applied Sciences Journal. 2014, 30 (5), pp. 617—623. Available at: http://www.idosi.org/wasj/wasj30(5)14/14.pdf. Date of access: 12.09.2014. DOI: http://dx.doi.org/10.5829/idosi.wasj.2014.30.05.14064.
- Maksimyuk V.A., Storozhuk E.A., Chernyshenko I.S. Variational Finite-difference Methods in Linear and Nonlinear Problems of the Deformation of Metallic and Composite Shells (Review). International Applied Mechanics. 2012, vol. 48, no. 6, pp. 613—687. DOI: http://dx.doi.org/10.1007/s10778-012-0544-8.
- Qatu M.S., Sullivan R.W., Wang W. Recent Research Advances on the Dynamic Analysis of Composite Shells: 2000—2009. Composite Structures. 2010, vol. 93, no. 1, pp. 14—31. DOI: http://dx.doi.org/10.1016/j.compstruct.2010.05.014.
- Trushin S.I., Sysoeva E.V., Zhuravleva T.A. Ustoychivost' nelineyno deformiruemykh tsilindricheskikh obolochek iz kompozitsionnogo materiala pri deystvii neravnomernykh nagruzok [Stability of Nonlinear Deformable Cylindrical Shells Made of Composite Material under Action of Nonuniform Loads]. Stroitel'naya mekhanika inzhenernykh konstruktsiy i sooruzheniy [Structural Mechanics of Engineering Structures and Constructions]. 2013, no. 2, pp. 3—10. (in Russian)
- Kirakosyan R.M. Ob odnoy utochnennoy teorii gladkikh ortotropnykh obolochek peremennoy tolshchiny [On One Improved Theory of Smooth Orthotropic Shells of Variable Thickness]. Doklady natsional'noy akademii nauk Armenii [Reports of National Academy of Sciences of Armenia]. 2011, no. 2, pp. 148—156. (in Russian)
- Antuf'ev B.A. Lokal'noe deformirovanie diskretno podkreplennykh obolochek [Local Deformation of Discretely Reinforced Shells]. Moscow, MAI Publ., 2013, 182 p. (in Russian)
- Moskalenko L.P. Effektivnost' podkrepleniya pologikh obolochek rebrami peremennoy vysoty [Reinforcement Efficiency of Shallow Shells by Ribs of Variable Height]. Vestnik grazhdanskikh inzhenerov [Bulletin of Civil Engineers]. 2011, no. 3 (28), pp. 46—50. (in Russian)
- Qu Y., Wu S., Chen Y., Hua H. Vibration Analysis of Ring-Stiffened Conical—Cylindrical—Spherical Shells Based on a Modified Variational Approach. International Journal of Mechanical Sciences. April 2013, vol. 69, pp. 72—84. Available at: http://dx.doi.org/10.1016/j.ijmecsci.2013.01.026/. Date of access: 29.08.2014.
- Maksimyuk V.A., Storozhuk E.A., Chernyshenko I.S. Nonlinear Deformation of Thin Isotropic and Orthotropic Shells of Revolution with Reinforced Holes and Rigid Inclusions. International Applied Mechanics. 2013, vol. 49, no. 6, pp. 685—692. DOI: http://dx.doi.org/10.1007/s10778-013-0602-x.
- Lindgaard E., Lund E. A Unified Approach to Nonlinear Buckling Optimization of Composite Structures. Computers & Structures. 2011, vol. 89, no. 3—4, pp. 357—370. DOI: http://dx.doi.org/10.1016/j.compstruc.2010.11.008.
- Tomás A., Martí P. Shape and Size Optimisation of Concrete Shells. Engineering Structures. 2010, vol. 32, no. 6, pp. 1650—1658. DOI: http://dx.doi.org/10.1016/j.engstruct.2010.02.013.
- Amiro I.Ya., Zarutskiy V.A. Issledovaniya v oblasti ustoychivosti rebristykh obolochek [Investigations in the Field of Ribbed Shells’ Stability]. Prikladnaya mekhanika [Applied Mechanics]. 1983, vol. 19, no. 11, pp. 3—20. (in Russian)
- Ignat'ev O.V., Karpov V.V., Filatov V.N. Variatsionno-parametricheskiy metod v nelineynoy teorii obolochek stupenchato-peremennoy tolshchiny [Variational and Parametric Method in Nonlinear Theory of Shells of Step-Variable Thickness]. Volgograd, VolgGASA Publ., 2001, 210 p. (in Russian)
- Bakouline N., Ignatiev O., Karpov V. Variation Parametric Research Technique of Variable by Step Width Shallow Shells with Finite Deflections. International Journal for Computational Civil and Structural Engineering. 2000, vol. I, no. 3, pp. 1—6.
- Karpov V.V., Ignat'ev O.V. Metod posledovatel'nogo izmeneniya krivizny [Method of Consequent Change in Curvature]. Matematicheskoe modelirovanie, chislennye metody i kompleksy programm : mezhvuzovskiy tematicheskiy sbornik trudov [Mathematical Modeling, Numerical Methods and Program System]. Saint Petersburg, SPbGASU Publ., 1996, no. 2, pp. 131—135. (in Russian)
- Karpov V.V. Prochnost' i ustoychivost' podkreplennykh obolochek vrashcheniya: v 2 ch. Ch. 1: Modeli i algoritmy issledovaniya prochnosti i ustoychivosti podkreplennykh obolochek [Stability and Reliability of Reinforced Rotational Shells: in 2 Parts. Part 1: Research Models and Algorithms of Stability and Reliability of Reinforced Shells]. Moscow, Fizmatlit Publ., 2010, 288 p. (in Russian)
- Karpov V.V., Semenov A.A. Matematicheskaya model' deformirovaniya podkreplennykh ortotropnykh obolochek vrashcheniya [Mathematical Deformation Model of Reinforced Orthotropic Rotational Shells]. Inzhenerno-stroitel'nyy zhurnal [Magazine of Civil Engineering]. 2013, no. 5, pp. 100—106. (in Russian)
- Petrov V.V. Metod posledovatel'nykh nagruzheniy v nelineynoy teorii plastinok I obolochek [Method of Consequent Loadings in Nonlinear Theory of Plates and Shells]. Saratov, SGU im. N.G. Chernyshevskogo Publ., 1975, 119 p. (in Russian)
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Kupavtsev Vladimir Vladimirovich -
Moscow State University of Civil Engineering (MGSU)
Candidate of Physical and Mathematical Sciences, Associated Professor, Department of Theoretical Mechanics and Aerodynamics, Moscow State University of Civil Engineering (MGSU), 26 Yaroslavskoe shosse, Мoscow, 129337, Russian Federation;
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.
The author considers the method of two-sided evaluations in solving the problems of stability of one-span elastic non-uniformly compressed rod with variable longitudinal bending rigidity in case of different classic conditions of fixation of the rod ends. The minimum critical value of the loading parameter for the rod is represented as a problem of calculating minimum value of the functional corresponding to the Euler equation, which is the same as the integral equation for the rod stability. Using the inequalities following from the problem of the best approximation of a Hilbert space element through the basic functions, the author constructs two sequences of functionals, the minimum values of which are the lower evaluations and the upper ones for the required value of the loading parameter. The basic functions here are the derivative forms of the stability loss for a rod with constant cross-section, compressed by longitudinal forces applied at the rod ends. The calculation of the lower bounds value is reduced to the determination of the maximum eigenvalues of block matrices. The elements of the aforesaid matrices are expressed through the integrals of basic functions depending on the type of the fixation of the rod ends. The calculation of the upper bound value is reduced to the determination of the maximum eigenvalue of the matrix, which almost coincides with one of the modular matrices. It is noted that the obtained upper bound evaluations are not worse than the evaluations obtained by the Ritz method with the use of the same basic functions.
DOI: 10.22227/1997-0935.2014.10.41-47
References
- Kupavtsev V.V. Variatsionnye formulirovki integral'nogo uravneniya ustoychivosti uprugikh sterzhney [Variational Formulations of the Integral Equation of Stability of Elastic Bars]. Vestnik MGSU [Proceedings of Moscow State University of Civil Engineering]. 2012, no. 9, pp. 137—143. (in Russian)
- Rzhanitsyn A.R. Ustoychivost' ravnovesiya uprugikh system [Stability of Equilibrium of Elastic Systems]. Moscow, GITTL Publ., 1955, 475 p. (in Russian)
- Alfutov N.A. Osnovy rascheta na ustoychivost' uprugikh system [Fundamentals of the Stability Analysis of the Elastic Systems]. 2-nd edition. Moscow, Mashinostroenie Publ., 1991, 336 p. (in Russian)
- Kupavtsev V.V. Bazisnye funktsii metoda dvustoronnikh otsenok v zadachakh ustoychivosti uprugikh neodnorodno-szhatykh sterzhney [Basic Functions for the Method of Two-sided Evaluations in the Problems of Stability of Elastic Non-uniformly Compressed Rods]. Vestnik MGSU [Proceedings of Moscow State University of Civil Engineering]. 2013, no. 6, pp. 63—70. (in Russian)
- Panteleev S.A. Dvustoronnie otsenki v zadachakh ob ustoychivosti szhatykh uprugikh blokov [Bilateral Assessments in the Stability Problem of Compressed Elastic Blocks]. Izvestiya RAN. Mekhanika tverdogo tela [News of the Russian Academy of Sciences. Solid Body Mechanics]. 2010, no. 1, pp. 51—63. (in Russian)
- Santos H.A., Gao D.Y. Canonical Dual Finite Element Method for Solving Post-Buckling Problems of a Large Deformation Elastic Beam. International Journal Non-linear Mechanics. 2012, vol. 47, no. 2, pp. 240—247. DOI: http://dx.doi.org/10.1016/j.ijnonlinmec.2011.05.012.
- Manchenko M.M. Ustoychivost' i kinematicheskie uravneniya dvizheniya dinamicheski szhatogo sterzhnya [Dynamically Loaded Bar: Stability and Kinematic Equations of Motion]. Vestnik MGSU [Proceedings of Moscow State University of Civil Engineering]. 2013, no. 6, pp. 71—76. (in Russian)
- Bogdanovich A.U., Kuznetsov I.L. Prodol'noe szhatie tonkostennogo sterzhnya peremennogo secheniya pri razlichnykh variantakh zakrepleniya tortsov. Soobshchenie 1 [Longitudinal Compression of a Thin-Walled Bar of Variable Cross Section with Different Variants of Ends Fastening (Information 1)]. Izvestiya vuzov. Stroitel'stvo [News of Institutions of Higher Education. Construction]. 2005, no. 10, pp. 19—25. (in Russian)
- Bogdanovich A.U., Kuznetsov I.L. Prodol'noe szhatie tonkostennogo sterzhnya peremennogo secheniya pri razlichnykh variantakh zakrepleniya tortsov. Soobshchenie 2 [Longitudinal Compression of a Thin-Walled Core of Variable Cross Section with Different Variants of Ends Fastening (Information 2)]. Izvestiya vuzov. Stroitel'stvo [News of Institutions of Higher Education. Construction]. 2005, no. 11, pp. 10—16. (in Russian)
- Selamet S., Garlock M.E. Predicting the Maximum Compressive Beam Axial During Fire Considering Local Buckling. Journal of Constructional Steel Research. 2012, vol. 71, pp. 189—201. DOI: http://dx.doi.org/10.1016/j.jcsr.2011.09.014.
- Vo Thuc P., Thai Huu-Tai. Vibration and Buckling Of Composite Beams Using Refined Shear Deformation Theory. International Journal of Mechanical Sciences. 2012, vol. 62, no. 1, pp. 67—76. DOI: http://dx.doi.org/10.1016/j.ijmecsci.2012.06.001.
- Kanno Yoshihiro, Ohsaki Makoto. Optimization-bazed Stability Analysis of Structures under Unilateral Constraints. International Journal for Numerical Methods in Engineering. 2009, vol. 77, no. 1, pp. 90—125.
- Doraiswamy Srikrishna, Narayanan Krishna R., Srinivasa Arun R. Finding Minimum Energy configurations for constrained beam buckling problems using the Viterbi algorithm. International Journal of Solids and Structures. 2012, vol. 49, no. 2, pp. 289—297.
- Rektoris К. Variational methods in Mathematics, Science and Engineering. Prague, SNTL-Publ., Techn. Liter., 1980. (in Russian)
- Kupavtsev V.V. Variatsionnye formulirovki zadach ustoychivosti uprugikh sterzhney cherez izgibayushchie momenty [Variational Formuliations of Stability Problems of Elastic Rods Using Bending Moments]. Vestnik MGSU [Proceedings of Moscow State University of Civil Engineering]. 2010, no. 4, vol. 3, pp. 285—289. (in Russian)
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Zhadanovskiy Boris Vasil’evich -
Moscow State University of Civil Engineering (National Research University) (MGSU)
Candidate of Technical Sciences, Senior Lecturer, Professor, Department of Technology and Organization of Construction Operations, Moscow State University of Civil Engineering (National Research University) (MGSU), 26 Yaroslavskoye Shosse, Moscow, 129337, Russian Federation.
The underground space is widely used in the construction in big cities of the Russian Federation. These works need the use of elevating-transfer vehicles. In this case the requirements of norms and regulations on operating safety should be strictly observed, because their breach often leads to emergency situations and injuries. The organizational and technological solutions when developing the design documentation and executing construction and assembly works should be primarily based on the stability of lifting facilities. The author states the requirements to installation of lifting tackles (cranes). The features of their installation in different operation conditions on construction sites are described. The crane stability depends on many different indicators, which are considered by the author. The calculation algorithms of crane stability are offered.
DOI: 10.22227/1997-0935.2016.5.52-58
References
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- Telichenko V.I., editor. Stroitel’stvo i rekonstruktsiya zdaniy i sooruzheniy gorodskoy infrastruktury [Construction and Reconstruction of Buildings and Structures of City Infrastructure]. Moscow, MGSU Publ.; ASV Publ., 2009, vol. 1: Organizatsiya i tekhnologiya stroitel’stva [Organization and Technology of the Construction]. 519 p. (In Russian)
- Cherednichenko N.D. Modelirovanie stroitel’nogo protsessa na etape predproektnoy podgotovki stroitel’stva [Simulation of a Construction Process on the Stage of Pre-design Preparation of the Construction]. Inzhenernyy vestnik Dona [Engineering Journal of Don]. 2012, vol. 22, no. 4—1 (22), article 174. (In Russian)
- Chulkov V.O., Kuzina O.N. Funktsional’noe modelirovanie stroitel’nogo pereustroystva neproizvodstvennykh ob”ektov [Functional Modeling of Redevelopment of Non-industrial Buildings]. Vestnik MGSU [Proceedings of Moscow State University of Civil Engineering]. 2012, no. 9, pp. 251—258. (In Russian)
- Kazaryan R.R., Nikol’skaya O.Yu. Sertifikatsiya sredstv mekhanizatsii ruchnogo truda i transportirovaniya stroitel’nykh gruzov [Certification of the Mechanization Means of Hand Labour and Transportation of Construction Loads]. Promyshlennoe i grazhdanskoe stroitel’stvo [Industrial and Civil Engineering]. 2008, no. 10, p. 51. (In Russian)
- Shirshikov B.F., Akulich V.V. Vybor ratsional’nogo kompleksa stroitel’nykh mashin dlya vypolneniya vosstanovitel’nykh rabot [Choosing the Justified Complex of Construction Machinery for Reconstruction Works]. Promyshlennoe i grazhdanskoe stroitel’stvo [Industrial and Civil Engineering]. 2010, no. 11, pp. 76—78. (In Russian)
- Shirshikov B.F., Akulich V.V. Model’ otsenki ratsional’nogo vybora organizatsionno-tekhnologicheskikh resheniy pri provedenii vosstanovitel’nykh rabot [Assessment Model of the Rational Choice of Organizational and Technological Solutions for Reconstruction Works]. Promyshlennoe i grazhdanskoe stroitel’stvo [Industrial and Civil Engineering]. 2011, no. 9, pp. 33—35. (In Russian)
- Abramov L.I., Abramov I.L. Modelirovanie tekhnologicheskikh protsessov stroitel’stva maloetazhnykh zhilykh zdaniy [Simulation of Technological Construction Processes of Low-rise Residential Buildings]. Zhilishchnoe stroitel’stvo [Residential Construction]. 2007, no. 5, pp. 1—3. (In Russian)
- Afanas’ev A.A., Matveev E.P., Monastyrev P.V. Industrial’nye metody oblitsovki fasadov zdaniy pri ikh uteplenii [Industrial Methods of Facing Building Faсades and Their Heat Insulation]. Promyshlennoe i grazhdanskoe stroitel’stvo [Industrial and Civil Engineering]. 1997, no. 6, pp. 49. (In Russian)
- Dzhalilov F.F., Kievskiy L.V. Razrabotka organizatsionnykh resheniy po sozdaniyu ob”ektov stroitel’stva i ikh ekspertiza: problemy i podkhody [Development of Organizational Solutions on Construction Objects’ Creation and Their Expertise: Problems and Approaches]. Promyshlennoe i grazhdanskoe stroitel’stvo [Industrial and Civil Engineering]. 1995, no. 4, p. 24. (In Russian)
- Ershov M.N., Shirshikov B.F. Rekonstruktsiya obshchestvennykh zdaniy bez osta-novki ikh ekspluatatsii [Reconstruction of Public Buildins without Stopping Their Operation]. Promyshlennoe i grazhdanskoe stroitel’stvo [Industrial and Civil Engineering]. 2004, no. 5, pp. 57—58. (In Russian)
- Vil’man Yu.A., Stepanov M.A. Distantsionno-upravlyaemye manipulyatory [Remote-Controlled Manipulative Devices]. Mekhanizatsiya stroitel’stva [Mechanization of the Construction]. 2006, no. 1, pp. 3—8. (In Russian)
- Vil’man Yu.A., Kagan P.B. Sovershenstvovanie urovnya mekhanizatsii i avtomatizatsii tekhnologiy montazha konstruktsiy [Advancing the Mechanization and Automation Level of Construction Installation Technologies]. Estestvennye i tekhnicheskie nauki [Natural and Technical Chiences]. 2014, no. 11—12 (78), pp. 397—398. (In Russian)
- Chirva M.A. Povyshenie kachestva razrabotki proektov proizvodstva rabot [Increasing the Quality of the Development of Work Performance Projects]. Transportnoe stroitel’stvo [Transport Construction]. 2015, no. 8, pp. 27—29. (In Russian)
- Margolin V.M. Metod opredeleniya osnovnykh tekhnologicheskikh parametrov in”ektsii vyazkikh rastvorov v peschanye grunty [Method of Determining the Main Technological Parametres of Cementing Mortar Injections into Sandy Soils]. Promyshlennoe i grazhdanskoe stroitel’stvo [Industrial and Civil Engineering]. 2013, no. 5, pp. 52—53. (In Russian)
- Spravochnik stroitelya. Stroitel’noe proizvodstvo [Reference Book of a Constructor. Construction Operations]. In 3 volumes. Moscow, Stroyizdat Publ., 1989, vol. 2. Organizatsiya i tekhnologiya rabot [Organization and Technology of Operations]. 527 p. (In Russian)
- Epifanov S.P., Polyakov V.I. Pnevmokolesnye i gusenichnye krany [Rubber-Tire and Caterpillar Cranes]. Moscow, Vysshaya shkola Publ., 1985, 312 p. (In Russian)
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Suraeva Ekaterina Nikolaevna -
Ogarev Mordovia State University (Ogarev MSU)
external degree-seeking student, Department of Construction Materials and Technologies, Ogarev Mordovia State University (Ogarev MSU), 68 Bolshevistskaya Str., Saransk 430005, Republic of Mordovia, Russian Federation; +7 (8342) 47-40-19;
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.
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Erofeev Vladimir Trofimovich -
Ogarev Mordovia State University (MGU im. Ogareva)
Doctor of Technical Sciences, Professor, Chair, Department of Construction Materials and Technologies, dean, Department of Architecture and Construction, Ogarev Mordovia State University (MGU im. Ogareva), 68 Bol’shevistskaya str., Saransk, 430005, Russian Federation; +7 (8342) 47-40-19;
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Korolev Evgeniy Valer'evich -
Moscow State University of Civil Engineering (MGSU)
Doctor of Technical Sciences, Professor, Adviser, Russian Academy of Architectural and Building Sciences (RAACS), director, Moscow State University of Civil Engineering (MGSU), 26 Yaroslavskoe shosse, Moscow, 129337, Russian Federation; +7-499-188-04-00;
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.
Dry construction mixes are today a product of high technologies. Depending on the purpose and requirements to the properties it is easy to produce dry construction mixes with different compositions and operating indicators in plant conditions using the necessary modifying additives. Cement, gypsum and other mineral binders are used in the construction mixes. Different types of cement are more heavily used in dry construction mixes. Such dry mixes are believed to be more effective materials comparing to traditional cement-sandy solutions of centralized preparation. The authors present the results of the investigations on obtaining biocidal cement-sand compositions. It was established, that introduction of sodium sulfate into the composition provides obtaining the materials with funginert and fungicide properties. The strength properties of the mixes modified by carbon nanotubes and biocide additive were investigated by mathematical planning methods. The results of the investigations showed that the modification of cement stone structure by carbon nanotubes positively influences their strength and technological properties. Nanomodifying of construction composites by introducing carbon nanotubes may be effectively used at different stages of structure formation of a construction material.
DOI: 10.22227/1997-0935.2015.4.104-114
References
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- Antonov V.B. Vliyanie biopovrezhdeniy zdaniy i sooruzheniy na zdorov'e cheloveka [Influence of Biodamages of Buildings and Structures on Human Health]. Biopovrezhdeniya i biokorroziya v stroitel'stve : materialy II Mezhdunarodnoy nauchno-tekhnicheskoy konferentsii [Biodamages and Biocorrosion in the Construction : Materials of the II International Science and Technical Conference]. Saransk, 2006, pp. 238—242. (In Russian)
- Erofeev V.T., Kaznacheev S.V., Bogatov A.D., Spirin V.A., Svetlov D.A. Biotsidnye tsementnye kompozity s dobavkami, soderzhashchimi guanidin [Biocide Cement Composites with Additives Containing Aminoethanamidine]. Privolzhskiy nauchnyy zhurnal [Volga Region Scientific Journal]. 2010, no. 4, pp. 87—94. (In Russian)
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- Ivanov F.M. Biokorroziya neorganicheskikh stroitel'nykh materialov [Biocorrosion of Nonorganic Construction Materials]. Biopovrezhdeniya v stroitel'stve : sbornik nauchnykh trudov [Biodamages in Construction : Collection of Scientific Works]. Moscow, Stroyizdat Publ., 1984, pp. 183—188. (In Russian)
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- Yudovich M.E., Ponomarev A.N. Nanomodifikatsiya plastifikatorov. Regulirovanie ikh svoystv i prochnostnykh kharakteristik litykh betonov [Nanomodification of Plastifiers. Regulation of their Properties and the Strength Characteristics of Liquid Concretes]. StroyPROFIl' [Construction Profile]. 2007, no. 6, pp. 49—51. (In Russian)
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- Kalashnikov V.I., Erofeev V.T., Moroz M.N.,Troyanov I.Yu., Volodin V.M., Suzdal'tsev O.V. Nanogidrosilikatnye tekhnologii v proizvodstve betonov [Nanohydrosilicate Technologies in Concrete Production]. Stroitel'nye materialy [Construction Materials]. 2014, no. 5, pp. 89—91. (In Russian)
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- Zanello L.P., Zhao B., Hu H., Haddon R.C. Bone Cell Proliferation on Carbon Nanotubes. Nano Lett. 2006, no. 6 (III), pp. 562—567. DOI: http://dx.doi.org/10.1021/nl051861e.
- Smart S.K., Cassady A.I., Lu G.Q., Martin D.J. The Biocompatibility of Carbon Nanotubes. Carbon. 2006, vol. 44, no. 6, pp. 1034—1047. DOI: http://dx.doi.org/10.1016/j.carbon.2005.10.011.
- Korolev E.V. Nanotekhnologiya v stroitel'nom materialovedenii. Analiz sostoyaniya i dostizheniy. Puti razvitiya [Nanotechnology in Construction Material Science. Analysis of the State and Achievements]. Stroitel'nye materialy [Construction Materials]. 2014, no. 11, pp. 47—79. (In Russian)
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Radzinskiy Aleksandr Vladimirovich -
LLC "Gidrospetsproekt"
engineer, LLC "Gidrospetsproekt", 11/10-3 Letnikovskaya str., 115114, Moscow, Russian Federation;
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Rasskazov Leonid Nikolaevich -
Moscow State University of Civil Engineering (MGSU)
Doctor of Technical Sciences, Professor, Department of Hydraulic Engineering, Honored Scientist of the Russian Federation, Moscow State University of Civil Engineering (MGSU), 26 Yaroslavskoe shosse, Moscow, 129337, Russian Federation;
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.
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Sainov Mikhail Petrovich -
Moscow State University of Civil Engineering (MGSU)
Candidate of Technical Sciences, Associate Professor, Department of Hydraulic Engineering, Moscow State University of Civil Engineering (MGSU), 26 Yaroslavskoe shosse, Moscow, 129337, Russian Federation;
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In the article the authors estimate the possibility of building a high (100 m high) stone dam with clay-cement concrete diaphragm. This diaphragm is used as an antifiltering element and it is made of secant piles method of clay-cement concrete (method of "slurry wall"). This diaphragm should be constructed in several phases, in our example example in three stages. Numerical studies of the stress-strain state of such a dam show that considerable compressive stresses can appear in the diaphragm. These stresses can be significantly (3...4 times) greater than the strength of clay-cement concrete in compression. However it should be taken into consideration that the diaphragm of such a high dam will be crimped by horizontal stresses, i.e. clay-cement concrete will operate in the triaxial compression. Under these conditions the strength of clay-cement concrete will be significantly higher, therefore, the diaphragm reliability might be provided with a margin. For this reason, the most important issue in the engineering of a high dam with such type of diaphragm is to select the required composition of clay-cement concrete. Increasing its strength by extension of the cement fraction could increase modulus of deformation. Therefore it could lead to compressive stress increase and the strength state degradation. Hydrostatic pressure generates the areas of tensile stresses in the clay-cement concrete diaphragm due to the arising bending deformation. It threatens the formation of cracks in the clay-cement concrete, especially in the nodes interface diaphragm queues. It is recommended to match the diaphragm queues using ferroconcrete galleries. This should ensure flexibility of deformation between the gallery and the diaphragm.
DOI: 10.22227/1997-0935.2014.9.106-115
References
- Korolev V.M., Smirnov O.E., Argal E.S., Radzinskiy A.V. Novoe v sozdanii protivofil'tratsionnogo elementa v tele gruntovoy plotiny [New Things in the Creation of Antifiltering Element in the Body of a Subsurface Dam]. Gidrotekhnicheskoe stroitel'stvo [Hydraulic Engineering]. 2013, no. 8, pp. 2—9.
- Kudrin K.P., Korolev V.M., Argal E.S., Solov'eva E.V., Smirnov O.E., Radzinskiy A.V. Ispol'zovanie innovatsionnykh resheniy pri sozdanii protivofil'tratsionnoy diafragmy v peremychke Nizhne-Bureyskoy GES [Using Innovative Solutions to Create Impervious Diaphragm in the Jumper of Lower Bureyskaya HPP]. Gidrotekhnicheskoe stroitel'stvo [Hydraulic Engineering]. 2014, no. 7, pp. 22—28.
- Radchenko V.G., Lopatina M.G., Nikolaychuk E.V., Radchenko S.V. Opyt vozvedeniya protivofil'tratsionnykh ustroystv i gruntotsementnykh smesey [Experience in the Construction of Antifiltering Devices and Soil-cement Compositions]. Gidrotekhnicheskoe stroitel'stvo [Hydraulic Engineering]. 2012, no. 6, pp. 46—54.
- Gol'din A.L., Rasskazov L.N. Proektirovanie gruntovykh plotin [Engineering of Soil Dams]. 2nd edition. Moscow, ASV Publ., 2001, 375 p.
- Rasskazov L.N., Radzinskiy A.V., Sainov M.P. Vybor sostava glinotsementobetona pri sozdanii «steny v grunte» [Choice of Clay Cement Concrete to Create "Slurry Trench" Cutoff Wall]. Gidrotekhnicheskoe stroitel'stvo [Hydraulic Engineering]. 2014, no. 3, pp. 16—23.
- Rasskazov L.N., Radzinskiy A.V., Sainov M.P. K prochnosti glinotsementobetona [To the Problem of Clay-cement Concrete Strength]. Gidrotekhnicheskoe stroitel'stvo [Hydraulic Engineering]. 2014, no. 8, pp. 26—28.
- Rasskazov L.N., Radzinskiy A.V., Sainov M.P. Prochnost' i deformativnost' glinotsementobetona v slozhnonapryazhennom sostoyanii [Strength and Deformability of Clay-cement Concrete in Complex Stress State]. Gidrotekhnicheskoe stroitel'stvo [Hydraulic Engineering]. 2014, no. 8, pp. 29—33.
- Rasskazov L.N., Radzinskiy A.V., Sainov M.P. Plotiny s glinotsementobetonnoy diafragmoy. Napryazhenno-deformirovannoe sostoyanie i prochnost' [Dams with Clay-cement Concrete Diaphragm. Stress-strain State and Strength]. Gidrotekhnicheskoe stroitel'stvo [Hydraulic Engineering]. 2014, no. 9, pp. 37—44.
- Malyshev L.I., Rasskazov L.N., Soldatov P.V. Sostoyanie plotiny Kureyskoy GES i tekhnicheskie resheniya po ee remontu [The Condition of Kureyskaya Hydraulic Power Station Dam and Technical Solutions for its Repair]. Gidrotekhnicheskoe stroitel'stvo [Hydraulic Engineering]. 1999, no. 1, pp. 31—36.
- O`Brien S., Dann C., Hunter G., Schwermer M. Construction of the Plastic Concrete Cut-off Wall at Hinze Dam. ANCOLD Proceedings of Technical Groups. Available at: http://www.bauerdamcontractors.com/export/sites/www.bauerdamcontractors.com/en/pdf/publications/Cutoff-Wall-Paper-09-ANCOLD-Conference---Final.pdf/. Date of access: 25.05.2014.
- Fedoseev V.I., Shishov I.N., Pekhtin V.A., Krivonogova N.F., Kagan A.A. Protivofil'tratsionnye zavesy gidrotekhnicheskikh sooruzheniy na mnogoletney. Opyt proektirovaniya i proizvodstva rabot merzlote [Antifiltering Curtain of Hydraulic Structures on Permafrost. Design Experience and Production]. Vol. 2, Saint Petersburg, VNIIG im. B.E. Vedeneeva Publ., 2009, pp. 303—316.
- Powell R.D., Morgenstern N.R. Use and Performance of Seepage Reduction Measures. Proc. Symp. Seepage and Leakage from Dams and Impoundments. American Society of Civil Engineers. Denver, CO, USA, 1985, pp. 158—182.
- Baltruschat M., Banzhaf P., Beutler S., Hechendorfer S. Cut-off Wall for the Strengthening of the Sylvenstein Reservoir (70 km south of Munich, Germany) : Cut-off Wall executed with BAUER cutter and grab and Plastic Concrete. BAUER Spezialtiefbau GmbH. Available at: http://www.bauerdamcontractors.com/export/sites/www.bauerdamcontractors.com/en/pdf/publications/paper_HYDRO-2013_bmi_2013_08_24_spa-bz_B_short.pdf. Date of access: 25.05.2014.
- Sainov M.P. Vychislitel'naya programma po raschetu napryazhenno-deformirovannogo sostoyaniya gruntovykh plotin: opyt sozdaniya, metodiki i algoritmy [Computer Program for the Calculation of the Stress-strain State of Soil Dams: the Experience of Creation, Techniques and Algorithms]. International Journal for Computational Civil and Structural Engineering. 2013, vol. 9, no. 4, pp. 208—225.
- Rasskazov L.N. Dzhkha Dzh. Deformiruemost' i prochnost' grunta pri raschete vysokikh gruntovykh plotin [Deformability and Strength of the Soil in the Calculation of High Soil Dams]. Gidrotekhnicheskoe stroitel'stvo [Hydraulic Engineering]. 1987, no. 7, pp. 31—36.
- Sainov M.P. Parametry deformiruemosti krupnooblomochnykh gruntov v tele gruntovykh plotin [Deformability Parameters of Coarse Soils in the Body of Soil Dams]. Stroitel'stvo: nauka i obrazovanie [Construction: Science and Education]. 2014, no. 2. Available at: http://www.nso-journal.ru/public/journals/1/issues/2014/02/2_Sainov.pdf. Date of access: 25.05.2014.
- Sainov M.P. Osobennosti chislennogo modelirovaniya napryazhenno-deformirovannogo sostoyaniya gruntovykh plotin s tonkimi protivofil'tratsionnymi elementami [Numerical Modeling of the Stress-Strain State of Earth Dams That Have Thin Rigid Seepage Control Elements]. Vestnik MGSU [Proceedings of Moscow State University of Civil Engineering]. 2012, no. 10, pp. 102—108.
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Morozenko Andrey Alexandrovich -
Moscow State University
of Civil Engineering
Candidate of Technical Sciences,
Associated Professor, Director, Youth Centre for Professional Labour Activity
8 (499) 183-25-83, Moscow State University
of Civil Engineering, 26 Yaroslavskoe shosse, Moscow, 129337, Russian Federation;
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.
In the article, the author proves that the resistance to crises that originate both inside the organization
and in the external environment has a great importance in terms of formation of stability
of the organizational structure. In this article, the issue of flexibility of the organizational structure is
considered; the author demonstrates that the rapidity of the system response to any internal and
external impacts is essential for the purpose of appraisal of the system properties. The analysis
performed by the author serves as the basis for his recommendations designated to assure the
organizational stability in the course of any potential crises.
DOI: 10.22227/1997-0935.2012.8.203 - 206
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Kupavtsev Vladimir Vladimirovich -
Moscow State University of Civil Engineering (MGSU)
Candidate of Physical and Mathematical Sciences, Associated Professor, Department of Theoretical Mechanics and Aerodynamics, Moscow State University of Civil Engineering (MGSU), 26 Yaroslavskoe shosse, Мoscow, 129337, Russian Federation;
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In the article, the author proposes an original method of identification of upper and lower bounds of critical values of loading parameters in respect of three stability problems for a non-uniformly compressed rectilinear one-span elastic rod with a varying longitudinal bending stiffness value.Initial variational formulations of stability problems under consideration are presented through internal bending moments that emerge at the moment of the rod stability loss and that satisfy uniform boundary conditions rather than additional integral conditions. The author has obtained forms of the bending moment and respective loading parameter values in case of the rod equilibrium bifurcation in the basic problem of stability of an elastic rectilinear rod with a constant cross section, compressed by longitudinal forces at the rod ends.The calculation of the lower bound is reduced to determination of the greatest eigenvalues for the matrices presented in the form of modular matrices of the second order with the elements expressed through the integrals of available forms of bending moments. The calculation of the upper bound is reduced to determination of the greatest eigenvalue for the matrix that almost coincides with one of modular matrices.
DOI: 10.22227/1997-0935.2013.2.47-54
References
- Rzhanitsyn A.R Ustoychivost’ ravnovesiya uprugikh system [Stability of Equilibrium of Elastic Systems]. Moscow, Gostekhizdat Publ., 1955, 475 p.
- Kupavtsev V.V. Variatsionnye formulirovki zadach ustoychivosti uprugikh sterzhney cherez izgibayushchie momenty [Variational Formulations of Problems of Stability of Elastic Rods Using Bending Moments]. Vestnik MGSU. [Proceedings of Ìoscow State University of Civil Engineering]. 2010, no. 4, vol. 3, pp. 285—289.
- Kupavtsev V.V. O variatsionnykh formulirovkakh zadach ustoychivosti sterzhney s uprugo zashchemlennymi i opertymi kontsami [Variational Formulations of Stability Problems for Rods That Have Elastically Fixed and Supported Ends]. Vestnik MGSU [Proceedings of Ìoscow State University of Civil Engineering]. 2011, vol. 3, no. 4, pp. 283—287.
- Kupavtsev V.V. K dvustoronnim otsenkam kriticheskikh nagruzok neodnorodno szhatykh sterzhney [On Bilateral Evaluations of Critical Loading Values in Respect of Non-uniformly Compressed Elastic Rods]. Izvestiya vuzov. Stroitel’stvo i arkhitektura. [News of Institutions of Higher Education. Construction and Architecture]. 1984, no. 8, pp. 24—29.
- Panteleev S.A. Dvustoronnie otsenki v zadachakh ob ustoychivosti szhatykh uprugikh blokov [Bilateral Assessments in the Stability Problem of Compressed Elastic Blocks]. Izvestiya RAN. MTT. [News of the Russian Academy of Sciences. Mechanics of Solids]. 2010, no. 1, pp. 51—63.
- Izhendeev A.V. Otsenka vnutrennikh usiliy tonkostennogo sterzhnya otkrytogo profilya [Assessment of Internal Forces of a Thin-walled Rod with an Open Profile]. Izvestiya vuzov. Stroitel’stvo. [News of Institutions of Higher Education. Construction]. 2004, no. 3, pp. 100—103.
- Chanyshev A.I., Igonina E.A. O potere ustoychivosti beskonechno dlinnoy polosy za predelom uprugosti pri szhatii [On the Loss of Stability of an Indefinitely Long Strip beyond the Elasticity in Compression]. Fizicheskaya mezomekhanika [Physical Mesomechanics]. 2010, vol. 13, no. 51, pp. 89—95.
- Paymushin V.N., Gyunal I.Sh., Lukankin S.A. Issledovanie kachestva nelineynykh uravneniy teorii uprugosti na zadachakh ustoychivosti ploskikh krivolineynykh sterzhney sloistoy struktury (postanovka zadachi) [Research into the Quality of Non-linear Equations of the Theory of Elasticity Exemplified by the Problems of Stability of Flat Curvilinear Rods That Have a Layered Structure (Problem Definition)]. Izvestiya vuzov. Aviatsionnaya tekhnika. [News of Institutions of Higher Education. Aeronautical Engineering]. 2010, no. 2, pp. 34—37.
- Dudchenko A.V., Kupavtsev V.V. Dvustoronnie otsenki ustoychivosti uprugogo konsol’nogo sterzhnya, szhatogo polusledyashchey siloy [Bilateral Estimates of Stability of an Elastic Cantilever Rod, Compressed by the Half-tracking Force]. Vestnik MGSU [Proceedings of Ìoscow State University of Civil Engineering]. 2011, no. 6, pp. 302—306.
- Dudchenko A.V., Kupavtsev V.V. Dvustoronnie otsenki ustoychivosti uprugogo konsol'nogo sterzhnya, szhatogo cherez shatun [Bilateral Estimates of Stability of an Elastic Cantilever Rod, Compressed over the Connecting Rod]. Vestnik MGSU [Proceedings of Ìoscow State University of Civil Engineering]. 2012, no. 7, pp. 75—81.
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Alekseev Evgenij Valer'evich -
Moscow State University of Civil Engineering (MSUCE)
Doctor of Technical Sciences, Professor, Head of Department of Water Supply and Aquatic Ecology
8 (499) 183-54-56, Moscow State University of Civil Engineering (MSUCE), 26 Jaroslavskoe shosse, Moscow, 129337, Russia;
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.
Discrete properties of substances found in the water can provide exhaustive information about the substances contained in it. However, they do not provide any information about the interaction between the substances and the water, or between themselves, or the overall properties of the aquatic system. Therefore, they cannot serve as the basis for the systemic approach to development of efficient water treatment technologies.
The author's suggestion is to introduce the term "aquatic system" as a description of the properties of natural and sewerage water. An aquatic system represents a collection of interconnected substances and phenomena in the aquatic medium. Therefore, natural and sewerage water represent aquatic systems, or mixtures of substances that have different origins, that interact with one another on a non-stop basis, and that are interrelated, and that interact with the water at one and the same time. Primary features of aquatic systems are considered in the article, including genesis, stability, and localization. Secondary features of aquatic systems, including their aggregate state, their biotic state, and their chemical composition.
The research of aquatic systems of natural and sewerage waters, their structure and interrelations identifies the top-priority subject of research in the aquatic ecology. Therefore, the subject matter of the aquatic ecology represents the area of research, learning and systematization of features and properties of natural and man-made aquatic systems. This area of research dives way to a new trend of the methodology of modeling and optimization of natural and sewerage water treatment technologies. Aquatic ecology is to develop the principal provisions aimed at the improvement of water treatment technologies based on the properties of aquatic systems.
DOI: 10.22227/1997-0935.2012.2.140 - 144
References
- Shvecov V.N., Morozova K.M., Mjasnikov I.N. and others. Klassifikator tehnologij ochistki stochnyh vod [Classified Technologies of Sewerage Water Treatment Technologies]. Vodosnabzhenie i sanitarnaja tehnika [Water Supply and Sanitation Machinery], 2004, Issue # 5, pp. 2—4.
- Zhurba M.G., Sokolov L.I., Govorova Zh.M. Vodosnabzhenie. Proektirovanie sistem i sooruzhenij [Water Supply. Design of Systems and Structures], methodological guide, edited by professor Zhurba M.G. Moscow, ASV, 2004, volume 2.
- Zhurba M.G., Nechaev A.P., Ivleva G.A. and others. Klassifikatory tehnologij ochistki prirodnyh vod [Classifiers of Natural Water Treatment Technologies]. Moscow, GPI Sojuzvodokanalproekt, 2000, 118 p.
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Kupavtsev Vladimir Vladimirovich -
Moscow
State University of Civil Engineering (MGSU)
Candidate of Physical and Mathematical
Sciences, Associated Professor, Department of Theoretical Mechanics and Aerodynamics
8 (499) 183-46-74, Moscow
State University of Civil Engineering (MGSU), 26 Yaroslavskoe shosse, Moscow, 129337, Russian
Federation;
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.
The author considers the variational formulations of the problem of stability of non-uniformly
compressed rectilinear elastic bars that demonstrate their variable longitudinal bending rigidity in the
event of different classical conditions of fixation of bar ends.
Identification of the critical bar loading value is presented as a minimax problem with respect
to the loading parameter and to the transversal displacement of the bar axis accompanied by the
loss of stability. The author demonstrates that the critical value of the loading parameter may be formulated
as a solution to the dual minimax problem. Further, the minimax formulation is transformed
into the problem of identification of eigenvalues in the bilinear symmetric and continuous form, which
is equivalent to the identification of eigenvalues of a strictly positive, linear and completely continuous
operator. The operator kernel is presented in the form of symmetrization of the non-symmetric
kernel derived in an explicit form.
Within the framework of the problem considered by the author, the bar ends are fixed as follows:
(1) both ends are rigidly fixed, (2) one end is rigidly fixed, while the other one is pinned, (3) one
end is rigidly fixed, while the other one is attached to the support displaceable in the transverse direction,
(4) one end is rigidly fixed, while the other one is free, (5) one end is pinned, while the other
one is attached to the support displaceable in the transverse direction, (6) both ends are pinned.
DOI: 10.22227/1997-0935.2012.9.137 - 143
References
- Rzhanitsyn A.R. Ustoychivost’ ravnovesiya uprugikh system [Stability of the Equilibrium State of Elastic Systems]. Moscow, Gostekhizdat Publ., 1955, 475 p.
- Alfutov N.A. Osnovy rascheta na ustoychivost’ uprugikh system [Principles of the Stability Analysis of Elastic Systems]. Moscow, Mashinostroenie Publ., 1991, 336 p.
- Rektoris K. Variatsionnye metody v matematicheskoy fi zike i tekhnike [Variational Methods in Mathematical Physics and Engineering]. Moscow, Mir Publ., 1985, 589 p.
- Litvinov V.G. Optimizatsiya v ellipticheskikh granichnykh zadachakh s prilozheniyami k mekhanike [Optimization in Elliptic Boundary-value Problems Applicable to Mechanics]. Moscow, Mir Publ., 1985, 368 p.
- Litvinov S.V., Klimenko E.S., Kulinich I.I., Yazyeva S.B. Ustoychivost’ polimernykh sterzhney pri razlichnykh variantakh zakrepleniya [Stability of Polymer Bars in Case of Various Methods of Their Fixation]. Vestnik MGSU [Proceedings of Moscow State University of Civil Engineering]. 2011, no. 4, vol. 2, pp. 153—157.
- Il’yashenko A.V. Lokal’naya ustoychivost’ tavrovykh neideal’nykh sterzhney [Local Stability of Tshaped Imperfect Bars]. Vestnik MGSU [Proceedings of Moscow State University of Civil Engineering]. 2010, no. 4, vol. 3, pp. 162—166.
- Tamarzyan A.G. Dinamicheskaya ustoychivost’ szhatogo zhelezobetonnogo elementa kak vyazkouprugogo sterzhnya [Dynamic Stability of a Compressed Reinforced Concrete Element as a Viscoelastic Bar]. Vestnik MGSU [Proceedings of Moscow State University of Civil Engineering]. 2011, no. 1, vol. 2, pp. 193—196.
- Dudchenko A.V., Kupavtsev V.V. Dvustoronnie otsenki ustoychivosti uprugogo konsol’nogo sterzhnya, szhatogo polusledyashchey siloy [Two-way Estimates of Stability of an Elastic Cantilever Bar, Compressed by a Half-tracking Force]. Vestnik MGSU [Proceedings of Moscow State University of Civil Engineering]. 2011, no. 1, vol. 6, pp. 302—306.
- Kupavtsev V.V. Variatsionnye formulirovki zadach ustoychivosti uprugikh sterzhney cherez izgibayushchie momenty [Variational Formulations of Problems of Stability of Elastic Bars Derived by Using Bending Moments]. Vestnik MGSU [Proceedings of Moscow State University of Civil Engineering]. 2010, no. 4, vol. 3, pp. 285—289.
- Kupavtsev V.V. O variatsionnykh formulirovkakh zadach ustoychivosti sterzhney s uprugo zashchemlennymi i opertymi kontsami [About the Variational Formulations of Stability Problems for Bars with Elastic Fixation of Supported Bar Ends]. Vestnik MGSU [Proceedings of Moscow State University of Civil Engineering]. 2011, no. 4, pp. 283—287.
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Litvinov Vladimir Vital'evich -
Rostov State University of Civil Engineering (RGSU)
Director, Laboratory of Department of Strength of Materials,
8 (863) 201-91-36, Rostov State University of Civil Engineering (RGSU), 162 Sotsialisticheskaya St., Rostov-Don, 344022, Russian Federation;
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.
-
Andreev Vladimir Igorevich -
Moscow State University of Civil Engineering (National Research University) (MGSU)
Doctor of Technical Sciences, Professor, corresponding member of Russian Academy of Architecture and Construction Sciences, chair, Department of Strength of Materials, Moscow State University of Civil Engineering (National Research University) (MGSU), 26 Yaroslavskoe shosse, Moscow, 129337, Russian Federation;
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-
Chepurnenko Anton Sergeevich -
Don State Technical University (DGTU)
Candidate of Engineering Science, teaching assistant of the strength of materials department, Don State Technical University (DGTU), 162 Sotsialisticheskaya str., Rostov-on-Don, 344022;
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.
The problem of stability of a freely supported truncated circular conical shell, compressed by the upper base of a uniformly distributed load per unit length , referred to the median shell surface and directed along the generatrix of the cone, was solved by the Ritz-Timoshenko energy method. The orthogonal system of curvilinear coordinates of the points of the middle surface of the shell was adopted to solve the problem. Possible displacements were selected in the form of double series approximation functions. The physical principle of inextensible generatrix of the cone exposed to buckling at the moment of instability was employed. In addition, the fundamental principle of continuum mechanics, or the principle of minimal total potential energy of the system, was taken as the basis. According to the linear elasticity theory, energy methods make it possible to replace the solution of complex differential equations by the solution of simple linear algebraic equations. As a result, the problem is reduced to the problem of identifying the eigenvalues in the algebraic theory of matrices. The numerical value of the critical load was derived through the employment of the software.
DOI: 10.22227/1997-0935.2012.10.95 - 101
References
- Vol’mir A.S. Ustoychivost’ deformiruemykh sistem [Stability of Deformable Systems]. Nauka Publ., 1967, 984 p.
- Birger I.A., Panovko Ya.G. Prochnost’. Ustoychivost’. Kolebaniya [Strength. Stability. Vibrations]. Reference book. Moscow, Mashinostroenie Publ., 1968, vol. 3, 568 p.
- Alfutov N.A. Osnovy rascheta na ustoychivost’ uprugikh sistem [Fundamentals of Analysis of Stability of Elastic Systems]. Moscow, Mashinostroenie Publ., 1991, 336 p.
- Gol’denveyzer A.L. Teoriya tonkikh uprugikh obolochek [Theory of Thin Elastic Shells]. Moscow – Leningrad, Gostekhizdat Publ., 1953, 544 p.
- Mushtari Kh.M. Priblizhennoe reshenie nekotorykh zadach ustoychivosti tonkostennoy konicheskoy obolochki krugovogo secheniya [Approximate Solution of Some Problems of Stability of Thin-walled Conical Shell with Circular Cross Section]. Prikladnaya matematika i mekhanika [Applied Mathematics and Mechanics]. 1943, vol. 7, no. 3, pp. 155—166.
- Grigolyuk E.I., Kabanov V.V. Ustoychivost’ obolochek [Stability of Shells]. Moscow, Nauka Publ., 1978.
- Timoshenko S.P. Ustoychivost’ uprugikh system [Stability of Elastic Systems]. Moscow, Gostekhizdat Publ., 1946.
- Baruch M., Harari O., Singer J. Low Buckling Loads of Axially Compressed Conical Shells. Trans. ASME, Ser. E., 1970, vol. 37, no. 2, pp. 384—392.
- Shtaerman I.Ya. Ustoychivost’ obolochek [Stability of Shells]. Works of Kiev Institute of Aviation. 1936, no. 1, pp. 12—16.
- Bryan G.N. Application of the Energy Test to the Collapse of a Thin Long Pipe under External Pressure. Proc. Cambridge Philos. Soc. 1988, vol. 6, pp. 287—292.