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

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

Pages 41-51

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

DOI: 10.22227/1997-0935.2014.1.41-51

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

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Using wavelet analysisto obtain characteristics of accelerograms

Vestnik MGSU 7/2013
  • Mkrtychev Oleg Vartanovich - Moscow State University of Civil Engineering (National Research University) (MGSU) Doctor of Technical Sciences, head, Scientific Laboratory of Reliability and Seismic Resistance of Structures, Professor, Department of Strength of Materials, Moscow State University of Civil Engineering (National Research University) (MGSU), ; This e-mail address is being protected from spambots. You need JavaScript enabled to view it .
  • Reshetov Andrey Aleksandrovich - Moscow State University of Civil Engineering (National Research University) (MGSU) Candidate of Technical Sciences, engineer, Research Laboratory “Reliability and Earthquake Engineering”, Moscow State University of Civil Engineering (National Research University) (MGSU), 26 Yaroslavskoe shosse, Moscow, 129337, Russian Federation; This e-mail address is being protected from spambots. You need JavaScript enabled to view it .

Pages 59-67

Application of accelerograms to the analysis of structures, exposed to seismic loads, and generation of synthetic accelerograms may only be implemented if their varied characteristics are available. The wavelet analysis may serve as a method for identification of the above characteristics. The wavelet analysis is an effective tool for identification of versatile regularities of signals. Wavelets can be used to detect inflection points, extremes, etc. Also, wavelets can be used to filter signals.The authors discuss particular theoretical principles of the wavelet analysis and the multiresolution analysis. The authors present formulas designated for the practical application. The authors implemented a wavelet transform in respect of a specific accelerogram.The recording of the horizontal component (N00E) of the Spitak earthquake (Armenia, 1988) was exposed to the analysis as an accelerogram. An accelerogram was considered as a non-stationary random process in the course of its decomposition into the envelope and the non-stationary part. This non-stationary random process was presented as a multiplication envelope of a stationary random process. Parameters of exposure of a construction site to the seismic impact can be used to synthesize accelerograms.

DOI: 10.22227/1997-0935.2013.7.59-67

References
  1. Blater K. Veyvlet-analiz. Osnovy teorii [Wavelet Analysis. Foundations of the Theory]. Moscow, Tekhnosfera Publ., 2007, 280 p.
  2. Percival D.B., Walden A.T. Wavelet Methods for Time Series Analysis. Cambridge University Press, 2000, 622 p.
  3. Dobeshi I. Desyat’ lektsiy po veyvletam [Ten Lectures on Wavelets]. Izhevsk, NITs «Regulyarnaya i khaoticheskaya dinamika» publ., 2001, 454 p.
  4. Addison P.S. The Illustrated Wavelet Transform Handbook. Institute of Physics, 2002, 358 p.
  5. Goswami J.C., Chan A.K., Fundamentals of Wavelets: Theory, Algorithms and Applications. John Wiley & Sons, Inc., 1999, 359 p.
  6. Chui C.K. Wavelets: A Mathematical Tool for Signal Analysis, SIAM. Philadelphia, 1997, 228 p.
  7. Mkrtychev O.V., Reshetov A.A. Primenenie veyvlet-preobrazovaniy pri analize akselerogramm [Application of Wavelet Transformations to the Analysis of Accelerograms]. International Journal for Computational Civil and Structural Engineering. 2011, vol. 7, no. 3, pp. 118—126.
  8. Mukherjee S., Gupta V.K. Wavelet-based Generation of Spectrum-compatible Time-histories. Soil Dynamics and Earthquake Engineering. 2002, vol. 22, no. 9-12, pp. 799—804.
  9. Bolotin V.V. Metody teorii veroyatnostey i teorii nadezhnosti v raschetakh sooruzheniy [Methods of the Theory of Probabilities and Theory of Reliability in Analysis of Structures]. Moscow, Stroyizdat Publ., 1982, 351 p.
  10. Bakalov V.P. Tsifrovoe modelirovanie sluchaynykh protsessov [Digital Modeling of Random Processes]. Moscow, MAI Publ., 2002, 88 p.

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