Error
  • Error loading Modules:Can't create/write to file '/var/lib/mysql/tmp/#sql_bd4_0.MYI' (Errcode: 30) SQL=SELECT id, title, module, position, content, showtitle, control, params FROM jos_modules AS m LEFT JOIN jos_modules_menu AS mm ON mm.moduleid = m.id WHERE m.published = 1 AND m.access <= 0 AND m.client_id = 0 AND ( mm.menuid = 8 OR mm.menuid = 0 ) ORDER BY position, ordering
  • Error loading Modules:Can't create/write to file '/var/lib/mysql/tmp/#sql_bd4_0.MYI' (Errcode: 30) SQL=SELECT id, title, module, position, content, showtitle, control, params FROM jos_modules AS m LEFT JOIN jos_modules_menu AS mm ON mm.moduleid = m.id WHERE m.published = 1 AND m.access <= 0 AND m.client_id = 0 AND ( mm.menuid = 8 OR mm.menuid = 0 ) ORDER BY position, ordering
  • Error loading Modules:Can't create/write to file '/var/lib/mysql/tmp/#sql_bd4_0.MYI' (Errcode: 30) SQL=SELECT id, title, module, position, content, showtitle, control, params FROM jos_modules AS m LEFT JOIN jos_modules_menu AS mm ON mm.moduleid = m.id WHERE m.published = 1 AND m.access <= 0 AND m.client_id = 0 AND ( mm.menuid = 8 OR mm.menuid = 0 ) ORDER BY position, ordering
  • Error loading Modules:Can't create/write to file '/var/lib/mysql/tmp/#sql_bd4_0.MYI' (Errcode: 30) SQL=SELECT id, title, module, position, content, showtitle, control, params FROM jos_modules AS m LEFT JOIN jos_modules_menu AS mm ON mm.moduleid = m.id WHERE m.published = 1 AND m.access <= 0 AND m.client_id = 0 AND ( mm.menuid = 8 OR mm.menuid = 0 ) ORDER BY position, ordering
  • Error loading Modules:Can't create/write to file '/var/lib/mysql/tmp/#sql_bd4_0.MYI' (Errcode: 30) SQL=SELECT id, title, module, position, content, showtitle, control, params FROM jos_modules AS m LEFT JOIN jos_modules_menu AS mm ON mm.moduleid = m.id WHERE m.published = 1 AND m.access <= 0 AND m.client_id = 0 AND ( mm.menuid = 8 OR mm.menuid = 0 ) ORDER BY position, ordering
  • Error loading Modules:Can't create/write to file '/var/lib/mysql/tmp/#sql_bd4_0.MYI' (Errcode: 30) SQL=SELECT id, title, module, position, content, showtitle, control, params FROM jos_modules AS m LEFT JOIN jos_modules_menu AS mm ON mm.moduleid = m.id WHERE m.published = 1 AND m.access <= 0 AND m.client_id = 0 AND ( mm.menuid = 8 OR mm.menuid = 0 ) ORDER BY position, ordering
  • Error loading Modules:Can't create/write to file '/var/lib/mysql/tmp/#sql_bd4_0.MYI' (Errcode: 30) SQL=SELECT id, title, module, position, content, showtitle, control, params FROM jos_modules AS m LEFT JOIN jos_modules_menu AS mm ON mm.moduleid = m.id WHERE m.published = 1 AND m.access <= 0 AND m.client_id = 0 AND ( mm.menuid = 8 OR mm.menuid = 0 ) ORDER BY position, ordering
  • Error loading Modules:Can't create/write to file '/var/lib/mysql/tmp/#sql_bd4_0.MYI' (Errcode: 30) SQL=SELECT id, title, module, position, content, showtitle, control, params FROM jos_modules AS m LEFT JOIN jos_modules_menu AS mm ON mm.moduleid = m.id WHERE m.published = 1 AND m.access <= 0 AND m.client_id = 0 AND ( mm.menuid = 8 OR mm.menuid = 0 ) ORDER BY position, ordering
  • Error loading Modules:Can't create/write to file '/var/lib/mysql/tmp/#sql_bd4_0.MYI' (Errcode: 30) SQL=SELECT id, title, module, position, content, showtitle, control, params FROM jos_modules AS m LEFT JOIN jos_modules_menu AS mm ON mm.moduleid = m.id WHERE m.published = 1 AND m.access <= 0 AND m.client_id = 0 AND ( mm.menuid = 8 OR mm.menuid = 0 ) ORDER BY position, ordering
  • Error loading Modules:Can't create/write to file '/var/lib/mysql/tmp/#sql_bd4_0.MYI' (Errcode: 30) SQL=SELECT id, title, module, position, content, showtitle, control, params FROM jos_modules AS m LEFT JOIN jos_modules_menu AS mm ON mm.moduleid = m.id WHERE m.published = 1 AND m.access <= 0 AND m.client_id = 0 AND ( mm.menuid = 8 OR mm.menuid = 0 ) ORDER BY position, ordering
  • Error loading Modules:Can't create/write to file '/var/lib/mysql/tmp/#sql_bd4_0.MYI' (Errcode: 30) SQL=SELECT id, title, module, position, content, showtitle, control, params FROM jos_modules AS m LEFT JOIN jos_modules_menu AS mm ON mm.moduleid = m.id WHERE m.published = 1 AND m.access <= 0 AND m.client_id = 0 AND ( mm.menuid = 8 OR mm.menuid = 0 ) ORDER BY position, ordering
  • Error loading Modules:Can't create/write to file '/var/lib/mysql/tmp/#sql_bd4_0.MYI' (Errcode: 30) SQL=SELECT id, title, module, position, content, showtitle, control, params FROM jos_modules AS m LEFT JOIN jos_modules_menu AS mm ON mm.moduleid = m.id WHERE m.published = 1 AND m.access <= 0 AND m.client_id = 0 AND ( mm.menuid = 8 OR mm.menuid = 0 ) ORDER BY position, ordering
  • Error loading Modules:Can't create/write to file '/var/lib/mysql/tmp/#sql_bd4_0.MYI' (Errcode: 30) SQL=SELECT id, title, module, position, content, showtitle, control, params FROM jos_modules AS m LEFT JOIN jos_modules_menu AS mm ON mm.moduleid = m.id WHERE m.published = 1 AND m.access <= 0 AND m.client_id = 0 AND ( mm.menuid = 8 OR mm.menuid = 0 ) ORDER BY position, ordering
  • Error loading Modules:Can't create/write to file '/var/lib/mysql/tmp/#sql_bd4_0.MYI' (Errcode: 30) SQL=SELECT id, title, module, position, content, showtitle, control, params FROM jos_modules AS m LEFT JOIN jos_modules_menu AS mm ON mm.moduleid = m.id WHERE m.published = 1 AND m.access <= 0 AND m.client_id = 0 AND ( mm.menuid = 8 OR mm.menuid = 0 ) ORDER BY position, ordering
  • Error loading Modules:Can't create/write to file '/var/lib/mysql/tmp/#sql_bd4_0.MYI' (Errcode: 30) SQL=SELECT id, title, module, position, content, showtitle, control, params FROM jos_modules AS m LEFT JOIN jos_modules_menu AS mm ON mm.moduleid = m.id WHERE m.published = 1 AND m.access <= 0 AND m.client_id = 0 AND ( mm.menuid = 8 OR mm.menuid = 0 ) ORDER BY position, ordering
  • Error loading Modules:Can't create/write to file '/var/lib/mysql/tmp/#sql_bd4_0.MYI' (Errcode: 30) SQL=SELECT id, title, module, position, content, showtitle, control, params FROM jos_modules AS m LEFT JOIN jos_modules_menu AS mm ON mm.moduleid = m.id WHERE m.published = 1 AND m.access <= 0 AND m.client_id = 0 AND ( mm.menuid = 8 OR mm.menuid = 0 ) ORDER BY position, ordering
  • Error loading Modules:Can't create/write to file '/var/lib/mysql/tmp/#sql_bd4_0.MYI' (Errcode: 30) SQL=SELECT id, title, module, position, content, showtitle, control, params FROM jos_modules AS m LEFT JOIN jos_modules_menu AS mm ON mm.moduleid = m.id WHERE m.published = 1 AND m.access <= 0 AND m.client_id = 0 AND ( mm.menuid = 8 OR mm.menuid = 0 ) ORDER BY position, ordering

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.

Download

Results 1 - 1 of 1