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

• Main Authors: Kurbatskiy Evgeniy Nikolaevich, Mai Duc Minh.
• Format: Article
• Language: English
• Published: Moscow State University of Civil Engineering (MGSU) 2014-01-01
• Series: Vestnik MGSU
• Subjects: finite function; Winkler elastic foundation; foundation calculation; beam; elastic foundation; elastic features; Fourier transform
• Online Access: http://vestnikmgsu.ru/files/archive/issues/2014/1/ru/5.pdf

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 famous 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.