Calculation of Foundation Mesh Slabs on an Elastic Layer

Bosakov S., Kozunova O.

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https://doi.org/10.35579/2076-6033-2020-12-01

ABSTRACT


In this work, the authors have developed the procedure for calculation of mesh slabs on an elastic base modeled by an elastic homogeneous isotropic layer affected by the external load. The history of development of calculations of structures on an elastic basis demonstrates that, due to the scientific and technical progress, methods for calculation of aforementioned structures were improved and refined. This can be traced on various models of the elastic foundation that were used to simulate real soils in their natural occurrence or in an artificial base when setting up fundamentally new problems of structural analysis.

Variety of practical tasks results in ambiguous modelling of the elastic base. The authors refer to the works of Tarasevich A. N., Kozunova O. V. and Semenyuk S. D. that provide extensive systematic review of elastic base models for calculation of foundation beams, beam and foundation slabs, as well as for calculation of cross tapes for shallow foundations.

The relevance and timeliness of the proposed work is due to the fact that the issues of calculation of mesh slabs and the system of cross tapes on an elastic base have not yet been fully studied. The authors are familiar with the works of M. I. Gorbunov-Posadov, I. A. Simvulidi, G. Ya. Popov, S. D. Semenyuk, S. N. Klepikov, where various approaches are used to conduct the researches in calculation of mesh slabs and spatial monolithic foundations as the system of cross tapes on an elastic base.

The procedure proposed is based on the Ritz variational method and the mixed method of structural mechanics using the Zhemochkin influence functions. To calculate the coefficients of canonical equations and the absolute terms for the mixed method of structural mechanics by way of the Zhemochkin method, the ratios of deflections with the normal restrained in the center of the slab are used in the calculation.

The numerical implementation of the new general-purpose approach is carried out, as an example, for the rectangular foundation slab with holes, symmetrically loaded by the uniformly distributed load, on the elastic uniform isotropic layer. Graphical results of calculations are given, describing the settlements of the foundation mesh slab and the distribution of contact stresses under the slab.

Keywords: foundation mesh slab, elastic base, elastic half-space, elastic uniform isotropic layer, Ritz variational method, Zhemochkin method, mixed method of structural mechanics, influence functions, settlements, contact stresses.

For citation: Bosakov S., Kozunova O. Calculation of foundation mesh slabs on an elastic layer. In: Contemporary Issues of Concrete and Reinforced Concrete: Collected Research Papers. Minsk. Institute BelNIIS. Vol. 12. 2020. pp. 11-27. https://doi.org/10.35579/2076-6033-2020-12-01

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References:

  1. Gorbunov-Posadov M. I. Balki i plity na uprugom osnovanii [Beams and plates on an elastic foundation] Moscow: Stroyizdat, 1949. 238 p. (rus)
  2. Gorbunov-Posadov M. I . and others. Raschet konstruktsiy na uprugom osnovanii [Calculation of structures on an elastic foundation]. Moscow: Stroyizdat, 1984. 680 p. (rus)
  3. Korenev B. G. Voprosy rascheta balok i plit na uprugom osnovanii [Issues of calculation of beams and slabs on an elastic foundation]. Moscow: Stroyizdat, 1954. 231 p. (rus)
  4. Klepikov S. N. Raschet konstruktsiy na uprugom osnovanii [Calculation of structures on an elastic foundation]. Kiev: Budivelnik, 1967. 184 p. (rus)
  5. Razvitiye teorii kontaktnykh zadach v SSSR [Development of the theory of contact problems in the USSR]. Academy of Sciences of the USSR, Institute of Problems in Mechanics; ed. by L. A. Galin. Moscow: Nauka, 1976. 496 p. (rus)
  6. Bosakov S. V. Staticheskiye raschety plit na uprugom osnovanii [Static calculations of plates on an elastic foundation]. Minsk: BNTU, 2002. 128 p. (rus)
  7. Tarasevich A. N. Izgib samonapryazhennykh plit na uprugom osnovanii :dis. … kand. tekhn. nauk : 05.23.17 [Bending of self-stressed plates on an elastic foundation: dis. ... Cand. tech. Sciences: 05.23.17]. Brest, 2001. 125 p. (rus)
  8. Kozunova O. V. Staticheskiy analiz sistemy “balochnaya plita – nelineyno-uprugoye neodnorodnoye osnovaniye” variatsionno-raznostnym metodom: dis. … kand. tekhn. nauk: 05.23.17 [Static analysis of the system “beam slab - nonlinear elastic inhomogeneous base” by the variational-difference method: dis. ... Cand. tech. Sciences: 05.23.17]. Minsk, 2017. 168 p. (rus)
  9. Semenyuk S. D. Zhelezobetonnyye prostranstvennyye fundamenty zhilykh i grazhdanskikh zdaniy na neravnomerno-deformiruyemom osnovanii [Reinforced concrete spatial foundations of residential and civil buildings on unevenly deformable foundations]. Mogilev: BRU, 2003. 269 p. (rus)
  10. Fuss N. I. (1790) Recherches sur un probleme de mecanique. Nova Acta Academiae Scientiarum Imperialis. Petropolis, 1790. Vol. 6 (1788). pp. 172–184.
  11. Winkler E. Die Lehre von der Elasticitaet und Festigkeit. Praga, 1867. 380 p. (de)
  12. Boussinesq I. Applications des patentiels a l’etude de l’equilibre et du movement des solides elastiques. Paris: Gauthiers-Villars, 1885. 721 p. (fr)
  13. Kogan B. I. Tr. HADI. 1953. No. 14. pp. 33-46. (rus)
  14. Bosakov S. V. and others. NTZh: Structural mechanics and calculation of structures. 2018. No. 4. pp. 2–5. (rus)
  15. Aleksandrov, A. V. and others. Osnovy teorii uprugosti i plastichnosti [Fundamentals of the theory of elasticity and plasticity]. Moscow: Higher school, 2002. 400 p. (rus)
  16. Vasilyeva A. B. Differentsialnyye i integralnyye uravneniya, variatsionnoye ischisleniye v primerakh i zadachakh [Differential and integral equations, calculus of variations in examples and problems]. Moscow: Fizmatlit, 2003. 432 p. (rus)
  17. Zhemochkin B. N. Prakticheskiye metody raschetov fundamentnykh balok i plit na uprugom osnovanii [Practical methods for calculating foundation beams and slabs on an elastic foundation]. Moscow: Gosstroyizdat, 1962. 240 p. (rus)
  18. Simvulidi I. A. Raschet inzhenernykh konstruktsiy na uprugom osnovanii [Calculation of engineering structures on an elastic foundation]. Moscow: Higher school, 1987. 576 p. (rus)
  19. Popov G. Ya. News of Higher Educational Institutions. Building and Architecture. 1959. No. 3. pp. 25–33. (rus)
  20. Rzhanitsyn R. A. Stroitelnaya mekhanika [Construction mechanics]. Moscow: Higher school, 1991. 439 p. (rus)
  21. Bosakov S. V. Metod Rittsa v kontaktnykh zadachakh teorii uprugosti [The Ritz method in contact problems of the theory of elasticity]. Brest: BrGTU, 2006. 107 p. (rus)
  22. Bosakov S., Kozunova O. (2019) Development of the Theory of Computation of Pivotally-Connected Beams on an Elastic Foundation Taking into Account Their Physical Nonlinearity. Contemporary Issues of Concrete and Reinforced Concrete: Collected Research Papers. Minsk. Institute BelNIIS. Vol. 11. 2019. pp. 11–24.
  23. Bosakov S. V. and others. Razvitiye teorii rascheta setchatykh plit na uprugom osnovanii [Development of the theory of calculating mesh plates on an elastic foundation]. NTZh: Structural mechanics and calculation of structures. 2020. No. 3. pp. 20–25. (rus)



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ISSN 2076-6033 (Print)

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