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Analysis of Beams on Pasternak Foundation Using Quintic Displacement Functions

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Abstract

Beams supported by elastic foundations one of the complex soil-structure interaction problems and analysis carried out using the concept of “beam on elastic foundation” approach. The structural foundation and the soil continuum must act together to support the loads. Developing more realistic foundation models and simplified methods are very important for safe and economical design of such type of structure. In the present study, a first order continuity three nodded beam based on Euler–Bernoulli assumptions and a workable approach for the analysis of beams on Pasternak foundation is attempted. A Matlab code is developed for present formulation. The results, thus obtained, are compared with similar studies done by other researchers, which show very good conformity. Parametric studies are carried out to obtain response for different loading conditions, boundary conditions and foundation parameter.It is concluded that the present formulation has rapid convergence regardless of boundary conditions, aspect ratio and foundation parameters. It behaves extremely well for Euler–Bernoulli beams effectively and efficiently. The effect of the soil coefficient on the response of beams on two parameter elastic foundation is generally larger than that of beam physical and material property.

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Code Availability

MATLAB 2011b, MathWorks Inc, 2011.

Availability of Data and Materials

Data supporting the result reported in the article: Parvanova, S. (2011). Lectures notes: Structural analysis II, Bulgaria: University of Architecture, Civil Engineering Geodesy, Sofia. Chen, W.Q., LÜ, C. F., and Bian, Z.G. A mixed method for bending and free vibration of beams resting on a Pasternak elastic foundation, Applied Mathematical Modelling 28 (2004) 877–890.

Abbreviations

EBBT:

Euler–Bernoulli beam theory

DOF:

Degree of freedom

C:

Clamped or fixed end

S:

Simply supported end

F:

Free end

PS:

Present study

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Authors and Affiliations

  1. Department of Construction Engineering, Jadavpur University, Salt Lake, Kolkata, 700098, India

    Ashis Kumar Dutta & Debasish Bandyopadhyay

  2. Department of Civil Engineering, National Institute of Technical Teachers’ Training and Research, Kolkata, 700106, India

    Jagat Jyoti Mandal

Authors
  1. Ashis Kumar Dutta
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  2. Jagat Jyoti Mandal
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  3. Debasish Bandyopadhyay
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Contributions

Ashis Kumar Dutta developed the theory, written the computer code and drafted the manuscript, Jagat Jyoti Mandal scrutinized the manuscript and checked the data analysis and Debasish Bandyopadhyay participated as research coordinator and scrutinized the manuscript. The Authors read and approved the final manuscript.

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Correspondence to Ashis Kumar Dutta.

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Dutta, A.K., Mandal, J.J. & Bandyopadhyay, D. Analysis of Beams on Pasternak Foundation Using Quintic Displacement Functions. Geotech Geol Eng 39, 4213–4224 (2021). https://doi.org/10.1007/s10706-021-01752-9

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  • DOI: https://doi.org/10.1007/s10706-021-01752-9

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