Formulas for an Infinitely Long Bernoulli-Euler Beam on the Pasternak Model

Tanahashi, Hideaki

doi:10.3208/sandf.44.5_109

Cited by 112 publications

(46 citation statements)

References 11 publications

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“…It proved that the stresses decrease to some extent owing to the shear rigidity. However, Pasternak's solution was only for a limited case; thus, Tanahashi gave a complete set of formulas for an infinitely long Bernoulli‐Euler Beam on a Pasternak Model and showed the differences in stresses depending on the shear rigidity.…”

Section: Mechanical Models Of Embedmentmentioning

confidence: 99%

Review on the mechanical models and formulations of embedment of traditional timber joints in Japan

Tanahashi

Suzuki

2020

Japan Architectural Review

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This paper reviews recent developments of the mechanical models and formulations for the embedment of traditional timber joints in Japan. In recent decades in Japan, seismic performance evaluation methods of traditional timber buildings have been actively researched, and useful findings have been obtained to evaluate the seismic performances of traditional timber buildings such as temples, shrines, and dwelling houses. The major seismic resisting elements of traditional timber buildings in Japan are restoring forces of thick column rocking, rotational resistances of column‐beam joints, and shear resistances of mud/wood walls. Among them, the restoring force of rotational resistances of column‐beam joints due to embedment plays an important role. Such restoring force characteristics depend primarily on the partial compression on continua. However, the partial compression on continua is difficult to analyze owing to the continua. In relation to the partial compression on continua, research results of beams on elastic foundations are reviewed. Subsequently, the recent developments of mechanical models and formulations of the traditional timber joints in Japan are reviewed and problems related to formulations are discussed, and the authors' comments are given.

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Section: Mechanical Models Of Embedmentmentioning

confidence: 99%

Review on the mechanical models and formulations of embedment of traditional timber joints in Japan

Tanahashi

Suzuki

2020

Japan Architectural Review

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“…e vertical displacement y 1 of a half infinitely long beam on the Pasternak model in the two-dimensional plain strain condition can be expressed as follows [14][15][16]:…”

Section: Calculation Model For the Buried Pipeline As Shown Inmentioning

confidence: 99%

“…e Pasternak model is called the "two-parameter model" as it includes the coefficient of the subgrade reaction and shear modules of the soil. Tanahashi [14] presented a set of equations to estimate the displacements and stress on an infinitely long Bernoulli-Euler beam using the Pasternak model.…”

Section: Introductionmentioning

confidence: 99%

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Analysis of Longitudinal Mechanical Properties of Buried Suspended Pipeline Resisting Collapse

Lin

Yanping

Liu

et al. 2019

Advances in Civil Engineering

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Ground subsidence caused by collapse leads to suspension or subsidence of the pipe, resulting in the stress concentration. It is a significant factor being a threat to safe operation of the pipeline. Based on Pasternak’s beam-on-elastic-foundation theory, this study presents a mechanical model of interaction between the buried suspended pipeline and the soil, which considers the effect of the beam width. The pipeline was modeled as a buried part and a suspended part. According to the compatibility conditions of suspended and nonsuspended parts, this paper solved differential equations describing the deflection of pipeline and derived the formulas of deflection and internal force. This solution involves whole cases of the Pasternak model. Connecting to the pipeline operation status, the formulas of piping stress were deduced by piping stress analysis. Meanwhile, piping stress analysis can define the scope of application of the model. Compared with the measured values and results of the Winkler model, the calculated results of the Pasternak model are more accurate and suitable for predicting the behavior of the pipeline in the limit state. In addition, according to normalized analysis of main affecting factors which comprise the pipe material, pipe dimension, pipe depth, and length of collapse, it was also found that the length of collapse dominates the stability of the pipeline.

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“…Despite the development of numerous commercial finite-element (FE) software, renewed interest in this topic of analytical foundation modeling is on the rise recently (Avramidis and Morfidis, 2006;Colasanti and Horvath, 2010;Failla et al, 2013;Horvath and Colasanti, 2011;Tanahashi, 2004;Wang et al, 2005;Worku, 2010;Worku and Degu, 2010;Worku, 2013;Yin, 2000). This could be attributed to a number of reasons including the mesh dependence of FE modeling, lack of accurate geotechnical data for use in advanced constitutive relationships, relative difficulty to use FE models to solve routine problems in design offices like modeling the soil and structure together as a unit, and need for controlling FE analysis results.…”

Section: Introductionmentioning

confidence: 99%

Development of a calibrated Pasternak foundation model for practical use

Worku

2013

International Journal of Geotechnical Engineering

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A calibrated continuum foundation model of the order same as those of Pasternak, Filonenko-Borodich, and Vlasov is developed. This is achieved by seeking equality of the surface deformation of a Pasternak-type model with that of a calibrated Kerr-type model presented recently without neglecting any stress, strain, or deformation component in the continuum. In order to alleviate the sensitiveness of the model parameters to the layer thickness, this is eliminated from the corresponding expressions through the introduction of a dimensionless calibration parameter. The superiority of the new model over existing models of similar order has been demonstrated. Closed-form calibrated relationships for the two parameters of the new model are provided together with values of the calibration factor. The use of the model is illustrated on a basic problem of a beam on an elastic foundation. As a Pasternak-type model is more familiar to engineers and much easier to handle in applications than a Kerr-type model, its use in practice is recommended. The new model completes a series of calibrated models at three different levels: Winkler, Pasternak, and Kerr as proposed recently by the author.

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Formulas for an Infinitely Long Bernoulli-Euler Beam on the Pasternak Model

Cited by 112 publications

References 11 publications

Review on the mechanical models and formulations of embedment of traditional timber joints in Japan

Review on the mechanical models and formulations of embedment of traditional timber joints in Japan

Analysis of Longitudinal Mechanical Properties of Buried Suspended Pipeline Resisting Collapse

Development of a calibrated Pasternak foundation model for practical use

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