Response of a finite beam on a tensionless Pasternak foundation under symmetric and asymmetric loading

Coşkun, İrfan; Engin, Hasan; Özmutlu, Aydin

doi:10.12989/sem.2008.30.1.021

Cited by 12 publications

(2 citation statements)

References 30 publications

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“…e solutions of equation ( 3) can be divided into three cases, which are ρ > 1, ρ � 1, and ρ < 1. e condition of ρ < 1 satisfies most projects, which is also proved in the following parameter analysis and calculation of engineering examples [26]. Considering the boundary condition (1), the solution of the differential equation ( 3) can be expressed [28][29][30]. In the AO section, the frost heave deformation is 0, and the solution of equation ( 3) is…”

Section: Model Solutionmentioning

confidence: 85%

Longitudinal Deformation Model and Parameter Analysis of Canal Lining under Nonuniform Frost Heave

Dong

Ren

et al. 2021

Advances in Materials Science and Engineering

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Due to the unique hydrothermal environments, the frost heave failure of the concrete lining of water conveyance canals in cold regions is still frequent. The deformation of lining after frost heaving and the stress distribution calculated by the mechanical model can be the reference for the lining design. However, previous research mainly focused on the mechanical model of the cross-section while having little attention for the longitudinal nonuniform frost heave damage. In this study, a mechanical model of the bottom lining under the nonuniform frost heave deformation is built based on the Euler–Bernoulli beam and the Pasternak foundation model, and the analytical solution of the model is obtained. The internal stress of the lining is analyzed during the changes of subgrade coefficient, shear rigidity, transition section length, and frost heave amount inside the model. Also, the calculation process is proved to be correct. The result shows that dangerous cross-sections are at the start and the end of the transition sections. The maximum normal stress and the tangential stress increase when the subgrade coefficient and the frost heave amount increase and the shear modulus and transition section length decrease. The frost heave amount in the frozen ground subgrade increases constantly, while the temperature decreases, but at the same time, the shear rigidity of the subgrade increases with it. The former increases the stress of lining, and the latter decreases it. Therefore, during the frost heaving process, the internal force of lining is coupled with these two elements. By analyzing a water conveyance canal lining under the nonuniform frost heave in the Xinjiang Tarim irrigation district, the maximum normal stress of the dangerous lining cross-section is greater than its tensile strength when the transition section length smaller than 7 m at the frost heave amount is 0.031 m.

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Section: Model Solutionmentioning

confidence: 85%

Longitudinal Deformation Model and Parameter Analysis of Canal Lining under Nonuniform Frost Heave

Dong

Ren

et al. 2021

Advances in Materials Science and Engineering

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“…Due to these reasons the number of the publications on a two-parameter foundation model that reacts in compression only is very limited. Rings, beams and plates resting on a twoparameter foundation are investigated by Güler (2004), Celep et al (2005), Co kun et al (2008 and Ma et al (2009). Nonlinear oscillations take place, when the external loads depend on time.…”

Section: Introductionmentioning

confidence: 99%

Response of a completely free beam on a tensionless Pasternak foundation subjected to dynamic load

Celep¹,

Güler²,

Demir³

2011

Structural Engineering and Mechanics

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Static and dynamic responses of a completely free elastic beam resting on a two-parameter tensionless Pasternak foundation are investigated by assuming that the beam is symmetrically subjected to a uniformly distributed load and concentrated load at its middle. Governing equations of the problem are obtained and solved by paying attention on the boundary conditions of the problem including the concentrated edge foundation reaction in the case of complete contact and lift-off condition of the beam in a two-parameter foundation. The nonlinear governing equation of the problem is evaluated numerically by adopting an iterative procedure. Numerical results are presented in figures to demonstrate the non-linear behavior of the beam-foundation system for various values of the parameters of the problem comparatively by considering the static and dynamic loading cases.

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Thermally stressed thermoelectric microbeam supported by Winkler foundation via the modified Moore–Gibson–Thompson thermoelasticity theory

2023

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This article offers the first investigation into the thermoelectric vibration of microscale Euler‐Bernoulli beams resting on an elastic Winkler base. We developed the system of equations for thermoelastic microbeams using elastic basis theory and the generalized Moore–Gibson–Thompson (MGT) thermal transport framework with a single‐phase delay. At the front of the microbeam, a graphene strip connected to an electrical power source was employed to generate heat. In addition, the influence of an ultra‐short‐pulsed laser on the vibration of a microbeam is studied, taking into account its heating effect. The microbeam system variables were analyzed after solving the mathematical equations by applying the Laplace transform technique. Graphs showing how different inputs affect different mechanical fields, such as Winkler substrate stiffness, voltage, electrical resistance, and temperature modulus pulses, are also presented. An increase in the Winkler modulus and the shear modulus of the foundation was found to decrease the amount of deflection and axial deformation in the microbeams. The increased beam stiffness has resulted in this decrease.

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Response of a finite beam on a tensionless Pasternak foundation under symmetric and asymmetric loading

Cited by 12 publications

References 30 publications

Longitudinal Deformation Model and Parameter Analysis of Canal Lining under Nonuniform Frost Heave

Longitudinal Deformation Model and Parameter Analysis of Canal Lining under Nonuniform Frost Heave

Response of a completely free beam on a tensionless Pasternak foundation subjected to dynamic load

Thermally stressed thermoelectric microbeam supported by Winkler foundation via the modified Moore–Gibson–Thompson thermoelasticity theory

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