Shear stress concentrations in tramway rails: Results from beam theory-based cross-sectional 2D Finite Element analyses

Hasslinger, Patricia; Kurfürst, Aleš; Hammer, Thomas; Fischmeister, Edgar; Hellmich, Christian; Scheiner, Stefan

doi:10.1016/j.engstruct.2019.03.081

Cited by 3 publications

(8 citation statements)

References 52 publications

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“…(184) degenerates to a 2D problem in y and z, which can be solved again by means of the FE method, using four-noded quadrilateral elements and bilinear shape functions, see Ref. [13] for details.…”

Section: Finite Element Method-based Determination Of Displacements Amentioning

confidence: 99%

“…Equation (78) is solved by means of a 2D FE analysis based on isoparametric four-noded quadrilateral finite elements with bilinear shape functions approximating the warping function and the coordinates y and z (for more details, see Refs. [11,13]). This gives access to the primary warping function with respect to the geometrical center, w GC I ðy; zÞ.…”

Section: Actual Beam Deformations-cross-sectional Boundary Value Probmentioning

confidence: 99%

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Sequential 1D/2D Finite Element analyses of tramway rails under bending and restrained torsion, based on the principle of virtual power

Kuttke¹,

Kurfürst²,

Scheiner

et al. 2019

Mechanics of Advanced Materials and Structures

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The increased incidence of fractures in aging tramway rails has motivated the development of a new, efficient numerical tool for studying structural mechanics problems related to such rails. We introduce virtual velocity fields reflecting axial, bending, shear, and torsional deformations, which are then translated, via the principle of virtual power, into corresponding equilibrium conditions. The resulting equations are numerically solved by means of sequential 1D and 2D Finite Element analyses, providing displacement quantities and stress resultants along the beam axis, as well as cross-sectional stress distributions. Finally, the key advantages of this modeling approach, including excellent efficiency and reliability, as well as straightforward applicability to a wide range of cross-sectional shapes and structural settings, are demonstrated via numerical examples. ARTICLE HISTORY

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Section: Finite Element Method-based Determination Of Displacements Amentioning

confidence: 99%

Section: Actual Beam Deformations-cross-sectional Boundary Value Probmentioning

confidence: 99%

Sequential 1D/2D Finite Element analyses of tramway rails under bending and restrained torsion, based on the principle of virtual power

Kuttke¹,

Kurfürst²,

Scheiner

et al. 2019

Mechanics of Advanced Materials and Structures

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“…Both Eqs. (59) and (62) are solved based on a two-dimensional (2D) Finite Element (FE) analysis [43,44], using for that purpose isoparametric four-noded quadrilateral finite elements with bilinear shape functions [30,45], giving, eventually, access to ψ I (y, z) and ψ II (y, z), respectively, and to warping-related cross-sectional quantities such as the center of twist.…”

Section: Computation Of Primary and Secondary Warping Functionsmentioning

confidence: 99%

“…(88) and (89), are inserted into a suitable equilibrium condition, and into a boundary condition reflecting traction-free lateral surfaces, both of which can be expressed in terms of a corresponding weak form, see [28] for details. The latter is again solved by means of a 2D FE analysis, using four-noded quadrilateral elements and bilinear shape functions, see [30] for details.…”

Section: Computation Of Cross-sectional Stress Distributionsmentioning

confidence: 99%

“…In this work, we took a new path towards consideration of elastically supported beams in general, and of tramway rails in particular, tying in with the approach recently published by the present paper's authors [28], where virtual kinematics were introduced reflecting stretching, bending, as well as primary and secondary warping deformations of a beam, and through rigorous application of the principle of virtual power [29] respective equilibrium equations and natural boundary conditions could be derived, including higher-order torsion-related force quantities. Eventually, this mathematical framework was utilized for computing displacement quantities along the longitudinal axis of the beam, and corresponding stress distributions in selected cross sections, both by means of the Finite Element method, see also [30] for further details. In order to extend this approach, elastic foundation-related traction force vectors are introduced, leading to respective extensions in the model-governing equations, see Sect.…”

Section: Introductionmentioning

confidence: 99%

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A principle of virtual power-based beam model reveals discontinuities in elastic support as potential sources of stress peaks in tramway rails

2020

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This paper addresses the question to which extent the stiffness of an elastic foundation in general, and of a discontinuity occurring in the foundation in particular, affects the stresses to which a beam resting on such a foundation is exposed to. This is particularly relevant for tramway rails, where foundation discontinuities may be generated in the course of maintenance works. In the presented work, the underlying mathematical framework was derived based on the principle of virtual power, using a suitable virtual velocity field and a foundation-related traction force vector as input quantities. The resulting mathematical expressions for the virtual powers performed by the internal and external forces were approximated based on Finite Element discretizations, and eventually solved correspondingly, in the format of sequential Finite Element analyses. Numerical studies, performed on a tramway rail-shaped beam, have confirmed that foundation discontinuities indeed induce substantial increases in the stress tensor components, when moving from regions of a high-stiffness foundation to regions of a low-stiffness foundation; as it may occur if specific sections of the tramway network get renewed.

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Feasibility study of calculation methods for tram track stiffness

Dudkin

Mohsin

Sultanov

2023

jour

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Nowadays, design and construction of new urban tramlines require feasibility study of calculation methods for stiffness. A calculation method for tram track stiffness with noise and vibration insulation systems has been developed in this paper. Theoretical analysis of the impact of rail insulation systems on tram-to-slab load transfer has revealed the potential options and factors influencing the choice of a system. The new design method obtained makes it possible to predict the distribution of loads on the load-bearing foundation surface. Different variants of rail/slab load distribution have been determined depending on the mechanical characteristics of rail profiles. Tram track slab stiffness has been calculated for three design models such as rigid surface pavement, bridge structure and foundation slab. The design of the tram track as foundation slab allows calculating slab reinforcement as accurately as possible because the surface pavement takes into account the planned service life and tram flow density in the area under survey.Field experiments have demonstrated a better convergence of theoretical and experimental data when designing the slab as foundation. As a result, a new method for calculating the foundation slab stiffness of a tram track has been proposed taking into account planned service life, tram flow density and other factors.

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Shear stress concentrations in tramway rails: Results from beam theory-based cross-sectional 2D Finite Element analyses

Cited by 3 publications

References 52 publications

Sequential 1D/2D Finite Element analyses of tramway rails under bending and restrained torsion, based on the principle of virtual power

Sequential 1D/2D Finite Element analyses of tramway rails under bending and restrained torsion, based on the principle of virtual power

A principle of virtual power-based beam model reveals discontinuities in elastic support as potential sources of stress peaks in tramway rails

Feasibility study of calculation methods for tram track stiffness

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