Analytical calculation of internal forces in orthotropic plated bridge decks based on the slope-deflection method

The stress-strain state of a small railway bridge with a beam design is considered in the article for the case of offsetting the track panel axis relative to the bridge axis by the value exceeding the limit determined by regulatory documents. The differential equation is considered in the analytical calculation of the behavior parameters and the state of the span under the action of the load. This equation describes the vertical vibrations of the beam and allows considering them as a combination of forced and free vibrations. In numerical modeling, the finite element method is used as the solution procedure. Determining equations of the method contain linear and angular displacements of nodes in the model as unknowns. As a result of the calculations, graphical dependences for normal and horizontal displacements, internal forces, principal and equivalent stresses at various points of the span are obtained. Values are presented that show an increase in bending and torsional forces, as well as in principal stresses when the axis of the railway track is displaced relative to the bridge axis.

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Proposal Of Simplified Way of Applying Wind Load on Circular Cross-Section

IOP Conference Series Materials Science and Engineering ◽

10.1088/1757-899x/1203/3/032075 ◽

2021 ◽

Vol 1203 (3) ◽

pp. 032075

Author(s):

Maciej Wiśniowski

Keyword(s):

Cross Section ◽

Load Distribution ◽

Analytical Calculation ◽

Circular Cross Section ◽

Flow Simulation ◽

Accurate Method ◽

Wind Load ◽

Fe Model ◽

Complicated Model ◽

Internal Forces

Abstract Wind action on circular cross section was described in many publications. It finds an application for flue gas ducts, pipelines, silo or chimneys. This study concentrate on elements with diameter greater than 1m. There are well recognized analytical solutions of static calculation with uses Fourier-series for wind distribution. Although during last 10 years numerical methods of solving problems get more popular, especially among young engineers. For surface structures ability of analytical finding internal forces disappears, and Finish Element Method substitutes analytical calculation. Modelling of wind load in FEM programs cause several problems. Using wind load distribution proposed in Eurocode 1-4, or from laboratory test, it is usually necessary to divide circular cross-section into 32 up to 72 rectangular elements. Applying load in that way is the most accurate method to imitate wind load in FE model. From the other hand that take much time, and requires preparing data about distribution before modelling. Applying wind on complicated model, with many independent parts of piping, for at least 2 load cases cause faults and slows down work. This paper shows and compares a few proposal wind load models for numerical calculation. Those models were built to obtain accurate internal forces in compare to Eurocode procedure. Proposed models offers simplification of Geometry in numerical model, and saves of time. It also helps to make FE mesh become independent from structural nodes, lines or divisions. This paper concern on one case of one Reynolds number, with refers to 2m wide cylinder, wind velocity of 22m/s and surface roughness of steel plate – 0,05 mm. This paper compares different wind load distributions, in terms of required number of division of model, time consuming, precision of results. Author selected one proposal load distribution, with give equivalent internal forces as wind load distribution obtained from Wind Flow simulation (for example CFD method). Proposed model is useful for structural engineers and statics in offer stage of project. With some safety factor it can be also used as wind load as case for detailing cylindrical structures.

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Monte Carlo Modelling of Secondary Electron Yield from Rough Surfaces

Proceedings, annual meeting, Electron Microscopy Society of America ◽

10.1017/s0424820100180860 ◽

1990 ◽

Vol 48 (1) ◽

pp. 422-423

Author(s):

John C. Russ

Keyword(s):

Monte Carlo ◽

Energy Loss ◽

Secondary Electron ◽

Secondary Electron Emission ◽

Analytical Calculation ◽

Mean Free Path ◽

Single Scattering ◽

High Energy ◽

Secondary Electron Yield ◽

Electron Yield

Monte-Carlo programs are well recognized for their ability to model electron beam interactions with samples, and to incorporate boundary conditions such as compositional or surface variations which are difficult to handle analytically. This success has been especially powerful for modelling X-ray emission and the backscattering of high energy electrons. Secondary electron emission has proven to be somewhat more difficult, since the diffusion of the generated secondaries to the surface is strongly geometry dependent, and requires analytical calculations as well as material parameters. Modelling of secondary electron yield within a Monte-Carlo framework has been done using multiple scattering programs, but is not readily adapted to the moderately complex geometries associated with samples such as microelectronic devices, etc.This paper reports results using a different approach in which simplifying assumptions are made to permit direct and easy estimation of the secondary electron signal from samples of arbitrary complexity. The single-scattering program which performs the basic Monte-Carlo simulation (and is also used for backscattered electron and EBIC simulation) allows multiple regions to be defined within the sample, each with boundaries formed by a polygon of any number of sides. Each region may be given any elemental composition in atomic percent. In addition to the regions comprising the primary structure of the sample, a series of thin regions are defined along the surface(s) in which the total energy loss of the primary electrons is summed. This energy loss is assumed to be proportional to the generated secondary electron signal which would be emitted from the sample. The only adjustable variable is the thickness of the region, which plays the same role as the mean free path of the secondary electrons in an analytical calculation. This is treated as an empirical factor, similar in many respects to the λ and ε parameters in the Joy model.

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Mean-field analytical calculation of the segregation profile around grain boundaries and free surfaces in binary alloys

Philosophical Magazine A ◽

10.1080/014186100300012607 ◽

2000 ◽

Vol 80 (12) ◽

pp. 2871-2897

Author(s):

I. P. Antoniades, G. L. Bleris

Keyword(s):

Grain Boundaries ◽

Binary Alloys ◽

Mean Field ◽

Analytical Calculation ◽

Free Surfaces ◽

Segregation Profile

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A novel analytical calculation of magnetic field in the slotted air gap of spoke-type permanent-magnet machines using conformal mapping

International Journal of Applied Electromagnetics and Mechanics ◽

10.3233/jae-201505 ◽

2020 ◽

pp. 1-15

Author(s):

Jianqi Li ◽

Yu Zhou ◽

Jianying Li

Keyword(s):

Magnetic Field ◽

Conformal Mapping ◽

Permanent Magnet ◽

Flux Density ◽

Analytical Method ◽

Electromotive Force ◽

Analytical Calculation ◽

Air Gap ◽

Permanent Magnet Machines ◽

Peak Value

This paper presented a novel analytical method for calculating magnetic field in the slotted air gap of spoke-type permanent-magnet machines using conformal mapping. Firstly, flux density without slots and complex relative air-gap permeance of slotted air gap are derived from conformal transformation separately. Secondly, they are combined in order to obtain normalized flux density taking account into the slots effect. The finite element (FE) results confirmed the validity of the analytical method for predicting magnetic field and back electromotive force (BEMF) in the slotted air gap of spoke-type permanent-magnet machines. In comparison with FE result, the analytical solution yields higher peak value of cogging torque.

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Produktivkraft als Versprechen

PROKLA Zeitschrift für kritische Sozialwissenschaft ◽

10.32387/prokla.v46i185.135 ◽

2016 ◽

Vol 46 (185) ◽

pp. 621-638 ◽

Cited By ~ 3

Author(s):

Christian Siefkes

Keyword(s):

Private Consumption ◽

Minor Role ◽

Progressive Reduction ◽

Internal Forces ◽

A Minor

The ‘Fragment on Machines’ from Marx’s Grundrisse is often cited as an argument that the internal forces of capitalism will lead to its doom. But the argument that the progressive reduction of labor must doom capitalism lacks a proper foundation, as a comparison with the ‘Schemes of Reproduction’ given in Capital II shows. The latter, however, aren’t fully convincing either. In reality, more depends on the private consumption of capitalists than either model recognizes. Ultimately, most can be made of the ‘Fragment on Machines’ by reading it not as an exposure of capitalism’s internal contractions, but as a discussion of a possible communist future where labor (or work) will play but a minor role.

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