• Title/Summary/Keyword: functions of loading

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Formulating the Local Displacement and Local Moments of a Plate Stiffened with Open Ribs According to the Loading Sizes (재하 크기에 따른 개단면 리브 보강판의 국부 처짐과 국부 모멘트의 정형화)

  • Chu, Seok Beom
    • Journal of Korean Society of Steel Construction
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    • v.25 no.3
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    • pp.267-278
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    • 2013
  • In this study, stiffened plates with open ribs are analyzed to estimate and formulate the local displacement and local moments according to square loading sizes. For the local behaviors of plates stiffened with rectangular and reverse T ribs, the ratio functions according to the dimensions of stiffened plates are obtained at each square loading size. Analytical results show that values of the basic stiffened plates are different but the ratio functions of each square loading size are similar and the difference of the ratio functions between rectangular ribs and reverse T ribs are small, so the ratio functions can be unified by integrating the loading sizes regardless of the rib type. The application of the unioned ratio functions to L type ribs and rectangular loading shows good accuracies. Therefore, the local behaviors of plates stiffened with open ribs can easily be obtained by using the unioned ratio functions proposed in this study.

Non-linear rheology of tension structural element under single and variable loading history Part I: Theoretical derivations

  • Kmet, S.
    • Structural Engineering and Mechanics
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    • v.18 no.5
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    • pp.565-589
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    • 2004
  • The present paper concerns the macroscopic overall description of rheologic properties for steel wire and synthetic fibre cables under variable loading actions according to non-linear creep and/or relaxation theory. The general constitutive equations of non-linear creep and/or relaxation of tension elements - cables under one-step and the variable stress or strain inputs using the product and two types of additive approximations of the kernel functions are presented in the paper. The derived non-linear constitutive equations describe a non-linear rheologic behaviour of the cables for a variable stress or strain history using the kernel functions determined only by one-step - constant creep or relaxation tests. The developed constitutive equations enable to simulate and to predict in a general way non-linear rheologic behaviour of the cables under an arbitrary loading or straining history. The derived constitutive equations can be used for the various tension structural elements with the non-linear rheologic properties under uniaxial variable stressing or straining.

The Local Behavior Characteristics of a Plate Stiffened with Closed Ribs (폐단면 리브 보강판의 국부 거동 특성)

  • Chu, Seok Beom
    • Journal of Korean Society of Steel Construction
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    • v.26 no.4
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    • pp.277-288
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    • 2014
  • In this study, the local displacement and moment characteristics of a plate stiffened with closed ribs are analyzed according to the dimensions of stiffened plates. The analyzed results of various stiffened plates under square distributed load show that the effect of the loading panel width to the local behavior is dominant but that of the next panel width is very small. And the local behavior of reference stiffened plates can be expressed by the angle between the plate and the rib, and that of other stiffened plates can be obtained by multiplying ratio functions of the loading panel width, plate thickness, rib thickness, rib height and next panel width and they give good results. Applying ratio functions to other loading sizes shows that the applicability of ratio functions except for the loading panel width is proved and the modified ratio functions of the loading panel width improve error ratios. Therefore, the local displacement and moments of a plate stiffened with closed ribs can easily achieve proper results regardless of the dimensions using ratio functions proposed in this study.

Analysis of elastic wave propagation in long beam using Fourier transformation

  • Mohammad Tahaye Abadi
    • Structural Engineering and Mechanics
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    • v.87 no.2
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    • pp.165-172
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    • 2023
  • This paper presents a novel method for modeling elastic wave propagation in long beams. The proposed method derives a solution for the transient transverse displacement of the beam's neutral axis without assuming the separation of variables (SV). By mapping the governing equation from the space domain to the frequency domain using Fourier transformation (FT), the transverse displacement function is determined as a convolution integral of external loading functions and a combination of trigonometric and Fresnel functions. This method determines the beam's response to general loading conditions as a linear combination of the analytical response of a beam subjected to an abrupt localized loading. The proposed solution method is verified through finite element analysis (FEA) and wave propagation patterns are derived for tone burst loading with specific frequency contents. The results demonstrate that the proposed solution method accurately models wave dispersion, reduces computational cost, and yields accurate results even for high-frequency loading.

Probabilistic Fatigue Crack Growth Analysis under Random Loading (불규칙 하중하의 확률론적 피로균열 성장 해석)

  • Song, Sam-Hong;Chang, Doo-Soo
    • Journal of the Korean Society for Precision Engineering
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    • v.11 no.1
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    • pp.192-200
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    • 1994
  • The methodology of a simple probabilistic fatigue crack under random loading is proposed. Using the crack closure concept, the crack opening stress is assumed to be constant during random loading. The loading history was analyzed to determine the probability density functions, probability distribution functions and other related parameters for the probabilistic fatigue crack growth analysis. Fatigue crack growth using the exisiting available data was predicted by the proposed probabilistic analysis and compared with experimental data.

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Application of Variational Method to the Elastic Foundation (변분법에 의한 탄성지반 해석)

  • Lee, Seung-Hyun;Han, Jin-Tae
    • Journal of the Korea Academia-Industrial cooperation Society
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    • v.12 no.10
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    • pp.4642-4647
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    • 2011
  • Solution for elastic foundation of plane strain state was derived by the application of variational method. Functions of the transverse distribution of the displacements for the analysis were chosen as linear functions. Loading conditions considered for the analysis were concentrated load and distributed load. Under the loading condition of the concentrated load, surface displacement was decreased drastically as the distance from the point of the loading increased. Under the loading condition of the distributed load, surface displacements were more uniformly distributed beneath the loading area when the ratio of the half of the loading width to the depth(B/H) of the compressible layer was greater. The surface displacement was more quickly converged from the edge of the loading area as the ratio(B/H) increased.

Modelling the dynamic response of railway track to wheel/rail impact loading

  • Cai, Z.;Raymond, G.P.
    • Structural Engineering and Mechanics
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    • v.2 no.1
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    • pp.95-112
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    • 1994
  • This paper describes the formulation and application of a dynamic model for a conventional rail track subjected to arbitary loading functions that simulate wheel/rail impact forces. The rail track is idealized as a periodic elastically coupled beam system resting on a Winkler foundation. Modal parameters of the track structure are first obtained from the natural vibration characteristics of the beam system, which is discretized into a periodic assembly of a specially-constructed track element and a single beam element characterized by their exact dynamic stiffness matrices. An equivalent frequency-dependent spring coefficient representing the resilient, flexural and inertial characteristics of the rail support components is introduced to reduce the degrees of freedom of the track element. The forced vibration equations of motion of the track subjected to a series of loading functions are then formulated by using beam bending theories and are reduced to second order ordinary differential equations through the use of mode summation with non-proportional modal damping. Numerical examples for the dynamic responses of a typical track are presented, and the solutions resulting from different rail/tie beam theories are compared.

Stress state around cylindrical cavities in transversally isotropic rock mass

  • Lukic, Dragan C.;Prokic, Aleksandar D.;Brcic, Stanko V.
    • Geomechanics and Engineering
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    • v.6 no.3
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    • pp.213-233
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    • 2014
  • The present paper is dealing with the investigation of the stress field around the infinitely long cylindrical cavity, of a circular cross section, contained in the transversally isotropic elastic continuum. Investigation is based upon the determination of the stress function that satisfies the biharmonic equation, for the given boundary conditions and for rotationaly symmetric loading. The solution of the partial differential equation of the problem is given in the form of infinite series of Bessel's functions. Determination of the stress-strain field around cavities is a common requirement for estimation of safety of underground rock excavations.

Experiment study of structural random loading identification by the inverse pseudo excitation method

  • Guo, Xing-Lin;Li, Dong-Sheng
    • Structural Engineering and Mechanics
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    • v.18 no.6
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    • pp.791-806
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    • 2004
  • The inverse pseudo excitation method is used in the identification of random loadings. For structures subjected to stationary random excitations, the power spectral density matrices of such loadings are identified experimentally. The identification is based on the measured acceleration responses and the structural frequency response functions. Numerical simulation is used in the optimal selection of sensor locations. The proposed method has been successfully applied to the loading identification experiments of three structural models, two uniform steel cantilever beams and a four-story plastic glass frame, subjected to uncorrelated or partially correlated random excitations. The identified loadings agree quite well with actual excitations. It is proved that the proposed method is quite accurate and efficient in addition to its ability to alleviate the ill conditioning of the structural frequency response functions.