• Structural Engineering and Mechanics
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• v.73 no.1
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• pp.83-95
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• 2020

In this work, a mathematical model of beam-column system carrying a double eccentric end mass system is investigated, and solved analytically based on the exact solution analysis. The model considers the case in which the double eccentric end mass is a rigid storage tank containing fluid. Both Timoshenko and Bernoulli-Euler beam bending theories are considered. Equation of motion, general solution and boundary conditions for the present system model are developed and presented in dimensional and non-dimensional format. Several important non-dimensional design parameters are introduced. Symbolic and/or explicit formulae of the frequency and mode shape equations are formulated. To the authors knowledge, the present reduced closed form symbolic and explicit frequency equations have not appeared in literature. For different applications, the results are validated using commercial finite element package, namely ANSYS. The beam-column system investigated in this paper is significant for many engineering applications, especially, in mechanical and structural systems.

• Structural Engineering and Mechanics
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• v.52 no.1
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• pp.173-203
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• 2014

The cross-section warping due to the passage of high-speed trains can be a relevant issue to consider in the dynamic analysis of bridges due to (i) the usual layout of railway systems, resulting in eccentric moving loads; and (ii) the use of cross-sections prone to warping deformations. A thin-walled beam formulation for the dynamic analysis of bridges including the cross section warping is presented in this paper. Towards a numerical implementation of the beam formulation, a finite element with seven degrees of freedom is proposed. In order to easily consider the compatibility between elements, and since the coupling between flexural and torsional effects occurs in non-symmetric cross-sections due to dynamic effects, a single axis is considered for the element. The coupled flexural-torsional free vibration of thin-walled beams is analysed through the presented beam model, comparing the results with analytical solutions presented in the literature. The dynamic analysis due to an eccentric moving load, which results in a coupled flexural-torsional vibration, is considered in the literature by analytical solutions, being therefore of a limited applicability in practice engineering. In this paper, the dynamic response due to an eccentric moving load is obtained from the proposed finite element beam model that includes warping by a modal analysis.

• Structural Engineering and Mechanics
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• v.8 no.1
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• pp.85-102
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• 1999

With the advent of computer, the finite element method has become a most powerful numerical method for structural analysis. However, bridge designers are reluctant to use it in their designs because of its complex nature and its being time consuming in the preparation of the input data and analyzing the results. This paper describes the development of a computer based finite element model using the idea of eccentric beam elements for the analysis of slab-on-girder bridges. The proposed method is supported by a laboratory test using a reinforced concrete bridge model. Other bridge analytical schemes are also introduced and compared with the proposed method. The main aim of the comparison is to prove the effectiveness of the shell and eccentric beam modelling in the studies of lateral load distribution of slab-on-girder bridges. It is concluded that the proposed finite element method gives a closer to real idealization and its developed computer program, SHECAN, is also very simple to use. It is highly recommended to use it as an analytical tool for the design of slab-on-girder bridges.

• Earthquakes and Structures
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• v.15 no.2
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• pp.145-153
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• 2018

Extensive reinforced concrete interior beam-column joints with beams of different depths have been used in large industrial buildings and tall building structures under the demand of craft or function. The seismic behavior of the joint, particularly the relationship between deformation and strength in the core region of these eccentric reinforced concrete beam-column joints, has rarely been investigated. This paper performed a theoretical study on the effects of geometric features on the shear strength of the reinforced concrete interior beam-column joints with beams of different depths, which was critical factor in seismic behavior. A new model was developed to analyze the relationship between the shear strength and deformation based on the Equivalent Strut Mechanism (ESM), which combined the truss model and the diagonal strut model. Additionally, this paper developed a simplified calculation method to estimate the shear strength of these type eccentric joints. The accuracy of the model was verified as the modifying analysis data fitted to the test results, which was a loading test of 6 eccentric joints conducted previously.

• Steel and Composite Structures
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• v.35 no.1
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• pp.13-27
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• 2020

To investigate the stress-strain relation of PVC-FRP Confined Concrete (PFCC) column with RC ring beam joint subjected to eccentric compression, the experiment of 13 joint specimens, which were designed with principle of "strong joint and weak column", were presented. Several variable parameters, such as reinforcement ratio, width and height of ring beam, FRP strips spacing and eccentricity, were considered. The specimens were eventually damaged by the crushing of concrete, the fracture of PVC tube and several FRP strips. With the FRP strips spacing or eccentricity increased, the ultimate carrying capacity of specimens declined. The strain of FRP strips and axial strain of PVC tube decreased as FRP strips spacing decreased. The decrease of eccentricity would slow down the development of strain of FRP strips and axial strain of PVC tube. The slope of stress-strain curve of PFCC column decreased as FRP strips spacing or eccentricity increased. The ultimate strain of PFCC column reduced as FRP strips spacing increased, while the effect of eccentricity on the ultimate strain of PFCC was not distinct. Considering the influence of eccentricity on the stress-strain relation, a modified stress-strain model for conveniently predicting the weak PFCC column and strong RC ring beam joint under eccentric compression was proposed and it was in good agreement with the experimental data.

• Structural Engineering and Mechanics
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• v.57 no.6
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• pp.989-1014
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• 2016

This paper deals with the analysis of the natural frequencies, mode shapes of an axially loaded beam system carrying ends consisting of non-concentrated tip masses and three spring-two mass sub-systems. The influence of system design and sub-system parameters on the combined system characteristics is the major part of this investigation. The effect of material properties, rotary inertia and shear deformation of the beam system is included. The end masses are elastically supported against rotation and translation at an offset point from the point of attachment. Sub-systems are attached to center of gravity eccentric points out of the beam span. The boundary conditions of the ordinary differential equation governing the lateral deflections and slope due to bending of the beam system including developed shear force frequency dependent terms, due to the sub.system suspension, have been formulated. Exact formulae for the modal frequencies and the modal shapes have been derived. Based on these formulae, detailed parametric studies are carried out. The geometrical and mechanical parameters of the system under study have been presented in non-dimensional analysis. The applied mathematical model is presented to cover wide range of mechanical, naval and structural engineering applications.

• Structural Engineering and Mechanics
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• v.58 no.3
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• pp.515-532
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• 2016

The elastoplastic response of functionally graded material (FGM) beams resting on a nonlinear elastic foundation to an eccentric axial load is investigated by using the finite element method. The FGM is assumed to be formed from ceramic and metal phases with their volume fraction vary in the thickness direction by a power-law function. A bilinear elastoplastic behavior is assumed for the metallic phase, and the effective elastoplastic properties of the FGM are evaluated by Tamura-Tomota-Ozawa (TTO) model. Based on the classical beam theory, a nonlinear finite beam element taking the shift in the neutral axis position into account is formulated and employed in the investigation. An incremental-iterative procedure in combination with the arc-length control method is employed in computing the equilibrium paths of the beams. The validation of the formulated element is confirmed by comparing the equilibrium paths obtained by using the present element and the one available in the literature. The numerical results show that the elastoplastic post-buckling of the FGM beams is unstable, and the post-buckling strength is higher for the beams associated with a higher ceramic content. Different from homogeneous beams, yielding in the FGM beam occurs in the layer near the ceramic layer before in the layer near metal surface. A parametric study is carried out to highlight the effect of the material distribution, foundation support and eccentric ratio on the elastoplastic response of the beams.

• Interaction and multiscale mechanics
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• v.5 no.2
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• pp.91-104
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• 2012

There is relatively little numerical study on the behavior of eccentrically loaded high strength rectangular concrete-filled steel tubular (CFST) slender beam-columns with large depth-to-thickness ratios, which may undergo local and global buckling. This paper presents a multiscale numerical model for simulating the interaction local and global buckling behavior of high strength thin-walled rectangular CFST slender beam-columns under eccentric loading. The effects of progressive local buckling are taken into account in the mesoscale model based on fiber element formulations. Computational algorithms based on the M$\ddot{u}$ller's method are developed to obtain complete load-deflection responses of CFST slender beam-columns at the macroscale level. Performance indices are proposed to quantify the performance of CFST slender beam-columns. The accuracy of the multiscale numerical model is examined by comparisons of computer solutions with existing experimental results. The numerical model is utilized to investigate the effects of concrete compressive strength, depth-to-thickness ratio, loading eccentricity ratio and column slenderness ratio on the performance indices. The multiscale numerical model is shown to be accurate and efficient for predicting the interaction buckling behavior of high strength thin-walled CFST slender beam-columns.

• Journal of the Society of Naval Architects of Korea
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• v.28 no.2
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• pp.307-317
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• 1991

A displacement-based finite element method is presented for the geometrically nonlinear analysis of eccentrically stiffened plates. The nonlinear degenerated shell and eccentric isobeam(isoparametric beam) elements are formulated on the basis of total Lagrangian and updated Lagrangian descriptions. To describe the stiffener's local plate buckling mode, some additional local degrees of freedom are used in the eccentric isobeam element. The eccentric isobeam element can be affectively employed to model the eccentric stiffener just like the case of the degenerated shell element. A detailed nonlinear analysis including the effects of stiffener's eccentricity is performed to estimate the critical load and the post buckling behaviour of an eccentrically stiffened plate. The critical buckling loads are found higher than analytic plate buckling load but lower than Euler buckling load which are the buckling strength requirements of classification society.

• Steel and Composite Structures
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• v.18 no.4
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• pp.853-871
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• 2015

Up to now, Japan has more than 200 corrugated steel web composite beam bridges which are under construction and have been constructed, and China has more than 30 corrugated steel web composite beam bridges. The bridge type includes the simply supported beam, continuous beam, continuous rigid frame and cable stayed bridge etc. The section form has developed to the single box and multi-cell box girder from the original single box and single chamber. From the stress performance and cost saving, the span range of 50~150 m is the most competitive. At present, the design mostly adopts the computational analytical method combining the spatial bar system model, plane beam grillage model and solid model. However, the spatial bar system model is short of the refinement analysis on the space effect, such as the shear lag effect, effective distribution width problem, and eccentric load factor problem etc. Due to the similarity of the plane beam grillage method in the equivalence principle, it cannot accurately reflect the shearing stress distribution and local stress of the top and bottom plates of the box type composite beam. The solid model is very difficult to combine with the overall calculation. Moreover, the spatial grid model can achieve the refinement analysis, with the integrity of the analysis and the comprehensiveness of the stress checking calculation, and can make up the deficiency of the analytical method currently. Through the example verification of the solid model and spatial grid model, it can be seen that the calculation results for the stress and the displacement of two models are almost consistent, indicating the applicability and precision of the spatial grid model.