• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2000.06a
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• pp.689-694
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• 2000

This paper presents a modeling method for the vibration analysis of cantilever beams with an elastically restrained root. Mass and stiffness matrices are derived explicitly by considering the elastically restrained root coupling effect between stretching and bending motion. Numerical results show that the two effects influence the vibration characteristics of rotating beams significantly. The results also present the magnitude of the elastic stiffness of the root to avoid the dynamic buckling. The method presented in this paper can be used to provide accurate predictions of the variations of natural frequencies of rotating beams with an elastically restrained root.

• Nuclear Engineering and Technology
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• v.52 no.5
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• pp.1066-1078
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• 2020

The present paper describes an analytic solution procedure for flexural vibration of a rotationally restrained hinged-hinged Timoshenko beam at the supports during an earthquake. Focusing on maximal magnitudes of internal loads such as bending moment and shearing force under wide variations of two parameters, kL/EI and kGAL²/EI, various beams under synchronous and asynchronous support motions are simulated. The simulations under asynchronous support motions show the following facts. The variations of the maximal magnitudes of internal loads of stocky beams due to the variation of kL/EI from zero to infinity show much wider variations than those of slender beams as kGAL²/EI decreases. The maximal magnitudes of internal loads of a beam tend to be governed by their static components as kL/EI increases and kGAL²/EI decreases. When the internal loads are governed by their static components, maximal magnitudes of internal loads of the stocky tend to increase monotonically as the value of kL/EI increases. However, the simulations under synchronous support motions show the static components of the internal loads vanish and the internal loads are governed by dynamic components irrespective of the two parameters.

• Nuclear Engineering and Technology
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• v.52 no.12
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• pp.2939-2948
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• 2020

This paper presents an analytic solution procedure of the rotationally restrained hinged-hinged beam subjected to transverse motions at supports based on EBT (Euler-Bernoulli beam theory). The EBT solutions are compared with the solutions based on TBT (Timoshenko beam theory) for a wide range of the rotational restraint parameter (kL/EI) of slender beams whose slenderness ratio is greater than 100. The comparison shows the followings. The internal loads such as bending moment and shearing force of an extremely thin beam obtained by EBT show a good agreement with those obtained by TBT. But the discrepancy between two solutions of internal loads tends to increase as the slenderness ratio decreases. A careful examination shows that the discrepancy of the internal loads originates from their dynamic components whereas their static components show a little difference between EBT and TBT. This result suggests that TBT should be employed even for slender beams to consider the rotational effect and the shear deformation effect on dynamic components of the internal loads. The influence of the parameter on boundary conditions is examined by manipulating the spring stiffness from zero to a sufficiently large value.

• Journal of the Korean Society of Manufacturing Process Engineers
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• v.10 no.3
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• pp.79-86
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• 2011

The dynamic instability and natural frequency of elastically restrained pipe conveying fluid with the attached mass and crack are investigated. The pipe system with a crack is modeled by using extended Hamilton's Principle with consideration of bending energy. The crack on the pipe system is represented by a local flexibility matrix and two undamaged beam segments are connected. In this paper, the influence of attached mass, its position and crack on the dynamic stability of a elastically restrained pipe system is presented. Also, the critical flow velocity for the flutter and divergence due to the variation in the position and stiffness of supported spring is studied. Finally, the critical flow velocities and stability maps of the pipe conveying fluid with the attached mass are obtained by the changing parameters.

• Steel and Composite Structures
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• v.4 no.1
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• pp.23-36
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• 2004

The inelastic lateral-distortional buckling of doubly-symmetric hot-rolled I-section beam-columns subjected to a concentric axial force and uniform bending with elastic restraint which produce single curvature is investigated in this paper. The numerical model adopted in this paper is an energy-based method which leads to the incremental and iterative solution of a fourth-order eigenproblem, with very rapid solutions being obtained. The elastic restraint considered in this paper is full restraint against translation, but torsional restraint is permitted at the tension flange. Hitherto, a numerical method to analyse the elastic and inelastic lateral-distortional buckling of restrained or unrestrained beam-columns is unavailable. The prediction of the inelastic lateral-distortional buckling load obtained in this study is compared with the inelastic lateral-distortional buckling of restrained beams and the inelastic lateral-torsional buckling solution, by suppressing the out-of-plane web distortion, is published elsewhere and they agree reasonable well. The method is then extended to the lateral-distortional buckling of continuously restrained doubly symmetric I-sections to illustrate the effect of web distortion.

• Structural Engineering and Mechanics
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• v.4 no.4
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• pp.383-396
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• 1996

In this paper, the behavior of plates partially restrained against rotation under stress gradient is investigated. As a first stage, an energy formulation is presented to model this boundary condition and a general expression is derived for the prediction of the elastic buckling of the plate under this general loading condition. The accuracy of the derived expression is compared numerically using the Galerkin method with other available data for the two limiting conditions of rotationally free and clamped boundaries. Results show that the prediction is within a 5% difference. The influence of rotational restraint and stress gradient upon the buckling load and the associated buckling mode is investigated. Numerical results show sensitivity of the buckling mode to the degree of rotational restraint and the variation of the buckling load with the stress gradient.

• Earthquakes and Structures
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• v.12 no.4
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• pp.469-478
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• 2017

This paper summarizes estimated seismic response results from three-dimensional nonlinear inelastic time-history analyses of some steel buckling-restrained braced (BRB) structures taking into account soil-structure interaction (SSI). The response results involve mean values for peak interstorey drift ratios, peak interstorey residual drift ratios and peak floor accelerations. Moreover, mean seismic demands in terms of axial force and rotation in columns, of axial and shear forces and bending moment in BRB beams and of axial displacement in BRBs are also discussed. For comparison purposes, three separate configurations of the BRBs have been considered and the aforementioned seismic response and demands results have been obtained firstly by considering SSI effects and then by neglecting them. It is concluded that SSI, when considered, may lead to larger interstorey and residual interstorey drifts than when not. These drifts did not cause failure of columns and of the BRBs. However, the BRB beam may fail due to flexure.

• Computational Structural Engineering
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• v.10 no.1
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• pp.135-148
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• 1997

The main objective of this paper is to analyze the rectangular stiffened plates with two opposite ends elastically restrained and the others simply supported subjected to in-plane bending by Finite Element Method. Another objective is to develope Classical Method analyzing the unstiffened rectangular plates with the above boundary conditions. In order to validate finite element and classical methods, the buckling strengths of the rectangular plates with four simply supported ends, and with two simply supported and the others fixed ends by finite element method and classical method are compared with those of references. In finite element method, elastically restrained ends can be obtained as considering torsional and warping rigidities of end stiffeners. The buckling strengths of the rectangular plates with elastically restrained ends by finite element and classical methods are calculated and compared with each other. In case of stiffened plates, to validate finite element method, the buckling strengths of the rectangular stiffened plates with four simply supported ends, and with two simply supported and the others fixed ends are also compared with those of references. The buckling strengths of the rectangular stiffened plates with elastically restrained ends by finite element method are calculated as solving eigenvalue problems which are obtained as assembling rectangular plate elements and beam elements considered torsional and warping rigidities. The buckling strengths of rectangular stiffened plates according to various positions of rectangular intermediate stiffener, J and I/sub w/ of end stiffeners are also obtained, which are compared to determine the efficient position of intermediate stiffener.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.31 no.2 s.257
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• pp.277-284
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• 2007

The steam generator in a nuclear power plant is a large heat exchanger that uses heat from a reactor to generate steam to drive the turbine generator. Rupture of a steam generator tube can result in release of fission products to environment outside. Therefore, an accurate integrity assessment of the steam generator tubes with cracks is of great importance for maintaining the safety of a nuclear power plant. The steam generator tubes are supported at regular intervals by support plates and rotations of the tubes are restrained. Although it has been reported that the limit load for a circumferential crack is significantly affected by boundary condition of the tube, existing limit load solutions do not consider the restraining effect of support plate correctly. In addition, there are no limit load solutions for circumferential cracks in U-bend region with the effect of the support plate. This paper provides detailed limit load solutions for circumferential cracks in top of tube sheet and the U-bend regions of the steam generator tube with the actual boundary conditions to simulate the restraining effect of the support plate. Such solutions are developed based on three dimensional finite element analyses. The resulting limit load solutions are given in a polynomial form, and thus can be simply used in practical integrity assessment of the steam generator tubes.

• Smart Structures and Systems
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• v.30 no.2
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• pp.173-181
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• 2022

The current paper presents a technique to detect crack in non-uniform cantilever-type pipe beams, that have step changes in the properties of their cross sections, restrained by a translational and rotational spring with a tip mass at the free end. An equation for estimating the natural frequencies for the non-uniform beams is derived using the boundary and continuity conditions, and an equivalent bending stiffness for cracked beam is applied to calculate the natural frequencies of the cracked beam. An experimental study for a step-changed non-uniform cantilever-type pipe beam restrained by bolts with a tip mass is carried out to verify the proposed method. The translational and rotational spring constants are updated using the neural network technique to the results of the experiment for intact case in order to establish a baseline model for the subsequent crack detection. Then, several numerical simulations for the specimen are carried out using the derived equation for estimating the natural frequencies of the cracked beam to construct a set of training patterns of a neural network. The crack locations and sizes are identified using the trained neural network for the 5 damage cases. It is found that the crack locations and sizes are reasonably well estimated from a practical point of view. And it is considered that the usefulness of the proposed method for structural health monitoring of the step-changed non-uniform cantilever-type pipe beam-like structures elastically restrained in the ground and have a tip mass at the free end could be verified.