• 한국농공학회지
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• 제41권1호
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• pp.106-114
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• 1999

This paper explores the geometrical non-linear behavior of the simply supported tapered beams subject to the trapezoidal distributed load and end moments. In order to apply the Bernoulli -Euler beam theory to this tapered beam, the bending moment equation on any point of the elastical is obtained by the redistribution of trapezoidal distributed load. On the basis of the bending moment equation and the BErnoulli-Euler beam theory, the differential equations governging the elastical of such beams are derived and solved numerically by using the Runge-Jutta method and the trial and error method. The three kinds of tapered beams (i.e. width, depth and square tapers) are analyzed in this study. The numerical results of non-linear behavior obtained in this study from the simply supported tapered beams are appeared to be quite well according to the results from the reference . As the numerical results, the elastica, the stress resultants and the load-displacement curves are given in the figures.

• 대한조선학회지
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• 제15권2호
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• pp.1-11
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• 1978

Using the elliptical cylindrical function, the added masses of thin rectangular plates vibrating elastically in an infinite ideal fluid are calculated. For the boundary conditions of the plates, two models are adopted. The plate which is simply-supported on two opposite edges while the other edges are clamped is one and the other is the plate which is simply-supported on two opposite edges while the other edges are free. Same examples are calculated numerically for the fundamental mode in each cases. And the effect of the boundary condition on the added mass are investigated by comparing these data with those of Kim's[4] which were calculated for the simply-supported plates by the same method. It is concluded that it is possible to predict the added mass of a rectangular plate, whose boundary condition is not treated in this report, by using the result of this investigation.

• 한국전산구조공학회:학술대회논문집
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• 한국전산구조공학회 1996년도 봄 학술발표회 논문집
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• pp.135-142
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• 1996

In this paper, a simple tut accurate method of vibration analysis of structural elements with or without attached mass/masses is presented. The method used has been developed by the senior author since 1974. This method is very effective for the plates with arbitrary boundary conditions and irregular sections. This method is applied to the special orthotropic Plate with two opposite edges simply supported and the other two opposite edges free. Such plate represents the most of the simply supported bridges/decks, including concrete and girders-cross beam systems. Detailed illustration is given for beams and plates for easy understanding. Some laminate orientation for which the special orthotropic equations can be applied are identified.

• Structural Engineering and Mechanics
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• 제32권6호
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• pp.811-833
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• 2009

In the present article bending, buckling and vibration analyses of tapered beams using Eringen non-local elasticity theory are being carried out. The associated governing differential equations are solved employing Rayleigh-Ritz method. Both Euler-Bernoulli and Timoshenko beam theories are considered in the analyses. Present results are in good agreement with those reported in literature. Beam material is considered to be made up of functionally graded materials (fgms). Non-local analyses for tapered beam with simply supported - simply supported, clamped - simply supported and clamped - free boundary conditions are carried out and discussed. Further, effect of length to height ratio on maximum deflections, vibration frequencies and critical buckling loads are studied.

• Structural Engineering and Mechanics
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• 제17권6호
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• pp.879-898
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• 2004

A method of making simply supported girders continuous is described for bridges with spans of 30-45 m. The splicing method takes advantage of an induced secondary moment to transform the self-weight stresses in the precast simply supported girders into values representative of a continuous girder. The secondary moment results from prestressing of continuity tendons and detensioning of temporary tendons in the girders. Preliminary sections are selected for spliced U-girder bridges with a range of span lengths. Use of the proposed technique results in girder depth reductions of 500-800 mm when compared to standard simply supported I-girder bridges. The flexural behavior of an example bridge with 40-m spans is examined to illustrate the necessary considerations for determining the optimum sequence of splicing operations.

• Structural Engineering and Mechanics
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• 제25권6호
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• pp.691-716
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• 2007

The purpose of the present work is to establish a method for predicting the location and depth of a crack in a circular cross section beam by only considering the frequencies of the cracked beam. An accurate knowledge of the material properties is not required. The crack location and size is identified by finding the point of intersection of pulsation ratio contour lines of lower vertical and horizontal modes. This process is presented and numerically validated in the case of a simply supported beam with various crack locations and sizes. If the beam has structural symmetry, the identification of crack location is performed by adding an off-center placed mass to the simply supported beam. In order to avoid worse diagnostic, it was demonstrated that a robust identification of crack size and location is possible if two tests are undertaken by adding the mass at the left and then right end of the simply supported beam. Finally, the pulsation ratio contour lines method is generalized in order to be extended to the case of rectangular cross section beams or more complex structures.

• Advances in nano research
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• 제10권2호
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• pp.165-174
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• 2021

This paper based on Sanders theory aims to investigate the vibration of SWCNTs considering the clamped-simply supported, clamped-free, clamped-clamped and simply supported-simply supported end conditions. After developing the governing equation of the objective system, the Rayleigh-Ritz technique is implemented for the purpose of obtaining the frequency equation in the eigen form. In addition, the applicability of this model for the analysis of vibration of CNTs is examined with the effect of length and ratio of height-to-radius. A detailed description of different types of SWCNTs with different indices is provided in the theoretical methodology. The effect of extended length is stimulated with increasing the radii and the model is effective because it also predicts the effect of thickness on vibration of SWCNTs. For different boundary conditions, the present results are verified with earlier literature.

• Computers and Concrete
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• 제32권3호
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• pp.303-311
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• 2023

An analysis of the Poisson's ratios influence of single walled carbon nanotubes (SWCNTs) based on Sander's shell theory is carried out. The effect of Poisson's ratio, boundary conditions and different armchairs SWCNTs is discussed and studied. The Galerkin's method is applied to get the eigen values in matrix form. The obtained results shows that, the decrease in ratios of Poisson, the frequency increases. Poisson's ratio directly measures the deformation in the material. A high Poisson's ratio denotes that the material exhibits large elastic deformation. Due to these deformation frequencies of carbon nanotubes increases. The frequency value increases with the increase of indices of single walled carbon nanotubes. The prescribe boundary conditions used are simply supported and clamped simply supported. The Timoshenko beam model is used to compare the results. The present method should serve as bench mark results for agreeing the results of other models, with slightly different value of the natural frequencies.

• 대한기계학회논문집
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• 제7권2호
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• pp.186-192
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• 1983

The purpose of this study is to determine the general frequency expression for a rotating shaft of uniform cross section, supported by two bearings, and carrying flywheel at the free end. The bearing spacing and the ratio of the weight of flywheel to the total distributed weight are used as parameters. The data have thus been reduced to dimensionless form so that the results are generally applicable for this type of rotor. Frequencies for the first three modes of vibration are determined. Experimental investigation with rotor/flywheel model confirmed the critical speed frequencies lie between analytical models with simply supported-simply supported boundary conditions and spring supported-spring supported boundary conditions.

• Structural Engineering and Mechanics
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• 제69권2호
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• pp.193-204
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• 2019

This paper presents results from experimental and numerical studies on the response of steel-concrete composite box bridge girders under certain localized fire exposure conditions. Two composite box bridge girders, a simply supported girder and a continuous girder respectively, were tested under simultaneous loading and fire exposure. The simply supported girder was exposed to fire over 40% of its span length in the middle zone, and the two-span continuous girder was exposed to fire over 38% of its length of the first span and full length of the second span. A measurement method based on comparative rate of deflection was provided to predict the failure time in the hogging moment zone of continuous composite box bridge girders under certain localized fire exposure condition. Parameters including transverse and longitudinal stiffeners and fire scenarios were introduced to investigate fire resistance of the composite box bridge girders. Test results show that failure of the simply supported girder is governed by the deflection limit state, whereas failure of the continuous girder occurs through bending buckling of the web and bottom slab in the hogging moment zone. Deflection based criterion may not be reliable in evaluating failure of continuous composite box bridge girder under certain fire exposure condition. The fire resistance (failure time) of the continuous girder is higher than that of the simply supported girder. Data from fire tests is successfully utilized to validate a finite element based numerical model for further investigating the response of composite box bridge girders exposed to localized fire. Results from numerical analysis show that fire resistance of composite box bridge girders can be highly influenced by the spacing of longitudinal stiffeners and fire severity. The continuous composite box bridge girder with closer longitudinal stiffeners has better fire resistance than the simply composite box bridge girder. It is concluded that the fire resistance of continuous composite box bridge girders can be significantly enhanced by preventing the hogging moment zone from exposure to fire. Longitudinal stiffeners with closer spacing can enhance fire resistance of composite box bridge girders. The increase of transverse stiffeners has no significant effect on fire resistance of composite box bridge girders.