• KSCE Journal of Civil and Environmental Engineering Research
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• v.29 no.3A
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• pp.251-258
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• 2009

This paper deals with the strongest beams with the solid regular polygon cross-section, whose volumes are always held constant. The differential equation of the elastic deflection curve of such beam subjected to the concentrated and trapezoidal distributed loads are derived and solved by using the double integration method. The Simpson's formula was used to numerically integrate the differential equation. In the numerical examples, the clamped-clamped and clamped-hinged ends are considered as the end constraints and the linear, parabolic and sinusoidal tapers are considered as the shape function of cross sectional depth. As the numerical results, the configurations, i.e. section ratios, of the strongest beams are determined by reading the section ratios from the numerical data obtained in this study, under which static maximum behaviors become to be minimum.

• Magazine of the Korean Society of Agricultural Engineers
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• v.41 no.1
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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.

• KSCE Journal of Civil and Environmental Engineering Research
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• v.29 no.2A
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• pp.155-162
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• 2009

This paper deals with the strongest beams with the solid regular polygon cross-section, whose volumes are always held constant. The differential equation of the elastic deflection curve of such beam subjected to the concentrated and trapezoidal distributed loads are derived and solved numerically. The Runge-Kutta method and shooting method are used to integrate the differential equation and to determine the unknown initial boundary condition of the given beam. In the numerical examples, the simple beams are considered as the end constraint and also, the linear, parabolic and sinusoidal tapers are considered as the shape function of cross sectional depth. As the numerical results, the configurations, i.e. section ratios, of the strongest beams are determined by reading the section ratios from the numerical data related with the static behaviors, under which static maximum behaviors become to be minimum.

• Journal of the Society of Naval Architects of Korea
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• v.34 no.4
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• pp.99-107
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• 1997

A mixed type finite element method is applied to the nonuniform shear warping beam theory which is very useful for the structural analysis of thin-walled sectional beams considering the shear deformation. As known generally, it is shown that the mixed type finite element method, compared with the displacement type one, can give more balanced accuracy of results in calculating the stresses and displacements of the structure. In this paper, one typical example, the flexural-torsional problem of a discontinuously variable sectional beam under coupled end torsional moments, is selected and analyzed to validate the usefulness of the developed beam element.

• Journal of the Computational Structural Engineering Institute of Korea
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• v.27 no.3
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• pp.199-206
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• 2014

In this paper, a scheme to evaluate the response variability for functionally graded material (FGM) beam with varying sectional area is presented. The randomness is assumed to appear in a spatial domain along the beam axis in the elastic modulus. The functionally graded material categorized as composite materials, however without the drawbacks of delamination and occurrence of cracks due to abrupt change in material properties between layers in the conventional composite materials. The functionally graded material is produced by the gradual solidification through thickness direction, which endows continuous variation of material properties, which makes this material performs in a smooth way. However, due to difficulties in tailoring the gradients, to have uncertainty in material properties is unavoidable. The elastic modulus at the center section is assumed to be random in the spatial domain along the beam axis. Introducing random variables, defined in terms of stochastic integration, the first and second moments of responses are evaluated. The proposed scheme is verified by using the Monte Carlo simulation based on the random samples generated employing the spectral representation scheme. The response variability as a function of correlation distance, the effects of material and geometrical parameters on the response variability are investigated in detail. The efficiency of the proposed scheme is also addressed by comparing the analysis time of the proposed scheme and MCS.

• Proceeding of EDISON Challenge
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• 2015.03a
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• pp.269-273
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• 2015

처음 에디슨 경진대회를 준비할 때 업로드 되어 있는 다양한 프로그램을 보면서 어떤 주제를 선정할 지 고민을 하던 중, 눈에 들어온 프로그램은 서울대학교에서 제작한 Co-rotational Plane beam-Dynamic tip load이란 프로그램이었다. 위 프로그램은 한쪽 단이 고정된 외팔보(cantilever beam)의 끝단에 하중을 시간에 관련된 함수(sin, cos)로 주어 각 절점에서의 변위(X, Y), 속도 그리고 가속도를 알려주는 프로그램이다. 우리는 이 프로그램을 이용해서 외팔보 끝단의 진동 형태와 주기가 어떤 요인(단면의 모양, 재료의 성질, 가하는 하중의 진동수 등)에 의해서 변하는지 분석할 수 있었다. 거기서 더 나아가 하중을 실제 지진상황에서의 크기와 유사하게 주고 위 프로그램에서의 보의 거동(진동 주기, 진동 변위 등)을 건물의 거동이라 가정했을 때 면진 주기를 얼마로 설정해야하는지도 알 수 있었다.

• Journal of Korean Society of Steel Construction
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• v.22 no.1
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• pp.67-74
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• 2010

The cases of collapse of greenhouses in rural areas have been increasing due to the unexpected heavy snow load. Studies on how to prevent the collapse of greenhouses are rare, however, and the damages are repeated annually. This studysuggests two reinforcing methods: the use of ahigh-strength tapered module, and the addition of a pre-tension tie. The high-strength tapered section is installed where the bending moment is maximum. The design of a plastic greenhouse is controlled by its strength rather than its deflection. The shape of a greenhouse resembles that of an arch system, but its actual structural behavior is the frame behavior, because it is non-continually composed of a curved element (a beam) and vertical elements (columns). This system is too weak and slender to resist a vertical load, because an external load is resisted by the moment rather than by axial force. In this study, a new method, the installation of a temporary tie at the junction of the arch and the column only during snow accumulation, is proposed. The tie changes the action of the greenhouse frame to an arch action. The arch action is more effective when the pre-tension force is applied in the tie, which results in a very strong temporary structural system during snowfall. As a result of using this high-strength tapered section, the combined strength ratio of what? decreased from 10% to 30%. In the case of the additional reinforcement with a tie, it was reduced by half.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2002.11a
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• pp.394.1-394
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• 2002

The purpose of this paper is to investigate the natural frequencies and mode shapes of tapered beams with general boundary condition(translational and rotational elastic support) at one end and carrying a tip mass of rotatory inertia at the other end. The beam model is based on the classical Bernoulli-Euler beam theory which neglects the effects of rotatory inertia and shear deformation. (omitted)

• Computational Structural Engineering
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• v.6 no.1
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• pp.99-105
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• 1993

A Stepped beam with immovable ends under forced vibrations with large amplitude is investigated by using the finite element method and the Ritz vectors. Unlike the Eigen vectors, the Ritz vectors are generated by a simple recurrence relation. Moreover the Ritz vectors yield much faster convergence with respect to the number of vectors used than the use of Eigen vectors. The computer program is developed for nonlinear analysis using Ritz vectors instead of Eigen vectors and numerical examples are analysed for deflections and natural frequencies of stepped beam under various support conditions. Results show that the proposed method is valid and efficient.

• Proceedings of the Computational Structural Engineering Institute Conference
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• 2002.04a
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• pp.115-122
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• 2002

The main purpose of this paper is to determine the static optimal shapes of tapered beams with constant volume. The linear, parabolic and sinusoidal tapers with the regular polygon cross-section are considered, whose material volume and span length are always held constant. The Runge-Kutta method is used to integrate the differential equation and also Shooting method is used to calculate the unknown boundary condition. Then the static optimal shapes are determined by reading the minimum values of the deflection versus section ratio curves plotted by the deflection data. In numerical examples, the various tapered beams are analyzed and those numerical results of this study are shown in figures.