• Magazine of the Korean Society of Agricultural Engineers
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• v.38 no.6
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• pp.42-50
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• 1996

이 논문은 step기둥의 자유진동 및 좌굴하중에 관한 연구이다. 축하중을 받는 변단면 기둥의 자유진동을 지배하는 편미분방정식을 이용하여 축하중을 받는 step기둥의 자유진동을 지배하는 상미분방정식을 유도하였다. 또한 이 자유진동을 지배하는 미분방정식을 이용하여 step기둥의 좌굴하중을 지배하는 상미분방정식을 유도하였다. 유도된 미분방정식들을 Heun방법과 Regula-Falsi방법을 이용하여 고유진동수 및 좌굴하중을 산출할 수 있는 수치해석방법을 개발하였다. 실제 수치해석 예에서는 2개의 step구간을 갖는 회전-회전, 회전-고정, 고정-고정 기둥에 대한 무차원 고유진동수화 무차원변수들과의 관계 및 무차원 좌굴하중과 무차원 변수들과의 관계를 그림에 나타내었다.

• KSCE Journal of Civil and Environmental Engineering Research
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• v.31 no.1A
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• pp.1-7
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• 2011

This paper deals with buckling loads of the column with the constant surface area. The shape function of variable column depth is chosen as the linear taper. The ordinary differential equation governing buckled shapes of the column is derived based on the dynamic equilibrium equation of such column subjected to an axial load. Three kinds of end constraint of hinged-hinged, hinged-clamped and clamped-clamped are considered in numerical examples. Effects of the column parameters on buckling loads are extensively discussed. Especially, section ratios of the strongest column are calculated, under which the maximum, i.e. strongest, buckling loads are achieved. Also the buckled shapes are obtained for searching the nodal points where the inner transverse supports are simply installed to increase the buckling loads.

• Journal of KSNVE
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• v.10 no.6
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• pp.1067-1074
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• 2000

Numerical methods for calculating both the natural frequencies and buckling loads of columns with the multiple elastic springs are developed. In order to derive the governing equations of such columns, each elastic spring is modeled as a discrete elastic foundation with the finite longitudinal length. By using this model, the differential equations governing both the free vibrations and buckled shapes, respectively, of such columns are derided. These differential equations are solved numerically. The Runge- Kutta method is used to integrate the differential equations, and the determinant search method combined with Regula-Falsi method is used to determine the eingenvalues. namely natural frequencies and buckling loads. In the numerical examples, the clamped-clamped. clamped-hinged, hinged-clamped and hinged-hinged end constraints are considered. Extensive numerical results including the frequency parameters, mode shapes of free vibrations and buckling load parameters are presented in the non-dimensional forms.

• Journal of KSNVE
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• v.6 no.5
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• pp.587-594
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• 1996

The differential equation governing both the free vibrations and buckling loads of tapered beam-columns of regular polygon cross-section with constant volume were derived and solved numerically. The parabolic and sinusoidl tapers were chosen as the variable depth of cross-section for the tapered beam-column. In numerical examples, the clamped-clamped, hinged-clamped and hinged-hinged end constraints were considered. The variations of frequency parameters and first buckling load parameters with the non-dimensional system parameters are reported in figures, and typical vibrating mode shapes are presented. Also, the configurations of strongest columns were determined.

• Computational Structural Engineering
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• v.9 no.3
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• pp.135-143
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• 1996

The differential equations governing both the free vibrations and buckling loads of tapered beam-columns of circular cross-section with constant volume are derived and solved numerically. The effects of axial load are included in the differential equations. The parabolic equation is chosen as the variable radius of circular cross-section for the tapered beam-column. In numerical examples, the clamped-clamped, clamped-hinged and hinged-hinged end constraints are considered. The variations of the frequency parameters and buckling load parameters with the non-dimensional system parameters are presented in figures and the configurations of strongest columns are obtained.

• KSCE Journal of Civil and Environmental Engineering Research
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• v.28 no.6A
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• pp.827-833
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• 2008

This paper deals with the free vibrations of elastica shaped arches. The elastica shaped arches are formed by the post-buckled column whose arc length is always constant. The equations governing free, planar vibration of general arch in open literature are modified for applying the free vibrations of elastica shaped arch and solved numerically to obtain frequencies and mode shapes for hinged-hinged, clamped-hinged and clamped-clamped end constraints. The effects of rotatory inertia, rise ratio and slenderness ratio on natural frequencies are presented. The frequencies of elastica shaped arches are greater than those of parabolic shaped ones. Also, typical mode shapes are presented in figures.

• Transactions of the Korean Society for Noise and Vibration Engineering
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• v.16 no.10 s.115
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• pp.1074-1081
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• 2006

This paper deals with the dynamic stability analysis of clamped-hinged columns with constant volume. Numerical methods are developed for solving natural frequencies and buckling loads of such columns, subjected to an axial compressive load. The parabolic taper with the regular polygon cross-section is considered, whose material volume and column length are always held constant. Differential equations governing both free vibrations and buckled shapes of such columns are derived. The Runge-Kutta method is used to integrate the differential equations, and the Regula-Falsi method is used to determine natural frequencies and buckling loads, respectively. The numerical methods developed herein for computing natural frequencies and buckling loads are found to be efficient and robust. From the numerical results, dynamic stability regions, dynamic optimal shapes and configurations of strongest columns are reported in figures and tables.

• Journal of the Computational Structural Engineering Institute of Korea
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• v.15 no.1
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• pp.165-172
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• 2002

Generally, the steel rigid frame has been analyzed using finite element analysis tools. While many efforts have been poured into the understanding and accurate prediction for the nonlinear behavior of the columns and beam-columns connections, the base of the columns are modeled as simply hinged or fixed. However, the base of the steel columns practically is neither fixed not hinged. It behaves as semi-rigid. In this paper, the supports of the columns we modeled as semi-rigid and the importance of such approach in moment-resisting columns is evaluated. Two typical buildings designed by the US specification are modeled and analyzed by the finite element based on stiffness method and flexibility method. The column bases of three-story buildings are modeled as rotational springs with a varying degree of stiffness and strength that simulates the semi-rigidity of the base. Depending on the degree of stiffness and strength, the semi-rigidity varies from the hinged to the fixed. Buildings with semi-rigid column bases behaves similarly to the building with fixed bases. It has been numerically observed through the pushover and nonlinear time history analyses that the decrease of the stiffness of the column base induces the rotational demand on the int air beams. an increase of rotation demands on the first store connections and lead to a soft-story mechanists Due often to the construction and environmental effects, undesired reduction of column base stiffness may cause an increase of rotation demands on the first store connections and lead to a soft-story mechanism.

• Journal of the Korean Institute of Intelligent Systems
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• v.5 no.2
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• pp.86-96
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• 1995

In this paper the fuzzy extension for the classical engineering mechanics problems is studied. The governing differential equation is derived for the buckling loads of the columns with uncertain mediums: the their own weight and the flexural rigidity. The columns with one typical end constraint(hinged1 clarnped/free) and the other finite rotational spring with fuzzy constant are considered in numerical examples. The vertex method is used to evaluate the fuzzy functions. The Runge-Kutta method and Determinant Search method are used to solve the differential equation and determine the buckling loads, respectively. The membership functions of the buckling load are calculated. The index of fuzziness to quantitatively describe the propagation of fuzziness is defined. According to the fuzziness of governing factors, the varlation of index of fuzziness for buckling load is investigated, and the sensitivity for the end constraints is analyzed.

• Transactions of the Korean Society of Mechanical Engineers
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• v.9 no.5
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• pp.606-612
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• 1985

On the stability of the Beck's column with a tip mass, the influence of the characteristics of the springs at the fixed end of the column are studied. The equations of motion and boundary conditions of this system are established by using the Hamiton's principle. On the evaluation of the stability of the column, t he effect of the shear deformation and rotatory inertial is considered in calculation. For the maintenance of the stability of the column, it is proved that the constant of the translational spring at the fixed end must be very large while th magnitude of the constant of the rotational spring at the fixed end has no effect. When the constants of the springs at the fixed end are small, it is also proved that the influence of the moment of inertial of the tip mass on the stability of the column are decreased and for the translational spring the degree of the decrease is more and more. Therefore it is found that the characteristics of the springs at the fixed end are very effective elements for the stability of the column when the columns subjected to a compressive follower force are designed.