• 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.

• KSCE Journal of Civil and Environmental Engineering Research
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• v.29 no.2A
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• pp.145-153
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• 2009

The lateral-torsional buckling strengths of the parabolic arches are investigated in this study. The curvatures of a parabolic arch vary along the center line of the arch. Thus, the problem is much more complicated comparing that of arches with constant curvature such as circular arches. Moreover, most of previous studies are limited to the circular arches. In this study, lateral-torsional buckling equations are derived for the arches with varying curvatures considering the warping effects. To obtain the buckling strength of parabolic arches, numerical solutions based on the finite difference technique are provided. The numerical solutions are compared with the those of previous researchers and finite element analyses. Then, the lateral-torsional strengths of parabolic arches are successfully verified. Finally, comparison study of critical buckling loads of parabolic arches with those of circular arches for the various rise to span ratios are discussed.

• Journal of the Computational Structural Engineering Institute of Korea
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• v.21 no.4
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• pp.357-364
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• 2008

This paper deals with the free vibrations of arches with rectangular hollow section having constant area. The differential equations governing free vibrations of arches are derived in polar coordinates, in which the effect of rotatory inertia is included. Natural frequencies is computed numerically for parabolic arches with clamped-clamped, clamped-hinged and hinged-hinged ends. Comparisons of natural frequencies between this study and reference are made to validate theories and numerical methods developed herein. The lowest four natural frequency parameters are reported, with the rotatory inertia, as functions of three non-dimensional system parameters: the breadth ratio, the thickness ratio and the shape ratio

• Transactions of the Korean Society for Noise and Vibration Engineering
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• v.18 no.2
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• pp.215-223
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• 2008

The differential equations governing free vibrations of the elastic arches with hollow section are derived in polar coordinates, in which the effect of rotatory inertia is included. Natural frequencies is computed numerically for parabolic arches with both clamped ends and both hinged ends. Comparisons of natural frequencies between this study and reference are made to validate theories and numerical methods developed herein. The lowest four natural frequency parameters are reported, with the rotatory inertia, as functions of three non-dimensional system parameters: the breadth ratio, the thickness ratio and the rise to span length ratio.

• Magazine of the Korean Society of Agricultural Engineers
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• v.37 no.2
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• pp.53-63
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• 1995

본 논문의 다경간 연속아치의 자유진동에 관한 연구이다. 다경간 연속아치의 고유진 동수 및 진ㄷㅇ형을 산출하기 위하여 내부지점의 지점조건에 다른 경계조건식을 유도하였다. 아치의 선형은 포물선을 택하였으며, 회전-로울러-회전, 고정-회전-고정의 지점 조건을 갖는 2경간 연속아치에 대한 수치해석 결과를 제시하였다. Runge-Kutta maethod을 이용 하였다. 실제 수치해석예에서는 회전관성이 고유진동수에 미치는 영향을 고찰 하였으며, 무차원 고유진동수와 아치높이 지간길이비 및 세장비 사이의 관계를 분석하였다. 또한 실험을 토아여 이론적인 해석결과를 검증하였다.

• Journal of Korean Society of Steel Construction
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• v.17 no.4 s.77
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• pp.439-447
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• 2005

When arch ribs are subjected to vertical loading, they may buckle suddenly towards the in-plane direction. Therefore, the designer should consider their in-plane stability. In this paper, the in-plane elastic and inelastic buckling strength of parabolic, fixed arch ribs subjected to vertical distributed loading were investigated using the finite element method. A finite element model for the snap-through and inelastic behavior of arch ribs was verified using other researchers' test results. The ultimate strength of arch ribs was determined by taking into account their large deformation, material inelasticity, and residual stress. Finally, the finite element analysis results were compared with the EC3 design code.

• Transactions of the Korean Society for Noise and Vibration Engineering
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• v.12 no.12
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• pp.970-978
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• 2002

The differential equations governing free vibrations of the elastic arches with unsymmetric axis are derived in Cartesian coordinates rather than in polar coordinates. in which the effect of rotatory inertia is included. Frequencies and mode shapes are computed numerically for parabolic arches with both clamped ends and both hinged ends. Comparisons of natural frequencies between this study and SAP 2000 are made to validate theories and numerical methods developed herein. The convergent efficiency is highly improved under the newly derived differential equations in Cartesian coordinates. The lowest four natural frequency parameters are reported, with and without the rotatory inertia, as functions of three non-dimensional system parameters the rise to chord length ratio. the span length to chord length ratio, and the slenderness ratio. Also typical mode shapes of vibrating arches are presented.

• Journal of Korean Society of Steel Construction
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• v.9 no.4 s.33
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• pp.673-682
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• 1997

The main purpose of this paper is to investigate the effects of rotatory inertia and shear deformation on the natural frequencies of arches with variable curvature. The differential equations are derived for the in-plane free vibration of linearly elastic arches of uniform stiffness and constant mass per unit length. The governing equations are solved numerically for parabolic, circular and elliptic geometries with hinged-hinged, hinged-clamped and clamped-clamped end constraints. For each cases, the four lowest frequency parameters are presented as functions of the two dimensionless system parameters; the arch rise to span length ratio, and the slenderness ratio.

• Journal of Korean Association for Spatial Structures
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• v.12 no.1
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• pp.87-98
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• 2012

In this study, mechanical role of edge beams in the gabled hyperbolic paraboloid shells was investigated through the comparisons of Finite element(FE) analysis results between the shells structures with and without edge beams. In addition, the effects of roof slope was studied. FE analysis showed that roof loads was directly transferred to the supports at corners by the arch action in the diagonal direction of the shells, thus, less member forces in the edge and ridge beams but higher stresses near supports were estimated than those from the membrane theory. When the edge beams were removed, stress concentration in the shells near the supports and the deflections along the shell edge were increased. Such phenomenon were intensified as the roof slope decrease. Thus, in gable hyperbolic paraboloid shell, the thickness of the shell near supports needs to be increased and careful investigation should be made in the cases when the roof height is low and/or the edge beams are removed.

• KSCE Journal of Civil and Environmental Engineering Research
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• v.12 no.2
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• pp.43-54
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• 1992

For shallow arches with large dynamic loading, linear analysis is no longer considered as practical and accurate. In this study, a method is presented for the dynamic analysis of shallow arches in which geometric nonlinearity must be considered. A program is developed for the analysis of the nonlinear dynamic behavior and for evaluation of critical buckling loads of shallow arches. Geometric nonlinearity is modeled using Lagrangian description of the motion. The finite element analysis procedure is used to solve the dynamic equation of motion and Newmark method is adopted in the approximation of time integration. A shallow arch subject to radial step loads is analyzed. The results are compared with those from other researches to verify the developed program. The behavior of arches is analyzed using the non-dimensional time, load, and shape parameters. It is shown that geometric nonlinearity should be considered in the analysis of shallow arches and probability of buckling failure is getting higher as arches are getting shallower. It is confirmed that arches with the same shape parameter have the same deflection ratio at the same time parameter when arches are loaded with the same parametric load. In addition, it is proved that buckling of arches with the same shape parameter occurs at the same load parameter. Circular arches, which are under a single or uniform normal load, are analyzed for comparison. A parabolic arch with radial step load is also analyzed. It is verified that the developed program is applicable for those problems.