• KSCE Journal of Civil and Environmental Engineering Research
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• v.26 no.3A
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• pp.533-538
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• 2006

This study deals with the static and dynamic stability analyses of simple tapered columns with constant volume. The crosssections of column taper are the regular polygons whose depths are varied with the parabolic functional fashion. The hingedhinged end constraint is chosen as the boundary condition of the column. The non-dimensional ordinary differential equation governing free vibrations of such column subjected to an axial load is derived and solved numerically. From numerical results, the relationships between natural frequencies and section ratios are obtained, from which the configurations of dynamic optimal shapes of columns and the strongest columns are extracted.

• Magazine of the Korean Society of Agricultural Engineers
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• v.41 no.5
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• pp.112-122
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• 1999

이 논문은 일정체적을 갖는 양단고정 변단면 기둥의 좌굴하중 및 후좌굴 거동에 관한 연구이다. 기둥의 변단면으로는 직선형, 포물선형, 정현의 선형을 갖는세 가지 변단면을 채택하였다. Bernoulli-Euler 보 이론을 이용하여 압축하중이 작용하여 좌굴된 기둥이 정확탄성곡선을 지배하는 미분방정식을 유도하였다. 유도된 미분방정식을 Runge-Kutta 법과 REgula-Falsi법을 이용하여 수치해석하였다. 수치해석의 결과로 좌굴하중, 좌굴기둥의 평형경로 및 정확탄성곡선을 산출하였다. 또한 좌굴하중-단면비 곡선으로부터 최강기둥의 좌굴하중과 단면비를 산출하였다.

• Journal of the Computational Structural Engineering Institute of Korea
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• v.19 no.1 s.71
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• pp.85-92
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• 2006

This paper investigates critical loads of the tapered Beck's columns with clamped and spring supports, subjected to a subtangential follower force. The linearly tapered columns with the solid rectangular cross-section is adopted as the column taper. The differential equation governing free vibrations of such Beck's columns is derived using the Bemoulli-Euler beam theory. Both divergence and flutter critical loads are calculated from the load-frequency curves which are obtained by solving the differential equation. The critical loads are presented as functions of various non-dimensional system parameters: the taper type, the subtangential parameter and the spring stiffness.

• Journal of Korean Society of Steel Construction
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• v.13 no.6
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• pp.683-691
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• 2001

Numerical methods are developed for solving the elastica and buckling load of tapered columns with shear deformation, subjected to a compressive end load. The linear, parabolic and sinusoidal tapers with the regular polygon cross-sections are considered, whose material volume and span length are always held constant. The differential equations governing the elastica of buckled column are derived. The Runge-Kutta method is used to integrate the differential equations, and the Regula-Falsi method is used to determine the rotation at left end and the buckling load, respectively. The numerical methods developed herein for computing the elastica and the buckling loads of the columns are found to be efficient and reliable.

• Journal of Korean Society of Steel Construction
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• v.8 no.3 s.28
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• pp.79-87
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• 1996

본 논문에서는 단순지지된 일정체적의 정다각형 단면을 갖는 변단면 기둥의 정확탄성곡선(elastica)을 산출할 수 있는 수치해석법을 개발하였다. 정확탄성곡선의 미분방정식은 Bernoulli-Euler 보 이론으로 유도하였고, 미분방정식의 수치적분은 Runge-Kutta method를 이용하였다. 미분방정식의 고유치인 지점의 단면회전각은 Regula-Falsi method를 이용하여 계산하였다. 변단면의 단면 깊이의 변화식으로는 직선식, 포물선식 및 정현식의 3가지 함수식을 채택하였다. 또한 유도된 미분방정식을 이용하여 대상기둥의 좌굴하중을 산출하고 이로부터 최강기둥의 단면비와 좌굴하중을 결정하였다.

• KSCE Journal of Civil and Environmental Engineering Research
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• v.29 no.1A
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• pp.53-60
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• 2009

This paper deals with the geometrical nonlinear analyses of post-buckled columns with variable cross-section. The objective columns having variable cross-section of the width, depth and square tapers are supported by both hinged ends. By using the Bernoulli-Euler beam theory, differential equations governing the elastica of post-buckled column and their boundary conditions are derived. The solution methods of these differential equations which have two unknown parameters are developed. As the numerical results, equilibrium paths, elasticas and stress resultants of the post-buckled columns are presented. Laboratory scaled experiments were conducted for validating the theories developed in this study.

• Journal of Korean Society of Steel Construction
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• v.17 no.6 s.79
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• pp.699-705
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• 2005

This paper investigates critical loads of tapered cantilever columns with a tip mass, subjected to a follower force. The linearly tapered solid rectangular cross-sections are adopted as the column taper. The differential equation governing free vibrations of such columns, also called Beck's columns, is derived using the Bernoulli-Euler beam theory. Both divergence and flutter critical loads are calculated from the load-frequency curves that are obtained by solving the differential equation. The critical loads are presented as functions of various non-dimensional system parameters, namely, the taper type, the subtangential parameter, and the mass ratio.

• 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.

• KSCE Journal of Civil and Environmental Engineering Research
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• v.11 no.4
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• pp.17-26
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• 1991

Numerical methods are developed to obtain the critical loads and to analyze the post-buckling behaviour of the linearly varying tapered columns. The non-dimensional differential equations governing the elastica of post buckled column are derived by third order and solved numerically using the Runge-Kutta method and Regula-Falsi method. Three kinds of cross-sectional shape with simply supported end constraint are applied in unmerical examples. As the numerical results, the equlibrium paths. the typical elastica of post buckled columns and the critical load vs. section ratio curves are presented in figures. Also, the effects of cross-sectional shape factor on critical loads and postbuckling behaviour are presented in tables.

• KSCE Journal of Civil and Environmental Engineering Research
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• v.33 no.5
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• pp.1935-1946
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• 2013

In this study, the behavior characteristics of bent pile structures with varying cross-section was examined through the measured results of field load test. A framework for determining the bending stress is calculated based on the stresses in the circumference of the pile using 3D finite element analysis. It is found that the bending stress near the pile-column joint changes rapidly and fracture zones occurs easily at variable cross-sections in bent pile structures. Also, the optimized column-pile diameter ratio was analyzed through the relationship between the column-pile diameter ratio and lateral crack load ratio. Based on this study, the optimized column-pile diameter ratio can be obtained near the inflection point of the curve between the column-pile diameter ratio and lateral crack load ratio. Therefore, a present study by considering the optimized variable cross-section condition would be improved bent pile structures design.