• 한국소음진동공학회:학술대회논문집
• /
• 한국소음진동공학회 2002년도 추계학술대회논문집
• /
• pp.1054-1059
• /
• 2002

A linearly tapered beam immersed partially in other material is considered and is modelled as a linearly tapered Bernoulli-Euler beam fixed at the bottom with a concentrated mass at the top. Its governing equations is derived and its free vibration analysis is performed for various boundary conditions. And the rotatory inertia of the eccentric lumped tip mass is considered. The problem of determining the natural frequencies leads to an eighth order determinant. The solutions of the frequency equations are obtained numerically. The non-dimensional frequency parameters are given in tabular form and the influence of non-dimensional parameters on natural frequency is discussed for various conditions.

• 한국전산구조공학회:학술대회논문집
• /
• 한국전산구조공학회 2000년도 가을 학술발표회논문집
• /
• pp.59-66
• /
• 2000

It is generally known that the lateral frequency( ω) of the vibration of a prismatic beam-column decreases according to the rele (equation omitted) (ω/sub 0/=natural frequency). In the cases of tapered members, the determination of P/ sub/ cr/(elastic critical load) and ω/ sub 0/ are not easy. Furthermore, the relationship between the compressive load and frequency can not be determined by the conventional analytical method. The axial force-frequency relationship of sinusolidally non-symmetrically tapered members with different shapes were investigated using the finite element method. To obtain the two eigenvalues, the axial thrust was increased step by step and the corresponding frequency was calculated. The result indicated that the axial thrust of the elastic critical load ratio and the square of the frequency ratio can be approximately represented in any case by a straight line. Finally, the linear relationship is also applicable to the sinusolidally non-symmetrically tapered member.

• 한국강구조학회 논문집
• /
• 제17권6호통권79호
• /
• pp.699-705
• /
• 2005

이 논문은 자유단에 집중질량을 갖고 종동력이 작용하는 변단면 캔틸레버 기둥의 임계하중에 관한 연구이다. 기둥의 단면을 중실 직사각형 단면을 갖는 선형 변단면으로 채택하고, Bernoulli-Euler 보 이론에 의한 자유단 집중질량을 갖고 종동력을 받는 소위 Beck 기둥의 자유진동을 지배하는 미분방정식을 유도하였다. 이 미분방정식을 수치해석하여 하중-고유진동수 곡선을 얻고 이로부터 발산임계하중 및 동요임계하중을 산출하였다. 수치해석의 결과로부터 변단면 형태, 경사변수 및 질량비가 임계하중에 미치는 영향을 고찰하였다.

• 대한토목학회논문집
• /
• 제4권1호
• /
• pp.93-101
• /
• 1984

본(本) 논문(論文)에서는 일정변단면장주(一定變斷面長柱)의 탄성임좌굴하중(彈性臨挫屈荷重)을 구하는 각산식(咯算式)을 제시(提示)하였다. 특히, 고가도로설계시(高架道路設計時) 자주 나타나는 일단고정(一端固定) 타단자유(他端自由)인 중실원형(中實圓形) 및 구형단면(矩形斷面)에 한(限)하였다. 처짐곡선 미분방정식(微分方程式)의 정밀해(精密解)는 Bessel 함수(凾數)로 나타나는데, Bisection method를 이용하여 Computer로 수치해석(數値解析)하였다. 또 자중(自重)고려시 F.E.M에 의한 해석(解析)은 고유치(固有値) 문제(問題)가 되므로 Jacobi method를 이용하여 수치해석(數値解析)하였고, 균일단면장주(均一斷面長柱)의 정밀해(精密解)와 비교(比較)하여 F.E.M에 의한 근사해(近似解)의 신뢰도(信賴度)를 높였다. 그 결과(結果) 일정변단면장주(一定變斷面長柱)의 임계좌굴하중(臨界挫屈荷重)은 형상계수(形狀係數)와 단면변화율(斷面變化率)에 대해 균일단면장주(均一斷面長柱)의 비례식(比例式)으로 나타낼 수 있었다.

• 한국소음진동공학회:학술대회논문집
• /
• 한국소음진동공학회 2002년도 춘계학술대회논문집
• /
• pp.417-422
• /
• 2002

The main purpose of this paper is to determine the dynamic optimal shapes of tapered column 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 ordinary differential equation including the effect of axial load is applied to calculate the natural frequencies. The Runge-Kutta method and Regula-Falsi methods are used to integrate the differential equation and compute the frequencies, respectively. Then the dynamic optimal shape whose lowest natural frequency is highest is determined by reading the critical value of the frequency versus section ratio curve plotted by the frequency data. In the numerical examples, the tapered columns are analysed and the numerical result of this study are shown in table and figures.

• 한국소음진동공학회:학술대회논문집
• /
• 한국소음진동공학회 2001년도 추계학술대회논문집 II
• /
• pp.1000-1004
• /
• 2001

This study explores the free vibrations of tapered column with hinged end restricted by rotational spring. The ordinary differential equation governing the free vibration of such column is derived as nondimensional form in which three kinds of cross-sectional shape are considered. In order to obtain the natural frequencies of column, the governing differential equation is solved by numerical procedures. Numerical results are compared with existing solutions by other methods. It is expected that the results obtained herein can be practically utilized in the structural and the vibration control fields.

• Computers and Concrete
• /
• 제9권6호
• /
• pp.403-426
• /
• 2012

This paper deals with the structural behaviour of tapered concrete-filled steel composite (TCFSC) columns under eccentric loading. Finite element software LUSAS is used to perform the nonlinear analyses to predict the structural behaviour of the columns. Results from the finite element modelling and existing experimental test are compared to verify the accuracy of the modelling. It is demonstrated that they correlate reasonably well with each other; therefore, the proposed finite element modelling is absolutely accurate to predict the structural behaviour of the columns. Nonlinear analyses are carried out to investigate the behaviour of the columns where the main parameters are: (1) tapered angle (from $0^{\circ}$ to $2.75^{\circ}$); (2) steel wall thickness (from 3 mm to 4 mm); (3) load eccentricity (15 mm and 30 mm); (4) L/H ratio (from 10.67 to 17.33); (5) concrete compressive strength (from 30 MPa to 60 MPa); (6) steel yield stress (from 250 MPa to 495 MPa). Results are depicted in the form of load versus mid-height deflection plots. Effects of various tapered angles, steel wall thicknesses, and L/H ratios on the ultimate load capacity, ductility and stiffness of the columns are studied. Effects of different load eccentricities, concrete compressive strengths and steel yield stresses on the ultimate load capacity of the columns are also examined. It is concluded from the study that the parameters considerably influence the structural behaviour of the columns.

• 한국전산구조공학회:학술대회논문집
• /
• 한국전산구조공학회 2002년도 가을 학술발표회 논문집
• /
• pp.244-251
• /
• 2002

The purpose of this paper is to investigate the stability of tapered columns with general boundary condition(translational and rotational elastic support) at one end and carrying a tip mass of rotatory inertia with translational elastic support at the other end. The column model is based on the classical Bernoulli-Euler beam theory which neglects the effects of rotatory inertia and shear deformation. The governing differential equation for the free vibrations of linearly tapered columns subjected to a subtangential follower force is solved numerically using the corresponding boundary conditions. And the bisection method is used to calculate the critical divergence/flutter load. After having verified the results of the present study, the frequency and critical divergence/flutter load are presented as functions of various nondimensional system parameters.

• 한국전산구조공학회:학술대회논문집
• /
• 한국전산구조공학회 2007년도 정기 학술대회 논문집
• /
• pp.223-226
• /
• 2007

In current specification, modification factor(B) for web-tapered beam is used to account for the stress gradient and the restraining effect for adjacent spans. However, because these effects are considered together in modification factor, this paper revaluate the accuracy of the modification factor used in current specification. Also this paper investigate the flexural torsional buckling strength of laterally fixed thin-walled arch with doubly symmetric section using the analytical and numerical method. From this investigate the concept of effective length to consider the out-of-plane boundary condition for straight column or beam is not applicate for the flexural-torsional buckling of laterally fixed arches.

• 한국구조물진단유지관리공학회 논문집
• /
• 제9권3호
• /
• pp.139-150
• /
• 2005

유한요소법을 이용하여 기둥단면이 직선형태로 변화하는 3경간 단층 골조의 두 고유치 (탄성임계하중과 횡방향 기본진동수)를 산정하였다. 수치해석에서 고려한 변수는 기둥의 taper 비 ($={\alpha}$), 경간대 층고비 ($={\beta}$), 보와 기둥의 단면2차 모멘트 비(=Y)이다. 또한 주각의 지지상태와 주두의 수평동(side-sway)유무가 고유치에 미치는 영향도 고려하였다. 하나의 연속함수로부터 고유치의 변화 추정이 가능한 대수 함수식을 제안하였다. 대수함수식의 변수는 수치해석에서의 변수 즉 ${\alpha}$, ${\beta}$ 및 Y 이다. 골조에 작용하는 축방향력의 크기를 점차 증가시켜 가면서 여기에 대응하는 진동수의 감소현상을 검토하였다.