• Title/Summary/Keyword: Regular Polygon Cross-section

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Static and Dynamic Stability Analyses of Simple Tapered Columns with Constant Volume (일정체적 단순지지 변단면 기둥의 정·동적 안정해석)

  • Lee, Byoung Koo;Kim, Suk Ki
    • 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.

Free Vibrations of Timoshenko Beam with Constant Volume (일정체적 Timoshenko 보의 자유진동)

  • Lee, Byoung-Koo;Lee, Tae-Eun;Yoon, Hee-Min
    • Transactions of the Korean Society for Noise and Vibration Engineering
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    • v.22 no.3
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    • pp.223-233
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    • 2012
  • This paper deals with free vibrations of the tapered Timoshenko beam with constant volume, in which both the rotatory inertia and shear deformation are included. The cross section of the tapered beam is chosen as the regular polygon cross section whose depth is varied with the parabolic function. The ordinary differential equations governing free vibrations of such beam are derived based on the Timoshenko beam theory by decomposing the displacements. Governing equations are solved for determining the natural frequencies corresponding with their mode shapes. In the numerical examples, three end constraints of the hinged-hinged, hinged-clamped and clamped-clamped ends are considered. The effects of various beam parameters on natural frequencies are extensively discussed. The mode shapes of both the deflections and stress resultants are presented, in which the composing rates due to bending rotation and shear deformation are determined.

Elastica of Tapered Columns of Regular Polygon Cross-Section with Constant Volume (정다각형 단면을 갖는 일정체적 변단면 기둥의 정확탄성곡선)

  • LEE, Byoung Koo;OH, Sang Jin;MO, Jeong Man
    • 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.

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Dynamic Stability Analysis of Clamped-Hinged Columns with Constant Volume (일정체적 고정-회전 기둥의 동적안정 해석)

  • Kim, Suk-Ki;Lee, Byoung-Koo
    • 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.

Free Vibrations and Buckling Loads of Column with Clamped-Spring Ends and Constant Volume (고정-스프링 일정체적 기둥의 자유진동 및 좌굴하중)

  • Yoon, Hee-Min;Lee, Tae-Eun;Park, Kwang-Kyu;Lee, Byoung-Koo
    • Proceedings of the Computational Structural Engineering Institute Conference
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    • 2007.04a
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    • pp.117-120
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    • 2007
  • This study deals with the free vibrations and buckling loads of column with clamped-spring ends and constant volume. The column has the regular polygon cross-section whose depth is varied with the linear functional fashion. The differential equation governing the free vibration of such column is derived in which the effect of axial load is included. The differential equation is solved numerically for calculating frequencies. By using the relationship between loads and frequencies, the buckling loads are also obtained.

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Strongest Simple Beams with Constant Volume (일정체적 단순지지 최강보)

  • Lee, Byoung Koo;Lee, Tae Eun;Kim, Young Il
    • 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.

Strongest Beams having Constant Volume Supported by Clamped-Clamped and Clamped-Hinged Ends (고정-고정 및 고정-회전 지점으로 지지된 일정체적 최강보)

  • Lee, Byoung Koo;Lee, Tae Eun;Shin, Seong Cheol
    • 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.

Buckling Loads and Post-Buckling Behaviors of Shear Deformable Columns with Regular Cross-Section (전단변형을 고려한 정다각형 단면 기둥의 좌굴하중 및 후좌굴 거동)

  • Lee, Byeoung Koo;Lee, Tae Eun;Kwon, Yun Sil;Kim, Sun Gi
    • 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.

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Static and Dynamic Optimal Shapes of Both Clamped Columns with Constant Volume (일정체적 양단고정 기둥의 정·동적 최적형상)

  • Lee, Byoung Koo;Kim, Suk Ki
    • Journal of Korean Society of Steel Construction
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    • v.19 no.1
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    • pp.99-106
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    • 2007
  • This paper deals with the static and dynamic optimal shapes of both clamped columns with constant volume. The parabolic taper with the regular polygon cross-section is considered, whose material volume and column length are held constant. Numerical methods are developed for solving natural frequencies and buckling loads of columns subjected to an axial compressive load. Differential equations governing the free vibrations of such column 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. From the numerical results, dynamic stability regions, dynamic optimal shapes and configurations of strongest columns are presented in figures and tables.