• 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.

• Proceedings of the Computational Structural Engineering Institute Conference
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• 2006.04a
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• pp.689-696
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• 2006

This paper deals with the geometrical non-linear analyses of the buckled columns. Differential equations governing elasticas of the buckled columns are derived, in which both effects of taper type and shear deformation are included. Three kinds of taper types such as breadth, depth and square tapers are considered. Differential equations are solved numerically to obtain the elasticas and buckling loads of such columns. End constraint of both clamped ends and both hinged ends are considered. The effects of shear deformation on the elastica of the buckled column and buckling load of column are investigated extensively. Experimental studies are presented that complement theoretical results of non-linear responses of the elasticas.

• 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.

• Earthquakes and Structures
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• v.24 no.2
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• pp.97-109
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• 2023

This experimental study investigates the effectiveness of applying carbon fiber reinforced polymer (CFRP) jackets for the retrofit of short reinforced concrete (RC) columns with inadequate transverse reinforcement and stirrup spacing to longitudinal rebar diameter equal to 12. RC columns scaled at 1/3, with round and square section, were subjected to axial compression up to failure. A damage scale is introduced for the assessment of the damage severity, which focusses on the extent of buckling of the longitudinal rebars. The damaged specimens were subsequently repaired with unidirectional CFRP jackets without any treatment of the buckled reinforcing bars and were finally re-tested to failure. Test results indicate that CFRP jackets may be effectively applied to rehabilitate RC columns (a) with inadequate transverse reinforcement constructed according to older practices so as to meet modern code requirements, and (b) with moderately buckled bars without the need of previously repairing the reinforcement bars, an application technique which may considerably facilitate the retrofit of earthquake damaged RC columns. Factors for the estimation of the reduced mechanical properties of the repaired specimens compared to the respective values for intact CFRP-jacketed specimens, in relation to the level of damage prior to retrofit, are proposed both for the compressive strength and the average modulus of elasticity. It was determined that the compressive strength of the retrofitted CFRP-jacketed columns is reduced by 90% to 65%, while the average modulus of elasticity is lower by 60% to 25% in respect to similar undamaged columns jacketed with the same layers of CFRP.

• 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.

• Proceedings of the Computational Structural Engineering Institute Conference
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• 2001.10a
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• pp.369-374
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• 2001

This paper deals with the buckling loads of column with rotation end restricted by rotational spring. The ordinary differential equations governing the buckling loads of such column is derived as nondimensional forms, and also its boundary conditions are derived. The buckled column model is based on the classical Bemoulli-Euler beam theory. The Runge-Kutta method and Regula-Falsi method are used to perform the integration of the differential equations and to determine the eigenvalue. The numerical methods developed herein for the buckling loads of the such column are found to be efficient and reliable. It is expected that the results obtained herein can be practically utilized in the structural engineering field.

• Proceedings of the Computational Structural Engineering Institute Conference
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• 2006.04a
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• pp.935-940
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• 2006

Numerical methods are developed for solving the elastica and buckling load of cantilever column with constant volume, 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 horizontal deflection at free 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.

• Structural Engineering and Mechanics
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• v.28 no.2
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• pp.221-238
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• 2008

Numerical solution to buckling analysis of beams and columns are obtained by the method of differential quadrature (DQ) and harmonic differential quadrature (HDQ) for various support conditions considering the variation of flexural rigidity. The solution technique is applied to find the buckling load of fully or partially embedded columns such as piles. A simple semi- inverse method of DQ or HDQ is proposed for determining the flexural rigidities at various sections of non-prismatic column ( pile) partially and fully embedded given the buckling load, buckled shape and sub-grade reaction of the soil. The obtained results are compared with the existing solutions available from other numerical methods and analytical results. In addition, this paper also uses a recently developed technique, known as the differential transformation (DT) to determine the critical buckling load of fully or partially supported heavy prismatic piles as well as fully supported non-prismatic piles. In solving the problem, governing differential equation is converted to algebraic equations using differential transformation methods (DT) which must be solved together with applied boundary conditions. The symbolic programming package, Mathematica is ideally suitable to solve such recursive equations by considering fairly large number of terms.

• Proceedings of the Computational Structural Engineering Institute Conference
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• 1996.10a
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• pp.3-10
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• 1996

Numerical methods are developed for solving the buckling loads and the elastica of clamped- free columns of circular cross-section with constant volume. The column model is based rut the Timoshenko beam theory. The Runge-Kutta and Regula-Falsi methods, respectively, are used to solve the governing differential equations and to compute the eigenvalues. Extensive numerical results, including buckling loads, elastica of buckled shapes and effects of shear de-formation, are presented in non-dimensional form for elastic columns whose radius of circular cross-section varies both linearly and parabolically with column length.

• 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.