• Steel and Composite Structures
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• v.16 no.1
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• pp.45-58
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• 2014

EC3 provides several methodologies for the stability verification of members and frames. However, when dealing with the verification of non-uniform members in general, with tapered cross-section, irregular distribution of restraints, non-linear axis, castellated, etc., several difficulties are noted. Because there are yet no guidelines to overcome any of these issues, safety verification is conservative. In recent research from the authors of this paper, an Ayrton-Perry based procedure was proposed for the flexural buckling verification of web-tapered columns. However, in order to apply this procedure, Linear Buckling Analysis (LBA) of the tapered column must be performed for determination of the critical load. Because tapered members should lead to efficient structural solutions, it is therefore of major importance to provide simple and accurate formula for determination of the critical axial force of tapered columns. In this paper, firstly, the fourth order differential equation for non-uniform columns is derived. For the particular case of simply supported web-tapered columns subject to in-plane buckling, the Rayleigh-Ritz method is applied. Finally, and followed by a numerical parametric study, a formula for determination of the critical axial force of simply supported linearly web-tapered columns buckling in plane is proposed leading to differences up to 8% relatively to the LBA model.

• Journal of KSNVE
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• v.2 no.3
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• pp.203-211
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• 1992

The main purpose of this paper is to present both the natural frequencies and the first critical loads of tapered columns. The ordinary differential equation governing the free vibration for tapered columns under compressive axial force is derived. Three kinds of cross sectional shape are considered in the governing equation. The Runge-Kutta method and determinant search method are used to perform the integration of the differential equation and to determine the natural frequencies, respectively. Additionally, the bisection method is used to determine the critical loads. In numerical examples, the effects of compressive axial force on the natural frequencies of tapered columns are investigated varying the end conditions. The first critical loads of tapered columns are determined on the basis of dynamic concepts. The first critical loads of tapered columns are determined on the basis of dynamic concept. The effects of cross sectional shapes are shown and some typical mode shapes are also presented.

• Steel and Composite Structures
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• v.17 no.5
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• pp.667-686
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• 2014

Tapered concrete filled double skin steel tubular (CFDST) columns have been used in China for structures such as electricity transmission towers. In practice, the bearing capacity related to the connection details on the top of the column is not fully understood. In this paper, the experimental behaviour of tapered CFDST stub columns subjected to axial partial compression is reported, sixteen specimens with top endplate and ten specimens without top endplate were tested. The test parameters included: (1) tapered angle, (2) top endplate thickness, and (3) partial compression area ratio. Test results show that the tapered CFDST stub columns under axial partial compression behaved in a ductile manner. The axial partial compressive behaviour and the failure modes of the tapered CFDST stub columns were significantly influenced by the parameters investigated. Finally, a simple formula for predicting the cross-sectional capacity of the tapered CFDST sections under axial partial compression is proposed.

• Architectural research
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• v.8 no.1
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• pp.47-56
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• 2006

In this research, the analysis of post-buckling behavior of tapered columns has been performed under a combined load of uniformly distributed axial load along the length and concentric axial load at free end by solving the nonlinear differential equation with the differential transformation technique. The buckling load at various slopes at free end of column is calculated and the results of the analysis using the differential transformation technique is verified with those of previous studies. It is also shown through the results that the buckling load of sinusoidal tapered columns is largest, the linear is second largest, and the parabolic is small in the all ranges of slopes at free end and the deflection of parabolic tapered columns in the x coordinates is largest, the sinusoidal is second largest, and the linear is smallest in the range of slope 0 to 140 degrees at free end. However, when the range of the slope is 160 to 176 degrees at the free end, the deflection of sinusoidal tapered columns in the x coordinates is largest, the linear is second largest, and the parabolic is smallest. In addition, for the linear tapered column, the buckling load increases along with the flexural stiffness ratio. Also, for the parabolic and the sinusoidal tapered column, the buckling loads increase and decrease as the flexural ratios increase in the range of flexural stiffness ratio n = 1.0 to n = 2.0. Through this research, it is verified that the differential transformation technique can be applied to solve the nonlinear differential equation problems, such as analysis of post-buckling behavior of tapered columns. It is also expected that the differential transformation technique apply to various more complicated problems in future.

• Structural Engineering and Mechanics
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• v.10 no.5
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• pp.479-489
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• 2000

Based on the stiffness equation of the tapered beam element involving the effects of axial force and shear deformation, numerical investigations are carried out on elastic instability for web-linearly tapered columns with I-section of steel portal frames. Effects of shear deformation on the effective length of the tapered columns with I-section are studied. An efficient approach for determining the effective length of the tapered portal frame columns considering effects of shear deformation is proposed.

• Proceedings of the Computational Structural Engineering Institute Conference
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• 2006.04a
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• pp.949-954
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• 2006

The purpose of this paper is to investigate the stability of tapered columns with clamped one end and carrying a tip mass of rotatory inertia with translational elastic support at the other end. 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 columns is derived using the Bernoulli-Euler beam theory. Both the 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, mass ratio and spring stiffness.

• Computers and Concrete
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• v.9 no.6
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• pp.403-426
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• 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.

• Proceedings of the Computational Structural Engineering Institute Conference
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• 2003.10a
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• pp.243-250
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• 2003

A method for the determination of effective length factors of the framed columns with sinusoidally tapered sections is proposed. In the study, the stability analysis of the single story-two equal bay, frame with tapered columns is performed first by finite element method. The changes of the critical load coefficients of frames are reprersented by algebraic equations of the analysis parameters. The effective length factor formula is expressed in terms of proposed algebraic equation. The effective length factors for the prismatic columns (α=0.0) estimated by the proposed method coincide fairly well with those determined by the analytical method.

• 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.

• Magazine of the Korean Society of Agricultural Engineers
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• v.34 no.4
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• pp.97-105
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• 1992

The main purpose of this paper is to present the buckling loads of tapered columns due to dynamic concept. The ordinary differential equation governing the bucking loads for tapered columns is derived on the basis of dynamic concept. Three kinds of cross sectional shape are considered in the governing equation. The Improved Euler method and Determinant Search method are used to perform the integration of the differential equation and to determine the buckling loads, respectively. The hinged-hinged, hinged-clamped, clamped-clamped and free-clamped end constraints are applied in numerical examples. The buckling loads are reported as the function of section ratio, and the effects of cross-sectional shapes are investigated. The buckling load equation, which are fitted by numerical data, are proposed as a function of section ratio. It is expected that these equations can be utilized in structural engineering field.