• Structural Engineering and Mechanics
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• v.48 no.2
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• pp.275-289
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• 2013

The cross sections of multi-span beams are sometimes suddenly increased at the interior support of continuous beams to resist high negative moment. An earlier study on elastic lateral torsional buckling of stepped beams was conducted to propose new design equations. This research aims to continue the earlier study by considering the effect of inelastic buckling of stepped beams subjected to pure bending and general loading condition. A three-dimensional finite element-program ABAQUS and a statistical program MINITAB were used in the development of new design equations. The inelastic lateral torsional buckling strengths of 36 and 27 models for singly and doubly stepped beams, respectively, were investigated. The general loading condition consists of 15 loading cases based on the number of inflection point within the unbraced length of the stepped beams. The combined effects of residual stresses and geometrical imperfection were also considered to evaluate the inelastic buckling strengths. The proposed equations in this study will definitely improve current design methods for the inelastic lateral-torsional buckling of stepped beams and will increase efficiency in building and bridge design.

• Steel and Composite Structures
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• v.4 no.1
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• pp.23-36
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• 2004

The inelastic lateral-distortional buckling of doubly-symmetric hot-rolled I-section beam-columns subjected to a concentric axial force and uniform bending with elastic restraint which produce single curvature is investigated in this paper. The numerical model adopted in this paper is an energy-based method which leads to the incremental and iterative solution of a fourth-order eigenproblem, with very rapid solutions being obtained. The elastic restraint considered in this paper is full restraint against translation, but torsional restraint is permitted at the tension flange. Hitherto, a numerical method to analyse the elastic and inelastic lateral-distortional buckling of restrained or unrestrained beam-columns is unavailable. The prediction of the inelastic lateral-distortional buckling load obtained in this study is compared with the inelastic lateral-distortional buckling of restrained beams and the inelastic lateral-torsional buckling solution, by suppressing the out-of-plane web distortion, is published elsewhere and they agree reasonable well. The method is then extended to the lateral-distortional buckling of continuously restrained doubly symmetric I-sections to illustrate the effect of web distortion.

• Steel and Composite Structures
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• v.43 no.3
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• pp.341-351
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• 2022

This paper presents an inelastic buckling behavior analysis of rectangular hollow steel tubes with geometrical imperfections under elevated temperatures. The main variables are the temperature loads, slenderness ratios, and exposure conditions at high temperatures. The material and structural properties of steels at different temperatures are based on Eurocode (EN 1993-1-2, 2005). In the elastic buckling analysis, the buckling strength decreases linearly with the exposure conditions, whereas the inelastic buckling analysis shows that the buckling strength decreases in clusters based on the exposure conditions of strong and weak axes. The buckling shape of the rectangular steel column in the elastic buckling mode, which depicts geometrical imperfection, shows a shift in the position at which bending buckling occurs when the lower section of the member is exposed to high temperatures. Furthermore, lateral torsional buckling occurs owing to cross-section deformation when the strong axial plane of the model is exposed to high temperatures. The elastic buckling analysis indicates a conservative value when the model is exposed to a relatively low temperature, whereas the inelastic buckling analysis indicates a conservative value at a certain temperature or higher. The comparative results between the inelastic buckling analysis and Eurocode 3 show that a range exists in which the buckling strength in the design equation result is overestimated at elevated temperatures, and the shapes of the buckling curves are different.

• Structural Engineering and Mechanics
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• v.26 no.6
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• pp.651-672
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• 2007

This study presents an improved method that uses the elastic and inelastic system buckling analyses for determining the K-factors of steel column members. The inelastic system buckling analysis is based on the tangent modulus theory for a single column and the application is extended to the frame structural system. The tangent modulus of an inelastic column is first derived as a function of nominal compressive stress from the column strength curve given in the design codes. The tangential stiffness matrix of a beam-column element is then formulated by using the so-called stability function or Hermitian interpolation functions. Two inelastic system buckling analysis procedures are newly proposed by utilizing nonlinear eigenvalue analysis algorithms. Finally, a practical method for determining the K-factors of individual members in a steel frame structure is proposed based on the inelastic and/or elastic system buckling analyses. The K-factors according to the proposed procedure are calculated for numerical examples and compared with other results in available references.

• Structural Engineering and Mechanics
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• v.27 no.4
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• pp.477-499
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• 2007

The main purpose of this paper is to investigate the ultimate behavior of steel cable-stayed bridges with design variables and compare the validity and applicability of computational methods for evaluating ultimate load capacity of cable-stayed bridges. The methods considered in this paper are elastic buckling analysis, inelastic buckling analysis and nonlinear elasto-plastic analysis. Elastic buckling analysis uses a numerical eigenvalue calculation without considering geometric nonlinearities of cable-stayed bridges and the inelastic material behavior of main components. Inelastic buckling analysis uses an iterative eigenvalue calculation to consider inelastic material behavior, but cannot consider geometric nonlinearities of cable-stayed bridges. The tangent modulus concept with the column strength curve prescribed in AASHTO LRFD is used to consider inelastic buckling behavior. Detailed procedures of inelastic buckling analysis are presented and corresponding computer codes were developed. In contrast, nonlinear elasto-plastic analysis uses an incremental-iterative method and can consider both geometric nonlinearities and inelastic material behavior of a cable-stayed bridge. Proprietary software ABAQUS are used and user-subroutines are newly written to update equivalent modulus of cables to consider geometric nonlinearity due to cable sags at each increment step. Ultimate load capacities with the three analyses are evaluated for numerical models of cable-stayed bridges that have center spans of 600 m, 900 m and 1200 m with different girder depths and live load cases. The results show that inelastic buckling analysis is an effective approximation method, as a simple and fast alternative, to obtain ultimate load capacity of long span cable-stayed bridges, whereas elastic buckling analysis greatly overestimates the overall stability of cable-stayed bridges.

• Steel and Composite Structures
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• v.3 no.1
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• pp.1-12
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• 2003

Cantilevers are unique statically determinate structural elements with respect to their mode of overall buckling, in that the tension flange is the critical flange under gravity loading, and is the flange that deflects greatest during overall buckling. While this phenomenon does not complicate the calculation of the lateral buckling load, either theoretically or in structural design codes, it has been shown in previous research that the influence of distortion in the elastic buckling of cantilevers is not the same as that experienced in the elastic buckling of simply supported beams. This paper extends the study of the distortional buckling of cantilevers into the hitherto unconsidered inelastic range of structural response. A finite element method for studying the inelastic bifurcative instability of members whose cross-sections may distort during buckling is described, and the efficacy of the method is demonstrated. It is then used to study the inelastic distortional buckling of hot-rolled I-section cantilevers with two common patterns of residual stresses, and which may be restrained elastically from buckling by other structural elements.

• Journal of Korean Society of Steel Construction
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• v.12 no.1 s.44
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• pp.29-43
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• 2000

In this study, the computationally efficient inelastic buckling analysis program is developed to be used as the research tool in finding buckling strength of inelastic members. The program can determine buckling loads and buckled shapes of elastic and inelastic members which failed by flexural, lateral-torsional and/or local buckling. It can analyze singly and doubly symmetric I-shape members. In the program, the web of the member is modeled using the plate element and the flanges are modeled by beam elements. Multilinear isotropic hardening rule and the incremental theory of plasticity are used to simulate the inelastic stress-strain relationship from material tests. The program is verified using theoretical solutions and experimental results. The results from the program show good agreement with those from experiments and theory.

• Steel and Composite Structures
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• v.2 no.4
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• pp.297-314
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• 2002

An energy method of analysis is presented which can be used to study the inelastic lateral-distortional buckling of hot-rolled I-sections continuously restrained at the level of the tension flange. The numerical modelling leads to the incremental and iterative solution of a fourth-order eigenproblem, with very rapid solutions being obtainable, so as to enable a study of the factors that influence the strength of continuously restained I-beams to be made. Although hot-rolled I-sections generally have stocky webs and are not susceptible to reductions in their overall buckling loads as a result of cross-sectional distortion, the effect of elastic restraints, particularly against twist rotation, can lead to buckling modes in which the effect of distortion is quite severe. While the phenomenon has been studied previously for elastic lateral-distortional buckling, it is extended in this paper to include the constitutive relationship characteristics of mild steel, and incorporates both the so-called 'polynomial' and 'simplified' models of residual stresses. The method is validated against inelastic lateral-torsional buckling solutions reported in previous studies, and is applied to illustrate some inelastic buckling problems. It is noted that over a certain range of member slenderness the provisions of the Australian AS4100 steel standard are unconservative.

• Steel and Composite Structures
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• v.5 no.4
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• pp.305-326
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• 2005

The inelastic buckling behaviour of continuously restrained two and three-span continuous beams subjected to concentrated loads and uniformly distributed loads are studied in this paper. The restraint type considered in this paper is fully restrained against translation and elastic twist applied at the top flange. These types of restraints are most likely experienced in industrial structures, for example steel-concrete composite beams and half through girders. The buckling analysis of continuous beam consists of two parts, firstly the moment and shear distribution along the member are determined by employing force method and the information is then used for an out-of-plane buckling analysis. The finite element method is incorporated with so-called simplified and the polynomial pattern of residual stress. Owing to the inelastic response of the steel, both the in-plane and out-of-plane analysis, which is treated as being uncoupled, extend into the nonlinear range. This paper presents the results of inelastic lateral-torsional and lateral-distortional buckling load and finally conclusions are drawn regarding the web distortion.

• Structural Engineering and Mechanics
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• v.9 no.1
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• pp.51-68
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• 2000

The paper presents theoretical and experimental investigations on three varying thickness circular cylinders, which were tested to destruction under external hydrostatic pressure. The five buckling theories that were presented were based on inelastic shell instability. Three of these inelastic buckling theories adopted the finite element method and the other two theories were based on a modified version of the much simpler von Mises theory. Comparison between experiment and theory showed that one of the inelastic buckling theories that was based on the von Mises buckling pressure gave very good results while the two finite element solutions, obtained by dividing the theoretical elastic instability pressures by experimentally determined plastic knockdown factors gave poor results. The third finite element solution which was based on material and geometrical non-linearity gave excellent results. Electrical resistance strain gauges were used to monitor the collapse mechanisms and these revealed that collapse occurred in the regions of the highest values of hoop stress, where considerable deformation took place.