• Structural Engineering and Mechanics
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• v.6 no.4
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• pp.411-425
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• 1998

The effective length factor of a framed column may be determined by means of the alignment chart procedure. This method is based on many unrealistic assumptions, among which is that all columns have the same stiffness parameter, which is dependent on the length, axial load, and moment of inertia of the column. A new approximate method is developed for the determination of effective length factors for columns in unbraced frames. This method takes into account the effects of inelastic column behaviour, far end conditions of the restraining beams and columns, semi-rigid beam-to-column connections, and differentiated stiffness parameters of columns. This method may be implemented on a microcomputer. A numerical study was carried out to demonstrate the extent to which the involved parameters affect the K factor. The beam-to-column connection stiffness, the stiffness parameter of columns, and the far end conditions of restraining members have a significant effect on the K factor of the column under investigation. The developed method is recommended for design purposes.

• Structural Engineering and Mechanics
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• v.19 no.6
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• pp.679-705
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• 2005

This paper presents a practical method to evaluate the effective length factors for columns in multi-storey unbraced frames based on the concept of storey-based elastic buckling by means of decomposing a multi-storey frame into a series of single-storey partially-restrained (PR) frames. The lateral stiffness of the multi-storey unbraced frame is derived and expressed as the product of the lateral stiffness of each storey. Thus, the stability analysis for the multi-storey frame is conducted by investigating the lateral stability of each individual storey, which is facilitated through decomposing the multi-storey frame into a series of single-storey PR frames and applying the storey-based stability analysis proposed by the authors (Xu and Liu 2002) for each single-storey PR frame. Prior to introducing decomposition approaches, the end rotational stiffness of an axially load column is derived and rotational stiffness interaction between the upper and lower columns is investigated. Three decomposition approaches, characterized by means of distributing beam-to-column rotational-restraining stiffness between the upper and lower columns, are proposed. The procedure of calculating storey-based column effective length factors is presented. Numerical examples are then given to illustrate the effectiveness of the proposed procedure.

• Structural Engineering and Mechanics
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• v.11 no.3
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• pp.287-299
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• 2001

Columns in multi-storey frames are presently categorised as either braced or unbraced, usually by means of the stability index criterion, for estimating their effective length ratios by design aids such as 'alignment charts'. This procedure, however, ignores the transition in buckling behaviour between the braced condition and the unbraced one. Hence, this results in either an overestimation or an underestimation of effective length estimates of columns in frames that are in fact 'partially braced'. It is shown in this paper that the transitional behaviour is gradual, and can be approximately modelled by means of a 'fuzzy logic' based technique. The proposed technique is simple and intuitively agreeable. It fills the existing gap between the braced and unbraced conditions in present codal provisions.

• Steel and Composite Structures
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• v.8 no.5
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• pp.389-402
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• 2008

In December 2005, one(A) of the two pre-engineered warehouse buildings in the port of K City of Korea was completely destroyed and the other(B) was seriously damaged to be demolished. Over-loaded snow and unexpected blast of wind were the causes of the accident and destructive behavior was brittle fracture caused by web local buckling and lateral torsional buckling at the flange below rafter. However, the architectural design technology of today based on material non-linear method does not consider the tolerances to solve the problem of such brittle fracture. So, geometric non-linear evaluation which includes initial deformation, width-thickness ratio, web stiffener and unbraced length is required. This study evaluates the structural safety of 4 models in terms of width-thickness ratio and unbraced length using ANSYS 9.0 with parameters such as width-thickness ratio of web, existence/non-existence of stiffener and unbraced length. The purpose of this study is to analyze destructive mechanism of the above-mentioned two warehouse buildings and to provide ways to promote the safety of pre-engineered buildings.

• Journal of Korean Society of Steel Construction
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• v.25 no.2
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• pp.115-130
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• 2013

In this study, lateral-torsional buckling (LTB) strength of high-strength H-beams built up from 800MPa tensile-strength steel was experimentally and analytically evaluated according to current lateral stability provisions (KBC 2009, AISC-LRFD 2010). The motivation was to evaluate whether or not current LTB provisions, which were originally developed for ordinary steel with different stress-strain characteristics, are still applicable to high-strength steel. Two sets of compact-section specimens with relatively low (Set A) or high (Set B) warping stiffness were prepared and tested under uniform moment loading. Laterally unbraced lengths of the test specimens were controlled such that inelastic LTB could be induced. All specimens exhibited LTB strength exceeding the minimum limit required by current provisions by a sufficient margin. Moreover, some specimen in Set A reached a rotation capacity required for plastic design, although its laterally unbraced length belonged to the inelastic LTB range. All the test results indicated that extrapolation of current provisions to high-strength steel is conservative. In order to further analyze the test results, the relationship between inelastic moment and laterally unbraced length was also derived in explicit form for both ordinary- and high-strength steel based on the effective tangent modulus of inelastic section. The analytical relationship derived again showed that extrapolation of current laterally unbraced length limit leads to a conservative design in the case of high-strength steel and that the laterally unbraced length to control the inelastic LTB behavior of high-strength steel beam should be specified by including its unique post-yield strain-hardening characteristics.

• Structural Engineering and Mechanics
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• v.19 no.1
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• pp.55-71
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• 2005

In several design codes and specifications, simplified formulae and diagrams are given for determining the buckling lengths of frame columns. It is shown that these formulae may yield rather erroneous results in certain cases. This is due to the fact that, the code formulae utilise only local stiffness distributions. In this paper, a simplified procedure for determining approximate values for the buckling loads of multi-storey frames is developed. The procedure utilises lateral load analysis of frames and yields errors in the order of 10%, which may be considered suitable for design purposes. The proposed procedure is applied to several numerical examples and it is shown that all the errors are in the acceptable range and on the safe side.

• Journal of Korean Society of Steel Construction
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• v.23 no.3
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• pp.327-335
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• 2011

This study has two objectives: (1) to evaluate the degradation characteristics of symmetric unbraced steel frames by using analytical approach, and (2) to suggest equation which can approximately estimate the effect of degradation during the schematic design stage. For the analytical approach, the refined plastic hinge method with an arc length algorithm was adopted. The subject of analysis was one story one-bay, multistory one-bay, and multistory three-bay unbraced steel frames. The main parameters of the analytical approach include the stiffness ratio of column to beam and the axial force ratio. The study led to the following conclusions. The normalized stiffness of degradations is affected by both stiffness ratio of column to beam and the axial load ratio; however, the major influence on degradations is the axial force ratio. The equation, which can approximately estimate the effect of degradation, was suggested together with the research results.

• Steel and Composite Structures
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• v.30 no.5
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• pp.483-492
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• 2019

In the current study, the influence of the initial lateral (sweep) shape and the cross-sectional twist imperfection on the lateral torsional buckling (LTB) response of doubly-symmetric steel I-beams was investigated. The material imperfection (residual stress) was not considered. For this objective, standard European IPN 300 beam with different unbraced span was numerically analyzed for three imperfection cases: (i) no sweep and no twist (perfect); (ii) three different shapes of global sweep (half-sine, full-sine and full-parabola between the end supports); and (iii) the combination of three different sweeps with initial sinusoidal twist along the beam. The first comparison was done between the results of numerical analyses (FEM) and both a theoretical solution and the code lateral torsional buckling formulations (EC3 and AISC-LRFD). These results with no imperfection effects were then separately compared with three different shapes of global sweep and the presence of initial twist in these sweep shapes. Besides, the effects of the shapes of initial global sweep and the inclusion of sinusoidal twist on the critical buckling load of the beams were investigated to unveil which parameter was considerably effective on LTB response. The most compatible outcomes for the perfect beams was obtained from the AISC-LRFD formulation; however, the EC-3 formulation estimated the $P_{cr}$ load conservatively. The high difference from the EC-3 formulation was predicted to directly originate from the initial imperfection reduction factor and high safety factor in its formulation. Due to no consideration of geometric imperfection in the AISC-LFRD code solution and the theoretical formulation, the need to develop a practical imperfection reduction factor for AISC-LRFD and theoretical formulation was underlined. Initial imperfections were obtained to be more influential on the buckling load, as the unbraced length of a beam approached to the elastic limit unbraced length ($L_r$). Mode-compatible initial imperfection shapes should be taken into account in the design and analysis stages of the I-beam to properly estimate the geometric imperfection influence on the $P_{cr}$ load. Sweep and sweep-twist imperfections led to 10% and 15% decrease in the $P_{cr}$ load, respectively, thus; well-estimated sweep and twist imperfections should considered in the LTB of doubly-symmetric steel I-beams.

• Steel and Composite Structures
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• v.5 no.5
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• pp.407-420
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• 2005

This study presents the strength of braced and unbraced cold-formed steel wall frames consisting of several wall studs acting as columns, top and bottom tracks, and bracing members. The strength and the buckling mode of steel wall frames were found to be different due to the change of bracing type. In addition, the spacing of wall studs is a crucial factor to the strength of steel wall frames. The comparisons were made between the test results and the predictions computed based on AISI Code. The related specifications do not clearly provides the effective length factors for the member of cold-formed steel frame under compression. This paper proposes effective length factors for the steel wall frames based on the test results. A theoretical model is also derived to obtain the modulus of elastic support provided by the bracing at mid-height of steel wall frames in this research.

• Journal of Korean Society of Steel Construction
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• v.19 no.5
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• pp.493-501
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• 2007

Recently, in the domestic amount of materials,curtailment and economic efficiency security by purpose, tapered beam application is achieved, but the architectural design technology of today based on the material non-linear method does not consider solutions to problems such as brittle fracture. So, geometric non-linear evaluation thatincludes initial deformation, width-thickness ratio, web stiffener and unbraced length is required. Therefore, in this study, we used ANSYS, a proven finite elementanalysis program,and material and geometric non-linear analysis to study existing and completed tapered H-section as deep beam's analysis model. Main parameters include the width-thickness ratio of web, stiffener, and flange brace, with the experimental result obtained by main variable buckling and limit strength evaluation. We made certain that a large width-thickness ratio of the web decreases the buckling strength and short unbraced web significantly improves ductility.