• Structural Engineering and Mechanics
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• v.11 no.1
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• pp.1-16
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• 2001

This paper discusses the elastic stability of unbraced frames under non-proportional loading based on the concept of storey-based buckling. Unlike the case of proportional loading, in which the load pattern is predefined, load patterns for non-proportional loading are unknown, and there may be various load patterns that will correspond to different critical buckling loads of the frame. The problem of determining elastic critical loads of unbraced frames under non-proportional loading is expressed as the minimization and maximization problem with subject to stability constraints and is solved by a linear programming method. The minimum and maximum loads represent the lower and upper bounds of critical loads for unbraced frames and provide realistic estimation of stability capacities of the frame under extreme load cases. The proposed approach of evaluating the stability of unbraced frames under non-proportional loading has taken into account the variability of magnitudes and patterns of loads, therefore, it is recommended for the design practice.

• Journal of Korean Society of Steel Construction
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• v.17 no.4 s.77
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• pp.469-479
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• 2005

The nonlinear behavior of a connection has an influence on the behavior (the $P-\Delta$ effect) and the stability of a steel unbraced frame when a semi-rigid connection is applied as a beam-to-column connection. Therefore, the effects of a connection's non-linear behavior on the behavior and stability of a steel unbraced frame were investigated using second-order inelastic analysis, after which the main influence factors and their behavioral tendencies were studied. The study results showed that the nonlinear behavior of a connection directly affects the stability of a steel unbraced frame, and that the main influence factors are the rotational stiffness of the connection and the location of a semi-rigid connection.

• 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.

• Structural Engineering and Mechanics
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• v.4 no.4
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• pp.365-381
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• 1996

Stability equations that evaluate the elastic critical axial load of columns in any type of construction with sidesway uninhibited, partially inhibited, and totally inhibited are derived in a classical manner. These equations can be applied to the stability of frames (unbraced, partially braced, and totally braced) with rigid, semirigid, and simple connections. The complete column classification and the corresponding three stability equations overcome the limitations and paradoxes of the well known alignment charts for braced and unbraced columns and frames. Simple criteria are presented that define the concept of partially braced columns and frames, as well as the minimum lateral bracing required by columns and frames to achieve non-sway buckling mode. Various examples are presented in detail that demonstrate the effectiveness and accuracy of the complete set of stability equations.

• 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.

• Proceedings of the Computational Structural Engineering Institute Conference
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• 2002.10a
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• pp.685-693
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• 2002

This bridge was planed to be located in Geuk-rak river at south of Kwangju city. And it is very important to emphasis the beauty of bridge appearance. So Ive adopted unbraced tube arch type those linear beauty is elegance and simple. Actually, foreign bridges similar to this won various prizes for excellence of design. But there is no similar precedent in domestic highway bridge. therefore we intended to certify the security of this bridge through computational analysis. In this paper, approximate introduction of this bridge, design procedure and principal examination item is mentioned.

• Journal of Korean Society of Steel Construction
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• v.13 no.4
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• pp.363-372
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• 2001

The objective of this study is to evaluate the $P-{\Delta}$ effect in the case of weak beam unbraced frames by experimental approach. To evaluate $P-{\Delta}$ effect, four specimens were tested under monotonic loading condition. The parameters of tests are the stiffness of column and the axial load ratio. The results show that the value of axial load affects frame stability because $P-{\Delta}$ effects promote the yielding of beam. The maximum lateral load increases in proportion to the increment of column stiffness and rotational stiffness of supports, The collapse mechanism of weak beam unbraced frames is stably formed in the condition of low axial load ratio. The $B_2$ factor of limit state design code does not properly consider the $P-{\Delta}$ effect in inelastic region.

• Journal of Korean Society of Steel Construction
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• v.22 no.1
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• pp.87-97
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• 2010

The purpose of this study was to evaluate the validity of the second-order analysis for asymmetric unbraced frame using the load amplification factor suggested by design codes. For this purpose, the first-order analysis with the B1 and B2 factors suggested by KBC 2005 and the direct analysis with the load amplification factors suggested by KBC 2009 were performed for five story - two bay and five story - four bay asymmetric unbraced steel frames. The results of the analyses were compared with the results of the second-order inelastic analysis to evaluate the validity of the suggested methods. The main parameters of the analysis were the shape of the frame, the axial load ratio of the column, the methods of analysis and the location of column. The research results show that the asymmetric shape of the frame deteriorates the validity of the factor B2 and the suggested methods. The range of error is increased in case of irregular or inclined column.

• Structural Engineering and Mechanics
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• v.5 no.4
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• pp.415-431
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• 1997

Stability equations that evaluate the elastic critical axial load of stepped columns under extreme and intermediate concentrated axial loads in any type of construction with sidesway totally inhibited, partially inhibited and uninhibited are derived in a classical manner. These equations can be utilized in the stability analysis of framed structures (totally braced, partially braced, and unbraced) with stepped columns with rigid, semirigid, and simple connetions. The proposed column classification and the corresponding stability equations overcome the limitations of current methods which are based on a classification of braced and unbraced columns. The proposed stability equations include the effects of: 1) semirigid connections; 2) step variation in the column cross section at the point of application of the intermediate axial load; and 3) lateral and rotational restraints at the intermediate connection and at the column ends. The proposed method consists in determining the eigenvalue of a $2{\times}2$ matrix for a braced column at the two ends and of a $3{\times}3$ matrix for a partially braced or unbraced column. The stability analysis can be carried out directly with the help of a pocket calculator. The proposed method is general and can be extended to multi-stepped columns. Various examples are include to demonstrate the effectiveness of the proposed method and to verify that the calculated results are exact. Definite minimum bracing criteria for single stepped columns is also presented.