• 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.

• Steel and Composite Structures
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• v.19 no.5
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• pp.1203-1219
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• 2015

'Distortional buckling' is one of the predominant buckling types that may occur in a steel-concrete composite box beam (SCCBB) under a negative moment. The key factors, which affect the buckling modes, are the torsional and lateral restraints of the bottom plate of a SCCBB. Therefore, this article investigates the equivalent lateral and torsional restraint rigidity of the bottom plate of a SCCBB under a negative moment; the results of which show a linear coupling relationship between the applied forces and the lateral and/or torsional restraint stiffness, which are not depended on the cross-sectional properties of a SCCBB completely. The mathematical formulas for calculating the lateral and torsional restraint rigidity of the bottom plate can be used to estimate: (1) the critical distortional buckling stress of SCCBBs under a negative moment; and (2) the critical distortional moment of SCCBBs. This article develops an improved calculation method for SCCBBs on an elastic foundation, which takes into account the coupling effect between the applied forces and the lateral and/or torsional restraint rigidity of the bottom plate. This article analyzes the accuracy of the following calculation methods by using 24 examples of SCCBBs: (1) the conventional energy method; (2) the improved calculation method, as it has been derived in this article; and (3) the ANSYS finite element method. The results verify that the improved calculation method, as it has been proved in this article, is more accurate and reliable than that of the current energy method, which has been noted in the references.

• Earthquakes and Structures
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• v.12 no.5
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• pp.515-527
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• 2017

Recently, Friction dampers become popular due to the desirable performance in the energy dissipation of lateral loads. A lot of research which has been conducted on these dampers results in developing friction dampers with low sensitivity to the number of cycles and temperature increases. Friction dampers impose high residual drifts to the buildings because of low post-yield stiffness of the damper which results from increasing lateral displacement and period of buildings. This issue can be more critical under strong aftershocks which results in increasing of structural damages. In this paper, in addition to the assessment of aftershock on steel buildings equipped with friction dampers, methods for controlling residual drifts and decreasing the costs of retrofitting are investigated. Utilizing rigid connections as a lateral dual system and activating lateral stiffness of gravity columns by adding elastic braces are as an example of effective methods investigated in this research. The results of nonlinear time history analyses on the low to medium rise steel frames equipped with friction dampers illustrate a rise in residual drifts as the result of aftershocks. In addition, the results show that different slip loads of friction damper can affect the residual drifts. Furthermore, elastic stories in comparison to rigid connections can reduce residual drifts of buildings in an effective fashion, when most slip loads of friction dampers are considered.

• Coupled systems mechanics
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• v.9 no.2
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• pp.183-200
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• 2020

Connection of adjacent buildings with stiff links is an efficient approach for seismic pounding mitigation. However, use of highly rigid links might alter the torsional response in asymmetric plans and although this was mentioned in the literature, no quantitative study has been done before to investigate the condition numerically. In this paper, the effect of rigid coupling on the elastic lateral-torsional response of two adjacent one-story column-type buildings has been studied by comparison to uncoupled structures. Three cases are considered, including two similar asymmetric structures, two adjacent asymmetric structures with different dynamic properties and a symmetric system adjacent to an adjacent asymmetric one. After an acceptable validation against the actual earthquake, the traditional random vibration method has been utilized for dynamic analysis under Ideal white noise input. Results demonstrate that rigid coupling may increase or decrease the rotational response, depending on eccentricities, torsional-to-lateral stiffness ratios and relative uncoupled lateral stiffness of adjacent buildings. Results are also discussed for the case of using identical cross section for all columns supporting eachplan. In contrast to symmetric systems, base shear increase in the stiffer building may be avoided when the buildings lateral stiffness ratio is less than 2. However, the eccentricity increases the rotation of the plans for high rotational stiffness of the buildings.

• Structural Engineering and Mechanics
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• v.21 no.4
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• pp.451-468
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• 2005

Effective beam width models are commonly used to obtain the lateral stiffness of flat plate structures. In these models, an effective beam width is defined as the width when the flexural stiffness of the beam element equals the slab stiffness. In this present study, a method to obtain effective beam widths that considers the effects of connection geometry and slab cracking is analytically proposed. The rectangularity of the vertical member for the connection geometry and the combined effects of creep and shrinkage for the slab cracking are considered. The results from the proposed method are compared with experimental results from a test structure having nine slab-column connections.

• Steel and Composite Structures
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• v.23 no.3
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• pp.285-302
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• 2017

Buckling-restrained braced frames (BRBFs) are commonly used as the lateral force-resisting systems in building structures in the seismic regions. The nearly-symmetric hysteretic response and the delayed brace core fracture of buckling-restrained braces (BRBs) under the axial cyclic loading provide the adequate lateral force and deformation capacity to BRBFs under the earthquake excitation. However, the smaller axial stiffness of BRBs result in the undesirable higher residual drift response of BRBFs in the post-earthquake scenario. Two alternative approaches are investigated in this study to improve the elastic axial stiffness of BRBs, namely, (i) by shortening the yielding cores of BRBs; and (ii) by reducing the BRB assemblies and adding the elastic brace segments in series. In order to obtain the limiting yielding core lengths of BRBs, a modified approach based on Coffin-Manson relationship and the higher mode compression buckling criteria has been proposed in this study. Both non-linear static and dynamic analyses are carried out to analytically evaluate the seismic response of BRBFs fitted with short-core BRBs of two medium-rise building frames. Analysis results showed that the proposed brace systems are effective in reducing the inter-story and residual drift response of braced frames without any significant change in the story shear and the displacement ductility demands.

• Structural Engineering and Mechanics
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• v.6 no.3
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• pp.305-325
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• 1998

A method that determines the minimum stiffness of baracing to achieve non-sway buckling conditions at a given story level of a multi-column elastic frame is proposed. Condensed equations that evaluate the required minimum stiffness of the lateral and torsional bracing are derived using the classical stability functions. The proposed method is applicable to elastic framed structures with rigid, semirigid, and simple connections. It is shown that the minimum stiffness of the bracing required by a multi-column system depends on: 1) the plan layout of the columns; 2) the variation in height and cross sectional properties among the columns; 3) the applied axial load pattern on the columns; 4) the lack of symmetry in the loading pattern, column layout, column sizes and heights that cause torsion-sway and its effects on the flexural bucking capacity; and 5) the flexural and torsional end restrains of the columns. The proposed method is limited to elastic framed structures with columns of doubly symmetrical cross section with their principal axes parallel to the global axes. However, it can be applied to inelastic structures when the nonlinear behavior is concentrated at the end connections. The effects of axial deformations in beams and columns are neglected. Three examples are presented in detail to show the effectiveness of the proposed method.

• Structural Engineering and Mechanics
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• v.33 no.4
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• pp.447-484
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• 2009

The spatially coupled buckling, in-plane, and lateral bucking analyses of thin-walled Timoshenko curved beam with non-symmetric, double-, and mono-symmetric cross-sections resting on elastic foundation are performed based on series solutions. The stiffness matrices are derived rigorously using the homogeneous form of the simultaneous ordinary differential equations. The present beam formulation includes the mechanical characteristics such as the non-symmetric cross-section, the thickness-curvature effect, the shear effects due to bending and restrained warping, the second-order terms of semitangential rotation, the Wagner effect, and the foundation effects. The equilibrium equations and force-deformation relationships are derived from the energy principle and expressions for displacement parameters are derived based on power series expansions of displacement components. Finally the element stiffness matrix is determined using force-deformation relationships. In order to verify the accuracy and validity of this study, the numerical solutions by the proposed method are presented and compared with the finite element solutions using the classical isoparametric curved beam elements and other researchers' analytical solutions.

• Steel and Composite Structures
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• v.30 no.5
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• pp.471-481
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• 2019

Beam-columns are structural members subjected to a combination of axial and bending forces. Lateral-torsional buckling is one of the main failure modes. Beam-columns that are bent about its strong axis may buckle out of the plane by deflecting laterally and twisting as the values of the applied loads reach a limiting state. Lateral-torsional buckling failure occurs suddenly in beam-column elements with a much greater in-plane bending stiffness than torsional or lateral bending stiffness. This study intends to establish a unique convenient closed-form equation that it can be used for calculating critical elastic lateral-torsional buckling load of beam-column in the presence of a known axial load. The presented equation includes first order bending distribution, the position of the loads acting transversely on the beam-column and mono-symmetry property of the section. Effects of axial loads, slenderness and load positions on lateral torsional buckling behavior of beam-columns are investigated. The proposed solutions are compared to finite element simulations where thin-walled shell elements including warping are used. Good agreement between the analytical and the numerical solutions is demonstrated. It is found out that the lateral-torsional buckling load of beam-columns with mono-symmetric sections can be determined by the presented equation and can be safely used in design procedures.

• Journal of Ocean Engineering and Technology
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• v.11 no.4
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• pp.7-22
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• 1997

A finite element analysis is performed for lateral buckling problems on the basis of a geometrically nonlinear formulation for a beam with small elastic strain but with possibly large rotations. The total Lagrangian formulation for a general large deformation, which involves finite rotations, is chosen and the exponential map is used to treat finite rotations from the Eulerian point of view. For lateral buckling, the point of vanishing determinant of the resulting unsymmetric tangent stiffness is traced to examine its relationship to bifurcation points. It is found that the points of vanishing determinant is not corresponding to bifurcation points for large deformations in general, which suggests that the present unsymmetric tangent stiffness is not an exact first derivative of internal forces with respect to displacement. This is illustrated through several numerical examples and followed by appropriate discussion.