计算长度系数的物理意义及对各种钢框架稳定设计方法的评论

本将有侧移失稳的框架柱计算长度系数与结构力学的D值法联系，论证了柱子计算长度系数计算柱子抗侧刚度系数．通过柱子计算长度系数可以较精确地确定整个楼层的抗侧刚度。本计算表明考虑同层各柱的相互支援对框架柱计算长度系数进行修正后，薄弱层柱子的计算长度系数能够得到略偏安全的精度。利用整体分析时各个柱子的计算长度系数存在的关系就可以得到所有其它非薄弱层柱子的计算长度系数，且同样略偏安全。通过例子发现框架层与层相互作用的一个重要性质：层对层的支援，对同一层的每个柱子而言．获得的好处(临界力增加)或贡献出来的刚度(临界荷栽的减小)具有相同的比例。本对当前各种框架稳定性计算方法(传统的线性分析计算长度系数法、线性分析层整体稳定计算法、结构整体稳定计算法和二阶分析法)进行了简单的讨论。     

Mechanics and effective lengths of columns with positive and negative end restraints

In approximate buckling analysis of frame structures, it is common practice to simplify by considering compression members in isolation with end restraints that supposedly reflect the interaction with the surrounding structure. Buckling modes and effective lengths of such members have traditionally been limited to modes that can be associated with positive end restraints. A wider range of realistic buckling modes, that also imply negative end restraints, are reviewed and discussed, and approximate formulas for effective lengths and inflection point locations are developed from simple physical models for unbraced and fully braced compression members. The formulas are expressed in terms of convenient end fixity factors that allow for simple and elegant formulations. The range of applicability of the formulas is identified by comparisons with exact results for a reasonably wide range of positive and negative restraints, and applications to special structures are demonstrated.     

考虑层与层相互支援的框架柱计算长度系数

框架稳定计算的传统假定导致梁对柱子的约束在上下柱之间按照柱子的线刚度分配，因此强柱反而得到更多的约束，与实际情况可能不符。本文放弃了传统计算长度系数法的三个理想化假定，提出了考虑层与层相互作用的框架柱计算长度的几乎精确的简单代数方法。对于两层框架，通过求解一个一元二次方程得到分配给各柱柱端的转动约束；对于三层框架，通过求解一个一元三次方程得到各柱柱端的转动约束；进而由传统公式计算或从规范附表查得μ值。对于更多层的情况，假设相邻层柱子远端的梁约束在上下柱之间按线刚度分配。可以得到很精确的薄弱层柱子计算长度系数。其它层柱子的计算长度系数则从各柱子计算长度之间存在的关系得到。由于这个模型引入了相邻层柱子远端的梁约束。因此可以考虑远端铰支或固定的情况。获得的结果在所有情况下满足工程要求的精度。     

Buckling lengths of irregular frame columns

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, especially for irregular frames. 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 both regular and irregular frames is developed. The procedure utilises lateral load analysis of frames and yields errors on the order of 5%, 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.     

Buckling of frames braced by flexural bracing

This paper investigates the buckling of multistory frames braced by vertical beams. The sectional properties of the frames and the bracing beam are assumed to vary linearly along the height; the axial forces in the columns and the bracing beam are also assumed to linearly change along the height. A relationship between the buckling load and the bracing rigidity is established. The threshold rigidity for the vertical bracing beam which is just enough to make the frames buckle in a non-sway mode is obtained. The result may be used as a rational basis for classifying sway frames and non-sway frames after taking the influence of initial imperfections and lateral loads into account.     

Buckling strength of multi-story sway, non-sway and partially-sway frames with semi-rigid connections

The objective of this paper is to propose a simplified approach to the evaluation of the critical buckling load of multi-story frames with semi-rigid connections. To that effect, analytical expressions and corresponding graphs accounting for the boundary conditions of the column under investigation are proposed for the calculation of the effective buckling length coefficient for different levels of frame sway ability. In addition, a complete set of rotational stiffness coefficients is derived, which is then used for the replacement of members converging at the bottom and top ends of the column in question by equivalent springs. All possible rotational and translational boundary conditions at the far end of these members, featuring semi-rigid connection at their near end as well as the eventual presence of axial force, are considered. Examples of sway, non-sway and partially-sway frames with semi-rigid connections are presented, where the proposed approach is found to be in excellent agreement with the finite element results, while the application of codes such as Eurocode 3 and LRFD leads to significant inaccuracies.     

钢结构稳定设计的新进展

本文介绍了近年来框架和冷弯型钢构件稳定承载力计算的新问题和新方法，包括框架先进分析法的实用化，当前广泛应用的计算长度法的改进，弱支撑框架和半刚性连接框架的稳定．大跨度框架无侧移失稳的可能性和计算方法，陡坡山形门式刚架的稳定，冷弯薄壁型钢板件局部相关屈曲．开口截面的畸变屈曲．以及局部和整体的相关屈曲。     

江苏太仓广播电视发射塔塔柱的稳定性分析

在钢塔结构中,塔柱是主要的受力构件,其稳定性直接关系到结构整体的安全,在工程设计中不容忽视。对于节点连接复杂的塔体结构,由于考虑到其他相连杆件的约束作用,一般不能简单将塔柱两端视为铰接,此时钢塔柱的计算长度在现行设计规范中没有明确说明,不能简单按照规范方法进行设计。为此,本文以江苏太仓市电视塔工程为例,选取其代表性结构单元,通过线性和非线性屈曲分析方法对钢塔柱在整体结构中的稳定性进行了计算。通过本文的研究,给出了塔柱的计算长度系数的估算方法,并针对太仓塔工程给出了合理的塔柱计算长度系数值。     

Stability of multi-storey unbraced steel frames subjected to variable loading

Proposed in this paper is an approach of evaluating the elastic buckling loads for multi-storey unbraced steel frames subjected to variable loading or non-proportional loading. In the case of variable loading, the conventional assumption of proportional loading is abandoned, and different load patterns may cause the frame to buckle at different levels of critical loads. In light of the use of the storey-based buckling concept to characterize the lateral sway buckling of unbraced framed structures, the problems of determining the lower and upper bounds among all of the frame buckling loads associated with different load patterns are presented as a pair of minimization and maximization problems subjected to elastic stability constraints. The problems take into account the semi-rigid behaviour of beam-to-column connections and the lateral stiffness reduction of columns due to the presence of an axial compressive load. The minimization and maximization problems are then solved by a linear programming method; thus, the lower and upper bounds of the frame buckling loads subjected to variable loading are obtained. Parametrical studies on the influence of the connection rigidity to the lower and upper bounds of critical loads and the comparisons to the conventional proportional loading are also presented in this paper.     

The effect of semi-rigid joints and an elastic bracing system on the buckling load of simple rectangular steel frames

A linear stability analysis for establishing the combined effect of joint flexibility and an elastic bracing system on the buckling load of steel plane frames is presented herein. Based on the beam-to-column model of Eurocode 3, the subsequent study shows that joint flexibility is a very important parameter that needs to be incorporated into the stability analysis of frames with semi-rigid connections. It was found that assuming flexible connections in such frames always leads to a reduction of their buckling load, which is proven to be significant in many characteristic cases. Numerical results for simple elastically braced or unbraced frames with semi-rigid connections, in tabular and graphical form, reveal the pronounced effect of joint flexibility and elastic bracing on their buckling load. The results presented herein can be readily used for the design of simple frames against buckling, while the flexible connection concept can be applied to all types of steel frames.     

钢框架考虑二阶效应的层间侧移限值取值及可靠度分析

分析钢框架结构时考虑二阶效应,得到的截面内力及位移通常比采用一阶分析方法计算的结果偏大。对于承受相同荷载、具有相同几何条件的结构,如采用一阶分析方法计算得到的位移满足现行规范的水平侧移限值,但采用二阶分析方法后不一定满足该侧移限值的规定,因此在规范中补充有关二阶分析时侧移限值的相关规定尤为必要。针对钢框架结构考虑二阶效...     

考虑竖向力影响时侧移框架的修正计算长度系数

推导了竖向力对框架的抗侧刚度影响系数α,并分别对计算侧移框架二阶效应的P-Δ法、二阶弹性分析法和双二阶效应法的计算长度系数进行修正。通过与《钢结构设计规范》(GB50017—2003)比较得知,双二阶效应法计算长度系数取值比规范安全,修正后的P-Δ法和二阶弹性分析法与规范最为接近,而二阶弹性分析法和P-Δ法在梁柱线刚度比K1大于1时偏于不安全。     

关于连续梁桥墩计算长度系数的探讨

首先,在深入研究连续梁桥墩屈曲机理的基础上,结合实际工程特点,建立力学模型,根据欧拉公式进行理论推导分析得出桥墩计算长度系数的超越方程;然后进一步分析桥墩计算长度系数的影响因素及其与桥墩计算长度系数间的相互关系;最后,利用有限元建模对某高速公路桥梁进行稳定分析,求解出桥墩计算长度系数,并与理论计算结果进行对比分析。结果表明:有限元计算结果与理论计算结果吻合很好,验证了桥墩计算长度系数求解的正确性。     

An efficient method for computation of effective length factor of columns in a steel gabled frame with tapered members

The concept of effective length is the only available common method for column design without non-linear structural analysis. Researches conducted for determination of effective length of members are mainly related to a constant moment of inertia. In many investigations related to members with variable moment of inertia, finite element and approximation methods are used. In this article, a method for quick calculation of the effective length factor of columns in steel gabled frames with tapered members is proposed. The method is based on two-dimensionless design-oriented charts relating the critical load of columns to frame characteristics and boundary conditions. Since I-sections are usually used for gabled frames members, the variation of moment of inertia along the length of members (beams or columns) is approximated as a parabolic function. As is demonstrated in the Numerical studies, these calculations can yield, in a very efficient way, accurate results for gabled frames consisting of tapered elements.     

Numerical study on the mean velocity distribution law of air backflow and the effective interaction length of airflow in forced ventilated tunnels

The effective interaction length of airflow (L_e) is the key factor in the determination of the distance between an air duct nozzle and the working face in dead-end tunnels. At present, the current calculation methods of L_e consider only the tunnel cross section dimension and are therefore not suitable for large underground cavern groups. Because air backflow is the direct promoting factor in the removal of pollutants and the construction specifications in underground space require a minimum wind speed, this paper proposed that L_e is the distance between the nozzle and the critical cross section, where the mean velocity of the air backflow equals the minimum wind speed required. For this purpose, a computational study was conducted to investigate the flow pattern of air backflow in ventilated tunnels. Semi-empirical equations of the mean velocity distribution law of air backflow were derived based on the numerical results. By solving the equations, the location of the critical cross section can then be acquired. Accordingly, the value of L_e could be obtained. The proposed method is related to the tunnel width, the tunnel height, the air duct diameter and the efflux velocity. Thus, it is more comprehensive and applicable compared to the current methods.     

Experimental optimization studies on steel core lengths in buckling restrained braces

Concentric braced frames are commonly used in steel structures to withstand lateral forces. However, brace hysteretic behavior is asymmetric in tension and compression. These frames typically exhibit substantial strength deterioration when loaded in compression. Consequently, the concept of Buckling Restrained Brace (BRB) has been introduced to overcome this deficiency.The length of a BRB steel core could have a significant effect on its overall behavior since it directly influences the energy dissipation of the member. Furthermore, BRB could be effectively utilized as a damper to dissipate seismic input energy, particularly when used as a fuse within the brace in a frame. Modified BRBs with shorter lengths may be called damper BRBs, because they function as if a typical damper is utilized along any brace member. These damper BRBs are fabricated and tested in this study both experimentally and analytically. Useful insights into local retrofitting of core plates and connections are also provided.     

Analysis of composite connections in unbraced frames subjected to wind and gravity loading

A comparison between a simplified and an advanced method of elastoplastic analysis is made for unbraced frames with composite connections. The advanced method implements a mechanical model to represent the composite node in unbraced frames, which allows considering the behavior of each component of the composite connection individually. This method includes the determination of a moment-rotation curve for loading-unloading-reloading, considering gravity and wind loading. Physical and geometrical nonlinearities are taken into account in the analysis. In the simplified method an appropriate analysis for practical purposes is implemented, on which the connections are considered semirigid for unloading and flexible for loading, after yielding by gravity loads. Second order effects are included using the P-Δ procedure. Finally, a comparison is made between the two methods attempting to transform both methods in a useful tool for composite connection design.     

Elastic buckling and second-order behaviour of pitched-roof steel frames

The aims of this work are two-fold: (i) to present the results of a study concerning the elastic in-plane stability and second-order behaviour of unbraced single-bay pitched-roof steel frames and (ii) to propose, validate and illustrate the application of an efficient methodology to design this type of commonly used frame. After (i) characterizing the relevant frame buckling modes and P-Δ second-order effects, and (ii) addressing the exact and approximate calculation of the associated bifurcation loads and secondary bending moments, the paper deals with the incorporation of these concepts in the definition of an efficient design procedure. In particular, it is clearly shown that, due to the rafter slope, the geometrically nonlinear behaviours of orthogonal beam-and-column and pitched-roof frames are qualitatively different. Finally, the proposed concepts and methodologies are illustrated through the presentation and discussion of numerical results involving fixed and pinned-base frames.     

巴蜀穿斗构架的地域特色探究

在我国以木构为主的传统建筑大 木构架体系中,穿斗构架是南方地区常采用的 结构形式。而巴蜀地区的穿斗构架兼有南方 穿斗的共性,又有其个性。在特殊的地理条 件、民俗文化的影响下,巴蜀穿斗构架在构筑 技术、构架组合、审美特质与特色空间营造等 方面都体现出富有内涵的地域特色。     

Effects of the frame geometry on the weight and inelastic behaviour of eccentrically braced chevron steel frames

Many experimental and analytical studies about eccentrically braced frames (EBFs) have been carried out since the late 1970s. However, parametric studies about the effects of the frame geometry on the weight and global inelastic behaviour are still quite limited. Such kind of parametric studies require many number of designed EBFs for the purpose of generalization, in fact, optimization of design is also necessary for the conservatism of results. Therefore, a computer program based on an iterative optimization procedure is coded for the design of eccentrically braced chevron frames and the algorithm is given. In this research, 420 EBFs with shear yielding links, 105 EBFs with intermediate links, and 105 EBFs with flexural yielding links are designed. Inelastic dynamic analyses of each of these frames are performed under 20 SAC ground motions with DRAIN-2DX whose input files are prepared automatically by another program coded. Each earthquake record for each frame is scaled by the program by modifying the DRAIN input files in an automated manner until one of the links reaches the code-based limit rotation angle, and the resultant scale factors are utilized for comparison of the frames’ inelastic behaviours. The equation for plastic link rotation of EBFs given in AISC-2005, which does not consider the vertical displacements of the column ends is modified to include these displacements and used in the inelastic analyses. Effects of the geometry selection on the frames’ seismic behaviours and weights are given. Push-over analyses of some of the designed frames are also performed with DRAIN-2DX in order to compare their displacement ductilities.