竖向荷载下纵向柱列支撑的设计方法研究
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摘要
在钢结构中通常利用支撑来提高结构或构件的稳定性。单层厂房纵向柱列支撑体系通常由柱间交叉支撑和水平撑杆组成,其作用是保证框架的纵向稳定、减小框架柱平面外计算长度以及传递纵向水平力。过去国外学者对支撑设计方法的研究主要集中于单柱-支撑模型的试验和理论分析上;国内学者则集中于柱顶竖向荷载相等时的柱列支撑体系的理论分析上,尚没看到柱顶竖向荷载不等时柱中水平撑杆受力分析的研究报导。另外,国内外尚未见到有关纵向柱列支撑体系的试验资料。
在纵向柱列支撑体系中,柱子和水平撑杆的初始几何缺陷都是随机变量,两类构件初始几何缺陷的随机遇合可导致水平撑杆受压或受拉。但以往的研究大多是按照最不利初始几何缺陷组合对纵向柱列支撑体系进行受力分析的,仅假定水平撑杆受压,不符合实际情况。因此,有必要深入开展带有随机初始几何缺陷分布的纵向柱列支撑体系的各种受力问题的研究工作,寻求合理的设计方法。
本课题采用少量的试验验证与大量的有限元参数分析相结合的方法,对纵向柱列支撑体系在竖向荷载下的各种受力问题进行了较系统的研究。在进行有限元参数分析时,采用蒙特卡罗方法考虑了柱子和水平撑杆初始几何缺陷的随机遇合问题。以设计应用为目标,通过数值计算、参数分析和概率统计,提出了简化实用的设计公式,可供规范修订和设计时参考。
本文对带有不同初始几何缺陷分布的三种纵向柱列支撑体系的试验模型进行了一系列的静力试验研究。三种试验模型分别是柱脚铰接的单层纵向柱列支撑体系、柱脚铰接的双层纵向柱列支撑体系以及柱脚刚接的双层纵向柱列支撑体系。通过试验研究,得到了三种试验模型的失稳模式、极限承载力和水平撑杆受拉、压的随机性等受力特点。采用ANSYS有限元模型对试验进行了模拟验证,计算结果与试验结果吻合良好,验证了利用有限元方法分析该问题的可靠性,为后续理论研究工作的进一步开展打下了良好的基础。
采用蒙特卡罗方法,考虑实际工程中柱子和柱顶撑杆初始几何缺陷的随机遇合,应用有限元程序ANSYS对承受竖向荷载作用的单层纵向柱列支撑体系进行了大量的参数仿真分析,得到了体系的三种失稳模式,通过概率统计得到柱顶撑杆所受内力的三峰正态概率密度函数,据此确定了可用于实际工程设计的柱顶支撑力的大小,为传统的柱顶撑杆由纵向水平力决定的设计方法补充了竖向受力分析的验算办法。结果表明,柱子和柱顶撑杆初始几何缺陷的随机遇合作用导致柱顶撑杆受压、拉或零受力的随机性,因此,使确定的设计支撑力更加合理。
采用蒙特卡罗方法,考虑柱子和水平撑杆初始几何缺陷的随机遇合,应用有限元程序ANSYS对柱脚铰接的双层纵向柱列支撑体系进行了大量的参数仿真分析,得到了体系的四种失稳模式,通过概率统计得到柱中水平撑杆所受内力的概率密度函数,据此确定了可用于实际工程设计的柱中支撑力的大小,结果表明:考虑柱子和水平撑杆初始几何缺陷的随机遇合作用所得到的水平撑杆的设计内力,比国内外相关规范中规定值均小许多。
采用蒙特卡罗方法,考虑柱子和水平撑杆初始几何缺陷的随机遇合作用,确定了柱脚刚接的双层纵向柱列支撑体系的柱中撑杆设计要求,并与相同条件下柱脚铰接的柱中撑杆设计要求进行了对比研究,分析了后者高于前者的原因。所得结果有别于已有研究。
开展了柱顶竖向荷载不等时柱脚铰接的双层纵向柱列支撑体系柱中撑杆设计要求的研究,与柱顶竖向荷载相等时的情况进行了比较,提出了相应的设计建议公式。分析表明,柱顶竖向荷载不等时纵向柱列体系的失稳是缘于个别受荷载较大的柱子的失稳破坏,并非所有柱子均已达到其各自的极限承载力,这一结论有别于现行国家规范。
基于在竖向荷载下保证框架纵向稳定性的要求,得到了单层和双层纵向柱列支撑体系中交叉支撑的刚度要求,为交叉支撑通常由纵向水平力决定的传统设计方法提供了一种考虑竖向受力的补充验算办法。
Braces are widely used to increase the stability of steel structures. The longitudinal column-bracing systems of one-story industrial building usually consist of diagonal bracings and horizontal bracing bars whose primary roles are to maintain the longitudinal stability and reduce the out-of-plane effective length of columns and transfer the longitudinal horizontal loads. In past studies on the design methods of bracings, most experimental researches and theoretical analyses were focused on a single column-brace model by the foreign scholars. In our country, the researches were mainly focused on the theoretical studies of longitudinal column-bracing system under equally top vertical loading. The analysis of mid-height horizontal bracing forces under unequally top vertical loads on the braced columns has not been seen. Moreover, the related experimental data on the longitudinal column-bracing systems have not been found in the domestic and abroad.
The initial imperfections of both the columns and the horizontal bracing bars are random variables in the longitudinal column-bracing systems, and the random combination of the initial imperfections between the columns and the horizontal bracing bars can lead to the randomness of horizontal bracing bars in compression or in tension. However, in past studies, the longitudinal column-bracing systems were usually analyzed according to the worst combination of the above two initial imperfections and the horizontal bracing bars were only assumed to be in compression, so it was’t in conformity with actual situations. Therefore, the various analyses on the longitudinal column-bracing systems with random distributions of the initial imperfections should be carried out and the rational design method should be seeked.
A small amount of verification tests and a large number of finite element parametric analyses on the various problems of the longitudinal column-bracing systems under vertical loading were systematically conducted in this paper. In the finite element parametric analyses, the random combination of the initial imperfections between the columns and the horizontal bracing bars was well considered by the Monte Carlo method. Aiming to the design application, the simplified formulas have been proposed based on numerical calculations, parametric analyses and probability statistics. It is very useful for code revision and design application.
A series of static experimental studies have been conducted on the three kinds of test models of longitudinal column-bracing systems with different distributions of the initial imperfections. The three kinds of test models are one-story longitudinal column-bracing systems with pin-ended column bases, two-story longitudinal column-bracing systems with pin-ended column bases and two-story longitudinal column-bracing systems with fixed-ended column bases, respectively. The ultimate load carrying capacity, instability modes and randomness of horizontal bracing forces in compression or tension were obtained. Moreover, the finite element models were developed according to the tests, and results from the finite element analysis by ANSYS agreed well with the experimental data. The reliability of finite element analysis has been verified, which established well foundation for the further theoretical study.
A large number of simulation analyses for one-story longitudinal column-bracing systems under vertical loading have been studied using the ANSYS finite element program, in which the random combination of the initial imperfections between the columns and the horizontal bracing bars was well considered by the Monte Carlo method. According to the analysis results, three kinds of instability modes of one-story longitudinal column-bracing systems have been found, triple-normal probability density function of the bracing forces for top bracing bars was proposed through probability statistics, and the design bracing forces for the top bracing bars were also obtained. Moreover, a check method based on the vertical loads analysis was supplied for the top bracing bars which are usually designed by the longitudinal horizontal loads. The results indicate that the random combination of the initial imperfections between the columns and the top bracing bars leads to the randomness of the top bracing forces in compression or intension or zero, so that the design bracing forces can be more reasonably determined.
A large number of simulation analyses for two-story longitudinal column-bracing systems with pin-ended column bases have been studied using the ANSYS finite element program, in which the random combination of the initial imperfections between the columns and the horizontal bracing bars was well considered by the Monte Carlo method. According to the analysis results, four kinds of instability modes of two-story longitudinal column-bracing systems have been found, probability density function of the bracing forces for the mid-height horizontal bracing bars was proposed through probability statistics, and the design bracing forces for the mid-height horizontal bracing bars were also obtained. The results indicate the above design bracing forces are much smaller than that proposed by the related codes in the domestic and abroad.
The design requirements of the mid-height horizontal bracing bars for two-story longitudinal column-bracing systems with fixed-ended column bases have been obtained, in which the random combination of the initial imperfections between the columns and the horizontal bracing bars was well considered by the Monte Carlo method. The comparative studies on the design requirements of the mid-height horizontal bracing bars were carried out between the systems with fixed-ended column bases and pin-ended column bases, and the reasons that the latter are higher than the former were analyzed also. This conclusion is different from the existing researches.
The researches on the design requirements of the mid-height horizontal bracing bars for two-story longitudinal column-bracing systems with pin-ended column bases under unequally top vertical loads on the braced columns were carried out, the above design requirements were compared with that under equally top vertical loading, and the corresponding design recommendations were proposed also. The analysis results indicate that the instability of the longitudinal column-bracing systems is caused by the individual buckling failures of bigger vertically loaded columns, not by the all columns reaching their ultimate load carrying capacity simultaneously. The conclusion is different from the existing national code.
The stiffness requirements of the diagonal bracings for one-story and two-story longitudinal column-bracing systems were obtained based on maintaining the longitudinal frame stability under the vertical loading. A check method based on the vertical loading analysis was supplied for the diagonal bracings which are usually designed by the longitudinal horizontal loads.
在纵向柱列支撑体系中,柱子和水平撑杆的初始几何缺陷都是随机变量,两类构件初始几何缺陷的随机遇合可导致水平撑杆受压或受拉。但以往的研究大多是按照最不利初始几何缺陷组合对纵向柱列支撑体系进行受力分析的,仅假定水平撑杆受压,不符合实际情况。因此,有必要深入开展带有随机初始几何缺陷分布的纵向柱列支撑体系的各种受力问题的研究工作,寻求合理的设计方法。
本课题采用少量的试验验证与大量的有限元参数分析相结合的方法,对纵向柱列支撑体系在竖向荷载下的各种受力问题进行了较系统的研究。在进行有限元参数分析时,采用蒙特卡罗方法考虑了柱子和水平撑杆初始几何缺陷的随机遇合问题。以设计应用为目标,通过数值计算、参数分析和概率统计,提出了简化实用的设计公式,可供规范修订和设计时参考。
本文对带有不同初始几何缺陷分布的三种纵向柱列支撑体系的试验模型进行了一系列的静力试验研究。三种试验模型分别是柱脚铰接的单层纵向柱列支撑体系、柱脚铰接的双层纵向柱列支撑体系以及柱脚刚接的双层纵向柱列支撑体系。通过试验研究,得到了三种试验模型的失稳模式、极限承载力和水平撑杆受拉、压的随机性等受力特点。采用ANSYS有限元模型对试验进行了模拟验证,计算结果与试验结果吻合良好,验证了利用有限元方法分析该问题的可靠性,为后续理论研究工作的进一步开展打下了良好的基础。
采用蒙特卡罗方法,考虑实际工程中柱子和柱顶撑杆初始几何缺陷的随机遇合,应用有限元程序ANSYS对承受竖向荷载作用的单层纵向柱列支撑体系进行了大量的参数仿真分析,得到了体系的三种失稳模式,通过概率统计得到柱顶撑杆所受内力的三峰正态概率密度函数,据此确定了可用于实际工程设计的柱顶支撑力的大小,为传统的柱顶撑杆由纵向水平力决定的设计方法补充了竖向受力分析的验算办法。结果表明,柱子和柱顶撑杆初始几何缺陷的随机遇合作用导致柱顶撑杆受压、拉或零受力的随机性,因此,使确定的设计支撑力更加合理。
采用蒙特卡罗方法,考虑柱子和水平撑杆初始几何缺陷的随机遇合,应用有限元程序ANSYS对柱脚铰接的双层纵向柱列支撑体系进行了大量的参数仿真分析,得到了体系的四种失稳模式,通过概率统计得到柱中水平撑杆所受内力的概率密度函数,据此确定了可用于实际工程设计的柱中支撑力的大小,结果表明:考虑柱子和水平撑杆初始几何缺陷的随机遇合作用所得到的水平撑杆的设计内力,比国内外相关规范中规定值均小许多。
采用蒙特卡罗方法,考虑柱子和水平撑杆初始几何缺陷的随机遇合作用,确定了柱脚刚接的双层纵向柱列支撑体系的柱中撑杆设计要求,并与相同条件下柱脚铰接的柱中撑杆设计要求进行了对比研究,分析了后者高于前者的原因。所得结果有别于已有研究。
开展了柱顶竖向荷载不等时柱脚铰接的双层纵向柱列支撑体系柱中撑杆设计要求的研究,与柱顶竖向荷载相等时的情况进行了比较,提出了相应的设计建议公式。分析表明,柱顶竖向荷载不等时纵向柱列体系的失稳是缘于个别受荷载较大的柱子的失稳破坏,并非所有柱子均已达到其各自的极限承载力,这一结论有别于现行国家规范。
基于在竖向荷载下保证框架纵向稳定性的要求,得到了单层和双层纵向柱列支撑体系中交叉支撑的刚度要求,为交叉支撑通常由纵向水平力决定的传统设计方法提供了一种考虑竖向受力的补充验算办法。
Braces are widely used to increase the stability of steel structures. The longitudinal column-bracing systems of one-story industrial building usually consist of diagonal bracings and horizontal bracing bars whose primary roles are to maintain the longitudinal stability and reduce the out-of-plane effective length of columns and transfer the longitudinal horizontal loads. In past studies on the design methods of bracings, most experimental researches and theoretical analyses were focused on a single column-brace model by the foreign scholars. In our country, the researches were mainly focused on the theoretical studies of longitudinal column-bracing system under equally top vertical loading. The analysis of mid-height horizontal bracing forces under unequally top vertical loads on the braced columns has not been seen. Moreover, the related experimental data on the longitudinal column-bracing systems have not been found in the domestic and abroad.
The initial imperfections of both the columns and the horizontal bracing bars are random variables in the longitudinal column-bracing systems, and the random combination of the initial imperfections between the columns and the horizontal bracing bars can lead to the randomness of horizontal bracing bars in compression or in tension. However, in past studies, the longitudinal column-bracing systems were usually analyzed according to the worst combination of the above two initial imperfections and the horizontal bracing bars were only assumed to be in compression, so it was’t in conformity with actual situations. Therefore, the various analyses on the longitudinal column-bracing systems with random distributions of the initial imperfections should be carried out and the rational design method should be seeked.
A small amount of verification tests and a large number of finite element parametric analyses on the various problems of the longitudinal column-bracing systems under vertical loading were systematically conducted in this paper. In the finite element parametric analyses, the random combination of the initial imperfections between the columns and the horizontal bracing bars was well considered by the Monte Carlo method. Aiming to the design application, the simplified formulas have been proposed based on numerical calculations, parametric analyses and probability statistics. It is very useful for code revision and design application.
A series of static experimental studies have been conducted on the three kinds of test models of longitudinal column-bracing systems with different distributions of the initial imperfections. The three kinds of test models are one-story longitudinal column-bracing systems with pin-ended column bases, two-story longitudinal column-bracing systems with pin-ended column bases and two-story longitudinal column-bracing systems with fixed-ended column bases, respectively. The ultimate load carrying capacity, instability modes and randomness of horizontal bracing forces in compression or tension were obtained. Moreover, the finite element models were developed according to the tests, and results from the finite element analysis by ANSYS agreed well with the experimental data. The reliability of finite element analysis has been verified, which established well foundation for the further theoretical study.
A large number of simulation analyses for one-story longitudinal column-bracing systems under vertical loading have been studied using the ANSYS finite element program, in which the random combination of the initial imperfections between the columns and the horizontal bracing bars was well considered by the Monte Carlo method. According to the analysis results, three kinds of instability modes of one-story longitudinal column-bracing systems have been found, triple-normal probability density function of the bracing forces for top bracing bars was proposed through probability statistics, and the design bracing forces for the top bracing bars were also obtained. Moreover, a check method based on the vertical loads analysis was supplied for the top bracing bars which are usually designed by the longitudinal horizontal loads. The results indicate that the random combination of the initial imperfections between the columns and the top bracing bars leads to the randomness of the top bracing forces in compression or intension or zero, so that the design bracing forces can be more reasonably determined.
A large number of simulation analyses for two-story longitudinal column-bracing systems with pin-ended column bases have been studied using the ANSYS finite element program, in which the random combination of the initial imperfections between the columns and the horizontal bracing bars was well considered by the Monte Carlo method. According to the analysis results, four kinds of instability modes of two-story longitudinal column-bracing systems have been found, probability density function of the bracing forces for the mid-height horizontal bracing bars was proposed through probability statistics, and the design bracing forces for the mid-height horizontal bracing bars were also obtained. The results indicate the above design bracing forces are much smaller than that proposed by the related codes in the domestic and abroad.
The design requirements of the mid-height horizontal bracing bars for two-story longitudinal column-bracing systems with fixed-ended column bases have been obtained, in which the random combination of the initial imperfections between the columns and the horizontal bracing bars was well considered by the Monte Carlo method. The comparative studies on the design requirements of the mid-height horizontal bracing bars were carried out between the systems with fixed-ended column bases and pin-ended column bases, and the reasons that the latter are higher than the former were analyzed also. This conclusion is different from the existing researches.
The researches on the design requirements of the mid-height horizontal bracing bars for two-story longitudinal column-bracing systems with pin-ended column bases under unequally top vertical loads on the braced columns were carried out, the above design requirements were compared with that under equally top vertical loading, and the corresponding design recommendations were proposed also. The analysis results indicate that the instability of the longitudinal column-bracing systems is caused by the individual buckling failures of bigger vertically loaded columns, not by the all columns reaching their ultimate load carrying capacity simultaneously. The conclusion is different from the existing national code.
The stiffness requirements of the diagonal bracings for one-story and two-story longitudinal column-bracing systems were obtained based on maintaining the longitudinal frame stability under the vertical loading. A check method based on the vertical loading analysis was supplied for the diagonal bracings which are usually designed by the longitudinal horizontal loads.
引文
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38 Tong Gengshu, Chen Shaofan. Buckling of Laterally and Torsionally Braced Beams. Journal of Constructional Steel Research. 1988, 14(2): 87-105
39童根树.轴心杆偏心支撑的有效性及Hartford体育馆网架破坏原因分析.西安冶金建筑学院学报. 1990, 22(3): 221-223
40 Tong Gengshu, Chen Shaofan. On the Efficiency of an Eccentric Brace on a Column and the Collapse of the Hartford Coliseum. Journal of Constructional Steel Research. 1990, 42: 112-123
41施东,陈骥.钢压弯构件侧向水平偏心支撑的刚度条件.西安建筑科技大学学报. 1995, 27(3): 314-319
42童根树.平行压杆体系的侧向稳定性支撑.西安冶金建筑学院学报. 1991, 23(4): 425-431
43童根树,万红.斜平面内侧向支撑压杆的屈曲理论及其应用.西安冶金建筑学院学报. 1991, 23(2): 119-127
44童根树.锅炉构架刚性平台设计的刚度和强度要求.锅炉技术. 1991,12: 1-8
45童根树,陈胜平.柱列支撑的设计要求.工业建筑. 2003, 33(5): 9-12
46 GB50017-2003.钢结构设计规范.中国计划出版社, 2003: 44-45
47童根树.钢结构构件和框架的平面内稳定.中国建筑工业出版社, 2005: 219-312
48 AS4100-1998. Standards Australia, Steel Structures. Sydney, 1998: 80-85
49 Eurocode 3. Design of Steel Structure. Part 1.1: General Rules and Rules forBuildings. European Committee for Standardisation (CEN), 1992: 19-45
50童根树,陈海啸.厂房纵向抽撑时柱子的平面外计算长度.工业建筑. 2004, 34(5): 59-61
51童根树,饶芝英.双层纵向柱列支撑的设计要求.建筑钢结构进展. 2007, 9(3): 50-57
52李克寒.厂房柱压弯构件侧向支撑杆的分析.西安建筑科技大学硕士学位论文. 2004: 33-50
53赵金友.柱列支撑设计方法的研究.哈尔滨工业大学硕士学位论文. 2005: 12-39
54 GB50205-2001.钢结构工程施工质量验收规范.中国计划出版社, 2001: 10-82
55赵金友,张文元,张耀春.柱顶受轴力的柱列支撑受力分析.建筑结构学报. 2007, 28(S1): 171-178
56 Yaochun Zhang, Jinyou Zhao and Wenyuan Zhang. Parametric Studies on Inter-column Brace Forces. Advances in Structural Engineering. 2008, 11(3): 305-315
57国际标准ISO / DIS 10721.国外钢结构设计规范译编(八).全国钢结构标准技术委员会, 1999: 66-67
58 ANSI/AISC 360-05. Specification for Structural Steel Buildings. American Institute of Steel Construction, 2005: 19-30
59李国强,刘玉姝.钢结构框架体系整体非线性分析研究综述.同济大学学报. 2003, 31(2): 138-144
60舒兴平,沈蒲生.空间钢框架结构的非线性全过程分析.工程力学. 1997, 14(3): 36-45
61许红胜,周绪红,舒兴平.空间钢框架几何非线性分析的一种新单元.工程力学. 2003, 20(8): 39-44
62刘永华,张耀春.钢框架高等分析研究综述.哈尔滨工业大学学报. 2005, 37(9): 1283-1290
63 S. El-Tawil, E. Vidarsson, T. Mikesell, S. K. Kunnath. Inelastic Behavior and Design of Steel Panel Zones. Journal of Structural Engineering (ASCE). 1999, 125(2):183-193
64 L. H. The, M. J. Clarke. Plastic-Zone Analysis of 3D Steel Frames Using BeamElements. Journal of Structural Engineering (ASCE). 1999, 125(11): 1328-1337
65 M. Foley, S. Vinnakota. Inelastic Behavior of Multistory Partially Restrained Steel Frames. Part I and PartⅡ. Journal of Structural Engineering (ASCE). 1999, 125(8): 854-869
66 P. Avery, M. Mahendran. Distributed Plasticity Analysis of Steel Frame Structures Comprising Non-Compact Sections. Engineering Structures. 2000, 22(8): 901-919
67 S. E. Kim, D. H. Lee. Second-Order Distributed Plasticity Analysis of Space Steel Frames. Engineering Structures. 2002, 24(6): 735-744
68 W. F. Chen, S. Toma. Advanced Analysis of Steel Frames Theory. Software and Application, CRC Press INC, 1996, (2): 8210
69 A. Kassimali. Large Deformation Analysis of Elastic-Plastic Frames. Journal of Structural Engineering. 1983, 109(8): 1869-1886
70 J. Y. R. Liew, D. W. White, W. F. Chen. Notional-Load Plastic-Hinge Method for Frame Design. Journal of Structural Engineering. 1994, 120(5): 1434-1454
71 M. Abdel-Ghaffar, D. W. White, W. F. Chen. Simplified second-order inelastic analysis for steel fame design. Special Volume of Session on Approximate Methods and Verification Procedures of Structural Analysis and Design, Proceeding at Structures Congress91, ASCE, 1991: 47-62
72 W. S. King, D. W. White, W. F. Chen. On Second-order Inelastic Methods for Steel Fame Design. Journal of Structural Engineering, ASCE, 1991, 118: 408-428
73 M. N. Attala, G. G. Deierlein, W. McGuire. Spread of Plasticity: Quasi-Plastic- Hinge Approach. Journal of Structural Engineering (ASCE). 1994, 120(8): 2451-2473
74 J. Y. R. Liew, D. W. White, W. F. Chen. Second-Order Refined Plastic-Hinge Analysis for Frame Design. Part I. Journal of Structural Engineering. 1993, 119(11): 3196-3216
75刘永华.空间钢框架高等分析方法研究.哈尔滨工业大学博士学位论文. 2007: 6-9
76 M. J. Clarke, R. Q. Bridge, G. J. Hancock, N. J. Trahair. Advanced Analysis of Steel Building Frames. Journal of Constructional Steel Research. 1992, 23(1-3):1-29
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79 J. Y. R. Liew, D. W. White, W. F. Chen. Second-order Refined Plastic-Hinge Analyses for Frame Design. Part II. Journal of Structural Engineering. 1993, 119 (11): 3217-3237
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35童根树.柱间水平撑杆设计的统一方法.西安冶金建筑学院学报. 1988, 20(1): 87-93
36 Tong Geng-Shu, Chen Shao-Fan. A Unified Approach for Horizontal Inter-Column Braces. Structural Stability Research Council(SSRC) Annual Technical Session and Meeting, 1988: 128-130
37童根树.压杆侧向支撑设计的统一方法.西安冶金建筑学院学报. 1989, 21(1): 25-33
38 Tong Gengshu, Chen Shaofan. Buckling of Laterally and Torsionally Braced Beams. Journal of Constructional Steel Research. 1988, 14(2): 87-105
39童根树.轴心杆偏心支撑的有效性及Hartford体育馆网架破坏原因分析.西安冶金建筑学院学报. 1990, 22(3): 221-223
40 Tong Gengshu, Chen Shaofan. On the Efficiency of an Eccentric Brace on a Column and the Collapse of the Hartford Coliseum. Journal of Constructional Steel Research. 1990, 42: 112-123
41施东,陈骥.钢压弯构件侧向水平偏心支撑的刚度条件.西安建筑科技大学学报. 1995, 27(3): 314-319
42童根树.平行压杆体系的侧向稳定性支撑.西安冶金建筑学院学报. 1991, 23(4): 425-431
43童根树,万红.斜平面内侧向支撑压杆的屈曲理论及其应用.西安冶金建筑学院学报. 1991, 23(2): 119-127
44童根树.锅炉构架刚性平台设计的刚度和强度要求.锅炉技术. 1991,12: 1-8
45童根树,陈胜平.柱列支撑的设计要求.工业建筑. 2003, 33(5): 9-12
46 GB50017-2003.钢结构设计规范.中国计划出版社, 2003: 44-45
47童根树.钢结构构件和框架的平面内稳定.中国建筑工业出版社, 2005: 219-312
48 AS4100-1998. Standards Australia, Steel Structures. Sydney, 1998: 80-85
49 Eurocode 3. Design of Steel Structure. Part 1.1: General Rules and Rules forBuildings. European Committee for Standardisation (CEN), 1992: 19-45
50童根树,陈海啸.厂房纵向抽撑时柱子的平面外计算长度.工业建筑. 2004, 34(5): 59-61
51童根树,饶芝英.双层纵向柱列支撑的设计要求.建筑钢结构进展. 2007, 9(3): 50-57
52李克寒.厂房柱压弯构件侧向支撑杆的分析.西安建筑科技大学硕士学位论文. 2004: 33-50
53赵金友.柱列支撑设计方法的研究.哈尔滨工业大学硕士学位论文. 2005: 12-39
54 GB50205-2001.钢结构工程施工质量验收规范.中国计划出版社, 2001: 10-82
55赵金友,张文元,张耀春.柱顶受轴力的柱列支撑受力分析.建筑结构学报. 2007, 28(S1): 171-178
56 Yaochun Zhang, Jinyou Zhao and Wenyuan Zhang. Parametric Studies on Inter-column Brace Forces. Advances in Structural Engineering. 2008, 11(3): 305-315
57国际标准ISO / DIS 10721.国外钢结构设计规范译编(八).全国钢结构标准技术委员会, 1999: 66-67
58 ANSI/AISC 360-05. Specification for Structural Steel Buildings. American Institute of Steel Construction, 2005: 19-30
59李国强,刘玉姝.钢结构框架体系整体非线性分析研究综述.同济大学学报. 2003, 31(2): 138-144
60舒兴平,沈蒲生.空间钢框架结构的非线性全过程分析.工程力学. 1997, 14(3): 36-45
61许红胜,周绪红,舒兴平.空间钢框架几何非线性分析的一种新单元.工程力学. 2003, 20(8): 39-44
62刘永华,张耀春.钢框架高等分析研究综述.哈尔滨工业大学学报. 2005, 37(9): 1283-1290
63 S. El-Tawil, E. Vidarsson, T. Mikesell, S. K. Kunnath. Inelastic Behavior and Design of Steel Panel Zones. Journal of Structural Engineering (ASCE). 1999, 125(2):183-193
64 L. H. The, M. J. Clarke. Plastic-Zone Analysis of 3D Steel Frames Using BeamElements. Journal of Structural Engineering (ASCE). 1999, 125(11): 1328-1337
65 M. Foley, S. Vinnakota. Inelastic Behavior of Multistory Partially Restrained Steel Frames. Part I and PartⅡ. Journal of Structural Engineering (ASCE). 1999, 125(8): 854-869
66 P. Avery, M. Mahendran. Distributed Plasticity Analysis of Steel Frame Structures Comprising Non-Compact Sections. Engineering Structures. 2000, 22(8): 901-919
67 S. E. Kim, D. H. Lee. Second-Order Distributed Plasticity Analysis of Space Steel Frames. Engineering Structures. 2002, 24(6): 735-744
68 W. F. Chen, S. Toma. Advanced Analysis of Steel Frames Theory. Software and Application, CRC Press INC, 1996, (2): 8210
69 A. Kassimali. Large Deformation Analysis of Elastic-Plastic Frames. Journal of Structural Engineering. 1983, 109(8): 1869-1886
70 J. Y. R. Liew, D. W. White, W. F. Chen. Notional-Load Plastic-Hinge Method for Frame Design. Journal of Structural Engineering. 1994, 120(5): 1434-1454
71 M. Abdel-Ghaffar, D. W. White, W. F. Chen. Simplified second-order inelastic analysis for steel fame design. Special Volume of Session on Approximate Methods and Verification Procedures of Structural Analysis and Design, Proceeding at Structures Congress91, ASCE, 1991: 47-62
72 W. S. King, D. W. White, W. F. Chen. On Second-order Inelastic Methods for Steel Fame Design. Journal of Structural Engineering, ASCE, 1991, 118: 408-428
73 M. N. Attala, G. G. Deierlein, W. McGuire. Spread of Plasticity: Quasi-Plastic- Hinge Approach. Journal of Structural Engineering (ASCE). 1994, 120(8): 2451-2473
74 J. Y. R. Liew, D. W. White, W. F. Chen. Second-Order Refined Plastic-Hinge Analysis for Frame Design. Part I. Journal of Structural Engineering. 1993, 119(11): 3196-3216
75刘永华.空间钢框架高等分析方法研究.哈尔滨工业大学博士学位论文. 2007: 6-9
76 M. J. Clarke, R. Q. Bridge, G. J. Hancock, N. J. Trahair. Advanced Analysis of Steel Building Frames. Journal of Constructional Steel Research. 1992, 23(1-3):1-29
77 Eurocode 3. Design of Steel Structures-Part 1-1: General Rules and Rules for Buildings. PREN 1993-1-1. European Committee for Standardisation (CEN), 2003: 19-30
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