悬挑立体桁架平面外稳定分析
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摘要
近年来,立体桁架结构越来越多的被应用在航站楼、火车站及体育场馆等大型公共建筑,悬挑型立体桁架则主要被应用于体育场。稳定性能是影响钢结构承载能力的一个关键因素,而现行规范对立体桁架在平面外的整体稳定性并没有统一的规定,因此,对立体桁架在平面外稳定性能的研究很有意义。
本文首先将悬挑立体桁架简化为闭口薄壁悬臂梁模型,采用能量法建立微分方程,求出该结构在平面外稳定临界荷载的近似解析解,并将其与简化模型的强度临界荷载进行对比,以获得悬挑立体桁架极限荷载由强度控制而不发生平面外失稳的条件。随后,采用有限元方法通过大量计算分析立体桁架各截面几何参数对平面外稳定性能的影响,并将其与解析解的结论进行对比。最后,采用有限元方法分析悬挑立体桁架在地震作用下的动力稳定性。
研究表明:上、下弦杆截面面积对悬挑立体桁架平面外的稳定性影响不大,随着斜腹杆截面面积的增大,立体桁架面外稳定性增强;当节间长度等于截面高度时,悬挑立体桁架的平面外稳定性最好;对每个选定的高挑比h l,都存在一个临界截面宽高比b h,当h l≥110时,临界截面宽高比可取为b h < 1 2.5,当1 20 < h l< 1 10时,临界截面宽高比可取为b h < 1 2, h l不宜小于1 20;悬挑仰角在工程常用角度范围内对悬挑立体桁架平面外稳定的影响不大。
In recent years, the tube-truss structure is applied more and more in large public buildings, e.g. the terminal, the railway station, and the sports stadium etc., and the cantilever tube-truss structure is mainly applied in the sports stadium. Stability is a key factor which could affect the carrying capacity of steel structure, however, there is no provision about the out-plane stability of tube-truss structure, so it is meaningful that the out-plane stability of tube-truss structure is studied in this paper.
Firstly, the tube-truss structure is simplified to a model of thin-walled closed cantilever, then the differential equations are established by the energy law, and the approximate analytical solution of out-plane stability ultimate load is obtained. Compared to out-plane stability ultimate load and strength ultimate load, this paper obtain the condition that the cantilever tube-truss structure couldn’t lose the out-plane stability. Secondly, the impact of geometric parameters on the out-plane stability of tube-truss structure is analyzed by the finite element method, and then, it is compared with the conclusions of analytical solution. Finally, the dynamic stability of cantilever tube-truss structure under earthquake is also analyzed by the element method.
The study indicates the following conclusions: the top chords and bottom chords have little impact on the out-plane stability of tube-truss structure, although with the increase of belly bar’s section area, the out-plane stability of tube-truss structure increase; when the internode length equals to the section height, the out-plane stability of cantilever tube-truss structure would be best; for each h/l, there is a critical aspect ratio b/h, when h / l 1/10, the critical aspect ratio b / h < 1/ 2.5, when 1/ 20 < h / l< 1/10, the critical aspect ratio b / h < 1/ 2, and h / l< 1/ 20 is inappropriate; within the range commonly used in engineering, the elevation has little impact on the out-plane stability of cantilever tube-truss structure.
本文首先将悬挑立体桁架简化为闭口薄壁悬臂梁模型,采用能量法建立微分方程,求出该结构在平面外稳定临界荷载的近似解析解,并将其与简化模型的强度临界荷载进行对比,以获得悬挑立体桁架极限荷载由强度控制而不发生平面外失稳的条件。随后,采用有限元方法通过大量计算分析立体桁架各截面几何参数对平面外稳定性能的影响,并将其与解析解的结论进行对比。最后,采用有限元方法分析悬挑立体桁架在地震作用下的动力稳定性。
研究表明:上、下弦杆截面面积对悬挑立体桁架平面外的稳定性影响不大,随着斜腹杆截面面积的增大,立体桁架面外稳定性增强;当节间长度等于截面高度时,悬挑立体桁架的平面外稳定性最好;对每个选定的高挑比h l,都存在一个临界截面宽高比b h,当h l≥110时,临界截面宽高比可取为b h < 1 2.5,当1 20 < h l< 1 10时,临界截面宽高比可取为b h < 1 2, h l不宜小于1 20;悬挑仰角在工程常用角度范围内对悬挑立体桁架平面外稳定的影响不大。
In recent years, the tube-truss structure is applied more and more in large public buildings, e.g. the terminal, the railway station, and the sports stadium etc., and the cantilever tube-truss structure is mainly applied in the sports stadium. Stability is a key factor which could affect the carrying capacity of steel structure, however, there is no provision about the out-plane stability of tube-truss structure, so it is meaningful that the out-plane stability of tube-truss structure is studied in this paper.
Firstly, the tube-truss structure is simplified to a model of thin-walled closed cantilever, then the differential equations are established by the energy law, and the approximate analytical solution of out-plane stability ultimate load is obtained. Compared to out-plane stability ultimate load and strength ultimate load, this paper obtain the condition that the cantilever tube-truss structure couldn’t lose the out-plane stability. Secondly, the impact of geometric parameters on the out-plane stability of tube-truss structure is analyzed by the finite element method, and then, it is compared with the conclusions of analytical solution. Finally, the dynamic stability of cantilever tube-truss structure under earthquake is also analyzed by the element method.
The study indicates the following conclusions: the top chords and bottom chords have little impact on the out-plane stability of tube-truss structure, although with the increase of belly bar’s section area, the out-plane stability of tube-truss structure increase; when the internode length equals to the section height, the out-plane stability of cantilever tube-truss structure would be best; for each h/l, there is a critical aspect ratio b/h, when h / l 1/10, the critical aspect ratio b / h < 1/ 2.5, when 1/ 20 < h / l< 1/10, the critical aspect ratio b / h < 1/ 2, and h / l< 1/ 20 is inappropriate; within the range commonly used in engineering, the elevation has little impact on the out-plane stability of cantilever tube-truss structure.
引文
[1]陈骥,钢结构稳定理论与设计,北京:科学出版社,2006
[2]童根树,钢结构的平面外稳定,北京:中国建筑工业出版社,2007
[3]刘锡良,现代空间结构,天津:天津大学出版社,2003
[4]沈世钊,陈昕,网壳结构稳定性,北京:科学出版社,1999
[5]包世华,周坚,薄壁杆件结构力学,北京:中国建筑工业出版社,2006
[6]董石麟,罗尧治,赵阳,大跨度空间结构的工程实践与学科发展,空间结构,2005,11(4):3~10
[7]刘殿中,刘灿军,三角形钢管桁架的应用研究,吉林建筑工程学院学报,2000,(3):1~4
[8]刘玉姝,张耀春,张福海,三角形空间格构式刚架平面外稳定参数分析,哈尔滨建筑大学学报,2002,35(2):11~15
[9]张耀春,刘玉姝,张福海,三角形空间格构式刚架平面外稳定的实用算法,哈尔滨建筑大学学报,2002,35(3):5~8
[10]董一萌,管桁架的平面外稳定问题的研究,结构工程师,2006,22(4):18~23
[11]Paul,J.C., Ultimate Resistance of unstiffened Multiplanar Tubular TT-and KK-Joints, J. Struct engrg, ASCE, 1994
[12]Murtha-Smith E, Aurnal of Structural Engineering, 1988, 114(9):1978~1999
[13]European Committee for Standardization (CEN ) : Eurocode3. Design of Steel Structures, Part 1. 1. ENV, 1993
[14]Gong, Yanglin, Design optimization of long-span king-post trusses, ADVANCES IN STRUCTURAL ENGINEERING, 2007, 10(6): 3.623~633
[15]Malla R, Wang B, Nalluri B, Dynamic effects of progressive member failure on the response of truss structures[C]//Dynamic Response and Progressive Failure of Special Structures.Reston:ASCE, 1993
[16]K J Bathe. Finite Element Procedures in Engineering Analysis. Prentice-Hall Inc, 1982
[17]兰艳妮,黄志尚,空间管桁在实际工程中的应用,大众科技,2005,(11):87~88
[18]李泽文,段树金,杨喜文,均布荷载作用下具有初始几何位移悬臂梁的承载力分析,石家庄铁道学院学报,2007,20(2):40~44
[19]张耀春,张秀华,截面为三角形的空间格构式圆拱平面内整体稳定性能分析,现代钢结构,2004,34(4):76~78
[20]郭海山,沈世钊,单层网壳结构动力稳定性分析方法,建筑结构学报,2003,24(3):1~9
[21]李一松,唐柏鉴,裴波,大跨度空间桁架梁整体稳定的参数分析,钢结构,2005,20(3):12~14
[22]唐小弟,冯郑红,大跨度钢管桁架屋盖结构的抗震性能分析,中南林业科技大学学报,2008,28(3):123~126
[23]罗永峰,杨木旺,大跨度刚性空间结构地震反应的静力弹塑性分析方法,建筑科学与工程学报,2008,25(3):73~80
[24]刘慧娟,弦支穹顶结构在地震作用下的动力稳定性研究:[硕士学位论文],天津;天津大学,2005
[25]周全智,大跨空间结构考虑行波效应的弹塑性地震反应分析:[硕士学位论文],天津;天津大学,2006
[26]芦燕,强震作用下大跨度拱形立体桁架结构动力强度破坏研究:[硕士学位论文],天津;天津大学,2009
[27]王秀丽,沈世钊,朱彦鹏等,轻型钢管拱形屋盖结构体系的优化设计,建筑结构,2002,(07):60~62
[28]李海旺,李建仙,钢管拱桁架在地震作用下的动力响应研究,科技情报开发与经济,2007,17(8):144~146
[29]顾祥林,彭斌,黄庆华,结构抗震分析中的计算机仿真技术,自然灾害学报,2007,16(2):92~99
[30]中华人民共和国建设部,GB 50011-2001,建筑抗震设计规范,北京:中国计划出版社,2002
[31]王庆扬,王传甲,陈志强等,基于材料本构关系的动力弹塑性时程分析方法及其工程应用,第十九届余国高层建筑结构学术会议论文,2006:684~689
[32]杨志勇,黄吉锋,弹性、弹塑性时程分析法在结构设计中的应用,建筑结构.技术通讯,2007:11~13
[33]苏少卿,网壳结构基于性能的动力失效判定准则,合肥工业大学学报(自然科学版),2007,30(6):777~780
[34]李海旺,李春艳,三角形钢管拱桁架在脉冲荷载作用下的动力稳定性,科学之友,2005(9/10):13~16
[35]博弈创作室,ANSYS9.0经典产品高级分析技术与实例详解,北京:中国水利水电出版社,2005
[36]祝效华,余志祥等,ANSYS高级工程有限元分析范例精选,北京:电子工业出版社,2004
[37]李国豪,桥梁结构稳定与振动,北京:中国铁道出版社,1992
[38]谷邛英,北京站无站台柱雨棚主桁架设计研究,铁道工程学报,2006,09:78~81
[39]杨惠东,李娜,王士裴等,某火车站无站台柱雨棚钢结构设计,铁道工程学报,2007,02:17~24
[40]王策,沈世钊,单层球面网壳动力稳定性,土木工程学报,2001,36(6):17~24
[41]郭海山,王林安,沈世钊,水平阶跃荷载作用下单层球面网壳结构的动力稳定性,哈尔滨建筑大学学报,2002,35(5):12~17
[42]刘慧娟,韩庆华,王永跃,弦支穹顶结构在地震荷载作用下的动力稳定性研究,工业建筑(增),2005
[43]郭海山,钱宏亮,沈世钊,地震作用下单层球面网壳结构的动力稳定性,地震工程与工程振动, 2003,23(1):31~37
[44]李中学,李元齐,严慧等,结构非线性动力稳定性研究中的关键问题探讨,空间结构,2000,6(4)
[45]张其林,Udo Peil,任意激励下弹性结构的动力稳定分析,土木工程学报,1998,31(1):26~32
[2]童根树,钢结构的平面外稳定,北京:中国建筑工业出版社,2007
[3]刘锡良,现代空间结构,天津:天津大学出版社,2003
[4]沈世钊,陈昕,网壳结构稳定性,北京:科学出版社,1999
[5]包世华,周坚,薄壁杆件结构力学,北京:中国建筑工业出版社,2006
[6]董石麟,罗尧治,赵阳,大跨度空间结构的工程实践与学科发展,空间结构,2005,11(4):3~10
[7]刘殿中,刘灿军,三角形钢管桁架的应用研究,吉林建筑工程学院学报,2000,(3):1~4
[8]刘玉姝,张耀春,张福海,三角形空间格构式刚架平面外稳定参数分析,哈尔滨建筑大学学报,2002,35(2):11~15
[9]张耀春,刘玉姝,张福海,三角形空间格构式刚架平面外稳定的实用算法,哈尔滨建筑大学学报,2002,35(3):5~8
[10]董一萌,管桁架的平面外稳定问题的研究,结构工程师,2006,22(4):18~23
[11]Paul,J.C., Ultimate Resistance of unstiffened Multiplanar Tubular TT-and KK-Joints, J. Struct engrg, ASCE, 1994
[12]Murtha-Smith E, Aurnal of Structural Engineering, 1988, 114(9):1978~1999
[13]European Committee for Standardization (CEN ) : Eurocode3. Design of Steel Structures, Part 1. 1. ENV, 1993
[14]Gong, Yanglin, Design optimization of long-span king-post trusses, ADVANCES IN STRUCTURAL ENGINEERING, 2007, 10(6): 3.623~633
[15]Malla R, Wang B, Nalluri B, Dynamic effects of progressive member failure on the response of truss structures[C]//Dynamic Response and Progressive Failure of Special Structures.Reston:ASCE, 1993
[16]K J Bathe. Finite Element Procedures in Engineering Analysis. Prentice-Hall Inc, 1982
[17]兰艳妮,黄志尚,空间管桁在实际工程中的应用,大众科技,2005,(11):87~88
[18]李泽文,段树金,杨喜文,均布荷载作用下具有初始几何位移悬臂梁的承载力分析,石家庄铁道学院学报,2007,20(2):40~44
[19]张耀春,张秀华,截面为三角形的空间格构式圆拱平面内整体稳定性能分析,现代钢结构,2004,34(4):76~78
[20]郭海山,沈世钊,单层网壳结构动力稳定性分析方法,建筑结构学报,2003,24(3):1~9
[21]李一松,唐柏鉴,裴波,大跨度空间桁架梁整体稳定的参数分析,钢结构,2005,20(3):12~14
[22]唐小弟,冯郑红,大跨度钢管桁架屋盖结构的抗震性能分析,中南林业科技大学学报,2008,28(3):123~126
[23]罗永峰,杨木旺,大跨度刚性空间结构地震反应的静力弹塑性分析方法,建筑科学与工程学报,2008,25(3):73~80
[24]刘慧娟,弦支穹顶结构在地震作用下的动力稳定性研究:[硕士学位论文],天津;天津大学,2005
[25]周全智,大跨空间结构考虑行波效应的弹塑性地震反应分析:[硕士学位论文],天津;天津大学,2006
[26]芦燕,强震作用下大跨度拱形立体桁架结构动力强度破坏研究:[硕士学位论文],天津;天津大学,2009
[27]王秀丽,沈世钊,朱彦鹏等,轻型钢管拱形屋盖结构体系的优化设计,建筑结构,2002,(07):60~62
[28]李海旺,李建仙,钢管拱桁架在地震作用下的动力响应研究,科技情报开发与经济,2007,17(8):144~146
[29]顾祥林,彭斌,黄庆华,结构抗震分析中的计算机仿真技术,自然灾害学报,2007,16(2):92~99
[30]中华人民共和国建设部,GB 50011-2001,建筑抗震设计规范,北京:中国计划出版社,2002
[31]王庆扬,王传甲,陈志强等,基于材料本构关系的动力弹塑性时程分析方法及其工程应用,第十九届余国高层建筑结构学术会议论文,2006:684~689
[32]杨志勇,黄吉锋,弹性、弹塑性时程分析法在结构设计中的应用,建筑结构.技术通讯,2007:11~13
[33]苏少卿,网壳结构基于性能的动力失效判定准则,合肥工业大学学报(自然科学版),2007,30(6):777~780
[34]李海旺,李春艳,三角形钢管拱桁架在脉冲荷载作用下的动力稳定性,科学之友,2005(9/10):13~16
[35]博弈创作室,ANSYS9.0经典产品高级分析技术与实例详解,北京:中国水利水电出版社,2005
[36]祝效华,余志祥等,ANSYS高级工程有限元分析范例精选,北京:电子工业出版社,2004
[37]李国豪,桥梁结构稳定与振动,北京:中国铁道出版社,1992
[38]谷邛英,北京站无站台柱雨棚主桁架设计研究,铁道工程学报,2006,09:78~81
[39]杨惠东,李娜,王士裴等,某火车站无站台柱雨棚钢结构设计,铁道工程学报,2007,02:17~24
[40]王策,沈世钊,单层球面网壳动力稳定性,土木工程学报,2001,36(6):17~24
[41]郭海山,王林安,沈世钊,水平阶跃荷载作用下单层球面网壳结构的动力稳定性,哈尔滨建筑大学学报,2002,35(5):12~17
[42]刘慧娟,韩庆华,王永跃,弦支穹顶结构在地震荷载作用下的动力稳定性研究,工业建筑(增),2005
[43]郭海山,钱宏亮,沈世钊,地震作用下单层球面网壳结构的动力稳定性,地震工程与工程振动, 2003,23(1):31~37
[44]李中学,李元齐,严慧等,结构非线性动力稳定性研究中的关键问题探讨,空间结构,2000,6(4)
[45]张其林,Udo Peil,任意激励下弹性结构的动力稳定分析,土木工程学报,1998,31(1):26~32