联方型双撑杆索穹顶考虑自重的预应力计算方法
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摘要
为了改善传统索穹顶结构的受力性能,该文提出了一种联方型双撑杆索穹顶结构,该索穹顶的上弦节点与两根斜撑杆相连,稳定性好并且便于张拉施工。针对联方型双撑杆索穹顶的找力分析问题,根据节点平衡方程,推导出考虑结构自重时索穹顶的预应力计算公式;给出了不同参数下联方型双撑杆索穹顶的预应力计算表,分析了该结构的受力特性;比较了考虑结构自重和不考虑结构自重时索穹顶初始预应力的差别,并采用有限元迭代法对比验证了理论公式的准确性。分析结果表明:随着矢跨比和撑杆高度的增大,结构中所有构件的初始预应力将减小;在自重荷载下,内圈脊索内力降低,最外圈斜索和环索内力显著增加;采用该文提出的理论公式可快速准确的获得考虑结构自重时联方型双撑杆索穹顶的实际预应力分布,为工程设计提供参考。
A type of Levy cable dome with double struts is presented to improve the mechanical behavior of cable domes. This structure has a good stability and is convenient for construction due to the fact that each upper node is connected to two inclined struts. To solve its force finding problem, according to the balanced equations of connections, the calculation formulas of prestress distribution with self-weight considered are deduced. The calculation tables of cable dome under different parameters are given to investigate the mechanical behavior. The differences of prestress-state with and without self-weight are compared, and the proposed formulas are checked using finite element iteration method. The results show that with the increase of rise-span ratio and height of struts, the initial prestress decreases for all components. Under self-weight, the internal force of inner ridge cables decreases, while the internal force of the most outer diagonal cables and hoop cables increases significantly. Using the formulas deduced in this paper, the actual initial prestress distribution considering self-weight for Levy cable dome with double struts can be obtained rapidly and accurately, providing a reference for engineering design.
A type of Levy cable dome with double struts is presented to improve the mechanical behavior of cable domes. This structure has a good stability and is convenient for construction due to the fact that each upper node is connected to two inclined struts. To solve its force finding problem, according to the balanced equations of connections, the calculation formulas of prestress distribution with self-weight considered are deduced. The calculation tables of cable dome under different parameters are given to investigate the mechanical behavior. The differences of prestress-state with and without self-weight are compared, and the proposed formulas are checked using finite element iteration method. The results show that with the increase of rise-span ratio and height of struts, the initial prestress decreases for all components. Under self-weight, the internal force of inner ridge cables decreases, while the internal force of the most outer diagonal cables and hoop cables increases significantly. Using the formulas deduced in this paper, the actual initial prestress distribution considering self-weight for Levy cable dome with double struts can be obtained rapidly and accurately, providing a reference for engineering design.
引文
[1]Geiger D H,Stefaniuk A,Chen D.The design and construction of two cable domes for the Korean Olympics[C]//Shells,Membranes and Space Frame,Proceedings IASS Symposium.Madrid,Spain:IASS,1986:265―272.
[2]Levy M P.The Georgia dome and beyond achieving lightweight-long span structures[C]//Proceedings of IASS-ASCE International Symposium.Madrid,Spain:IASS,1994:560―562.
[3]张国军,葛家琪,王树,等.内蒙古伊旗全民健身体育中心索穹顶结构体系设计研究[J].建筑结构学报,2012,33(4):12―22.Zhang Guojun,Ge Jiaqi,Wang Shu,et al.Design and research on cable dome structural system of the National Fitness Center in Ejin Horo Banner,Inner Mongolia[J].Journal of Building Structures,2012,33(4):12―22.(in Chinese)
[4]Yuan X,Chen L,Dong S.Prestress design of cable domes with new forms[J].International Journal of Solids and Structures,2007,44(9):2773―2782.
[5]陆金钰,武啸龙,赵曦蕾,等.基于环形张拉整体的索杆全张力穹顶结构形态分析[J].工程力学,2015,32(增刊):66―71.Lu Jinyu,Wu Xiaolong,Zhao Xilei,et al.Form finding analysis of cable-strut tensile dome based on tensegrity torus[J].Engineering Mechanics,2015,32(Suppl):66―71.(in Chinese)
[6]张爱林,刘学春,张庆亮,等.索杆弦支穹顶[P].中国:CN200720104045.9,2007-03-30.Zhang Ailin,Liu Xuechun,Zhang Qingliang,et al.Cable-strut suspendome[P].China:CN200720104045.9,2007-03-30.(in Chinese)
[7]薛素铎,高占远,李雄彦,等.一种新型预应力空间结构——劲性支撑穹顶[J].空间结构,2013,19(1):3―9.Xue Suduo,Gao Zhanyuan,Li Xiongyan,et al.A new prestressed spatial structure——Rigid bracing dome[J].Spatial Structures,2013,19(1):3―9.(in Chinese)
[8]Pellegrino S.Structural computations with the singular value decomposition of the equilibrium matrix[J].International Journal of Solids and Structures,1993,30(21):3025―3035.
[9]袁行飞,董石麟.索穹顶结构整体可行预应力概念及其应用[J].土木工程学报,2001,34(2):33―37.Yuan Xingfei,Dong Shilin.Application of integrity feasible prestressing to tensegrity cable domes[J].China Civil Engineering Journal,2001,34(2):33―37.(in Chinese)
[10]Tran H C,Park H S,Lee J.A unique feasible mode of prestress design for cable domes[J].Finite Elements in Analysis&Design,2012,59(5):44―54.
[11]董智力,何广乾,林春哲.张拉整体结构平衡状态的寻找[J].建筑结构学报,1995,20(5):24―28.Dong Zhili,He Guangqian,Lin Chunzhe.Finding of equilibrium states of tensegrity systems[J].Journal of Building Structures,1995,20(5):24―28.(in Chinese)
[12]Wang Z,Yuan X,Dong S.Simple approach for force finding analysis of circular Geiger domes with consideration of self-weight[J].Steel Construction,2010,66(2):317―322.
[13]姚云龙,董石麟,马广英.一种新型内外双重张弦网壳结构形状确定问题的研究[J].工程力学,2014,31(4):102―111.Yao Yunlong,Dong Shilin,Ma Guangying.Discussion on shape determination of a new double inner and outer latticed shell string-structure[J].Engineering Mechanics,2014,31(4):102―111.(in Chinese)
[14]Koohestani K,Guest S D.A new approach to the analytical and numerical form-finding of tensegrity structures[J].International Journal of Solids&Structures,2013,50(19):2995―3007.
[15]Lee S,Woo B H,Lee J.Self-stress design of tensegrity grid structures using genetic algorithm[J].International Journal of Mechanical Sciences,2014,79(1):38―46.
[16]葛家琪,张爱林,刘鑫刚,等.索穹顶结构张拉找形与承载全过程仿真分析[J].建筑结构学报,2012,33(4):1―11.Ge Jiaqi,Zhang Ailin,Liu Xingang,et al.Analysis of tension form-finding and whole loading process simulation of cable dome structure[J].Journal of Building Structures,2012,33(4):1―11.(in Chinese)
[17]Fu F.Structural behavior and design methods of tensegrity domes[J].Journal of Constructional Steel Research,2005,61(1):23―35.
[18]Pugh A.An introduction to tensegrity[M].Oakland,California:University of California Press,1976:10―11.
[19]Wang B B,Yan-Yun L.From tensegrity grids to cable-strut grids[J].International Journal of Space Structures,2001,16(4):279―314.
[20]董石麟,王振华,袁行飞.Levy型索穹顶考虑自重的初始预应力简捷计算法[J].工程力学,2009,26(4):1―6.Dong Shilin,Wang Zhenhua,Yuan Xingfei.A simplified calculation method for initial prestress of Levy cable domes with the consideration of self-weight[J].Engineering Mechanics,2009,26(4):1―6.(in Chinese)
[2]Levy M P.The Georgia dome and beyond achieving lightweight-long span structures[C]//Proceedings of IASS-ASCE International Symposium.Madrid,Spain:IASS,1994:560―562.
[3]张国军,葛家琪,王树,等.内蒙古伊旗全民健身体育中心索穹顶结构体系设计研究[J].建筑结构学报,2012,33(4):12―22.Zhang Guojun,Ge Jiaqi,Wang Shu,et al.Design and research on cable dome structural system of the National Fitness Center in Ejin Horo Banner,Inner Mongolia[J].Journal of Building Structures,2012,33(4):12―22.(in Chinese)
[4]Yuan X,Chen L,Dong S.Prestress design of cable domes with new forms[J].International Journal of Solids and Structures,2007,44(9):2773―2782.
[5]陆金钰,武啸龙,赵曦蕾,等.基于环形张拉整体的索杆全张力穹顶结构形态分析[J].工程力学,2015,32(增刊):66―71.Lu Jinyu,Wu Xiaolong,Zhao Xilei,et al.Form finding analysis of cable-strut tensile dome based on tensegrity torus[J].Engineering Mechanics,2015,32(Suppl):66―71.(in Chinese)
[6]张爱林,刘学春,张庆亮,等.索杆弦支穹顶[P].中国:CN200720104045.9,2007-03-30.Zhang Ailin,Liu Xuechun,Zhang Qingliang,et al.Cable-strut suspendome[P].China:CN200720104045.9,2007-03-30.(in Chinese)
[7]薛素铎,高占远,李雄彦,等.一种新型预应力空间结构——劲性支撑穹顶[J].空间结构,2013,19(1):3―9.Xue Suduo,Gao Zhanyuan,Li Xiongyan,et al.A new prestressed spatial structure——Rigid bracing dome[J].Spatial Structures,2013,19(1):3―9.(in Chinese)
[8]Pellegrino S.Structural computations with the singular value decomposition of the equilibrium matrix[J].International Journal of Solids and Structures,1993,30(21):3025―3035.
[9]袁行飞,董石麟.索穹顶结构整体可行预应力概念及其应用[J].土木工程学报,2001,34(2):33―37.Yuan Xingfei,Dong Shilin.Application of integrity feasible prestressing to tensegrity cable domes[J].China Civil Engineering Journal,2001,34(2):33―37.(in Chinese)
[10]Tran H C,Park H S,Lee J.A unique feasible mode of prestress design for cable domes[J].Finite Elements in Analysis&Design,2012,59(5):44―54.
[11]董智力,何广乾,林春哲.张拉整体结构平衡状态的寻找[J].建筑结构学报,1995,20(5):24―28.Dong Zhili,He Guangqian,Lin Chunzhe.Finding of equilibrium states of tensegrity systems[J].Journal of Building Structures,1995,20(5):24―28.(in Chinese)
[12]Wang Z,Yuan X,Dong S.Simple approach for force finding analysis of circular Geiger domes with consideration of self-weight[J].Steel Construction,2010,66(2):317―322.
[13]姚云龙,董石麟,马广英.一种新型内外双重张弦网壳结构形状确定问题的研究[J].工程力学,2014,31(4):102―111.Yao Yunlong,Dong Shilin,Ma Guangying.Discussion on shape determination of a new double inner and outer latticed shell string-structure[J].Engineering Mechanics,2014,31(4):102―111.(in Chinese)
[14]Koohestani K,Guest S D.A new approach to the analytical and numerical form-finding of tensegrity structures[J].International Journal of Solids&Structures,2013,50(19):2995―3007.
[15]Lee S,Woo B H,Lee J.Self-stress design of tensegrity grid structures using genetic algorithm[J].International Journal of Mechanical Sciences,2014,79(1):38―46.
[16]葛家琪,张爱林,刘鑫刚,等.索穹顶结构张拉找形与承载全过程仿真分析[J].建筑结构学报,2012,33(4):1―11.Ge Jiaqi,Zhang Ailin,Liu Xingang,et al.Analysis of tension form-finding and whole loading process simulation of cable dome structure[J].Journal of Building Structures,2012,33(4):1―11.(in Chinese)
[17]Fu F.Structural behavior and design methods of tensegrity domes[J].Journal of Constructional Steel Research,2005,61(1):23―35.
[18]Pugh A.An introduction to tensegrity[M].Oakland,California:University of California Press,1976:10―11.
[19]Wang B B,Yan-Yun L.From tensegrity grids to cable-strut grids[J].International Journal of Space Structures,2001,16(4):279―314.
[20]董石麟,王振华,袁行飞.Levy型索穹顶考虑自重的初始预应力简捷计算法[J].工程力学,2009,26(4):1―6.Dong Shilin,Wang Zhenhua,Yuan Xingfei.A simplified calculation method for initial prestress of Levy cable domes with the consideration of self-weight[J].Engineering Mechanics,2009,26(4):1―6.(in Chinese)