大跨越输电塔线体系环境荷载与极限承载力分析
|
摘要
大跨越输电塔线体系可以跨越山川河谷等障碍,四回路钢管大跨越输电塔有四层横担,具有占地面积少、输送电力多的特点。由于四回路钢管大跨越输电塔塔身高度高,横担长度长,这使得塔线体系在环境荷载作用下的极限承载能力与普通塔线体系有所不同。
大跨越输电塔线体系承受的环境荷载主要有风荷载、雨荷载以及覆冰荷载。本文主要研究雨荷载对输电塔的作用以及大跨越输电塔线体系在环境荷载下的极限承载能力。
针对雨荷载的数值模拟,首先解决风速入口的问题：本文采用谐波叠加法,生成空旷场地的脉动风速时程,并以此作为流场模拟入口；其次要解决雨颗粒的模拟问题：利用离散相模拟雨滴,用离散涡模型模拟瞬态流场；最后求解雨滴荷载,根据冲量守恒定理,得到时间间隔为0.25s的平均雨荷载时程。结果显示：当降雨强度为709.2mm/h,风速为10m/s时,平均雨荷载与风荷载比值最大值为2.53%,出现在18m高度处；雨荷载与风荷载的比值随高度增加而减少。
针对大跨越输电塔线体系的静力极限承载能力,首先建立了三跨两塔的ANSYS有限元模型；其次依据现行规范,对该模型在四个风向角荷载作用下的静力极限承载能力进行分析,得到了最不利风向角以及各个风向角荷载作用下的破坏模式和极限承载能力。研究发现：塔线体系的破坏从塔底受压侧角柱开始；若考虑弯矩对轴力的影响,输电塔底层角柱发生应力屈服的荷载将减小；塔线体系的控制风向角为45度风向角,极限荷载为2.083倍的设计荷载。
为了研究塔线体系的动力极限承载能力,本文计算了塔线体系在三种风荷载工况下的时程响应。研究发现：在10m高平均风速为50m/s的动力风荷载作用下,输电塔达到极限承载能力状态,底层受压角柱最先屈服,破坏时10m高度处脉动风速为55.1m/s。
Large span transmission tower-line system can cross rivers and mountains. The four cross arms on the steel pipe large span transmission tower make the system transfer more power with less area. The tower is so high and the cross arms are so long that the ultimate carrying capacity of the system is different from the normal tower-line system.
Wind load, wind drive rain load and ice load are the major environmental loads of the large span transmission tower-line system. One subject of the paper is wind-driven rain load of the tower; another subject of the paper is the ultimate carrying capacity of the tower-line system under wind load.
In order to simulate the rain load, first, the fluctuating wind velocity inlet is needed. Based on harmonic wave superimposing method, the time history of fluctuating wind in open site was generated and used as the velocity inlet for flow field simulation. Second, the raindrops must be simulated properly, the fluctuating wind field and raindrops were respectively simulated by detached eddy model and discrete phase model. The rain load is solved at last. According to the impulse equivalence principle, rain load averaged over 0.25s time interval was calculated. The result shows that in all the load case, the biggest ration of rain load to wind load happens when the rain intensity is 709.2mm/h and the average wind velocity is 10m/s at the height of 18m. It's also seen that the ration of the rain load to wind load decreases with height.
The other subject of this paper is the ultimate carrying capacity of the tower-line system. The finite element model of a transmission tower-line system is established using ANSYS software. According to the standard of the state, the static ultimate carrying capacity of the system is calculated with four different wind attack angles. The static ultimate carrying capacity of the tower-line system is achieved and the break models of the tower-line system under the different wind attack angles are discussed. The result shows that bottom compressed columns yield first before all the other members. Considering the interrelationship between bending moment and axis stress, the yield load will be smaller. The ultimate carrying capacity of the system at the angle attack of 45 degree is smallest in all load case. The ultimate load is 2.083 times of the design load.
The dynamic capacity of the system is studied at last. The dynamic response of the system is calculated under three load cases. The tower-line system breaks when the fluctuating wind velocity reaches 55.1m/s at the height of 10m. The bottom compressed columns are the first members exceed the yield stress.
大跨越输电塔线体系承受的环境荷载主要有风荷载、雨荷载以及覆冰荷载。本文主要研究雨荷载对输电塔的作用以及大跨越输电塔线体系在环境荷载下的极限承载能力。
针对雨荷载的数值模拟,首先解决风速入口的问题：本文采用谐波叠加法,生成空旷场地的脉动风速时程,并以此作为流场模拟入口；其次要解决雨颗粒的模拟问题：利用离散相模拟雨滴,用离散涡模型模拟瞬态流场；最后求解雨滴荷载,根据冲量守恒定理,得到时间间隔为0.25s的平均雨荷载时程。结果显示：当降雨强度为709.2mm/h,风速为10m/s时,平均雨荷载与风荷载比值最大值为2.53%,出现在18m高度处；雨荷载与风荷载的比值随高度增加而减少。
针对大跨越输电塔线体系的静力极限承载能力,首先建立了三跨两塔的ANSYS有限元模型；其次依据现行规范,对该模型在四个风向角荷载作用下的静力极限承载能力进行分析,得到了最不利风向角以及各个风向角荷载作用下的破坏模式和极限承载能力。研究发现：塔线体系的破坏从塔底受压侧角柱开始；若考虑弯矩对轴力的影响,输电塔底层角柱发生应力屈服的荷载将减小；塔线体系的控制风向角为45度风向角,极限荷载为2.083倍的设计荷载。
为了研究塔线体系的动力极限承载能力,本文计算了塔线体系在三种风荷载工况下的时程响应。研究发现：在10m高平均风速为50m/s的动力风荷载作用下,输电塔达到极限承载能力状态,底层受压角柱最先屈服,破坏时10m高度处脉动风速为55.1m/s。
Large span transmission tower-line system can cross rivers and mountains. The four cross arms on the steel pipe large span transmission tower make the system transfer more power with less area. The tower is so high and the cross arms are so long that the ultimate carrying capacity of the system is different from the normal tower-line system.
Wind load, wind drive rain load and ice load are the major environmental loads of the large span transmission tower-line system. One subject of the paper is wind-driven rain load of the tower; another subject of the paper is the ultimate carrying capacity of the tower-line system under wind load.
In order to simulate the rain load, first, the fluctuating wind velocity inlet is needed. Based on harmonic wave superimposing method, the time history of fluctuating wind in open site was generated and used as the velocity inlet for flow field simulation. Second, the raindrops must be simulated properly, the fluctuating wind field and raindrops were respectively simulated by detached eddy model and discrete phase model. The rain load is solved at last. According to the impulse equivalence principle, rain load averaged over 0.25s time interval was calculated. The result shows that in all the load case, the biggest ration of rain load to wind load happens when the rain intensity is 709.2mm/h and the average wind velocity is 10m/s at the height of 18m. It's also seen that the ration of the rain load to wind load decreases with height.
The other subject of this paper is the ultimate carrying capacity of the tower-line system. The finite element model of a transmission tower-line system is established using ANSYS software. According to the standard of the state, the static ultimate carrying capacity of the system is calculated with four different wind attack angles. The static ultimate carrying capacity of the tower-line system is achieved and the break models of the tower-line system under the different wind attack angles are discussed. The result shows that bottom compressed columns yield first before all the other members. Considering the interrelationship between bending moment and axis stress, the yield load will be smaller. The ultimate carrying capacity of the system at the angle attack of 45 degree is smallest in all load case. The ultimate load is 2.083 times of the design load.
The dynamic capacity of the system is studied at last. The dynamic response of the system is calculated under three load cases. The tower-line system breaks when the fluctuating wind velocity reaches 55.1m/s at the height of 10m. The bottom compressed columns are the first members exceed the yield stress.
引文
[1]李宏男,白海峰.高压输电塔,线体系抗灾研究的现状与发展趋势[J].土木工程学报,2007,2,40(2)：39-46.
[2]鲁元兵.大跨越输电塔线体系覆冰脱落分析[D].杭州：浙江大学硕士学位论文,2010.
[3]赵桂峰.高压输电塔,线藕连体系风致非线性振动研究[D].上海：同济大学博士学位论文,2009.
[4]曾程.大跨越输电塔结构极限承载力分析[D].上海：同济大学硕士学位论文,2006.
[5]李宏男,石文龙等.高压输电塔-导线耦联体系的简化抗震计算方法[J].特种结构,2002,19(3)：58-61.
[6]邓洪洲,朱松晔,苏速等.大跨越输电塔线体系风振控制风洞试验[J].同济大学学报,2003,31(9)：1009-1013.
[7]邓洪洲,朱松晔,陈晓明等.大跨越输电塔线体系气弹模型风洞试验[J].同济大学学报,2003,31(2)：132-137.
[8]Blockena B, Carmeliet J. A review of wind-driven rain research in building science[J]. Journal of Wind Engineering and Industrial Aerodynamics.2004,92:1079-1130.
[9]S.Assouline, A.EI Idrissi, E. Persoons. Modeling the physical charactreistics of simulated rainfall:a comparison with natural rainfall[J]. Journal of Hydrology,1997(196):336-347.
[10]H. Hangan, Wind-driven rain studies. A C-FD-E approach[J]. Journal of Wind Engineering and Industrial Aerodynamics,1999(81):323-331.
[11]Bert Blockena, Jan Carmelieta, Jean Poesen. Numerical simulation of the wind-driven rainfall distributionover small-scale topography in space and time[J]. Journal of Hydrology, 2005(315):252-273.
[12]R. Sankaran, D.A. Paterson. Computation of rain falling on a tall rectangular building[J]. Journal of Wind Engineering and Industrial Aerodynamics,1997(72):127-136.
[13]R. G. Bea,T. Xu, J. Stear, R. Ramos, wave forces on decks of offshore platforms[J]. Journal of waterway, port, coastal, and ocean engineering, may/June 1999:136-144.
[14]Edmund C.C. Choi. Wind-driven rain on building faces and the driving-rain index[J]. Journal of Wind Engineering and Industrial Aerodynamics,1999(79):105-122.
[15]E.C.C. Choi. Numerical modelling of gust effect on wind-driven rain[J]. Journal of Wind Engineering and Industrial Aerodynamics,1997(72):107-116.
[16]Joel Wolf, Morgan Griffith. Wind-driven rain as a design parameter[J]. Structures 2008: Crossing Borders @ 2008 ASCE.
[17]James C. Y. Guo, Ben Urbonas, Kevin Stewart. Rain catch under wind and vegetal cover effects[J]. Journal of hydrologic engineering, January/February 2001:29-33.
[18]M. Gu, X.Q.Du, S.Y.Li. Experimental and theoretical simulations on wind-rain-induced vibration of 3-D rigid stay cables[J]. Journal of Sound and Vibration.2009,320:184-200.
[19]吴小平.低层房屋风雨作用效应的数值研究[D].杭州：浙江大学硕士学位论文,2008.
[20]赖宗鼎.强降雨对结构设计风力系数之影响[D].基隆,国立台湾海洋大学硕士学位论文,2005.
[21]李宏男,任月明,白海峰.输电塔体系风雨激励的动力分析模型[J].中国电机工程学报,2007,27(30)：43-48.
[22]李宏男,白海峰.输电塔线体系的风雨致振动响应与稳定性研究[J].土木工程学报,2008,41(11)：31-38.
[23]熊铁华,梁枢果,邹良浩.风荷载下输电铁塔的失效模式及其极限荷载[J].工程力学,2009,26(12)：100-111.
[24]潘兹勇,胡海舰,周筱.输电塔架结构的极限承载力分析[J].建筑与结构设计,2009,26(4),26-29.
[25]赵滇生,金三爱.有限元模型对输电塔架结构动力特性分析的影响[J].特种结构,2004,21(3)：8-11.
[26]N. Prasad Rao, V. Kalyanaraman. Non-linear behaviour of lattice panel of angle towers[J]. Journal of Constructional Steel Research,2001,57:1337-1357.
[27]N. Prasad Rao, G.M. Samuel Knight, N. Lakshmanan. Investigation of transmission line tower failures[J]. Engineering Failure Analysis,2010.
[28]谢强,张勇,李杰.华东电网500kV任上5237线飑线风致倒塔事故调查分析[J].电网技术,2006,30(10)：59-63.
[29]Byoung-Wook Moon, Ji-Hun Park, Sung-Kyung Lee. Performance evaluation of a transmission tower by substructure test[J]. Journal of Constructional Steel Research,2009, 65:1-19.
[30]王之宏.风荷载的模拟研究[J].建筑结构学报,1994,15(1)：44-52.
[31]刘锡良,周颖.风荷载的几种模拟方法[J].工业建筑,2005,35(5)：81-84.
[32]刘庆宽,降雨对基本构件气动特性影响的初步研究,第十三届全国结构风工程学术会议论文集,2007.
[33]赵振维.广州地区雨滴尺寸分布模型及雨衰减预报,电波科学学报,1995,4(10)：33-37.
[34]Marshall J S, Palmer W M. The distribution of raindrops with size[J]. Journal of Meteorology, 1948(5):165-166.
[35]姚文艺,陈国祥,雨滴降落速度及终极公式,河海大学学报,1993,3(21).
[36]吕宏兴,武春龙,熊运章,等.雨滴降落速度的数值模拟[J].土壤侵蚀与水土保持学报,1997,3(2)：14-21.
[37]Blocken B, Carmeliet J. Spatial and temporal distribution of driving rain on a low-rise building[J]. Wind and Structures,2002,5(5):441-462.
[38]Gunn R, KinzerG D. The terminal velocity of fall for water droplets in stagnant air[J]. Q.J.R.Meteorol.Soc,1949,6:243-248.
[39]FLUENT6.3. Documentation.
[40]邓洪洲,朱松晔,陈晓明,等.大跨越输电塔线体系气弹模型风洞试验[J].同济大学学报,2003,31(2)：132-137.
[41]楼文娟,孙炳楠,唐锦春.高耸格构式结构风振数值分析及风洞试验[J].振动工程学报,1996,9(3)：318-322.
[42]王世村,孙炳楠,楼文娟,等.单杆输电塔气弹模型风洞试验研究和理论分析[J].浙江大学学报(工学版),2005,39(1)：87-91.
[43]程志军,付国宏,楼文娟,等.高耸格构式塔架风荷载试验研究[J].实验力学,2005,15(1)：51-55.
[44]付国宏,程志军,孙炳楠,等.架空输电线路风振试验研究[J].流体力学试验与测量,2001,15(1)：15-21.
[45]何敏娟,杨必峰.江阴500kV拉线式输电塔脉动实测[J].结构工程,2003,(4)：74-79.
[46]李杰,阎启,谢强,等.台风“韦帕”风场实测及风致输电塔振动响应[J].建筑科学与工程学报,2009,26(2)：1-8.
[47]Y. Momomura, H. Marukawa, T. Okamura, et al. Full-scale measurements of wind-induced vibration of a transmission line system in a mountainous area[J]. Journal of wind engineering and industrial aerodynamics,1997, (72):241-252.
[48]凌道盛,徐兴.非线性有限元及程序[M].杭州,浙江大学出版社,2004.
[49]张琳琳,谢强,李杰.输电线路多塔祸联体系的风致动力响应分析[J].防灾减灾工程学报,2006,26(3)：261-267.
[50]李宏男,李雪,李钢,等.状覆冰输电塔-线体系风致动力响应分析[J].防灾减灾工程学报,2008,28(2)：128-134.
[51]H. Yasui, H. Marukawa, Y. Momomura. Analytical study on wind-induced vibration of power transmission towers[J]. Journal of Wind Engineering and Industrial Aerodynamics,1999(83): 431-441.
[52]郭勇,孙炳楠,叶尹,等.大跨越输电塔线体系风振响应频域分析及风振控制[J].空气动力学学报,2009,27(3)：288-295.
[53]梁枢果,朱继华,王力.大跨越输电塔-线体系动力特性分析[J].地震工程与工程振动,2006,23(6)：63-69.
[54]邵天晓.架空送电线路的电线力学计算[M].北京,中国电力出版社,2003.
[55]赵先德.输电线路基础[M].北京,中国电力出版社,2006.
[56]架空输电线路铁塔设计技术导则[S].北京,中国电力顾问集团公司,2009.
[57]建筑结构荷载规范[S].北京,北京,中国建筑出版社,2006.
[58]陈建宁,魏德敏.输电塔线体系分析方法现状及存在的问题[J].科技情报开发与经济,2009,19(21)：146-148.
[59]李春祥,李锦华,于志强.输电塔线体系抗风设计理论与发展[J].振动与冲击,2009,28(10)：15-25.
[60]李宏男,胡大柱,路颖超.输电铁塔交叉斜材非线性极限承载力研究[J].特种结构,2004,21(3)：22-24.
[2]鲁元兵.大跨越输电塔线体系覆冰脱落分析[D].杭州：浙江大学硕士学位论文,2010.
[3]赵桂峰.高压输电塔,线藕连体系风致非线性振动研究[D].上海：同济大学博士学位论文,2009.
[4]曾程.大跨越输电塔结构极限承载力分析[D].上海：同济大学硕士学位论文,2006.
[5]李宏男,石文龙等.高压输电塔-导线耦联体系的简化抗震计算方法[J].特种结构,2002,19(3)：58-61.
[6]邓洪洲,朱松晔,苏速等.大跨越输电塔线体系风振控制风洞试验[J].同济大学学报,2003,31(9)：1009-1013.
[7]邓洪洲,朱松晔,陈晓明等.大跨越输电塔线体系气弹模型风洞试验[J].同济大学学报,2003,31(2)：132-137.
[8]Blockena B, Carmeliet J. A review of wind-driven rain research in building science[J]. Journal of Wind Engineering and Industrial Aerodynamics.2004,92:1079-1130.
[9]S.Assouline, A.EI Idrissi, E. Persoons. Modeling the physical charactreistics of simulated rainfall:a comparison with natural rainfall[J]. Journal of Hydrology,1997(196):336-347.
[10]H. Hangan, Wind-driven rain studies. A C-FD-E approach[J]. Journal of Wind Engineering and Industrial Aerodynamics,1999(81):323-331.
[11]Bert Blockena, Jan Carmelieta, Jean Poesen. Numerical simulation of the wind-driven rainfall distributionover small-scale topography in space and time[J]. Journal of Hydrology, 2005(315):252-273.
[12]R. Sankaran, D.A. Paterson. Computation of rain falling on a tall rectangular building[J]. Journal of Wind Engineering and Industrial Aerodynamics,1997(72):127-136.
[13]R. G. Bea,T. Xu, J. Stear, R. Ramos, wave forces on decks of offshore platforms[J]. Journal of waterway, port, coastal, and ocean engineering, may/June 1999:136-144.
[14]Edmund C.C. Choi. Wind-driven rain on building faces and the driving-rain index[J]. Journal of Wind Engineering and Industrial Aerodynamics,1999(79):105-122.
[15]E.C.C. Choi. Numerical modelling of gust effect on wind-driven rain[J]. Journal of Wind Engineering and Industrial Aerodynamics,1997(72):107-116.
[16]Joel Wolf, Morgan Griffith. Wind-driven rain as a design parameter[J]. Structures 2008: Crossing Borders @ 2008 ASCE.
[17]James C. Y. Guo, Ben Urbonas, Kevin Stewart. Rain catch under wind and vegetal cover effects[J]. Journal of hydrologic engineering, January/February 2001:29-33.
[18]M. Gu, X.Q.Du, S.Y.Li. Experimental and theoretical simulations on wind-rain-induced vibration of 3-D rigid stay cables[J]. Journal of Sound and Vibration.2009,320:184-200.
[19]吴小平.低层房屋风雨作用效应的数值研究[D].杭州：浙江大学硕士学位论文,2008.
[20]赖宗鼎.强降雨对结构设计风力系数之影响[D].基隆,国立台湾海洋大学硕士学位论文,2005.
[21]李宏男,任月明,白海峰.输电塔体系风雨激励的动力分析模型[J].中国电机工程学报,2007,27(30)：43-48.
[22]李宏男,白海峰.输电塔线体系的风雨致振动响应与稳定性研究[J].土木工程学报,2008,41(11)：31-38.
[23]熊铁华,梁枢果,邹良浩.风荷载下输电铁塔的失效模式及其极限荷载[J].工程力学,2009,26(12)：100-111.
[24]潘兹勇,胡海舰,周筱.输电塔架结构的极限承载力分析[J].建筑与结构设计,2009,26(4),26-29.
[25]赵滇生,金三爱.有限元模型对输电塔架结构动力特性分析的影响[J].特种结构,2004,21(3)：8-11.
[26]N. Prasad Rao, V. Kalyanaraman. Non-linear behaviour of lattice panel of angle towers[J]. Journal of Constructional Steel Research,2001,57:1337-1357.
[27]N. Prasad Rao, G.M. Samuel Knight, N. Lakshmanan. Investigation of transmission line tower failures[J]. Engineering Failure Analysis,2010.
[28]谢强,张勇,李杰.华东电网500kV任上5237线飑线风致倒塔事故调查分析[J].电网技术,2006,30(10)：59-63.
[29]Byoung-Wook Moon, Ji-Hun Park, Sung-Kyung Lee. Performance evaluation of a transmission tower by substructure test[J]. Journal of Constructional Steel Research,2009, 65:1-19.
[30]王之宏.风荷载的模拟研究[J].建筑结构学报,1994,15(1)：44-52.
[31]刘锡良,周颖.风荷载的几种模拟方法[J].工业建筑,2005,35(5)：81-84.
[32]刘庆宽,降雨对基本构件气动特性影响的初步研究,第十三届全国结构风工程学术会议论文集,2007.
[33]赵振维.广州地区雨滴尺寸分布模型及雨衰减预报,电波科学学报,1995,4(10)：33-37.
[34]Marshall J S, Palmer W M. The distribution of raindrops with size[J]. Journal of Meteorology, 1948(5):165-166.
[35]姚文艺,陈国祥,雨滴降落速度及终极公式,河海大学学报,1993,3(21).
[36]吕宏兴,武春龙,熊运章,等.雨滴降落速度的数值模拟[J].土壤侵蚀与水土保持学报,1997,3(2)：14-21.
[37]Blocken B, Carmeliet J. Spatial and temporal distribution of driving rain on a low-rise building[J]. Wind and Structures,2002,5(5):441-462.
[38]Gunn R, KinzerG D. The terminal velocity of fall for water droplets in stagnant air[J]. Q.J.R.Meteorol.Soc,1949,6:243-248.
[39]FLUENT6.3. Documentation.
[40]邓洪洲,朱松晔,陈晓明,等.大跨越输电塔线体系气弹模型风洞试验[J].同济大学学报,2003,31(2)：132-137.
[41]楼文娟,孙炳楠,唐锦春.高耸格构式结构风振数值分析及风洞试验[J].振动工程学报,1996,9(3)：318-322.
[42]王世村,孙炳楠,楼文娟,等.单杆输电塔气弹模型风洞试验研究和理论分析[J].浙江大学学报(工学版),2005,39(1)：87-91.
[43]程志军,付国宏,楼文娟,等.高耸格构式塔架风荷载试验研究[J].实验力学,2005,15(1)：51-55.
[44]付国宏,程志军,孙炳楠,等.架空输电线路风振试验研究[J].流体力学试验与测量,2001,15(1)：15-21.
[45]何敏娟,杨必峰.江阴500kV拉线式输电塔脉动实测[J].结构工程,2003,(4)：74-79.
[46]李杰,阎启,谢强,等.台风“韦帕”风场实测及风致输电塔振动响应[J].建筑科学与工程学报,2009,26(2)：1-8.
[47]Y. Momomura, H. Marukawa, T. Okamura, et al. Full-scale measurements of wind-induced vibration of a transmission line system in a mountainous area[J]. Journal of wind engineering and industrial aerodynamics,1997, (72):241-252.
[48]凌道盛,徐兴.非线性有限元及程序[M].杭州,浙江大学出版社,2004.
[49]张琳琳,谢强,李杰.输电线路多塔祸联体系的风致动力响应分析[J].防灾减灾工程学报,2006,26(3)：261-267.
[50]李宏男,李雪,李钢,等.状覆冰输电塔-线体系风致动力响应分析[J].防灾减灾工程学报,2008,28(2)：128-134.
[51]H. Yasui, H. Marukawa, Y. Momomura. Analytical study on wind-induced vibration of power transmission towers[J]. Journal of Wind Engineering and Industrial Aerodynamics,1999(83): 431-441.
[52]郭勇,孙炳楠,叶尹,等.大跨越输电塔线体系风振响应频域分析及风振控制[J].空气动力学学报,2009,27(3)：288-295.
[53]梁枢果,朱继华,王力.大跨越输电塔-线体系动力特性分析[J].地震工程与工程振动,2006,23(6)：63-69.
[54]邵天晓.架空送电线路的电线力学计算[M].北京,中国电力出版社,2003.
[55]赵先德.输电线路基础[M].北京,中国电力出版社,2006.
[56]架空输电线路铁塔设计技术导则[S].北京,中国电力顾问集团公司,2009.
[57]建筑结构荷载规范[S].北京,北京,中国建筑出版社,2006.
[58]陈建宁,魏德敏.输电塔线体系分析方法现状及存在的问题[J].科技情报开发与经济,2009,19(21)：146-148.
[59]李春祥,李锦华,于志强.输电塔线体系抗风设计理论与发展[J].振动与冲击,2009,28(10)：15-25.
[60]李宏男,胡大柱,路颖超.输电铁塔交叉斜材非线性极限承载力研究[J].特种结构,2004,21(3)：22-24.