罕遇地震下考虑压杆屈曲的网壳弹塑性分析
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摘要
分析网壳结构在地震作用下的动力性能,应考虑杆件损伤后的性能和上下部结构协同工作的影响。本文提出了一种能考虑受拉屈服和受压屈曲的等效弹塑性杆单元模型,并借助此模型进一步考察了网壳结构在罕遇地震作用下的结构响应特点;其次,在采用反应谱法计算网壳的竖向地震作用时,文中指出了传统的振型质量参与系数在确定组合振型数时存在局限,并对振型质量参与系数的合理形式进行了探讨。论文包括以下三方面的工作:
(1)建立了有初弯曲压杆的屈曲荷载和屈曲后路径曲线,并将其转化成等效的材料应力应变关系。基于大量数值计算并统计不同条件下轴心受压杆件的节点相对位移、杆件轴力与杆件长细比的关系,建立一个杆单元的等效弹塑性模型。该模型仅使用材料非线性便可实现压杆屈曲过程中的几何和材料双重非线性。
(2)采用上述的等效弹塑性模型以及常规的理想弹塑性模型,计算网壳结构在罕遇地震作用下的动力响应特点,并比较了两者的差别。同时找出按常规设计的网壳结构在罕遇地震作用下的薄弱杆件和区域,并对薄弱区域的加强措施提出了建议。研究发现,常规设计荷载作用下的网壳内力分布与罕遇地震作用下的网壳内力分布并不一致。在支座附近以及等效壳体内力较小的区域,杆件在罕遇地震作用下容易发生屈曲破坏。
(3)在按上下部结构整体模型计算网壳的竖向地震作用时,传统的振型质量参与系数很难达到90%,从而造成组合振型数过多并大大增加了计算量。文中通过对结构动力学基本公式的分析,指出上部网壳较柔而导致下部结构竖向振型不能激发是主要原因。并针对上部屋盖结构的竖向地震作用计算定义了一个局部振型质量参与系数,通过对球面和柱面网壳模型的位移和内力响应结果统计,证明该参与系数比传统的振型质量参与系数更为合理和有效。
To analysis the dynamic behavior of the lattice shell structure in the earthquake, the damage of bar and combining work of the upper and lower parts of structures should be considered. In this paper, the equivalent elastic-plastic bar mode considering the yielding of tension link and the buckling of the compression bar is built up. And the dynamic responds of the lattice shell in the rare earthquake are further researched with this new model. In the calculation of the vertical response of the whole modeling of long-span roof structure in the earthquake using the response spectrum analysis, It is pointed out that there exist some limits using the traditional modal mass participation factor to determine the model numbers and its reasonable forms are discussed. The paper includes three main parts of researches as follow:
(1) this paper determines the buckling load and post buckling path of compression bar with the initial bending deformation and builds up the equivalent relationship of material modeσ-ε. The relationships between the relative node displacement of axial force member and slenderness ratio, the axial force and slenderness ratio are established and the simple material modeσ-εis defined accordingly, using which realizes the geometrical and material nonlinear in the buckling process of compression bar.
(2) the equivalent material mode and ideal elastic-plastic material model are applied to a lattice shell to calculate the dynamic response under the seismic action respectively and the difference is compared. The weaknesses of members and zones of the lattice shell designed by normal code under the rare earthquake are found out and reinforced, and the reference of refinement and reinforcement are supplied accordingly. It is find that inner force distributions of the lattice shell show the disagreement according to traditional designing and under the rare earthquake respectively, and some members near the supports and some members with lower inner force analyzed using the shell theory would buckle easily.
(3) In the vertical response analysis of the whole modeling of long-span roof structure in the earthquake, it is found that the demand for modal mass participation coefficient up to 90% in traditional Code could not be achieved. This is because the stiffness and quality of the supporting system are far greater than those of the upper roof system, which requires a higher frequency vibration load to excite the lower part of supporting systems to vibrate. Therefore, the concept of local modal mass participation factor is defined in this paper and examples of sphere and cylindrical lattice shell structures are calculated and prove that the local modal mass participation factor is more reasonable comparing with the traditional one.
(1)建立了有初弯曲压杆的屈曲荷载和屈曲后路径曲线,并将其转化成等效的材料应力应变关系。基于大量数值计算并统计不同条件下轴心受压杆件的节点相对位移、杆件轴力与杆件长细比的关系,建立一个杆单元的等效弹塑性模型。该模型仅使用材料非线性便可实现压杆屈曲过程中的几何和材料双重非线性。
(2)采用上述的等效弹塑性模型以及常规的理想弹塑性模型,计算网壳结构在罕遇地震作用下的动力响应特点,并比较了两者的差别。同时找出按常规设计的网壳结构在罕遇地震作用下的薄弱杆件和区域,并对薄弱区域的加强措施提出了建议。研究发现,常规设计荷载作用下的网壳内力分布与罕遇地震作用下的网壳内力分布并不一致。在支座附近以及等效壳体内力较小的区域,杆件在罕遇地震作用下容易发生屈曲破坏。
(3)在按上下部结构整体模型计算网壳的竖向地震作用时,传统的振型质量参与系数很难达到90%,从而造成组合振型数过多并大大增加了计算量。文中通过对结构动力学基本公式的分析,指出上部网壳较柔而导致下部结构竖向振型不能激发是主要原因。并针对上部屋盖结构的竖向地震作用计算定义了一个局部振型质量参与系数,通过对球面和柱面网壳模型的位移和内力响应结果统计,证明该参与系数比传统的振型质量参与系数更为合理和有效。
To analysis the dynamic behavior of the lattice shell structure in the earthquake, the damage of bar and combining work of the upper and lower parts of structures should be considered. In this paper, the equivalent elastic-plastic bar mode considering the yielding of tension link and the buckling of the compression bar is built up. And the dynamic responds of the lattice shell in the rare earthquake are further researched with this new model. In the calculation of the vertical response of the whole modeling of long-span roof structure in the earthquake using the response spectrum analysis, It is pointed out that there exist some limits using the traditional modal mass participation factor to determine the model numbers and its reasonable forms are discussed. The paper includes three main parts of researches as follow:
(1) this paper determines the buckling load and post buckling path of compression bar with the initial bending deformation and builds up the equivalent relationship of material modeσ-ε. The relationships between the relative node displacement of axial force member and slenderness ratio, the axial force and slenderness ratio are established and the simple material modeσ-εis defined accordingly, using which realizes the geometrical and material nonlinear in the buckling process of compression bar.
(2) the equivalent material mode and ideal elastic-plastic material model are applied to a lattice shell to calculate the dynamic response under the seismic action respectively and the difference is compared. The weaknesses of members and zones of the lattice shell designed by normal code under the rare earthquake are found out and reinforced, and the reference of refinement and reinforcement are supplied accordingly. It is find that inner force distributions of the lattice shell show the disagreement according to traditional designing and under the rare earthquake respectively, and some members near the supports and some members with lower inner force analyzed using the shell theory would buckle easily.
(3) In the vertical response analysis of the whole modeling of long-span roof structure in the earthquake, it is found that the demand for modal mass participation coefficient up to 90% in traditional Code could not be achieved. This is because the stiffness and quality of the supporting system are far greater than those of the upper roof system, which requires a higher frequency vibration load to excite the lower part of supporting systems to vibrate. Therefore, the concept of local modal mass participation factor is defined in this paper and examples of sphere and cylindrical lattice shell structures are calculated and prove that the local modal mass participation factor is more reasonable comparing with the traditional one.
引文
[1]董石麟.空间结构[M].北京:中国电力出版社,2008
[2]卢家森,张其林.基于可靠度的单层网壳稳定设计方法[J].建筑结构学报,2006,27(6),108-130
[3]沈世钊,陈昕.网壳结构稳定性能[M].北京:科学出版社,1999
[4]叶继红,沈祖炎.初始缺陷对网壳结构动力稳定性能的影响[J].土木工程学报,1997,30(1):37-43
[5]胡聿贤.地震工程学[M].北京:地震出版社,2006
[6]曹资,薛素铎.空间结构抗震设计理论与设计[M].北京:科学出版社,2005
[7]GB50017-2001.建筑抗震规范[S].北京:中国建筑工业出版社,2001
[8]林家浩.随机振动的虚拟激励法[M].北京:科学出版社,2006
[9]Krawinkler.H.Pots and cons of a pushover analysis of seismic performance evaluation[J].Journal of Engineering Structures,1998;452-464
[10]Freeman,S.A.,Nicoletti,J.P.,and Tyrell,J.V.Evaluations of Existing Buildings for Seismic Risk- A Case Study of Puget Sound Naval Shipyard,Bremerton,Washington[J].Proceedings of 1st U.S.National Conference on Earthquake Engineering,EERI,Berkeley,1975;113-122
[11]Building Seismic Safety Council.FEMA-273.NEHRP Guidelines for the Seismic Rehabilitation of Buildings,Federal Emergency Management Agency:Washington.DC,1997
[12]Applied Technology Council.ATC40.Seismic Evaluation and Retrofit of Concrete Buildings,Report No.ATC40:Redwood City,California,1996
[13]董石麟,钱若军.空间网格结构分析理论与计算方法[M].北京:中国建筑工业出版社,2000
[14]蓝天,张毅刚.大跨度屋盖结构抗震设计[M].北京:中国建筑工业出版社,2002
[15]范峰,崔航宇,沈世钊.单层球壳结构弹塑性抗震性能分析[J].第九届全国空间结构学术会议,2000
[16]崔航宇.单层球壳弹塑性抗震性能分析[硕士学位论文].哈尔滨:哈尔滨建筑大学,2000
[17]王健宁,薛素铎,曹资,张毅刚.双层柱面网壳在地震作用下的弹塑性性能[J].第九届全国空间结构学术会议,2000
[18]张锦虹,陈扬骥.双层圆柱面网壳的抗震性能研究[J].同济大学学报,1998,26(5):498-502
[19]陈猛,罗永峰,沈祖炎.大跨空间钢结构罕遇地震反应分析[J].结构工程师,2005,21(4):39-43
[20]范峰.网壳结构抗震性能、振动控制的理论与实验研究[博士学位论文].哈尔滨:哈尔滨建筑大学,1999
[21]范峰.空间网壳结构弹塑性地震响应及抗震性能分析[J].哈尔滨建筑大学学报,1999,32(1):132-37
[22]曹资,张毅刚.各类常用网壳结构的地震反应规律[J].国家自然基金重大项目专题年度研究报告,1999
[23]薛素铎,曹资,王建宁.单层柱面网壳弹塑性地震反应特征[J].地震工程与工程振动,2002,22(1):56-60
[24]薛素铎,王建宁,曹资.钢网壳弹塑性地震反应分析[J].北京工业大学学报,2001,27(1):50-53
[25]沈世钊,支旭东.球面网壳结构在强震下的失效机理[J].土木工程学报,2005,38(1):11-20
[26]丁阳,王波.大跨空间网格结构在地震行波作用下的响应[J].地震工程与工程振动,2002,22(5):71-76
[27]Ishikawa K.,Kato S.Earthquake Resistant Capacity and Collapse Mechanism of Dynamic Buckling Analysis on Double Layer Lattices Domes under Vertical Motions[J].Proceedings of the Seiken-IASS Symposium,1993,10,69-576
[28]Ishikawa K.,Kato S.Elastic-plastic Dynamic Buckling Analysis of Reticular Domes Subjected to Earthquake Motion,International Journal of Space Structures[J].1997(3 &4),205-215
[29]Ishikawa K.,Kato S.Dynamic Buckling Behavior of Single and Double Domes Lattices due to Vertical Earthquake Motions[J].Proceedings of the Fourth International Conference of Space Structures,1993,1,466-475
[30]JGJ61-2003.网壳结构技术规程[S].北京:中国建筑工业出版社,2003.
[31]潘汉明,梁硕,裴胜兴,梁伟盛.大型薄壁钢管构件的轴压稳定分析[J].钢结构,2006,4(21):5-8
[32]吴庆雄,陈宝春,韦建刚.三维杆系结构的几何非线性有限元分析[J].工程力学,2007, 24(12):19-24
[33]沈祖炎,叶继红.运动稳定性理论在结构动力分析中的应用[J].工程力学,1997,14(3):21-28
[34]陈骥.钢结构稳定理论与设计[M].北京:科学出版社,2001
[35]S.P.Timoshenko,J.M.Gere.Theory of Elastic Stability(2nd ed)[M].New York:McGraw-Hill Inc.196l
[36]尹越,黄鑫.基于振型分解反应谱法的大跨空间结构抗震设计研究[J].沈阳理工大学学报,2007,26(3):87-90
[37]史铁花,韦承基.振型分解法中合理振型数的确定[J].建筑科学,2002,18(2):29-31
[38]刘庆林,傅学怡.反应谱CQC法合理振型数确定的研究[J].建筑结构学报,2006,27(6):87-93
[39]R.W.Clough,J.Penzien.Dynamics of Structures[M].New York:Mcgraw-Hill Inc,1975
[40]爱德华.L.威尔逊(北京金土木软件技术有限公司,中国建筑标准设计研究院).结构静力与动力分析-强调地震工程学的物理方法[M].北京:中国建筑工业出版社,2006
[2]卢家森,张其林.基于可靠度的单层网壳稳定设计方法[J].建筑结构学报,2006,27(6),108-130
[3]沈世钊,陈昕.网壳结构稳定性能[M].北京:科学出版社,1999
[4]叶继红,沈祖炎.初始缺陷对网壳结构动力稳定性能的影响[J].土木工程学报,1997,30(1):37-43
[5]胡聿贤.地震工程学[M].北京:地震出版社,2006
[6]曹资,薛素铎.空间结构抗震设计理论与设计[M].北京:科学出版社,2005
[7]GB50017-2001.建筑抗震规范[S].北京:中国建筑工业出版社,2001
[8]林家浩.随机振动的虚拟激励法[M].北京:科学出版社,2006
[9]Krawinkler.H.Pots and cons of a pushover analysis of seismic performance evaluation[J].Journal of Engineering Structures,1998;452-464
[10]Freeman,S.A.,Nicoletti,J.P.,and Tyrell,J.V.Evaluations of Existing Buildings for Seismic Risk- A Case Study of Puget Sound Naval Shipyard,Bremerton,Washington[J].Proceedings of 1st U.S.National Conference on Earthquake Engineering,EERI,Berkeley,1975;113-122
[11]Building Seismic Safety Council.FEMA-273.NEHRP Guidelines for the Seismic Rehabilitation of Buildings,Federal Emergency Management Agency:Washington.DC,1997
[12]Applied Technology Council.ATC40.Seismic Evaluation and Retrofit of Concrete Buildings,Report No.ATC40:Redwood City,California,1996
[13]董石麟,钱若军.空间网格结构分析理论与计算方法[M].北京:中国建筑工业出版社,2000
[14]蓝天,张毅刚.大跨度屋盖结构抗震设计[M].北京:中国建筑工业出版社,2002
[15]范峰,崔航宇,沈世钊.单层球壳结构弹塑性抗震性能分析[J].第九届全国空间结构学术会议,2000
[16]崔航宇.单层球壳弹塑性抗震性能分析[硕士学位论文].哈尔滨:哈尔滨建筑大学,2000
[17]王健宁,薛素铎,曹资,张毅刚.双层柱面网壳在地震作用下的弹塑性性能[J].第九届全国空间结构学术会议,2000
[18]张锦虹,陈扬骥.双层圆柱面网壳的抗震性能研究[J].同济大学学报,1998,26(5):498-502
[19]陈猛,罗永峰,沈祖炎.大跨空间钢结构罕遇地震反应分析[J].结构工程师,2005,21(4):39-43
[20]范峰.网壳结构抗震性能、振动控制的理论与实验研究[博士学位论文].哈尔滨:哈尔滨建筑大学,1999
[21]范峰.空间网壳结构弹塑性地震响应及抗震性能分析[J].哈尔滨建筑大学学报,1999,32(1):132-37
[22]曹资,张毅刚.各类常用网壳结构的地震反应规律[J].国家自然基金重大项目专题年度研究报告,1999
[23]薛素铎,曹资,王建宁.单层柱面网壳弹塑性地震反应特征[J].地震工程与工程振动,2002,22(1):56-60
[24]薛素铎,王建宁,曹资.钢网壳弹塑性地震反应分析[J].北京工业大学学报,2001,27(1):50-53
[25]沈世钊,支旭东.球面网壳结构在强震下的失效机理[J].土木工程学报,2005,38(1):11-20
[26]丁阳,王波.大跨空间网格结构在地震行波作用下的响应[J].地震工程与工程振动,2002,22(5):71-76
[27]Ishikawa K.,Kato S.Earthquake Resistant Capacity and Collapse Mechanism of Dynamic Buckling Analysis on Double Layer Lattices Domes under Vertical Motions[J].Proceedings of the Seiken-IASS Symposium,1993,10,69-576
[28]Ishikawa K.,Kato S.Elastic-plastic Dynamic Buckling Analysis of Reticular Domes Subjected to Earthquake Motion,International Journal of Space Structures[J].1997(3 &4),205-215
[29]Ishikawa K.,Kato S.Dynamic Buckling Behavior of Single and Double Domes Lattices due to Vertical Earthquake Motions[J].Proceedings of the Fourth International Conference of Space Structures,1993,1,466-475
[30]JGJ61-2003.网壳结构技术规程[S].北京:中国建筑工业出版社,2003.
[31]潘汉明,梁硕,裴胜兴,梁伟盛.大型薄壁钢管构件的轴压稳定分析[J].钢结构,2006,4(21):5-8
[32]吴庆雄,陈宝春,韦建刚.三维杆系结构的几何非线性有限元分析[J].工程力学,2007, 24(12):19-24
[33]沈祖炎,叶继红.运动稳定性理论在结构动力分析中的应用[J].工程力学,1997,14(3):21-28
[34]陈骥.钢结构稳定理论与设计[M].北京:科学出版社,2001
[35]S.P.Timoshenko,J.M.Gere.Theory of Elastic Stability(2nd ed)[M].New York:McGraw-Hill Inc.196l
[36]尹越,黄鑫.基于振型分解反应谱法的大跨空间结构抗震设计研究[J].沈阳理工大学学报,2007,26(3):87-90
[37]史铁花,韦承基.振型分解法中合理振型数的确定[J].建筑科学,2002,18(2):29-31
[38]刘庆林,傅学怡.反应谱CQC法合理振型数确定的研究[J].建筑结构学报,2006,27(6):87-93
[39]R.W.Clough,J.Penzien.Dynamics of Structures[M].New York:Mcgraw-Hill Inc,1975
[40]爱德华.L.威尔逊(北京金土木软件技术有限公司,中国建筑标准设计研究院).结构静力与动力分析-强调地震工程学的物理方法[M].北京:中国建筑工业出版社,2006