中国国家大剧院结构抗震动力分析
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摘要
中国国家大剧院结构分析——该项目是太原理工大学与北京市建筑设计研究院合作项目，属国家大剧院结构设计中的一个工作环节。
国家大剧院属甲类建筑，在抗震设计与分析中，必然优先考虑其“安全性”而非“经济性”。该建筑结构占地面积大，高度为56m，充分利用地下空间，结构形式为多塔楼结构，其体形布置极其复杂，具体表现在：结构开间大，梁板跨度大，楼板开洞较大且不规则；平面布置以椭圆曲线为主，有较多剪力墙面为曲面；抗震设计以剪力墙为主，局部应用钢管混凝土柱形成的柔性框架与剪力墙共同作用；结构存在转换层，刚度突变层等。因此对该结构除进行常规必要的设计工作外，需进一步利用工程分析软件进行结构分析，本文利用有限元分析软件ANSYS对国家大剧院进行了结构抗震动力分析。
根据建筑抗震设计规范规定，对建筑结构应进行多遇地震作用下的内力与变形分析。其主要内容有：
1、有限元模型
该建筑结构采用三维空间有限元模型。
2、结构抗震验算
采用振型分解反应谱法进行小震作用下构件强度验算；采
太原理工大学硕士研究生学位论文
用时程分析法进行弹性变形计算。
3、弹塑性分析
对ConCert塔楼地上部分进行静力弹塑性分析，计算罕遇地
震下结构的变形。
通过对结构进行抗震动力分析，发现结构的基本动力特点
为:基频较高;频谱密集，局部振型明显;各振型中，主振型
频率附近各阶振型变形形状比较接近，彼此祸连较大，而且各
主振型之间存在较多次要振型;地震作用下，弹性层间位移角
较小，结构抗侧刚度大，抗震能力强。此外，本文找出了结构
主要薄弱部位，结构中出现材料刚度突变、大面积悬挑构件、
大跨度薄板、大跨度巨型梁以及大开洞板等情况时，均会导致
结构局部薄弱。
分析工作中，得出一些处理问题的新办法与经验，如:
1、钢管混凝土柱的简化建模
弹性分析中，根据侧向等刚度原则，将钢管混凝土柱简化
为等效普通混凝土柱进行建模与计算，在保证计算精度的前提
下，有效地减少了总自由度数。
2、主要模态的把握
大型结构有限元分析中，可根据结构各阶模态的参与系数、
模态系数及振型特点，找出结构分别在x、y、z方向的主要模
态。
3、结构薄弱部位的确定
针对每一构件—墙、梁、柱、板，对其单元节点应力、
太原理工大学硕士研究生学位论文
位移进行排序，找出其中前几十位较大值，根据这些节点的位
置坐标，即可找出结构的薄弱部位。
4、水平荷载模式的提出
在弹塑性分析中，首次提出和应用了空间结构有限元计算时
的水平加载模式，通过逐级加载进行分析，得出塑性铰分布和
发展情况，进一步判明结构的薄弱环节。
这些有益经验和结论对该类大型复杂结构抗震动力分析与
计算具有很好的参考价值。
The engineering, anti-seismic analysis of Chinese National Grand Theater is assumed together by Taiyuan University of Technology and Beijing Institute of Architectural Design Research. This work is a portion of the whole design work of National Grand Theater.
A first-rate building, National Grand Theater is designed and analyzed on account of the safety instead of the economy. The architecture area of this structure is 14952m2 and its height is 56m. The building is a multi-tower structure with a huge underground space and its structural shape is very complex, which is reflected by following items: big room width, long-span slabs, long-span beams, irregular slabs shape, slabs with big holes and many curved shear-walls. Main seismic members are reinforced concrete shear-walls, which is partially assisted by frames composed of concrete filled tubular columns. Considering the importance and complication of National Grand Theater, it is necessary that the analysis software be adopted apart from the normal software for engineering design. In this paper, the seismic analysis is performed by using software ANSYS, version 5.7.1.
According to code for seismic design of buildings, the structural bearing and anti-deformed capacity should be calculated and evaluated under the normal earthquake. The main analytical
substances are shown as following.
1. The Finite Element model
The 3-Dimentional Finite Element model is adopted here.
2. Anti-seismic analysis
The elastic analysis has been performed under normal earthquake. The response spectrum analysis and the time-history analysis are separately employed to check structural bearing and deformation capacity.
3. Elastoplastic analysis
The Concert's tower structure is analyzed by push-over method under major earthquake.
Above calculations have shown the structural dynamic characteristics as following: high fundamental frequency, dense spectra of frequencies and obviously partial modes. There are many secondary modes between two main modes and every mode is greatly correlative with its adjacent modes. The displacement distance of the adjacent stories is quilt small, which indicates that the seismic capacity of this structure is extremely strong. Additionally, the main weak parts have been found in this paper. There are many reasons to partial weak stiffness, such as sudden change of stiffness, big cantilever members, long-span thin slabs, long-span mega-beams, and so on.
From the analysis, some new experiences can be drawn.
1. Simplification of concrete filled tubular column
According to the equivalent lateral stiffness criterion, the concrete filled tubular column is converted into an equivalent reinforced concrete column. By using these methods, the degrees of freedom of the whole structure are reduced greatly as well as the accuracy of analysis can be ensured.
2. Determination of the main modes
In the analysis of large-sized structures, the main modes can be determined by participation factor, modal coefficient, and characteristic of modes in the excitation direction.
3. Determination of structural weak parts
For every element, such as beam, column and shell, the node's stress and displacement values are sorted, and then according to their order, locations of nodes within more values region would be found. Therefore, weak parts would be determined.
4. Definition of horizontal loading form
The horizontal loading form is firstly presented and applied for 3-D Finite Element elastoplastic analysis. Under push-over loading, the distributions and development of hinges are obtained and then the weak parts are distinguished.
The conclusions and experiences acquired in this paper provide some advices for seismic analysis of similar large-sized structures.
国家大剧院属甲类建筑，在抗震设计与分析中，必然优先考虑其“安全性”而非“经济性”。该建筑结构占地面积大，高度为56m，充分利用地下空间，结构形式为多塔楼结构，其体形布置极其复杂，具体表现在：结构开间大，梁板跨度大，楼板开洞较大且不规则；平面布置以椭圆曲线为主，有较多剪力墙面为曲面；抗震设计以剪力墙为主，局部应用钢管混凝土柱形成的柔性框架与剪力墙共同作用；结构存在转换层，刚度突变层等。因此对该结构除进行常规必要的设计工作外，需进一步利用工程分析软件进行结构分析，本文利用有限元分析软件ANSYS对国家大剧院进行了结构抗震动力分析。
根据建筑抗震设计规范规定，对建筑结构应进行多遇地震作用下的内力与变形分析。其主要内容有：
1、有限元模型
该建筑结构采用三维空间有限元模型。
2、结构抗震验算
采用振型分解反应谱法进行小震作用下构件强度验算；采
太原理工大学硕士研究生学位论文
用时程分析法进行弹性变形计算。
3、弹塑性分析
对ConCert塔楼地上部分进行静力弹塑性分析，计算罕遇地
震下结构的变形。
通过对结构进行抗震动力分析，发现结构的基本动力特点
为:基频较高;频谱密集，局部振型明显;各振型中，主振型
频率附近各阶振型变形形状比较接近，彼此祸连较大，而且各
主振型之间存在较多次要振型;地震作用下，弹性层间位移角
较小，结构抗侧刚度大，抗震能力强。此外，本文找出了结构
主要薄弱部位，结构中出现材料刚度突变、大面积悬挑构件、
大跨度薄板、大跨度巨型梁以及大开洞板等情况时，均会导致
结构局部薄弱。
分析工作中，得出一些处理问题的新办法与经验，如:
1、钢管混凝土柱的简化建模
弹性分析中，根据侧向等刚度原则，将钢管混凝土柱简化
为等效普通混凝土柱进行建模与计算，在保证计算精度的前提
下，有效地减少了总自由度数。
2、主要模态的把握
大型结构有限元分析中，可根据结构各阶模态的参与系数、
模态系数及振型特点，找出结构分别在x、y、z方向的主要模
态。
3、结构薄弱部位的确定
针对每一构件—墙、梁、柱、板，对其单元节点应力、
太原理工大学硕士研究生学位论文
位移进行排序，找出其中前几十位较大值，根据这些节点的位
置坐标，即可找出结构的薄弱部位。
4、水平荷载模式的提出
在弹塑性分析中，首次提出和应用了空间结构有限元计算时
的水平加载模式，通过逐级加载进行分析，得出塑性铰分布和
发展情况，进一步判明结构的薄弱环节。
这些有益经验和结论对该类大型复杂结构抗震动力分析与
计算具有很好的参考价值。
The engineering, anti-seismic analysis of Chinese National Grand Theater is assumed together by Taiyuan University of Technology and Beijing Institute of Architectural Design Research. This work is a portion of the whole design work of National Grand Theater.
A first-rate building, National Grand Theater is designed and analyzed on account of the safety instead of the economy. The architecture area of this structure is 14952m2 and its height is 56m. The building is a multi-tower structure with a huge underground space and its structural shape is very complex, which is reflected by following items: big room width, long-span slabs, long-span beams, irregular slabs shape, slabs with big holes and many curved shear-walls. Main seismic members are reinforced concrete shear-walls, which is partially assisted by frames composed of concrete filled tubular columns. Considering the importance and complication of National Grand Theater, it is necessary that the analysis software be adopted apart from the normal software for engineering design. In this paper, the seismic analysis is performed by using software ANSYS, version 5.7.1.
According to code for seismic design of buildings, the structural bearing and anti-deformed capacity should be calculated and evaluated under the normal earthquake. The main analytical
substances are shown as following.
1. The Finite Element model
The 3-Dimentional Finite Element model is adopted here.
2. Anti-seismic analysis
The elastic analysis has been performed under normal earthquake. The response spectrum analysis and the time-history analysis are separately employed to check structural bearing and deformation capacity.
3. Elastoplastic analysis
The Concert's tower structure is analyzed by push-over method under major earthquake.
Above calculations have shown the structural dynamic characteristics as following: high fundamental frequency, dense spectra of frequencies and obviously partial modes. There are many secondary modes between two main modes and every mode is greatly correlative with its adjacent modes. The displacement distance of the adjacent stories is quilt small, which indicates that the seismic capacity of this structure is extremely strong. Additionally, the main weak parts have been found in this paper. There are many reasons to partial weak stiffness, such as sudden change of stiffness, big cantilever members, long-span thin slabs, long-span mega-beams, and so on.
From the analysis, some new experiences can be drawn.
1. Simplification of concrete filled tubular column
According to the equivalent lateral stiffness criterion, the concrete filled tubular column is converted into an equivalent reinforced concrete column. By using these methods, the degrees of freedom of the whole structure are reduced greatly as well as the accuracy of analysis can be ensured.
2. Determination of the main modes
In the analysis of large-sized structures, the main modes can be determined by participation factor, modal coefficient, and characteristic of modes in the excitation direction.
3. Determination of structural weak parts
For every element, such as beam, column and shell, the node's stress and displacement values are sorted, and then according to their order, locations of nodes within more values region would be found. Therefore, weak parts would be determined.
4. Definition of horizontal loading form
The horizontal loading form is firstly presented and applied for 3-D Finite Element elastoplastic analysis. Under push-over loading, the distributions and development of hinges are obtained and then the weak parts are distinguished.
The conclusions and experiences acquired in this paper provide some advices for seismic analysis of similar large-sized structures.
引文
[1] 方鄂华，钱稼茹．我国高层建筑抗震设计的若干问题．土木工程学报．1999(1)，5-8．
[2] 李淮．我国高层建筑结构分析方法的演变及其作用．广东土木与建筑．2001，(9)，29-33．
[3] 张伟林．计算力学的研究现状与发展前景．安徽建筑工业学院学报．2001，9(2)3-9．
[4] Clough C W, Penzien J. Dynamics of structures. Second edition. McGram-Hill, Inc.1993.
[5] R.R.Craig, Jr..Structural Dynamics. An Introduction to Computer Methods. John Wiley & Sons. 1981,45-56.
[6] 崔俊芝，梁俊．现代有限元软件方法．北京，国防工业出版社．1995，124-138．
[7] ANSYS Inc.Modeling and Meshing Guide.ANSYS Release 5.7,001377.December 2000. SAS IR Inc.
[8] 徐培福，黄小坤．高层建筑混凝土结构技术规程理解与应用．北京．中国建筑工业出版社，2003，170．
[9] GB50011-2001．建筑抗震设计规范．北京科技出版社，2001．
[10] 潘友光．钢管混凝土受弯构件承载力研究．哈尔滨建筑工程学院学报．1990，(2)，41-49．
[11] 龚昌基．试论钢管混凝土柱应用于高层建筑的综合效益．哈尔滨建筑大学学报，1997(5)，27-31．
[12] 李珠．充液金属圆柱壳受弹体冲击的整体变形与局部破坏分析．固体力学学报．1999．20(4)．303-309．
[13] 李珠．内充高压液体钢管受弹体侧向冲击破坏的试验研究与理论分析．太原理工大学博士论文．2000．3．
[14] 李珠．单个与组合预制槽金属圆柱管能量吸收能力的试验研究．力学与实践．2001．23(1)，45-49．
[15] 韩林海．钢管混凝土结构．北京，科学出版社，2000，163-169．
[16] 王文亮，张文，罗惟德等．结构动力学．上海，复旦大学出版社．1993，78-85．
[17] 赵西安．钢筋混凝土高层建筑结构设计．北京，中国建筑工业出版社，1992．86-92．
[18] 赵西安．高层建筑结构在竖向地震作用下的时程分析．建筑结构学报．1994．15(1)，2-10．
[19] 刘大海，杨翠如，钟锡根．高层建筑抗震设计．北京，中国建筑工业出版社，1993，384-386．
[20] 郭继武．建筑抗震设计．北京，高等教育出版社．2001，44-58．
[21] 龚思礼．建筑抗震设计手册．北京，中国建筑工业出版社．2002，207．
[22] 马乐为，吴敏哲，谢异同．基于脉冲频响函数的MATLAB动力方程求解方法．世界地震工程，2003，19(2)，168-171．
[23] G Ayala, 叶献国. Analytical Evaluation of the Structural Seismic Damage of Reinforced Concrete Frames.第7届加拿大地震工程大会论文集.加拿大.1995,389-396.
[24] William Weaver, Jr..Paul R. Johnston. Structural Dynamics by Finite Elements.Prentice-Hall, Englewood Cliffs, New Jersey. 1987,144-154.
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[26] 李珠.The global deformation and local damage analysis of filled metallic cylindrical shells impacted by missiles. ACTA MECHANICA SOLIDA SINICA. 1999. Vol.12. No.3.
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[32] Pierre Leger and Serge Dussault. Seismic-Energy Dissipation MDOF Structures, J. Struc. Engrg., ASCE, 118(5), 1992.
[33] 李田．结构时程动力分析中的阻尼取值研究．土木工程学报．1997，30(3)，68-73．
[34] 黄宗明，白绍良，赖明．结构地震反应时程分析中的阻尼问题详述．地震工程与工程振动．1996，16(2)，95-105．
[35] 程绍革，王理，张允顺．弹塑性时程分析方法及其应用．建筑结构学报．2000，21(1)，52-56．
[36] 杨溥，李英民，王亚勇等．结构静力弹塑性分析(push-over)方法的改进．建筑结构学报．2000，21(1)，44-51．
[37] 方鄂华，何国松，容柏生等．广州天王中心大厦弹塑性地震反应分析．建筑结构学报．2000，21(6)，10-15．
[38] 徐永基，王润昌，鱼水滢等．陕西省信息大厦超高层结构设计和安全性分析．建筑结构学报．2002，23(1)，89-95．
[39] 张青，陈彬磊，丁宗梁．北京西站北站房主楼抗震设计与研究．建筑结构学报．1996，17(1)，14-16．
[2] 李淮．我国高层建筑结构分析方法的演变及其作用．广东土木与建筑．2001，(9)，29-33．
[3] 张伟林．计算力学的研究现状与发展前景．安徽建筑工业学院学报．2001，9(2)3-9．
[4] Clough C W, Penzien J. Dynamics of structures. Second edition. McGram-Hill, Inc.1993.
[5] R.R.Craig, Jr..Structural Dynamics. An Introduction to Computer Methods. John Wiley & Sons. 1981,45-56.
[6] 崔俊芝，梁俊．现代有限元软件方法．北京，国防工业出版社．1995，124-138．
[7] ANSYS Inc.Modeling and Meshing Guide.ANSYS Release 5.7,001377.December 2000. SAS IR Inc.
[8] 徐培福，黄小坤．高层建筑混凝土结构技术规程理解与应用．北京．中国建筑工业出版社，2003，170．
[9] GB50011-2001．建筑抗震设计规范．北京科技出版社，2001．
[10] 潘友光．钢管混凝土受弯构件承载力研究．哈尔滨建筑工程学院学报．1990，(2)，41-49．
[11] 龚昌基．试论钢管混凝土柱应用于高层建筑的综合效益．哈尔滨建筑大学学报，1997(5)，27-31．
[12] 李珠．充液金属圆柱壳受弹体冲击的整体变形与局部破坏分析．固体力学学报．1999．20(4)．303-309．
[13] 李珠．内充高压液体钢管受弹体侧向冲击破坏的试验研究与理论分析．太原理工大学博士论文．2000．3．
[14] 李珠．单个与组合预制槽金属圆柱管能量吸收能力的试验研究．力学与实践．2001．23(1)，45-49．
[15] 韩林海．钢管混凝土结构．北京，科学出版社，2000，163-169．
[16] 王文亮，张文，罗惟德等．结构动力学．上海，复旦大学出版社．1993，78-85．
[17] 赵西安．钢筋混凝土高层建筑结构设计．北京，中国建筑工业出版社，1992．86-92．
[18] 赵西安．高层建筑结构在竖向地震作用下的时程分析．建筑结构学报．1994．15(1)，2-10．
[19] 刘大海，杨翠如，钟锡根．高层建筑抗震设计．北京，中国建筑工业出版社，1993，384-386．
[20] 郭继武．建筑抗震设计．北京，高等教育出版社．2001，44-58．
[21] 龚思礼．建筑抗震设计手册．北京，中国建筑工业出版社．2002，207．
[22] 马乐为，吴敏哲，谢异同．基于脉冲频响函数的MATLAB动力方程求解方法．世界地震工程，2003，19(2)，168-171．
[23] G Ayala, 叶献国. Analytical Evaluation of the Structural Seismic Damage of Reinforced Concrete Frames.第7届加拿大地震工程大会论文集.加拿大.1995,389-396.
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