单多自由度体系R-μ规律对比分析中的若干问题
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摘要
R -μ规律既是基于强度的抗震设计中确定水平设计地震作用的关键因素,又是基于性态的抗震设计理论的主要依据。因此,合理的R -μ规律是保证结构抗震安全性的关键所在。
国内外研究者已对单自由度非弹性体系的R -μ- T规律作了广泛的研究,结论具有较好的一致性。但实际工程中的多高层结构由于受塑性机构类型、结构超强及多振型等多因素影响,其动力反应特征远比单自由度体系复杂,所以需要考察R -μ规律在多自由度非弹性体系中的适用性。近年来虽有少数研究成果,但仍缺少对这一适用性的明确结论。
在这一大背景下,本文主要完成了以下研究工作:
①总结和评述到目前为止已经完成的单自由度体系和多自由度体系R -μ规律的研究成果;
②采用新思路选波,从美国加利福尼亚大学Berkeley分校太平洋地震工程研究中心(PEER)数据库下载合适的地面运动记录;
③设计三个周期不同的单自由度体系,选择七档不同的地震力降低系数取值,通过非线性动力反应分析计算对应的位移延性μ值,初步验证单自由度体系的R -μ规律;
④以按中国规范设计的0.4g区钢筋混凝土多层框架为例,把多层框架等效成单自由度体系,在相当于该区大震强度水准的多条地面运动输入下对多自由度体系和等效单自由度体系分别进行非弹性动力反应分析。通过考察两者在相同地震力降低系数取值下不同层面的延性需求间的差异,初步验证从单自由度体系获得的R -μ规律在多自由度体系中的适用性。
通过上述研究工作,本文初步获得以下主要结论:
①国内外研究者提出的单自由度体系R -μ- T规律的主要研究成果表现出良好的一致性。在探索多自由度体系的R -μ规律时,这些研究者通常着眼于将单自由度体系的R -μ规律进行修正后用于多自由度体系,多数是从特定算例出发寻求多自由度体系R的修正系数,未能从理论上根本解决多自由度体系的R -μ关系问题。
②初步验证在多条地震波输入下计算得到的单自由度体系R -μ规律基本符合以往研究者提出的公式。对自振周期较长时算例与以往公式间存在的差异还有待进一步研究。
③多自由度体系的结构延性需求小于等效单自由度体系,初步认为单自由度体系的R -μ规律在中等周期的多自由度体系中是适用的。除了层间位移角偏大楼层的部分梁铰外,多自由度体系的梁铰转角延性需求普遍小于对应的单自由度体系,柱铰的转角延性基本上都小于等效单自由度体系。初步认为在地震力降低系数R取值相同的情况下,可以用单自由度体系的位移延性系数μ来近似估计多自由度体系的延性需求。同时认为在三个延性层面中,多自由度体系塑性铰的转角延性与单自由度体系单一塑性铰的转角延性更具可比性。
The R -μrelationship is not only the key factor in determining lateral design seismic force for force-based seismic design, but also the chief parameter for performance-based seismic design. So the proper R -μrelationship is the key factor to ensure the seismic security.
Domestic and foreign researchers have comprehensively studied the R -μ- T relationships of single-degree-of-freedom inelastic systems and drawn similar conclusion. However, dynamic response characteristics of multi-rise and high-rise buildings in practice projects are more complex than that of single-degree-of-freedom inelastic systems due to the influence of potential hinge mechanisms, structural overstrength and higher modes, so R -μrelationship has to be verified whether it can be used in multi-degree-of-freedom inelastic systems. Recently several research findings reported on it, but none of them given definite conclusions on the applicability of R -μrelationship.
Based on this background, the main research work finished in this thesis is as follows:
①Summary and commentary of the main research findings of R -μrelationships for single- and multi-degree-of-freedom systems which have been so far finished.
②Suitable ground motion records are downloaded from Berkeley Pacific Earthquake Engineering Research Center (PEER) database, which adopt new ideas.
③Three single-degree-of-freedom systems are designed with varied fundamental period, then seven different force reduction factors are selected and the corresponding values of displacement ductilityμare calculated through nonlinear dynamic response analysis. So the R -μrelationships of single-degree-of-freedom systems are initial examined.
④A multi-story reinforced concrete frame in earthquake intensity 0.4g zone is designed conforming to Chinese codes. Then the multi-storey structure is equivalent to a single-degree-of-freedom system, and the inelastic dynamic response analyses of the multi-degree-of-freedom system and the equivalent single-degree-of-freedom system when subjected to several ground motions in majoy earthquake intensity 0.4g zone are finished. Through the research of discrepancy between two systems on ductility demand of different levels with the same force reduction factor R , review the applicability of the R -μrelationship acquired from single-degree-of-freedom systems in multi-degree-of-freedom systems preliminarily have been verified.
From the finished research work above, the main conclusions can be drawn preliminarily as follows:
①The main research findings of the R -μ- Trelationships of single-degree-of-freedom systems proposed by domestic and foreign researchers are consistent. Researchers often focus on amending the R -μrelationship of single-degree-of-freedom systems to use in multi-degree-of-freedom systems, most of them seek for the modification factor of multi-degree-of-freedom systems from the specific examples. So the R -μtheoretical relation problems of multi-degree-of-freedom systems has not been ultimatly solved.
②It is verified that the R -μrelationship of single-degree-of-freedom systems calculated after a number of seismic wave inputting is consistent with formulas proposed by previous researchers. It requires further study to eliminate the discrepancy between examples in this article and the previous formulas when natural vibration period is longer.
③The structure ductility demand of multi-degree-of-freedom systems is less than the equivalent single-degree-of-freedom systems. The preliminary view is that the R -μrelationship of single-degree-of-freedom systems at the moderate period is suitable for multi-degree-of-freedom systems. The rotation ductility demand of beam hinges and column hinges of multi-degree-of-freedom systems is generally less than the equivalent single-degree-of-freedom systems, except some beam hinges on the story whose drift is larger. It is preliminary advised that the displacement ductility factorμof single-degree-of-freedom systems can be used to approximately estimate the ductility demand of multi-degree-of-freedom systems when two systems have the same force reduction factor R . And considering the three ductility levels, the rotation ductility of plastic hinges of multi-degree-of-freedom systems is more comparable with the rotation ductility of single-plastic hinge of single-degree-of-freedom systems.
国内外研究者已对单自由度非弹性体系的R -μ- T规律作了广泛的研究,结论具有较好的一致性。但实际工程中的多高层结构由于受塑性机构类型、结构超强及多振型等多因素影响,其动力反应特征远比单自由度体系复杂,所以需要考察R -μ规律在多自由度非弹性体系中的适用性。近年来虽有少数研究成果,但仍缺少对这一适用性的明确结论。
在这一大背景下,本文主要完成了以下研究工作:
①总结和评述到目前为止已经完成的单自由度体系和多自由度体系R -μ规律的研究成果;
②采用新思路选波,从美国加利福尼亚大学Berkeley分校太平洋地震工程研究中心(PEER)数据库下载合适的地面运动记录;
③设计三个周期不同的单自由度体系,选择七档不同的地震力降低系数取值,通过非线性动力反应分析计算对应的位移延性μ值,初步验证单自由度体系的R -μ规律;
④以按中国规范设计的0.4g区钢筋混凝土多层框架为例,把多层框架等效成单自由度体系,在相当于该区大震强度水准的多条地面运动输入下对多自由度体系和等效单自由度体系分别进行非弹性动力反应分析。通过考察两者在相同地震力降低系数取值下不同层面的延性需求间的差异,初步验证从单自由度体系获得的R -μ规律在多自由度体系中的适用性。
通过上述研究工作,本文初步获得以下主要结论:
①国内外研究者提出的单自由度体系R -μ- T规律的主要研究成果表现出良好的一致性。在探索多自由度体系的R -μ规律时,这些研究者通常着眼于将单自由度体系的R -μ规律进行修正后用于多自由度体系,多数是从特定算例出发寻求多自由度体系R的修正系数,未能从理论上根本解决多自由度体系的R -μ关系问题。
②初步验证在多条地震波输入下计算得到的单自由度体系R -μ规律基本符合以往研究者提出的公式。对自振周期较长时算例与以往公式间存在的差异还有待进一步研究。
③多自由度体系的结构延性需求小于等效单自由度体系,初步认为单自由度体系的R -μ规律在中等周期的多自由度体系中是适用的。除了层间位移角偏大楼层的部分梁铰外,多自由度体系的梁铰转角延性需求普遍小于对应的单自由度体系,柱铰的转角延性基本上都小于等效单自由度体系。初步认为在地震力降低系数R取值相同的情况下,可以用单自由度体系的位移延性系数μ来近似估计多自由度体系的延性需求。同时认为在三个延性层面中,多自由度体系塑性铰的转角延性与单自由度体系单一塑性铰的转角延性更具可比性。
The R -μrelationship is not only the key factor in determining lateral design seismic force for force-based seismic design, but also the chief parameter for performance-based seismic design. So the proper R -μrelationship is the key factor to ensure the seismic security.
Domestic and foreign researchers have comprehensively studied the R -μ- T relationships of single-degree-of-freedom inelastic systems and drawn similar conclusion. However, dynamic response characteristics of multi-rise and high-rise buildings in practice projects are more complex than that of single-degree-of-freedom inelastic systems due to the influence of potential hinge mechanisms, structural overstrength and higher modes, so R -μrelationship has to be verified whether it can be used in multi-degree-of-freedom inelastic systems. Recently several research findings reported on it, but none of them given definite conclusions on the applicability of R -μrelationship.
Based on this background, the main research work finished in this thesis is as follows:
①Summary and commentary of the main research findings of R -μrelationships for single- and multi-degree-of-freedom systems which have been so far finished.
②Suitable ground motion records are downloaded from Berkeley Pacific Earthquake Engineering Research Center (PEER) database, which adopt new ideas.
③Three single-degree-of-freedom systems are designed with varied fundamental period, then seven different force reduction factors are selected and the corresponding values of displacement ductilityμare calculated through nonlinear dynamic response analysis. So the R -μrelationships of single-degree-of-freedom systems are initial examined.
④A multi-story reinforced concrete frame in earthquake intensity 0.4g zone is designed conforming to Chinese codes. Then the multi-storey structure is equivalent to a single-degree-of-freedom system, and the inelastic dynamic response analyses of the multi-degree-of-freedom system and the equivalent single-degree-of-freedom system when subjected to several ground motions in majoy earthquake intensity 0.4g zone are finished. Through the research of discrepancy between two systems on ductility demand of different levels with the same force reduction factor R , review the applicability of the R -μrelationship acquired from single-degree-of-freedom systems in multi-degree-of-freedom systems preliminarily have been verified.
From the finished research work above, the main conclusions can be drawn preliminarily as follows:
①The main research findings of the R -μ- Trelationships of single-degree-of-freedom systems proposed by domestic and foreign researchers are consistent. Researchers often focus on amending the R -μrelationship of single-degree-of-freedom systems to use in multi-degree-of-freedom systems, most of them seek for the modification factor of multi-degree-of-freedom systems from the specific examples. So the R -μtheoretical relation problems of multi-degree-of-freedom systems has not been ultimatly solved.
②It is verified that the R -μrelationship of single-degree-of-freedom systems calculated after a number of seismic wave inputting is consistent with formulas proposed by previous researchers. It requires further study to eliminate the discrepancy between examples in this article and the previous formulas when natural vibration period is longer.
③The structure ductility demand of multi-degree-of-freedom systems is less than the equivalent single-degree-of-freedom systems. The preliminary view is that the R -μrelationship of single-degree-of-freedom systems at the moderate period is suitable for multi-degree-of-freedom systems. The rotation ductility demand of beam hinges and column hinges of multi-degree-of-freedom systems is generally less than the equivalent single-degree-of-freedom systems, except some beam hinges on the story whose drift is larger. It is preliminary advised that the displacement ductility factorμof single-degree-of-freedom systems can be used to approximately estimate the ductility demand of multi-degree-of-freedom systems when two systems have the same force reduction factor R . And considering the three ductility levels, the rotation ductility of plastic hinges of multi-degree-of-freedom systems is more comparable with the rotation ductility of single-plastic hinge of single-degree-of-freedom systems.
引文
[1]胡聿贤.地震工程学[M].北京:地震出版社,1988.
[2] Eurocode 8, Design Provisions for Earthquake Resistance of Structure[S]. ENV 1998-1,CEN, Brussels, 1994: 854-876.
[3] Standards New Zealand. General structural design and design loadings for buildings[S]. NZS 4203:1992, Standard New Zealand, Wellington, 1992:352-397.
[4] Uniform Building Code[S]. International Conference of Building official, Whittier, 1997: 1234-1253.
[5] IBC2000. International Building Code[S]. International Code Council. Inc. Mar 2000.
[6]建筑抗震设计规范(GB50011—2001)[S].北京:中国建筑工业出版社,2001.
[7] Designers’Guide to EN 1998-1 and 1998-5. Eurocode 8: Design of Structures for Earthquake Resistance[S]. 2005.
[8]李刚,程耿东.基于性能的结构抗震设计——理论、方法与应用[M].北京:科学出版社,2004.
[9] A.J. Kappos. Evaluation of behaviour factors on the basis of ductility and overstrength studies[J]. Engineering Structures. 1999, 21:823-835.
[10] Bertero VV. State-of-the-art report: based structural design[C]. In: Proceedings of 9th World Conference on Earthquake Engineering, Tokyo-Kyoto, Japan, Aug. 1988;VIII:673-86.
[11] FEMA 450, NEHRP Recommended Provisions for Seismic Regulations for New Buildings and Other Structures, Part 2: Commentar[S]. Buildings Seismic Safety Council of the National Institute of Building Sciences,Washington,D C,2004.
[12] Eurocode 8, Design of structures for earthquake resistance[S]. The European Standard EN 1998-1:2004.
[13] NBCC2005. National Building Code of Canada 2005[S]. Institute for Research in Construction. National Research Council of Canada. Ottawa. Ont. 2005.
[14] CECS 160:2004.建筑工程抗震性态设计通则(试用)[S].北京:中国计划出版社.2004.
[15] G.D.P.K. Seneviratna and H. Krawinkler. Modifications of seismic demands for MDOF systems[C]. Proc. 11th WCEE.IAEE.Acapulco.Mexico.1996: Paper1446.
[16]韦锋.钢筋混凝土框架和框架-剪力墙结构非弹性地震反应性态的识别[博士][D].重庆:重庆大学.2005.
[17]李刚强.抗震设计的R ?μ基本准则及钢筋混凝土典型框架结构超强特征分析[D].重庆:重庆大学,2006.
[18]刘兰花.多自由度体系R ?μ规律初步分析及超静定次数对结构超强的影响[D].重庆:重庆大学,2007.
[19]混凝土结构设计规范(GB50010—2002)[S].北京:中国建筑工业出版社,2002.
[20]高层建筑混凝土结构技术规程(JGJ3—2002)[S].北京:中国建筑工业出版社,2002.
[21] N.M. Newmark and W.J. Hall. Earthquake Spectra and Design[M]. EERI Monograph Series. Earthquake Engineering Research Institute. Oakland. California. USA. 1982.
[22] A.A. Nassar and H. Krawinkler. Seismic demands for SDOF and MDOF systems[R]. Report No. 95, The John A. Blume Earthquake Engineering Center, Stanford University, Stanford, California, 1991:12-45.
[23] E. Miranda and V.V. Bertero. Evaluation of strength reduction factor for earthquake-resistance design[J]. Earthquake Spectra. 1994, l0 (2):357-379.
[24] T. Vidic P. Fajfar and M. Fischinger. Consistent inelastic design spectra: strength and displacement[J].Earthquake Engineering and Structural Dynamics, 1994, 23(3):507-521.
[25] B. Borzi and A.S. Elnashai. Refined force reduction factors for seismic design[J]. Journal of Engineering Structures.2000, 22(5):1244-1260.
[26]卓卫东,范立础.结构抗震设计中的强度折减系数研究[J].地震工程与工程振动. 2001, 21(1):84-88.
[27]翟长海,公茂盛,张茂花,谢礼立和张敏政.工程结构等延性地震抗力谱研究[J].地震工程与工程振动.2004, 24(1):22-29.
[28]翟长海,谢礼立.考虑设计地震分组的强度折减系数的研究[J].地震学报.2006, 28(3):284-294.
[29]吕西林和周定松.考虑场地类别与设计分组的延性需求谱和弹塑性位移反应谱[J].地震工程与工程振动.2004, 24(1):39-48.
[30]刘文渊.强度折减系数及单层钢框架结构影响系数[D].苏州:苏州科技学院,2008.
[31]翟长海.最不利设计地面运动及强度折减系数研究[博士][D].哈尔滨:哈尔滨工业大学.2004.
[32] H. Moghaddam and R.K. Mohammadi. Ductility reduction factor of MDOF shear-building structures[J].Journal of Earthquake Engineering.2001, 5(3):425-440.
[33]翟长海,谢礼立.多自由度体系效应对强度折减系数的影响[J].工程力学.2006, 23(11):33-37.
[34]周靖,蔡健,方小丹.剪切型多自由度结构体系抗震延性折减系数[J].振动工程学报.2007, 20(3):309-315.
[35]卢文汀.框架-筒体连体结构的静力、动力特性和地震反应分析[D].武汉:武汉大学,2005.
[36]杨红.基于细化杆模型的钢筋混凝土抗震框架非线性动力反应规律研究[博士][D].重庆:重庆建筑大学,2000.
[37] Fib (CEB-FIP). Bulletin 25. Displacement-Based Seismic Design of Reinforced Concrete Buildings[R]. Sprint-Digital-Druck. Stuttgart. 2003.
[38] Fib (CEB-FIP). Bulletin 25.白绍良译.钢筋混凝土建筑结构基于位移的抗震设计[R].重庆大学土木工程学院.2004.
[39] T.B. Panagiotakos and M.N. Fardis. Deformations of reinforced concrete members at yielding and ultimate[J]. ACI Structural Journal. 2001, 98(2): 135-148.
[40] T. Paulay and M.J.N. Priestley著.戴瑞同,陈世鸣等译.钢筋混凝土和砌体结构的抗震设计[M].北京:中国建筑工业出版社.1999.
[41]杨溥,李英民,赖明.结构时程分析法输入地震波的选择控制指标[J].土木工程学报,2000,33(6): 33-37.
[42] J.E. Martinez-Rueda. Scaling procedure for natural accelerograms based on a system of spectrum intensity scales[J]. Earthquake Spectra. 1998, 14(1):135-152.
[43] Chopra. Elastic response spectrum: A historical note[J]. Earthquake Engng Struct. Dyn. 2007, 36: 3-12.
[44] Chopra. Dynamics of Structures[M].北京:清华大学出版社,2005.
[45] Priestley. Performance based seismic design[C].Proc.12th WCEE.IAEE.Auckland.New Zealand. 2000:Paper2831.
[46]李国强.建筑结构抗震设计[M].北京:中国建筑工业出版社,2002.
[47]袁波.地震作用下结构目标位移简化计算方法的研究[J].工程力学,2007,24(1): 117-122.
[48]马宏旺.一种简化的R.C框架结构地震位移反应分析方法[J].工程力学,2007,24(12):113-119.
[49]雷磊,韩小雷,郑宜.直接基于位移的抗震设计方法的研究[J].华南地震,2007,27(2): 26-32.
[50]方华丽,李寿明.延性在地震区房屋结构设计中的运用分析[J].中外建筑, 2007,(05): 84-85.
[51]韦锋,杨红,白绍良,王珍.柱增强系数取值对钢筋混凝土抗震框架塑性铰机构的控制效果[J].工程力学,2005,22(2):155-161.
[52]杨红,高文生,王志军.空间框架简化为平面模型的抗震分析[J].重庆大学学报,2008,31(11): 1267-1272.
[53]韦锋,李刚强,白绍良.各国设计规范对基准设防地震和结构超强的考虑[J].重庆大学学报,2007,30(6): 102-120.
[2] Eurocode 8, Design Provisions for Earthquake Resistance of Structure[S]. ENV 1998-1,CEN, Brussels, 1994: 854-876.
[3] Standards New Zealand. General structural design and design loadings for buildings[S]. NZS 4203:1992, Standard New Zealand, Wellington, 1992:352-397.
[4] Uniform Building Code[S]. International Conference of Building official, Whittier, 1997: 1234-1253.
[5] IBC2000. International Building Code[S]. International Code Council. Inc. Mar 2000.
[6]建筑抗震设计规范(GB50011—2001)[S].北京:中国建筑工业出版社,2001.
[7] Designers’Guide to EN 1998-1 and 1998-5. Eurocode 8: Design of Structures for Earthquake Resistance[S]. 2005.
[8]李刚,程耿东.基于性能的结构抗震设计——理论、方法与应用[M].北京:科学出版社,2004.
[9] A.J. Kappos. Evaluation of behaviour factors on the basis of ductility and overstrength studies[J]. Engineering Structures. 1999, 21:823-835.
[10] Bertero VV. State-of-the-art report: based structural design[C]. In: Proceedings of 9th World Conference on Earthquake Engineering, Tokyo-Kyoto, Japan, Aug. 1988;VIII:673-86.
[11] FEMA 450, NEHRP Recommended Provisions for Seismic Regulations for New Buildings and Other Structures, Part 2: Commentar[S]. Buildings Seismic Safety Council of the National Institute of Building Sciences,Washington,D C,2004.
[12] Eurocode 8, Design of structures for earthquake resistance[S]. The European Standard EN 1998-1:2004.
[13] NBCC2005. National Building Code of Canada 2005[S]. Institute for Research in Construction. National Research Council of Canada. Ottawa. Ont. 2005.
[14] CECS 160:2004.建筑工程抗震性态设计通则(试用)[S].北京:中国计划出版社.2004.
[15] G.D.P.K. Seneviratna and H. Krawinkler. Modifications of seismic demands for MDOF systems[C]. Proc. 11th WCEE.IAEE.Acapulco.Mexico.1996: Paper1446.
[16]韦锋.钢筋混凝土框架和框架-剪力墙结构非弹性地震反应性态的识别[博士][D].重庆:重庆大学.2005.
[17]李刚强.抗震设计的R ?μ基本准则及钢筋混凝土典型框架结构超强特征分析[D].重庆:重庆大学,2006.
[18]刘兰花.多自由度体系R ?μ规律初步分析及超静定次数对结构超强的影响[D].重庆:重庆大学,2007.
[19]混凝土结构设计规范(GB50010—2002)[S].北京:中国建筑工业出版社,2002.
[20]高层建筑混凝土结构技术规程(JGJ3—2002)[S].北京:中国建筑工业出版社,2002.
[21] N.M. Newmark and W.J. Hall. Earthquake Spectra and Design[M]. EERI Monograph Series. Earthquake Engineering Research Institute. Oakland. California. USA. 1982.
[22] A.A. Nassar and H. Krawinkler. Seismic demands for SDOF and MDOF systems[R]. Report No. 95, The John A. Blume Earthquake Engineering Center, Stanford University, Stanford, California, 1991:12-45.
[23] E. Miranda and V.V. Bertero. Evaluation of strength reduction factor for earthquake-resistance design[J]. Earthquake Spectra. 1994, l0 (2):357-379.
[24] T. Vidic P. Fajfar and M. Fischinger. Consistent inelastic design spectra: strength and displacement[J].Earthquake Engineering and Structural Dynamics, 1994, 23(3):507-521.
[25] B. Borzi and A.S. Elnashai. Refined force reduction factors for seismic design[J]. Journal of Engineering Structures.2000, 22(5):1244-1260.
[26]卓卫东,范立础.结构抗震设计中的强度折减系数研究[J].地震工程与工程振动. 2001, 21(1):84-88.
[27]翟长海,公茂盛,张茂花,谢礼立和张敏政.工程结构等延性地震抗力谱研究[J].地震工程与工程振动.2004, 24(1):22-29.
[28]翟长海,谢礼立.考虑设计地震分组的强度折减系数的研究[J].地震学报.2006, 28(3):284-294.
[29]吕西林和周定松.考虑场地类别与设计分组的延性需求谱和弹塑性位移反应谱[J].地震工程与工程振动.2004, 24(1):39-48.
[30]刘文渊.强度折减系数及单层钢框架结构影响系数[D].苏州:苏州科技学院,2008.
[31]翟长海.最不利设计地面运动及强度折减系数研究[博士][D].哈尔滨:哈尔滨工业大学.2004.
[32] H. Moghaddam and R.K. Mohammadi. Ductility reduction factor of MDOF shear-building structures[J].Journal of Earthquake Engineering.2001, 5(3):425-440.
[33]翟长海,谢礼立.多自由度体系效应对强度折减系数的影响[J].工程力学.2006, 23(11):33-37.
[34]周靖,蔡健,方小丹.剪切型多自由度结构体系抗震延性折减系数[J].振动工程学报.2007, 20(3):309-315.
[35]卢文汀.框架-筒体连体结构的静力、动力特性和地震反应分析[D].武汉:武汉大学,2005.
[36]杨红.基于细化杆模型的钢筋混凝土抗震框架非线性动力反应规律研究[博士][D].重庆:重庆建筑大学,2000.
[37] Fib (CEB-FIP). Bulletin 25. Displacement-Based Seismic Design of Reinforced Concrete Buildings[R]. Sprint-Digital-Druck. Stuttgart. 2003.
[38] Fib (CEB-FIP). Bulletin 25.白绍良译.钢筋混凝土建筑结构基于位移的抗震设计[R].重庆大学土木工程学院.2004.
[39] T.B. Panagiotakos and M.N. Fardis. Deformations of reinforced concrete members at yielding and ultimate[J]. ACI Structural Journal. 2001, 98(2): 135-148.
[40] T. Paulay and M.J.N. Priestley著.戴瑞同,陈世鸣等译.钢筋混凝土和砌体结构的抗震设计[M].北京:中国建筑工业出版社.1999.
[41]杨溥,李英民,赖明.结构时程分析法输入地震波的选择控制指标[J].土木工程学报,2000,33(6): 33-37.
[42] J.E. Martinez-Rueda. Scaling procedure for natural accelerograms based on a system of spectrum intensity scales[J]. Earthquake Spectra. 1998, 14(1):135-152.
[43] Chopra. Elastic response spectrum: A historical note[J]. Earthquake Engng Struct. Dyn. 2007, 36: 3-12.
[44] Chopra. Dynamics of Structures[M].北京:清华大学出版社,2005.
[45] Priestley. Performance based seismic design[C].Proc.12th WCEE.IAEE.Auckland.New Zealand. 2000:Paper2831.
[46]李国强.建筑结构抗震设计[M].北京:中国建筑工业出版社,2002.
[47]袁波.地震作用下结构目标位移简化计算方法的研究[J].工程力学,2007,24(1): 117-122.
[48]马宏旺.一种简化的R.C框架结构地震位移反应分析方法[J].工程力学,2007,24(12):113-119.
[49]雷磊,韩小雷,郑宜.直接基于位移的抗震设计方法的研究[J].华南地震,2007,27(2): 26-32.
[50]方华丽,李寿明.延性在地震区房屋结构设计中的运用分析[J].中外建筑, 2007,(05): 84-85.
[51]韦锋,杨红,白绍良,王珍.柱增强系数取值对钢筋混凝土抗震框架塑性铰机构的控制效果[J].工程力学,2005,22(2):155-161.
[52]杨红,高文生,王志军.空间框架简化为平面模型的抗震分析[J].重庆大学学报,2008,31(11): 1267-1272.
[53]韦锋,李刚强,白绍良.各国设计规范对基准设防地震和结构超强的考虑[J].重庆大学学报,2007,30(6): 102-120.