P-△效应对抗震框架非弹性动力反应影响的初步分析
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摘要
本文首先对结构二阶效应的研究进展进行了评述,在此基础上,指出静力二阶分析与动力二阶分析本质的区别,静力二阶分析无法体现结构的动力特征和动力荷载的性质;然后对各国研究者就P-△效应对结构动力反应的影响已完成的分析研究工作进行总结和评述;对美国、加拿大、欧盟、中国等的抗震规范考虑P-△效应的规定进行说明;最后通过非弹性动力分析手段考察P-△效应对三组稳定系数为0.042,0.055,0.07的抗震框架非弹性动力反应的影响。
基于上述研究工作,得到了一下几项初步认识:
①经动力分析表明:与静力P-△效应总是增大结构的反应不同,动力反应中的P-△效应在不同的结构动力特征下受动力荷载决定,有可能增大,也有可能减小结构的反应。
②多波输入下的非弹性动力分析结果表明,P-△效应对结构非弹性反应的影响在不同的地面运动输入下的离散性较大,总体来看,P-△效应对稳定系数分别为0.042,0.055,0.07的三组一级抗震等级框架的非弹性反应影响不大;分析也表明地震动特性对P-△效应影响显著。
③截面设计考虑了P-△效应的结构,其相对屈服水准提高,在同样强度水准的地面运动下,所受的地震作用增大,相应结构的层剪力增大;但各层层剪力增大系数与截面设计考虑P-△效应的内力增大系数的分布规律不同。
④目前世界上一些国家或国家集团如欧盟、加拿大、墨西哥等的设计规范或规程在抗震结构设计时考虑P-△效应的具体规定虽有不同,但思路是基本一致的,即实现结构在给定强震反应位移下的等承载力。这一思路是以单自由度体系理想双折线滞回特征为依据提出的。考虑到近期已经认识到的实际工程中各类超静定结构的整体超强特征,上述思路已显得过于保守。
The present paper reviews the research of the second order effect on the structure. Based on this, this paper points out the essential difference between the static p-delta effect and the dynamic p-delta effect and that the static p-delta effect can't manifest the structure's dynamic feature and the nature of the dynamic load; Then it summarizes and comments on various countries' research on the influence of effect on the dynamic p-delta effect, and elaborates on the p-delta effect used in earthquake resistance standard adopted by various countries such as US, Canada, European Union, China and so on; Finally, it reviews the influence of the inelastic dynamic response on earthquake resistance frame through the inelastic mechanical analysis method and stability coefficients of the three groups are 0.042, 0.055, 0.07, respectively.
Based on the research work stated above,there are found several preliminary understanding:
①The dynamic analysis shows that the P—Δeffects of the dynamic response under the different power characteristics depend on dynamic loads,which may increase or reduce the structural response. It is different from the P—Δeffects of the static response,which is always increase the structural response.
②The inelastic dynamic analysis results show that the influence about P—Δeffects on inelastic response of the structure exhibits higher dispersion with the different ground motion input, basically the influence about the P—Δeffects on inelastic response of three frames with first earthquake-resistance level is little, the stability factor are respectively 0.042, 0.055, 0.07; it is also found that the influence about the P—Δeffects on earthquake motion is significant.
③The structures considered the P—Δeffects in section design enhance their relative yield level, augment the earthquake action and the corresponding floor shear when they subject to the same intensity level of ground motion. However, it is different between the increment coefficient of every floor shear and the distribution of internal force increment coefficient considered the P—Δeffects in section design.
④At present, some nation or group of nations for instance, European Union, Canada, Mexico and so on, while there are some difference in aseismic structure when considering the effect on specific stipulations in their design codes or regulations, But the mentality is basic consistent, namely realizes the equal bearing capacity of structure under the given strong earthquake response displacement. This mentality is hysteresis the characteristic take the single degree-of-freedom system ideal double broken line to propose as the basis. In view of the recent already aware of the practical engineering exists overall overstrength features of all kinds of statically indeterminate structure, the idea above has become too conservative.
基于上述研究工作,得到了一下几项初步认识:
①经动力分析表明:与静力P-△效应总是增大结构的反应不同,动力反应中的P-△效应在不同的结构动力特征下受动力荷载决定,有可能增大,也有可能减小结构的反应。
②多波输入下的非弹性动力分析结果表明,P-△效应对结构非弹性反应的影响在不同的地面运动输入下的离散性较大,总体来看,P-△效应对稳定系数分别为0.042,0.055,0.07的三组一级抗震等级框架的非弹性反应影响不大;分析也表明地震动特性对P-△效应影响显著。
③截面设计考虑了P-△效应的结构,其相对屈服水准提高,在同样强度水准的地面运动下,所受的地震作用增大,相应结构的层剪力增大;但各层层剪力增大系数与截面设计考虑P-△效应的内力增大系数的分布规律不同。
④目前世界上一些国家或国家集团如欧盟、加拿大、墨西哥等的设计规范或规程在抗震结构设计时考虑P-△效应的具体规定虽有不同,但思路是基本一致的,即实现结构在给定强震反应位移下的等承载力。这一思路是以单自由度体系理想双折线滞回特征为依据提出的。考虑到近期已经认识到的实际工程中各类超静定结构的整体超强特征,上述思路已显得过于保守。
The present paper reviews the research of the second order effect on the structure. Based on this, this paper points out the essential difference between the static p-delta effect and the dynamic p-delta effect and that the static p-delta effect can't manifest the structure's dynamic feature and the nature of the dynamic load; Then it summarizes and comments on various countries' research on the influence of effect on the dynamic p-delta effect, and elaborates on the p-delta effect used in earthquake resistance standard adopted by various countries such as US, Canada, European Union, China and so on; Finally, it reviews the influence of the inelastic dynamic response on earthquake resistance frame through the inelastic mechanical analysis method and stability coefficients of the three groups are 0.042, 0.055, 0.07, respectively.
Based on the research work stated above,there are found several preliminary understanding:
①The dynamic analysis shows that the P—Δeffects of the dynamic response under the different power characteristics depend on dynamic loads,which may increase or reduce the structural response. It is different from the P—Δeffects of the static response,which is always increase the structural response.
②The inelastic dynamic analysis results show that the influence about P—Δeffects on inelastic response of the structure exhibits higher dispersion with the different ground motion input, basically the influence about the P—Δeffects on inelastic response of three frames with first earthquake-resistance level is little, the stability factor are respectively 0.042, 0.055, 0.07; it is also found that the influence about the P—Δeffects on earthquake motion is significant.
③The structures considered the P—Δeffects in section design enhance their relative yield level, augment the earthquake action and the corresponding floor shear when they subject to the same intensity level of ground motion. However, it is different between the increment coefficient of every floor shear and the distribution of internal force increment coefficient considered the P—Δeffects in section design.
④At present, some nation or group of nations for instance, European Union, Canada, Mexico and so on, while there are some difference in aseismic structure when considering the effect on specific stipulations in their design codes or regulations, But the mentality is basic consistent, namely realizes the equal bearing capacity of structure under the given strong earthquake response displacement. This mentality is hysteresis the characteristic take the single degree-of-freedom system ideal double broken line to propose as the basis. In view of the recent already aware of the practical engineering exists overall overstrength features of all kinds of statically indeterminate structure, the idea above has become too conservative.
引文
[1]中国建筑科学研究院主编.混凝土结构设计[S].北京:中国建筑工业出版社,2003,pp.90-120
[2]刘毅.钢筋混凝土框架柱二阶效应与稳定中若干问题的讨论[D].重庆大学,1999
[3]O.G Julian,L.S.Lawrence.Notes on J and L Nomographs for Determination of Effective Lengths.未公开发表的研究报告,1959
[4]Lian Duan,Wai-Fah Chen.Effective Length Factor for Columns in Braced Frames.Journal of Structural Engineering,ASCE,Vol.114,No.10,1988(10)
[5]Yu-Xia Hu,Ren-Gen Zhou,Won-Sun King.On Effective Length Factor of Framed Columns in the ACI Building Code.ACI Structural Journal,Vol.90,No.2,1993(3),pp.135-143
[6]Lian Duan,Wai-Fah Chen.Effective Length Factor for Columns in Unbraced Frames.Journal of Structural Engineering,ASCE,Vol.115,No.1,1989(1)
[7]魏巍.考虑非弹性及二阶效应特征的钢筋混凝土框架柱的强度问题与稳定问题[D].重庆大学,2004(4)
[8]Wai-Fah Chen.Cm Factor in Load and Resistance Factor Design.Journal of Structural Engineering,ASCE,Vol.113,No.8,1987(8)
[9]J.A.Yura.The Effective Length of Columns in Unbraced Frames.Engineering Journal of Structural Engineering,AISC,1971
[10]Emilio Rosenblueth.Slenderness Effects in Buildings[M].Journal of the Structural Division,ASCE,Vol.91,No.1,1965(1)
[11]L.K.Stevens.Elastic Stability of Practical Multistory Frame.Proceedings of the Institution of Civil Engineers,1967
[12]高晓莉.钢筋混凝土框架柱二阶效应实用设计方法研究[D].重庆大学,1996
[13]ACI Committee 318.Building Code Requirements for Structural Concrete(ACI 318-2008)and Commentary(ACI 318 R-2008).American Concrete Institute,Detroit,2008
[14]CSA 2004a.Design of Concrete Structure[S].Standard CSA-A23.3-04.Canadian Standard Association.Rexdale.Ont.2005.
[15]EC2(1994):Eurocode 8-Design Provisions for Earthquake Resistance of Structures[S].ENV 1998,CEN,Brussels,1994.
[16]刘毅 钢筋混凝土结构二阶效应及设计方法的研究[D].重庆大学,2007.7
[17]Mac Rae GA P-A effects on single-degree-of-freedom structures in earthquakes.Earthquake Spectra 1994;10:539-568
[18]Jennings,P,C and Huid,R(1968)."Collapse of yielding structures under earthquake."J.Engrg.Mesh.,ASCE,94(5)1045-1065
[19]Sun CK,Berg GV,Hanson RD.Gravity effect on single degree inelastic system.J.Engrg.Mesh.,ASCE,1973;99:183-200
[20]Bernal D.Amplification factors for inelastic dynamic P-Δ effects in earthquake analysis.Earthquake Engineering and Structural Dynamics 1987;15:635-651
[21]Williamson EB.Evaluation of damage and P-Δ effects for systems under earthquake excitation.Journal of sturctral Engineering(ASCE) 2003;129:1036-1046
[22]Mohamed Ahmed Mahgoub.A study of some issues related to seismic design provisions of national building code of Canada[D].Carleton University 2004.
[23]H.Takizawa and P.C Jennings,'Ultimate capacity of low-rise R/C buildings subjected to intense earthquake motions,Proc.6th world conf.earthquake eng.New Delhi,India 3,79-84(1977).
[24]ATC 3-06,1987."ATC3-06 Tentative Provisions for the Development of Seismic Regulations for Buildings" NBS SP-510,June 1978."NEHRP Recommended Provisions for New Buildings."FEMA95,February 1986.
[25]Ingham,J.M.,Priestley,M.J.N.,Seible,F.,1994.Seismic performance of bridge knee joints.Report No.SSRP 94/12,Structural System Research[D].University of California,San Diego,La Jolla,California.
[26]Paulay,T.2001.A redefinition of stiffness of reinforced concrete elements and its implications in seismic design[D].Structural Enggineering international,11(1):36-41.
[27]NRCC.2005.National building code of Canada,1995.Canadian Commission on Building and Fire Codes,institute for Research in Construction,National Research Council Canada(NRCC),Ottawa,Ont.
[28]李刚强.抗震设计的R-μ基本准则及钢筋混凝土典型结构超强特征分析[硕士][D].重庆:重庆大学,2006.
[29]GB 50011-2001.建筑抗震设计规范[S].北京:中国建筑工业出版社.2001.
[30]Akshay Gupta,Dynamic P-delta Efects for Flexible Inelastic Steel Structures[J],Journal of Structural Engineering 2000
[31]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.
[32]Fib(CEB-FIP).Sesmic Design of Reinforced Concrete Structures for Controlled Inelastic Response(Design concepts)[R].2003.
[33]Fib(CEB-FIP).白绍良译.控制非弹性反应的钢筋混凝土结构抗震设计(设计原理)[R].重庆大学土木工程学院,2003.
[34]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.
[35]李英民.工程地震动的模型化研究[博士][D].重庆:重庆建筑大学,2000.
[36]杨溥,李英民,赖明.结构时程分析法输入下地震波的选择控制指标[J].土木工程学报.2000.12.33(6).33-37.
[37]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[硕士][D].重庆:重庆大学.2007.
[38]Wilson E.L.,and Habibullah A.Static and dynamic analysis of multi-story buildings,including P-Delta effect[J].Earthquake Spectra,Vol.3,No.2.
[39]Neuss.C.F,Maison N.M.and Bouwkamp J.G.."A Study of Computer Modeling Formulation and Special Analytical Procedures for Earthquake Response of Multistorey Buildings",a report to the national science foundation[J].Washington,USA
[2]刘毅.钢筋混凝土框架柱二阶效应与稳定中若干问题的讨论[D].重庆大学,1999
[3]O.G Julian,L.S.Lawrence.Notes on J and L Nomographs for Determination of Effective Lengths.未公开发表的研究报告,1959
[4]Lian Duan,Wai-Fah Chen.Effective Length Factor for Columns in Braced Frames.Journal of Structural Engineering,ASCE,Vol.114,No.10,1988(10)
[5]Yu-Xia Hu,Ren-Gen Zhou,Won-Sun King.On Effective Length Factor of Framed Columns in the ACI Building Code.ACI Structural Journal,Vol.90,No.2,1993(3),pp.135-143
[6]Lian Duan,Wai-Fah Chen.Effective Length Factor for Columns in Unbraced Frames.Journal of Structural Engineering,ASCE,Vol.115,No.1,1989(1)
[7]魏巍.考虑非弹性及二阶效应特征的钢筋混凝土框架柱的强度问题与稳定问题[D].重庆大学,2004(4)
[8]Wai-Fah Chen.Cm Factor in Load and Resistance Factor Design.Journal of Structural Engineering,ASCE,Vol.113,No.8,1987(8)
[9]J.A.Yura.The Effective Length of Columns in Unbraced Frames.Engineering Journal of Structural Engineering,AISC,1971
[10]Emilio Rosenblueth.Slenderness Effects in Buildings[M].Journal of the Structural Division,ASCE,Vol.91,No.1,1965(1)
[11]L.K.Stevens.Elastic Stability of Practical Multistory Frame.Proceedings of the Institution of Civil Engineers,1967
[12]高晓莉.钢筋混凝土框架柱二阶效应实用设计方法研究[D].重庆大学,1996
[13]ACI Committee 318.Building Code Requirements for Structural Concrete(ACI 318-2008)and Commentary(ACI 318 R-2008).American Concrete Institute,Detroit,2008
[14]CSA 2004a.Design of Concrete Structure[S].Standard CSA-A23.3-04.Canadian Standard Association.Rexdale.Ont.2005.
[15]EC2(1994):Eurocode 8-Design Provisions for Earthquake Resistance of Structures[S].ENV 1998,CEN,Brussels,1994.
[16]刘毅 钢筋混凝土结构二阶效应及设计方法的研究[D].重庆大学,2007.7
[17]Mac Rae GA P-A effects on single-degree-of-freedom structures in earthquakes.Earthquake Spectra 1994;10:539-568
[18]Jennings,P,C and Huid,R(1968)."Collapse of yielding structures under earthquake."J.Engrg.Mesh.,ASCE,94(5)1045-1065
[19]Sun CK,Berg GV,Hanson RD.Gravity effect on single degree inelastic system.J.Engrg.Mesh.,ASCE,1973;99:183-200
[20]Bernal D.Amplification factors for inelastic dynamic P-Δ effects in earthquake analysis.Earthquake Engineering and Structural Dynamics 1987;15:635-651
[21]Williamson EB.Evaluation of damage and P-Δ effects for systems under earthquake excitation.Journal of sturctral Engineering(ASCE) 2003;129:1036-1046
[22]Mohamed Ahmed Mahgoub.A study of some issues related to seismic design provisions of national building code of Canada[D].Carleton University 2004.
[23]H.Takizawa and P.C Jennings,'Ultimate capacity of low-rise R/C buildings subjected to intense earthquake motions,Proc.6th world conf.earthquake eng.New Delhi,India 3,79-84(1977).
[24]ATC 3-06,1987."ATC3-06 Tentative Provisions for the Development of Seismic Regulations for Buildings" NBS SP-510,June 1978."NEHRP Recommended Provisions for New Buildings."FEMA95,February 1986.
[25]Ingham,J.M.,Priestley,M.J.N.,Seible,F.,1994.Seismic performance of bridge knee joints.Report No.SSRP 94/12,Structural System Research[D].University of California,San Diego,La Jolla,California.
[26]Paulay,T.2001.A redefinition of stiffness of reinforced concrete elements and its implications in seismic design[D].Structural Enggineering international,11(1):36-41.
[27]NRCC.2005.National building code of Canada,1995.Canadian Commission on Building and Fire Codes,institute for Research in Construction,National Research Council Canada(NRCC),Ottawa,Ont.
[28]李刚强.抗震设计的R-μ基本准则及钢筋混凝土典型结构超强特征分析[硕士][D].重庆:重庆大学,2006.
[29]GB 50011-2001.建筑抗震设计规范[S].北京:中国建筑工业出版社.2001.
[30]Akshay Gupta,Dynamic P-delta Efects for Flexible Inelastic Steel Structures[J],Journal of Structural Engineering 2000
[31]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.
[32]Fib(CEB-FIP).Sesmic Design of Reinforced Concrete Structures for Controlled Inelastic Response(Design concepts)[R].2003.
[33]Fib(CEB-FIP).白绍良译.控制非弹性反应的钢筋混凝土结构抗震设计(设计原理)[R].重庆大学土木工程学院,2003.
[34]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.
[35]李英民.工程地震动的模型化研究[博士][D].重庆:重庆建筑大学,2000.
[36]杨溥,李英民,赖明.结构时程分析法输入下地震波的选择控制指标[J].土木工程学报.2000.12.33(6).33-37.
[37]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[硕士][D].重庆:重庆大学.2007.
[38]Wilson E.L.,and Habibullah A.Static and dynamic analysis of multi-story buildings,including P-Delta effect[J].Earthquake Spectra,Vol.3,No.2.
[39]Neuss.C.F,Maison N.M.and Bouwkamp J.G.."A Study of Computer Modeling Formulation and Special Analytical Procedures for Earthquake Response of Multistorey Buildings",a report to the national science foundation[J].Washington,USA