基于凸集模型的不确定性钢筋混凝土桥墩抗震性能设计方法
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摘要
当对不确定变量的信息掌握较少时,由概率模型得到的结果是值得怀疑的。本文采用对信息要求少得多的凸集模型描述设计目标位移、水平地震基本加速度和反应谱特征周期的不确定性,结合直接基于位移的设计方法,针对钢筋混凝土桥墩,提出一种界限性能设计方法。该设计方法考虑不确定设计参数的界限范围,得到抗震设计结果的区间,从而可以评定现行抗震规范设计结果的可靠性或抗震设计结果对不确定性设防参数的敏感性。算例结果表明,由我国规范方法得到的设计结果均处于本文基于凸变量分析得到的结果的下半个区间;设计基底剪力对目标位移的变化最敏感,其次为反应谱特征周期,最后为水平地震基本加速度。
Results drawn from a probabilistic model are suspectable when inadequate information on uncertain variations are available.In this paper,the convex set model is employed to describe the uncertainties of the design target displacement,horizontal basic acceleration and characteristic period of response spectra,where much less information about these variables is needed.In combination with the direct displacement-based design method,a bound performance-based design method for RC bridge piers is developed.The sections of the anti-seismic design results are obtained by considering the bound of uncertain design parameters so that the reliability of the design results worked out under the current anti-seismic specifications and the sensitivity of the design results to the uncertainty of the anti-seismic parameters can be evaluated.The results of a computational example show that the design by the prevailing anti-seismic specifications falls into the lower bound of the convex set analysis results,and the foundation-base shear force is most sensitive to target displacement,less to the characteristic period of response spectra and the least to the horizontal basic acceleration.
Results drawn from a probabilistic model are suspectable when inadequate information on uncertain variations are available.In this paper,the convex set model is employed to describe the uncertainties of the design target displacement,horizontal basic acceleration and characteristic period of response spectra,where much less information about these variables is needed.In combination with the direct displacement-based design method,a bound performance-based design method for RC bridge piers is developed.The sections of the anti-seismic design results are obtained by considering the bound of uncertain design parameters so that the reliability of the design results worked out under the current anti-seismic specifications and the sensitivity of the design results to the uncertainty of the anti-seismic parameters can be evaluated.The results of a computational example show that the design by the prevailing anti-seismic specifications falls into the lower bound of the convex set analysis results,and the foundation-base shear force is most sensitive to target displacement,less to the characteristic period of response spectra and the least to the horizontal basic acceleration.
引文
[1]Kowalsky MJ,Priestley MJ N,Macrae G A.Displace-ment-based Design of RC Bridge Column in Seismic Re-gions[J].Earthquake Engineering and Structural Dynam-ics,1995,24(12):1623-1643.
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[14]Cornell C A,Krawinkler H.Progress and Challenges inSeismic Performance Assessment[Z].PEER CenterNews,3(2).Stanford:Stanford Univercity,2000.
[15]Chandler A M,Lam N T K.Performance-based Designin Earthquake Engineering:A Multi-disciplinary Review[J].Engineering Structures,2001,23:1525-1543.
[16]Cornell C A.Hazard,Ground and Probabilistic Assess-ments for PBSD[C]//Performance-based Seismic DesignConcepts and I mplementation Proceedings of An Interna-tional Workshop.Bled.Berkeley:PEER,2004:39-52.
[17]Ellishakoff I.Essay on Uncertainties Inelastic and Viscoe-lastic Structures:from A M Freudenthal's Criticisms toModern Convex Modeling[J].Computers&Structures,1995,56(6):87-89.
[18]Ben-hai m Y,Elishakoff I.Convex Models of Uncertaintyin Applied Mechanics[M].Newyork:Elesevier,1990:11-20.
[19]中华人民共和国铁道部.GB 50111-2006铁路工程抗震设计规范[S].北京:中国计划出版社,2006.
[20]胡聿贤.地震工程学[M].北京:地震出版社,1988:186-188.
[21]王光远,董明耀.结构优化设计[M].哈尔滨:哈尔滨工业大学出版社,1987:185-190.
[22]陈达生,卢荣俭,谢礼立.地震工程研究报告集第三集.抗震建筑的设计反应谱[M].北京:科学出版社,1997:73-94.
[23]吴健,高孟潭.场地相关设计反应谱特征周期的统计分析[J].中国地震,2004,20(3):263-268.WUJian,GAO Meng-tan.Statistical Analysis on CornerPeriod of Site-Related Design Spectrum[J].EarthquakeResearchin China.2004,20(3):263-268.
[2]Calvi G M,Kingsley G R.Displacement-based SeismicDesign of Multi-degree-of-freedom Bridge Structures[J].Earthquake Engineering and Structural Dynamics,1995,24(9):1247-1266.
[3]Kowalsky M J.A Displacement-based Approach for theSeismic Design of Continuous Concrete Bridges[J].Earthquake Engineering and Structural Dynamics,2002,31(3):719-747.
[4]Chopra A K,Goel R K.Direct Displacement-based De-sign:Use of Inelastic vs.Elastic Design Spectra[J].Earthquake Spectra,2001,17(1):47-64.
[5]Fajfar P.Capacity Spectrum Method Based onInelastic De-mand Spectra[J].Earthquake Engineering and StructuralDynamics.1999,28:979-993.
[6]Xue Q.A Direct displacement-based seismic design proce-dure of inelastic structures[J].Engineering Structures,2001,23:1453-1460.
[7]Xue Q,Chen C C.Performance-based Seismic Design ofStructures:A Airect Displacement-based Approach[J].Engineering Structures,2003,25:1803-1813.
[8]Xue Q,Wu C W.Preli minary Detailing for Displacement-based Seismic Design of Bbuildings[J].Engineering Struc-tures,2006,28:431-440.
[9]Collins K R,Wen Y K,Foutch D A.Dual-level SeismicDesign:A Reliability-based Methodology[J].EarthquakeEngineering and Structural Dynamics,1996,25:1433-1467.
[10]Foschi R O,Li H,Zhang J.Reliability and Performance-based Design:A Computational Approach and Applica-tions[J].Structural Safety,2002,24:203~218.
[11]Wen Y K.Reliability and Performance-based Design[J].Structural Safety,2001,23:407-428.
[12]Kunnath S K,Larson L,Miranda E.Modeling Consider-ations in Probabilistic Performance-based Seismic Evalua-tion:Case Study of the I-880 Viaduct[J].EarthquakeEngineering and Structural Dynamics,2006,35:57-75.
[13]BeckJ L,Irfanoglu A,Paradi mitriou C,Au S K.A Per-formance-based Opti mal Design Methodology Incorpora-ting Multiple Criteria[C]//Rocketbyte.12thWorld Con-ference on Earthquake Engineering,Paper No.344.Up-perhutt:Rocketbyte,2000:1-8.
[14]Cornell C A,Krawinkler H.Progress and Challenges inSeismic Performance Assessment[Z].PEER CenterNews,3(2).Stanford:Stanford Univercity,2000.
[15]Chandler A M,Lam N T K.Performance-based Designin Earthquake Engineering:A Multi-disciplinary Review[J].Engineering Structures,2001,23:1525-1543.
[16]Cornell C A.Hazard,Ground and Probabilistic Assess-ments for PBSD[C]//Performance-based Seismic DesignConcepts and I mplementation Proceedings of An Interna-tional Workshop.Bled.Berkeley:PEER,2004:39-52.
[17]Ellishakoff I.Essay on Uncertainties Inelastic and Viscoe-lastic Structures:from A M Freudenthal's Criticisms toModern Convex Modeling[J].Computers&Structures,1995,56(6):87-89.
[18]Ben-hai m Y,Elishakoff I.Convex Models of Uncertaintyin Applied Mechanics[M].Newyork:Elesevier,1990:11-20.
[19]中华人民共和国铁道部.GB 50111-2006铁路工程抗震设计规范[S].北京:中国计划出版社,2006.
[20]胡聿贤.地震工程学[M].北京:地震出版社,1988:186-188.
[21]王光远,董明耀.结构优化设计[M].哈尔滨:哈尔滨工业大学出版社,1987:185-190.
[22]陈达生,卢荣俭,谢礼立.地震工程研究报告集第三集.抗震建筑的设计反应谱[M].北京:科学出版社,1997:73-94.
[23]吴健,高孟潭.场地相关设计反应谱特征周期的统计分析[J].中国地震,2004,20(3):263-268.WUJian,GAO Meng-tan.Statistical Analysis on CornerPeriod of Site-Related Design Spectrum[J].EarthquakeResearchin China.2004,20(3):263-268.
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