基于性能的结构多维抗震设计方法研究
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摘要
理论研究与震害经验表明，扭转反应会加速偏心结构在地震作用下的破坏，在某些情况下甚至成为导致建筑物破坏的主要因素，平扭耦联是空间问题，不应简化为平面问题处理。目前，结构的抗震设计思想也由传统的基于力的强度设计方法发展到基于性能的延性抗震设计方法，但研究成果大都以单向地震输入的平面分析为前提，所以研究多维偏心结构在多维地震作用下的基于性能的抗震设计理论和方法具有重要现实意义。本文以基于性能的结构多维抗震设计思路为基础，着重完成以下几个方面的研究工作：
(1)提出了直接基于损伤性能目标的抗震设计方法。由于以往对累积耗能与最大位移关系的研究针对于单自由度系统，而不一定适用于层间反应，于是基于累积耗能参数推导了地震下层间最大位移与层间累积耗能的关系方程，并以Park双参数损伤准则为基础建立了结构层间损伤计算公式，将结构最薄弱楼层的预期损伤性能目标作为设计起点进行抗震设计，反推结构的刚度和强度。为满足小震下的使用要求，将小震不坏的承载力控制引入设计程序，并与中震、大震下的损伤控制有机结合起来，从而实现了多性能水准的设计思想。最后通过算例，证明了该方法具有一定的准确性。
(2)由于结构的总滞回耗能是反映结构整体累积损伤的重要参量，为此通过能量方程推导了结构与其等效单自由度系统的滞回耗能和变形能关系公式。建议了通过结构等效单自由度系统来估计地震下结构累积滞回耗能的方法。通过对结构剪切刚度分布和屈服剪力系数分布的均匀和不均匀的多个算例进行分析和比较，证明了该方法在一定范围内能够较为准确地估计地震下结构的滞回耗能。
(3)针对传统抗震设计中完全依赖于概念设计来设计构件截面尺寸的不合理性，提出了刚度设计思想。将传统的“两阶段抗震设计”发展为“三阶段抗震设计”，即刚度设计阶段、强度设计阶段、变形验算及调整加固阶段，其中后两阶段与传统方法相似。对经典的R-μ设计谱进行分析，给出了长周期弹塑性位移谱的简化公式，并在此基础上提出了基于位移的刚度设计方法。定义了刚度调整系数，通过刚度调整系数可以一次性地调整好结构的构件尺寸，使结构能够满足预期的目标要求，从而避免了反复迭代的设计过程。针对三阶段设计中的刚度设计，首先给出了对称结构的刚度设计方法，并通过算例进行验证；而对于平面不对称结构的刚度设计，提出了基于pushover方法的平面刚度分布调整程序，通过该程序来调整不对称结构的刚度分布，尽可能的使刚心与质心重合，然后按对称结构进行刚度设计。而对于很难实现质心与刚心近似重合的结构，提出了偏心结构直接基于位移的刚度设计方法。最后，在以上研究成果的基础上给出了多维结构的三阶段抗震设计流程。
(4)建立了双向地震作用下单质点双自由度系统的等延性强度折减系数反应谱。通过硬土、中硬(软)土、软土场地的178条地震记录作为地震输入，采用了不同以往的建立强度折减系数设计谱的方法，建立了统计平均的等延性强度折减系数设计谱。分析了场地类别、延性系数、两水平主轴方向周期比对强度折减系数谱的影响。并根据统计结果，给出了便于工程应用的等延性强度折减系数简化设计谱公式。通过比较分析可知，该简化公式比较准确，且能够较合理的反应各参量对强度折减系数设计谱的影响规律。
(5)提出了考虑双向地震作用的多维结构振型pushover分析方法。采用弹性振型分解的思路，将非线性多维结构反应近似为结构多振型弹塑性反应的叠加，进而将多维结构按振型等效为多个等效方程。将每一等效方程转化为以双向实际地震记录的组合为地震输入的等效单自由度系统，并通过弹塑性R-μ关系谱的统计分析，得出其与实际地震记录输入的单自由度系统具有近似的弹塑性反应特性。在此基础上给出了考虑双向地震作用的多维结构振型pushover分析程序，并阐述了该方法与传统pushover分析方法的区别，最后通过算例将该方法结果与时程分析方法结果进行比较，证明了该方法具有一定的准确性。
(6)在本文的双向地震下等延性强度折减系数设计谱和考虑双向地震作用的振型pushover分析的研究基础上提出了多维能力谱方法。提出了多维结构振型组合的分析思路。由考虑双向地震作用的多维结构振型pushover分析程序获得基于各振型的能力谱曲线；由双向地震下等延性强度折减系数设计谱和规范设计谱建立等延性弹塑性需求设计谱曲线；将能力谱曲线与需求谱曲线组合并通过一定算法即可获得双向地震下多维结构的目标位移。最后通过算例进行比较分析，说明了该方法能够比较准确地估计多维结构在双向地震下的反应需求。
Both theoretical analysis and seismic disasters indicate that the torsional response canaggravate destroying of the asymmetry plan structures. The torsional coupling response willinduce the structure's dimensional effects that shouldn't be resolved in the two dimensions(2D). Presently, the seismic design has been shifted from force-based seismic design(FBSD)to performance-based seismic design (PBSD), but the existing research findings of PBSDalmost belong to 2D analysis. So it is significant to develop performance-based seismicdesign theories and methods for the asymmetry plan structures subjected to multi-dimensionalearthquake excitations. The theories and procedures of PBSD for asymmetric plan structuressubjected to multi-dimensional earthquake excitations are established and discussed, the mainfindings are listed as follows:
(1) A seismic design approach is presented where the design procedure attempts to createstructures with a specified limited objective under a specified level of seismic intensity. Thelimited objective may be directly defined by limiting damage state of the weakness storey.The famous Park model, constant ductility inelastic response spectra and the traditionaryseismic design method are combined to determine families of structures whose initial strengthand stiffness characteristics will ensure that the desired limited damage performance objectivefor each seismic level is, as closely as possible, achieved. Furthermore, the applicability ofusing the parameterγ_h for storey response of multiple degree-of-freedom structures isanalyzed, and the corresponding equation is established. Finally, a design example shows thatthe design approach is feasible and accurate.
(2) The formula of hysteretic energy between the MDOF structures and equivalentSDOF systems is developed. The procedure for estimating hysteretic energy of MDOFstructures subjected to severe ground motions employing the energy relation equation basedon equivalent SDOF systems is proposed. Finally, eight examples for two regular and sixirregular MDOF structures which includes three stiffness distribution irregular structures andthree yield ratio distribution irregular structures show that the procedure to obtain thehysteretic energy demands of MDOF structures may be used as a simple and effective energyestimation method.
(3) The traditionary design for structural members' section sizes depends on the concept design absolutely which is difficult to answer the purpose of multi-performance objective forperformance-based seismic design. So, the constant ductility strength reduction factorinelastic statistical spectra is analyzed, and the simplified inelastic spectra equation ispresented, based on which the traditionary two stages seismic design is developed to threestages seismic design: stiffness design stage, strength design stage, displacement checkingstage. In the stiffness design stage, the displacement-based stiffness design procedure ofsymmetry structures is proposed, firstly. For asymmetry plan structures, the adjustmentprocedure of storey stiffness distribution is presented, by which the floor quality center andstiffness center are concurrent and the torsion response is reduced. The displacement-basedseismic design procedure of eccentric structures is presented for those which it is difficult toremove the structural eccentricity by adjusting stiffness distribution. Finally, the three stagesseismic design procedures for multi-dimensional structures are proposed.
(4) The constant ductility strength reduction factor inelastic statistical spectra forbi-directional ground motions is established and effects on structural nonlinear response underbi-directional earthquake excitations are discussed based on statistic analysis of 178recordings for hard site, medium site and soft site. By the sufficient statistic analysis, thesimplified model of constant ductility strength reduction factors design spectra is established,which is the foundation for forming the inelastic design demand spectra for structuressubjected to bi-directional ground motions.
(5) A multiple modal pushover analysis method to estimate seismic demands forasymmetric plan structures subjected to bi-directional ground motions is presented. Theassumption of equivalent systems for asymmetric plan structures is developed fromequivalent SDOF systems for symmetric structures. The displacement response of asymmetricplan structures is supposed to equate to the combined responses of modal equivalent systems.The multiple modal pushover analysis procedure is proposed, and an example for comparingstructural response results of multiple modal pushover analysis with the results of nonlineardynamic time history analysis shows that the multiple modal pushover analysis proceduremay be used as a simple and effective seismic demands estimation method for asymmetricplan structures subjected to bi-directional ground motions.
(6) The capacity spectra methods for estimating the earthquake demands of asymmetricplan structures which based on the multiple modal pushover analysis and bi-directionalinelastic response demand spectra presented in the paper is proposed. Finally, the engineeringexample is provided to show the method is simple, feasible and accurate.
(1)提出了直接基于损伤性能目标的抗震设计方法。由于以往对累积耗能与最大位移关系的研究针对于单自由度系统，而不一定适用于层间反应，于是基于累积耗能参数推导了地震下层间最大位移与层间累积耗能的关系方程，并以Park双参数损伤准则为基础建立了结构层间损伤计算公式，将结构最薄弱楼层的预期损伤性能目标作为设计起点进行抗震设计，反推结构的刚度和强度。为满足小震下的使用要求，将小震不坏的承载力控制引入设计程序，并与中震、大震下的损伤控制有机结合起来，从而实现了多性能水准的设计思想。最后通过算例，证明了该方法具有一定的准确性。
(2)由于结构的总滞回耗能是反映结构整体累积损伤的重要参量，为此通过能量方程推导了结构与其等效单自由度系统的滞回耗能和变形能关系公式。建议了通过结构等效单自由度系统来估计地震下结构累积滞回耗能的方法。通过对结构剪切刚度分布和屈服剪力系数分布的均匀和不均匀的多个算例进行分析和比较，证明了该方法在一定范围内能够较为准确地估计地震下结构的滞回耗能。
(3)针对传统抗震设计中完全依赖于概念设计来设计构件截面尺寸的不合理性，提出了刚度设计思想。将传统的“两阶段抗震设计”发展为“三阶段抗震设计”，即刚度设计阶段、强度设计阶段、变形验算及调整加固阶段，其中后两阶段与传统方法相似。对经典的R-μ设计谱进行分析，给出了长周期弹塑性位移谱的简化公式，并在此基础上提出了基于位移的刚度设计方法。定义了刚度调整系数，通过刚度调整系数可以一次性地调整好结构的构件尺寸，使结构能够满足预期的目标要求，从而避免了反复迭代的设计过程。针对三阶段设计中的刚度设计，首先给出了对称结构的刚度设计方法，并通过算例进行验证；而对于平面不对称结构的刚度设计，提出了基于pushover方法的平面刚度分布调整程序，通过该程序来调整不对称结构的刚度分布，尽可能的使刚心与质心重合，然后按对称结构进行刚度设计。而对于很难实现质心与刚心近似重合的结构，提出了偏心结构直接基于位移的刚度设计方法。最后，在以上研究成果的基础上给出了多维结构的三阶段抗震设计流程。
(4)建立了双向地震作用下单质点双自由度系统的等延性强度折减系数反应谱。通过硬土、中硬(软)土、软土场地的178条地震记录作为地震输入，采用了不同以往的建立强度折减系数设计谱的方法，建立了统计平均的等延性强度折减系数设计谱。分析了场地类别、延性系数、两水平主轴方向周期比对强度折减系数谱的影响。并根据统计结果，给出了便于工程应用的等延性强度折减系数简化设计谱公式。通过比较分析可知，该简化公式比较准确，且能够较合理的反应各参量对强度折减系数设计谱的影响规律。
(5)提出了考虑双向地震作用的多维结构振型pushover分析方法。采用弹性振型分解的思路，将非线性多维结构反应近似为结构多振型弹塑性反应的叠加，进而将多维结构按振型等效为多个等效方程。将每一等效方程转化为以双向实际地震记录的组合为地震输入的等效单自由度系统，并通过弹塑性R-μ关系谱的统计分析，得出其与实际地震记录输入的单自由度系统具有近似的弹塑性反应特性。在此基础上给出了考虑双向地震作用的多维结构振型pushover分析程序，并阐述了该方法与传统pushover分析方法的区别，最后通过算例将该方法结果与时程分析方法结果进行比较，证明了该方法具有一定的准确性。
(6)在本文的双向地震下等延性强度折减系数设计谱和考虑双向地震作用的振型pushover分析的研究基础上提出了多维能力谱方法。提出了多维结构振型组合的分析思路。由考虑双向地震作用的多维结构振型pushover分析程序获得基于各振型的能力谱曲线；由双向地震下等延性强度折减系数设计谱和规范设计谱建立等延性弹塑性需求设计谱曲线；将能力谱曲线与需求谱曲线组合并通过一定算法即可获得双向地震下多维结构的目标位移。最后通过算例进行比较分析，说明了该方法能够比较准确地估计多维结构在双向地震下的反应需求。
Both theoretical analysis and seismic disasters indicate that the torsional response canaggravate destroying of the asymmetry plan structures. The torsional coupling response willinduce the structure's dimensional effects that shouldn't be resolved in the two dimensions(2D). Presently, the seismic design has been shifted from force-based seismic design(FBSD)to performance-based seismic design (PBSD), but the existing research findings of PBSDalmost belong to 2D analysis. So it is significant to develop performance-based seismicdesign theories and methods for the asymmetry plan structures subjected to multi-dimensionalearthquake excitations. The theories and procedures of PBSD for asymmetric plan structuressubjected to multi-dimensional earthquake excitations are established and discussed, the mainfindings are listed as follows:
(1) A seismic design approach is presented where the design procedure attempts to createstructures with a specified limited objective under a specified level of seismic intensity. Thelimited objective may be directly defined by limiting damage state of the weakness storey.The famous Park model, constant ductility inelastic response spectra and the traditionaryseismic design method are combined to determine families of structures whose initial strengthand stiffness characteristics will ensure that the desired limited damage performance objectivefor each seismic level is, as closely as possible, achieved. Furthermore, the applicability ofusing the parameterγ_h for storey response of multiple degree-of-freedom structures isanalyzed, and the corresponding equation is established. Finally, a design example shows thatthe design approach is feasible and accurate.
(2) The formula of hysteretic energy between the MDOF structures and equivalentSDOF systems is developed. The procedure for estimating hysteretic energy of MDOFstructures subjected to severe ground motions employing the energy relation equation basedon equivalent SDOF systems is proposed. Finally, eight examples for two regular and sixirregular MDOF structures which includes three stiffness distribution irregular structures andthree yield ratio distribution irregular structures show that the procedure to obtain thehysteretic energy demands of MDOF structures may be used as a simple and effective energyestimation method.
(3) The traditionary design for structural members' section sizes depends on the concept design absolutely which is difficult to answer the purpose of multi-performance objective forperformance-based seismic design. So, the constant ductility strength reduction factorinelastic statistical spectra is analyzed, and the simplified inelastic spectra equation ispresented, based on which the traditionary two stages seismic design is developed to threestages seismic design: stiffness design stage, strength design stage, displacement checkingstage. In the stiffness design stage, the displacement-based stiffness design procedure ofsymmetry structures is proposed, firstly. For asymmetry plan structures, the adjustmentprocedure of storey stiffness distribution is presented, by which the floor quality center andstiffness center are concurrent and the torsion response is reduced. The displacement-basedseismic design procedure of eccentric structures is presented for those which it is difficult toremove the structural eccentricity by adjusting stiffness distribution. Finally, the three stagesseismic design procedures for multi-dimensional structures are proposed.
(4) The constant ductility strength reduction factor inelastic statistical spectra forbi-directional ground motions is established and effects on structural nonlinear response underbi-directional earthquake excitations are discussed based on statistic analysis of 178recordings for hard site, medium site and soft site. By the sufficient statistic analysis, thesimplified model of constant ductility strength reduction factors design spectra is established,which is the foundation for forming the inelastic design demand spectra for structuressubjected to bi-directional ground motions.
(5) A multiple modal pushover analysis method to estimate seismic demands forasymmetric plan structures subjected to bi-directional ground motions is presented. Theassumption of equivalent systems for asymmetric plan structures is developed fromequivalent SDOF systems for symmetric structures. The displacement response of asymmetricplan structures is supposed to equate to the combined responses of modal equivalent systems.The multiple modal pushover analysis procedure is proposed, and an example for comparingstructural response results of multiple modal pushover analysis with the results of nonlineardynamic time history analysis shows that the multiple modal pushover analysis proceduremay be used as a simple and effective seismic demands estimation method for asymmetricplan structures subjected to bi-directional ground motions.
(6) The capacity spectra methods for estimating the earthquake demands of asymmetricplan structures which based on the multiple modal pushover analysis and bi-directionalinelastic response demand spectra presented in the paper is proposed. Finally, the engineeringexample is provided to show the method is simple, feasible and accurate.
引文
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