钢筋混凝土高层建筑结构三维线性及非线性地震反应分析方法的研究
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摘要
随着经济与社会的发展,社会财富大量集中,大地震造成的经济损失越来越大。现行的以保证人的生命安全为一级设计准则的抗震设计理念,在控制结构破坏、减少财产损失方面显得越来越力不从心。为了更好地控制结构在地震中的反应,美国学者在20世纪90年代初率先提出了基于性能的抗震设计,并得到各国工程界的广泛认同。作为实现基于性能抗震设计主要工具的线性动力分析方法、非线性静力分析方法(即pushover分析方法)及非线性动力分析方法,得到了广泛的研究和改进。本文在总结前人研究成果的基础上,对钢筋混凝土不规则空间结构的三维线性动力分析方法、三维非线性静力pushover方法进行了系统的研究,具体工作有以下几个方面。
1、钢筋混凝土柱、梁、结点模型的研究与改进。建立了钢筋混凝土空间柱单元的纤维模型。与以往的纤维模型不同,本文根据柱的受力特征,假定其塑性变形均匀地发生在两端一定长度的塑性铰区内,将柱单元划分为三个区段,即两端的塑性铰区和中间的弹性区。塑性铰区用空间弹塑性柱单元模拟,中间弹性区用空间弹性柱单元模拟,再采用静力缩聚的方法得到整个柱单元的刚度矩阵。改进了钢筋混凝土平面梁单元的多区段单元模型,使区段数可以自由调整,每个区段的截面刚度根据截面分析的结果确定,整个梁单元的刚度矩阵由各个区段的刚度矩阵组合后通过静力缩聚而成。采用计算机数值模拟的方法研究了梁纵向钢筋在梁柱结点混凝土中的滑移,根据滑移分析与梁截面分析的结果,提出了确定梁端弯矩与附加滑移转角关系的方法。将梁两端的转动弹簧与梁一起,建立了超级梁单元。
2、改进了剪力墙多垂直杆模型。在材料本构关系层次上确定各个垂直杆中钢筋和混凝土的轴向刚度,用软化桁架模型确定剪切弹簧的剪切刚度。并根据剪力墙截面的开裂长度和压溃长度,提出了一种考虑墙体弯曲变形影响剪切刚度的新方式,该方式计算简便,又能较好地考虑弯曲变形对剪切变形的影响。建议了一种考虑墙底转动的新方法,它通过计入墙体端部约束构件纵向钢筋的滑移来考虑墙底的转动。采用改进后的多垂直杆模型对文献上提供的两个剪力墙试验结果进行了比较,结果显示对带暗柱墙计算承载力高于试验结果约20%,对带明柱墙两者相符较好。
3、三维线性地震反应分析方法的研究。采用刚性楼板假定,建立了三维结构的平面子结构平扭模型与杆系型平扭模型。通过一个9层框架结构和一个20层框筒双塔结构的动力时程分析,比较了这两种模型分析结果的差别并对其原因进行了探讨。针对平面子结构平扭模型的缺陷,从两个方面对其进行了改进,改进后模型的计算精度有较好的提高。
4、结构三维非线性静力pushover分析方法的研究及程序编制。研究了在不规则空间结构中进行静力pushover分析的两种方法,即N2方法与模态pushover方法;以本文建立的单元模型为基础,应用MATLAB语言编制了结构三维非线性pushover分析的计算机程序,对两个不规则的空间钢筋混凝土框架结构分别使用N2方法与模态pushover方法进行了抗震性能计算,比较了这两种方法计算结果的差别。并探讨了结点钢筋滑移对结构抗震性能的影响,在考虑钢筋滑移后,结构的目标位移增大,从而使层间变形也增大。
5、结构三维非线性pushover分析方法准确性评价。以通用软件CANNY为分析工具,采用多条地震波弹塑性时程分析的平均结果为标准,分别从目标位移、层间位移及层间扭转角三个方面对静力pushover分析结果的准确性进行了评估,揭示了现行三维pushover方法在抗震性能评估方面存在的缺点是:(1)高估结构下部的地震反应,低估结构上部的地震反应;(2)不能正确表现结构刚度突变层地震反应的突变情况。
6、结构三维非线性pushover分析方法的改进。对N2方法提出了两种改进方法:(1)双向同时推覆N2方法。该方法按照使扭转变形最大的原则组合两个方向的水平推覆力,同时施加于结构上,对结构的层间扭转角评估有较大的改善。(2)多模态N2方法。此方法在x、y方向明确考虑了高阶模态荷载分量的影响,故在最大层间位移和扭转角方面都有较明显的改善。对模态pushover方法建议了三种改进方法:(1)正反向MPA方法。它综合考虑了模态荷载从正向与反向施加时的最不利组合情况,对于扭转不明显的结构,其结果与原MPA方法很相近;对扭转明显的结构,则大于原MPA方法的结果。该方法更能表现结构在地震中最不利的受力与变形情况。(2)模态位移成比例的MPA方法。该方法根据“基本模态组”的目标位移来计算高阶模态目标位移,一方面克服了MPA中高阶模态推覆曲线可能出现怪异形状的困难,另一方面简化了高阶模态的目标位移计算方法,其计算精度与原MPA方法相当,是一种可取的改进方法。(3)增大高阶模态目标位移的荷载相关Ritz向量(LDR)MPA方法。该方法采用与荷载相关Ritz向量而非精确的特征向量作为结构的振型,并且通过考虑被截断模态的振型参与质量来提高选用的较高阶振型的目标位移,取得了很好的改进效果。
With the development of economy and society, the social wealth accumulates greatly, so the financial loss caused by intense earthquake becomes heavier and heavier. The current seismic design concept,which aims to protect people’s lives,does not work well on controlling the damage of structures and on decreasing the wealth loss. In order to control the response of structures in earthquakes, the idea of performance-based seismic design was developed the first time by the American scholars in early 1990s, then it got widespread acceptance in the world. The linear dynamic analysis method, the nonlinear static analysis (pushover analysis) and the nonlinear dynamic analysis, as the key tools of practicing the performance-based seismic design, were widely developed and improved. In this dissertation, based on the forerunner’s works, the author studies the 3D seismic response analysis methods of linear dynamic analysis and pushover analysis of irregular concrete reinforced spatial structures systematically. The main work is as follows:
1、Study and improvement on mechanic models of concrete reinforced columns, beams and beam-column joints.The 3D fibre model of concrete column is proposed in different type from the forerunner’s model.Based on the deformation characteristic of columns, it is assumed that column’s plastic deformation occurs evenly in the plastic hinge zones, and the column is divided into three parts, which are elastic zone in the middle and the plastic hinge zones with certain length in both ends. The elastic 3D column element is used to simulate the middle part, and the plastic 3D column element is used to simulate the plastic hinge zone. The column’s stiffness matrix is computed by condense the structural matrix of the super-column-element with three substructures.The multi-segment model of plane beam is improved in this dissertation. In this model, the beam is divided into some parts and the sum can be adjusted freely, the section stiffness in each part is computed by cross-section analysis, and the beam’s stiffness matrix is calculated by condensing the assembly matrix of all parts. Slippage of a rebar in the beam-column joints is studied by numerical simulating method. According to the result of slippage analysis and the result of the beam’s cross-section analysis,the method of computing the relation between bending moment and slipping rotation on the beam end is proposed.A model of evaluating the slipping effect, in which two rotation springs are added on the beam ends, is developed, in which the two springs and the beam constitute the super beam element.
2、The multiple vertical-line element model of shear wall is improved in this dissertation. In author’s work, the axial stiffness of vertical-line is calculated by two-parallel component model, in which the stiffness of concrete and the steel bar components is determined based on their constitutive relationship. The stiffness of shear spring is determined by softened-truss model. A new procedure considering the flexual deformation of the wall influencing its shear stiffness is proposed based on the wall’s horizontal crack length and its crash length.This method is not only simple in calculation, but also effective in considering the wall’s flexual deformation reducing its shear ability. A new method evaluating the effect of fixed-end rotation of the wall is developed, in which the fixed-end rotation is considered as the slippage of the longitudinal reinforcement in the foundation of the wall’s column. The improved multiple vertical-line element model of shear wall is used to computed the two test walls, the load result is beyond the test result about 20% in terms of rectangular section wall, and agrees well with the test result in terms of wall with edge columns.
3、Study on the 3D linear seismic response analysis method. Based on the rigid slab assumption, two types of 3D analysis model, which are the plane substructure model and the spatial pole-component-system model, are developed as the structural analysis model. The difference between the two types of 3D model and the reasons, studying by the dynamic analysis of a 9-story frame structure and a two-tower 20-story frame-tube structure, are discussed. Aiming at the deficiency of the plane substructure model, improvements at two perspectives are proposed, the improved model is more accurate.
4、Study on the 3D nonlinear static pushover analysis method and making of computing procedure. N2 method and modal pushover analysis method (MPA) are studied. Based on the models developed in this dissertation, a 3D pushover analysis computing procedure is developed with MATLAB language. Then the N2 method and MPA method are used to evaluate the seismic performance of two irregular spatial frame structures with the computing procedure. The difference between the two pushover methods are examined. The influence of rebar slippage in the beam column joint is assessed, and the result shows that the target displacement and the story drifts increase due to rebar slippage.
5、The accuracy evaluation of the 3D nonlinear static pushover analysis method. The accuracy of the 3D pushover method is evaluated from their target displacements, story drifts and story torsion rotations based on the average results of elasto-plastic time history analysis with multi earthquake waves, which use the common computing procedure CANNY as the analytical tool. The common drawbacks of 3D pushover method are disclosed, which are, (1) the seismic response in structural upper story is overestimated,and the seismic response in structural lower story is underestimated, (2) the deformation in the weaker story can not be discovered correctly.
6、The improvements of the 3D pushover method. Two improved procedures are developed for N2 method, and they are: (1) pushing in x and y direction simultaneously N2 method. The combination of pushing loads in x and y direction, which leads to maximal torsion rotation, is given to the structure at same time. With this modification, the story torsion rotations improve effectively. (2)multi modal N2 method. The pushover analysis in x and y direction is performed with multi modal load pattern in this method, so the maximal story drifts and story torsion rotation improve greatly. Three improved methods are proposed for MPA method, and they are: (1) positive-and-negative MPA method. The disadvantageous effect of the modal load combination in positive and negative direction is considered in this method. For the slight irregular structure, the result of this method is much the same as that of MPA. But for the severe irregular structure, the result of this method is larger than that of MPA. So the disadvantage of the structural load or deformation in earthquake is discovered appropriately. (2) modal target displacements ratio MPA method. The higher modal target displacements are calculated based on the target displacements of“basic mode group”with a coefficient in this method. For one thing, the difficult caused by the odd higher mode pushover curves is solved, for another, the calculation of higher modal target displacements is simplified.And the accuracy of this method is as that of MPA, so it is a effective improvement.(3)load dependent Ritz vector (LDR) MPA with magnified higher modal target displacements. In this modification method, the load dependent Ritz vectors are used as the modal vectors in lieu of the exact eigenvectors, and the higher modal target displacements are magnified base on the truncation modal participating mass. This improvement leads to good result.
1、钢筋混凝土柱、梁、结点模型的研究与改进。建立了钢筋混凝土空间柱单元的纤维模型。与以往的纤维模型不同,本文根据柱的受力特征,假定其塑性变形均匀地发生在两端一定长度的塑性铰区内,将柱单元划分为三个区段,即两端的塑性铰区和中间的弹性区。塑性铰区用空间弹塑性柱单元模拟,中间弹性区用空间弹性柱单元模拟,再采用静力缩聚的方法得到整个柱单元的刚度矩阵。改进了钢筋混凝土平面梁单元的多区段单元模型,使区段数可以自由调整,每个区段的截面刚度根据截面分析的结果确定,整个梁单元的刚度矩阵由各个区段的刚度矩阵组合后通过静力缩聚而成。采用计算机数值模拟的方法研究了梁纵向钢筋在梁柱结点混凝土中的滑移,根据滑移分析与梁截面分析的结果,提出了确定梁端弯矩与附加滑移转角关系的方法。将梁两端的转动弹簧与梁一起,建立了超级梁单元。
2、改进了剪力墙多垂直杆模型。在材料本构关系层次上确定各个垂直杆中钢筋和混凝土的轴向刚度,用软化桁架模型确定剪切弹簧的剪切刚度。并根据剪力墙截面的开裂长度和压溃长度,提出了一种考虑墙体弯曲变形影响剪切刚度的新方式,该方式计算简便,又能较好地考虑弯曲变形对剪切变形的影响。建议了一种考虑墙底转动的新方法,它通过计入墙体端部约束构件纵向钢筋的滑移来考虑墙底的转动。采用改进后的多垂直杆模型对文献上提供的两个剪力墙试验结果进行了比较,结果显示对带暗柱墙计算承载力高于试验结果约20%,对带明柱墙两者相符较好。
3、三维线性地震反应分析方法的研究。采用刚性楼板假定,建立了三维结构的平面子结构平扭模型与杆系型平扭模型。通过一个9层框架结构和一个20层框筒双塔结构的动力时程分析,比较了这两种模型分析结果的差别并对其原因进行了探讨。针对平面子结构平扭模型的缺陷,从两个方面对其进行了改进,改进后模型的计算精度有较好的提高。
4、结构三维非线性静力pushover分析方法的研究及程序编制。研究了在不规则空间结构中进行静力pushover分析的两种方法,即N2方法与模态pushover方法;以本文建立的单元模型为基础,应用MATLAB语言编制了结构三维非线性pushover分析的计算机程序,对两个不规则的空间钢筋混凝土框架结构分别使用N2方法与模态pushover方法进行了抗震性能计算,比较了这两种方法计算结果的差别。并探讨了结点钢筋滑移对结构抗震性能的影响,在考虑钢筋滑移后,结构的目标位移增大,从而使层间变形也增大。
5、结构三维非线性pushover分析方法准确性评价。以通用软件CANNY为分析工具,采用多条地震波弹塑性时程分析的平均结果为标准,分别从目标位移、层间位移及层间扭转角三个方面对静力pushover分析结果的准确性进行了评估,揭示了现行三维pushover方法在抗震性能评估方面存在的缺点是:(1)高估结构下部的地震反应,低估结构上部的地震反应;(2)不能正确表现结构刚度突变层地震反应的突变情况。
6、结构三维非线性pushover分析方法的改进。对N2方法提出了两种改进方法:(1)双向同时推覆N2方法。该方法按照使扭转变形最大的原则组合两个方向的水平推覆力,同时施加于结构上,对结构的层间扭转角评估有较大的改善。(2)多模态N2方法。此方法在x、y方向明确考虑了高阶模态荷载分量的影响,故在最大层间位移和扭转角方面都有较明显的改善。对模态pushover方法建议了三种改进方法:(1)正反向MPA方法。它综合考虑了模态荷载从正向与反向施加时的最不利组合情况,对于扭转不明显的结构,其结果与原MPA方法很相近;对扭转明显的结构,则大于原MPA方法的结果。该方法更能表现结构在地震中最不利的受力与变形情况。(2)模态位移成比例的MPA方法。该方法根据“基本模态组”的目标位移来计算高阶模态目标位移,一方面克服了MPA中高阶模态推覆曲线可能出现怪异形状的困难,另一方面简化了高阶模态的目标位移计算方法,其计算精度与原MPA方法相当,是一种可取的改进方法。(3)增大高阶模态目标位移的荷载相关Ritz向量(LDR)MPA方法。该方法采用与荷载相关Ritz向量而非精确的特征向量作为结构的振型,并且通过考虑被截断模态的振型参与质量来提高选用的较高阶振型的目标位移,取得了很好的改进效果。
With the development of economy and society, the social wealth accumulates greatly, so the financial loss caused by intense earthquake becomes heavier and heavier. The current seismic design concept,which aims to protect people’s lives,does not work well on controlling the damage of structures and on decreasing the wealth loss. In order to control the response of structures in earthquakes, the idea of performance-based seismic design was developed the first time by the American scholars in early 1990s, then it got widespread acceptance in the world. The linear dynamic analysis method, the nonlinear static analysis (pushover analysis) and the nonlinear dynamic analysis, as the key tools of practicing the performance-based seismic design, were widely developed and improved. In this dissertation, based on the forerunner’s works, the author studies the 3D seismic response analysis methods of linear dynamic analysis and pushover analysis of irregular concrete reinforced spatial structures systematically. The main work is as follows:
1、Study and improvement on mechanic models of concrete reinforced columns, beams and beam-column joints.The 3D fibre model of concrete column is proposed in different type from the forerunner’s model.Based on the deformation characteristic of columns, it is assumed that column’s plastic deformation occurs evenly in the plastic hinge zones, and the column is divided into three parts, which are elastic zone in the middle and the plastic hinge zones with certain length in both ends. The elastic 3D column element is used to simulate the middle part, and the plastic 3D column element is used to simulate the plastic hinge zone. The column’s stiffness matrix is computed by condense the structural matrix of the super-column-element with three substructures.The multi-segment model of plane beam is improved in this dissertation. In this model, the beam is divided into some parts and the sum can be adjusted freely, the section stiffness in each part is computed by cross-section analysis, and the beam’s stiffness matrix is calculated by condensing the assembly matrix of all parts. Slippage of a rebar in the beam-column joints is studied by numerical simulating method. According to the result of slippage analysis and the result of the beam’s cross-section analysis,the method of computing the relation between bending moment and slipping rotation on the beam end is proposed.A model of evaluating the slipping effect, in which two rotation springs are added on the beam ends, is developed, in which the two springs and the beam constitute the super beam element.
2、The multiple vertical-line element model of shear wall is improved in this dissertation. In author’s work, the axial stiffness of vertical-line is calculated by two-parallel component model, in which the stiffness of concrete and the steel bar components is determined based on their constitutive relationship. The stiffness of shear spring is determined by softened-truss model. A new procedure considering the flexual deformation of the wall influencing its shear stiffness is proposed based on the wall’s horizontal crack length and its crash length.This method is not only simple in calculation, but also effective in considering the wall’s flexual deformation reducing its shear ability. A new method evaluating the effect of fixed-end rotation of the wall is developed, in which the fixed-end rotation is considered as the slippage of the longitudinal reinforcement in the foundation of the wall’s column. The improved multiple vertical-line element model of shear wall is used to computed the two test walls, the load result is beyond the test result about 20% in terms of rectangular section wall, and agrees well with the test result in terms of wall with edge columns.
3、Study on the 3D linear seismic response analysis method. Based on the rigid slab assumption, two types of 3D analysis model, which are the plane substructure model and the spatial pole-component-system model, are developed as the structural analysis model. The difference between the two types of 3D model and the reasons, studying by the dynamic analysis of a 9-story frame structure and a two-tower 20-story frame-tube structure, are discussed. Aiming at the deficiency of the plane substructure model, improvements at two perspectives are proposed, the improved model is more accurate.
4、Study on the 3D nonlinear static pushover analysis method and making of computing procedure. N2 method and modal pushover analysis method (MPA) are studied. Based on the models developed in this dissertation, a 3D pushover analysis computing procedure is developed with MATLAB language. Then the N2 method and MPA method are used to evaluate the seismic performance of two irregular spatial frame structures with the computing procedure. The difference between the two pushover methods are examined. The influence of rebar slippage in the beam column joint is assessed, and the result shows that the target displacement and the story drifts increase due to rebar slippage.
5、The accuracy evaluation of the 3D nonlinear static pushover analysis method. The accuracy of the 3D pushover method is evaluated from their target displacements, story drifts and story torsion rotations based on the average results of elasto-plastic time history analysis with multi earthquake waves, which use the common computing procedure CANNY as the analytical tool. The common drawbacks of 3D pushover method are disclosed, which are, (1) the seismic response in structural upper story is overestimated,and the seismic response in structural lower story is underestimated, (2) the deformation in the weaker story can not be discovered correctly.
6、The improvements of the 3D pushover method. Two improved procedures are developed for N2 method, and they are: (1) pushing in x and y direction simultaneously N2 method. The combination of pushing loads in x and y direction, which leads to maximal torsion rotation, is given to the structure at same time. With this modification, the story torsion rotations improve effectively. (2)multi modal N2 method. The pushover analysis in x and y direction is performed with multi modal load pattern in this method, so the maximal story drifts and story torsion rotation improve greatly. Three improved methods are proposed for MPA method, and they are: (1) positive-and-negative MPA method. The disadvantageous effect of the modal load combination in positive and negative direction is considered in this method. For the slight irregular structure, the result of this method is much the same as that of MPA. But for the severe irregular structure, the result of this method is larger than that of MPA. So the disadvantage of the structural load or deformation in earthquake is discovered appropriately. (2) modal target displacements ratio MPA method. The higher modal target displacements are calculated based on the target displacements of“basic mode group”with a coefficient in this method. For one thing, the difficult caused by the odd higher mode pushover curves is solved, for another, the calculation of higher modal target displacements is simplified.And the accuracy of this method is as that of MPA, so it is a effective improvement.(3)load dependent Ritz vector (LDR) MPA with magnified higher modal target displacements. In this modification method, the load dependent Ritz vectors are used as the modal vectors in lieu of the exact eigenvectors, and the higher modal target displacements are magnified base on the truncation modal participating mass. This improvement leads to good result.
引文
[1]中华人民共和国建设部.建筑抗震设计规范.北京:中国建筑工业出版社,2001, 195-197
[2]中国地震信息网,www.csi.ac.cn,2006-8-10
[3]Federal Emergency Management Agency. Action plan for performance based seismic design. FEMA349,2000,1-3
[4]汪梦甫,周锡元.基于性能的建筑结构抗震设计.建筑结构,2003,33(3):59-61
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