考虑高振型和非弹性影响的DBSD目标位移改进方法研究
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摘要
随着对结构地震反应的不断研究以及基于性态的抗震设计理念的提出,人们越来越意识到位移这一指标在地震工程评价和设计中的重要地位,基于位移的抗震设计方法是现阶段实现基于性态的抗震设计最为便捷有效的方法,并有望成为
抗震设计实用方法,成为未来抗震设计的发展趋势。基于位移的抗震设计(DBSD)以结构的位移作为控制结构性能的参数,在进行设计时,首先根据抗震性态水准的要求确定结构的目标位移,进而依次确定等效单自由度体系的等效质量、等效阻尼比、等效刚度和地震作用,最后完成构件的强度设计。因此,在基于位移的抗震设计中,目标位移的确定非常重要。
目标位移的确定方法有很多种,然而这些方法都基于这样一个假设,即结构的反应由基本振型控制,并且在结构屈服前后侧向荷载分布模式保持不变,因此都不能考虑高阶振型的影响。根据已有研究成果可知,随着结构周期的增长,高阶振型对于结构的影响也逐渐增大,故这种只考虑第一振型的目标位移确定方法在用于周期较长或者说高振型参与比例较大的结构设计时,会有较大的误差,甚至可能出现对变形控制的失效。
本文以国外新近开发的结构非线性分析工具OpenSees为平台,分别从结构非线性反应下各振型对顶点位移的贡献,以及R取值不同对结构非线性反应顶点位移的影响两个方面进行分析,研究基于位移设计顶点目标位移确定中引入高振型和非弹性影响的方法,具体内容如下:
第一,以按我国7度0.15g区设计的5层和11层两个框架为例,以结构弹性反应为基础,介绍了将结构顶点位移按结构弹性振型分解的方法。进而深入到结构非线性地震反应,介绍了Chopra振型解耦的方法,并采用取结构顶点位移最大值时刻的特征值和对梁柱刚度进行折减两种方案,将结构非线性地震反应顶点位移进行分解,研究除基本振型外的高阶振型对结构顶点位移的影响,主要得出以下结论:
①结构非线性地震反应顶点位移最大值随结构高度的增加和地震作用水准的增大而增大。
②在同一地震水准下,随着结构高度增加,周期变长,第二振型和第三振型的参与比例明显增大;而同一结构在不同地震水准下第二和第三振型的参与比例没有明显规律。
③对于周期较短的结构,地震水准(即大震、中震或小震)对于高振型参与比例的影响较大,且规律是地震水准越高,高振型参与比例越大。
第二,以三个地震力降低系数Rd分别取2.5、3.25和4.0进行设计的框架为例,输入10条地震地面加速度记录进行非线性动力反应分析,对结构顶点位移最大值进行统计,得出以下主要结论:
随着Rd取值的增大,结构非线性反应顶点位移也系统性增大,且Rd越大,顶点位移的增大越明显。这意味着在基于位移的设计中,还应该以R取值为依据,对顶点目标位移的确定方法进行修正。
第三,根据以上结论,以FEMA356分项系数法为基础,引入高振型和R值的影响,对顶点目标位移的计算公式提出初步的改进建议。
With the continuous research on structural seismic response and the proposing of performance-based seismic design notion, people are more and more aware the important role of the indicator-displacement in earthquake engineering design and evaluation. Nowadays, displacement-based seismic design is the most convenient and effective way to achieve performance-based design and it is expected to become practical seismic design method and a future trend of seismic design.
Displacement-based seismic design takes displacement (deformation) of structure as the parameter controlling structural performance. The first step is to determine the target displacement of structure according to the seismic performance level, then in turn to determine the equivalent mass, equivalent damping ratio, equivalent stiffness and earthquake force of the equivalent single degree of freedom system. Finally, complete strength design of components. Therefore, in the displacement-based seismic design, the computation of the target displacement is very important.
There are various methods to determine the target displacement, but all of these methods are based on the assumption that the response of structure is controlled by the fundamental mode and that the mode shape remains unchanged after the structure yields. So they can not consider the effect of higher modes. According to the existing research results, we can see that, the effect of higher modes on structure increases gradually along with the growth of period of structure. So in the design for structures with longer period, the methods considering only the first modal effect will have greater error, even will be failure in the deformation controlling.
Based on the platform-OpenSees, which is a foreign newly developed tool used for structural nonlinear analysis, this paper analyzes two parts: the contribution of each modal to the roof displacement of structure in nonlinear seismic response, and the effect of different values of R on the roof displacement of structure in nonlinear seismic response, to research the method that may consider the effect of higher modals in the computation of target roof displacement. The specific contents include as follows:
First, with two frames designed according to Chinese 7 degree, 0.15g area for example, which are 5 layers and 11 layers, respectively, the paper introduces a method of decomposing roof displacement to each modal in elastic response. Further depth to the nonlinear seismic response of structure, the paper introduces three methods to decompose roof displacement to each modal, which are the uncoupled modal response history analysis method proposed by Chopra, the method using the characteristic values at the time of maximum roof displacement appearing, and the method considering reduction of rigid of beams and columns. Based on these methods, this paper decomposes roof displacement to each modal of the structures to research the effect of higher modes other than the first mode on roof displacement of structure. The main conclusions include as follows:
①The maximum roof displacement of structure in nonlinear seismic response increased with the growth of height of structure and the earthquake level.
②In the same earthquake level, with the growth of structure height and period, the participation ratio of the second and third modal increased significantly; and for the same structure in different earthquake levels, the participation ratio of the second and third modal have no obvious rule.
③For the structure with short period, the effect of earthquake levels for participation ratio of higher modes is obvious, and the rule is that, higher the earthquake level is, larger the participation ratio of higher modes are.
Second, with three frames which seismic force reduction factor Rd were respectively taken 2.5, 3.25 and 4.0 for example, input 10 ground motion acceleration records for the nonlinear dynamic response analysis, a statistics of the maximum roof displacements is done and conclusions are as follows:
With the value of Rd increasing, the roof displacement of structure in nonlinear response increases, and larger the Rd is, more obviously the roof displacement increases.
It shows that, in displacement-based seismic design, we also should improve the target roof displacement computing method based on the value of R.
Third, in view of these two conclusions, this paper propose a preliminary suggest on the improving of the target roof displacement computing method based on the subentry coefficient method in FEMA356, which can consider effect of higher modes and the value of R.
抗震设计实用方法,成为未来抗震设计的发展趋势。基于位移的抗震设计(DBSD)以结构的位移作为控制结构性能的参数,在进行设计时,首先根据抗震性态水准的要求确定结构的目标位移,进而依次确定等效单自由度体系的等效质量、等效阻尼比、等效刚度和地震作用,最后完成构件的强度设计。因此,在基于位移的抗震设计中,目标位移的确定非常重要。
目标位移的确定方法有很多种,然而这些方法都基于这样一个假设,即结构的反应由基本振型控制,并且在结构屈服前后侧向荷载分布模式保持不变,因此都不能考虑高阶振型的影响。根据已有研究成果可知,随着结构周期的增长,高阶振型对于结构的影响也逐渐增大,故这种只考虑第一振型的目标位移确定方法在用于周期较长或者说高振型参与比例较大的结构设计时,会有较大的误差,甚至可能出现对变形控制的失效。
本文以国外新近开发的结构非线性分析工具OpenSees为平台,分别从结构非线性反应下各振型对顶点位移的贡献,以及R取值不同对结构非线性反应顶点位移的影响两个方面进行分析,研究基于位移设计顶点目标位移确定中引入高振型和非弹性影响的方法,具体内容如下:
第一,以按我国7度0.15g区设计的5层和11层两个框架为例,以结构弹性反应为基础,介绍了将结构顶点位移按结构弹性振型分解的方法。进而深入到结构非线性地震反应,介绍了Chopra振型解耦的方法,并采用取结构顶点位移最大值时刻的特征值和对梁柱刚度进行折减两种方案,将结构非线性地震反应顶点位移进行分解,研究除基本振型外的高阶振型对结构顶点位移的影响,主要得出以下结论:
①结构非线性地震反应顶点位移最大值随结构高度的增加和地震作用水准的增大而增大。
②在同一地震水准下,随着结构高度增加,周期变长,第二振型和第三振型的参与比例明显增大;而同一结构在不同地震水准下第二和第三振型的参与比例没有明显规律。
③对于周期较短的结构,地震水准(即大震、中震或小震)对于高振型参与比例的影响较大,且规律是地震水准越高,高振型参与比例越大。
第二,以三个地震力降低系数Rd分别取2.5、3.25和4.0进行设计的框架为例,输入10条地震地面加速度记录进行非线性动力反应分析,对结构顶点位移最大值进行统计,得出以下主要结论:
随着Rd取值的增大,结构非线性反应顶点位移也系统性增大,且Rd越大,顶点位移的增大越明显。这意味着在基于位移的设计中,还应该以R取值为依据,对顶点目标位移的确定方法进行修正。
第三,根据以上结论,以FEMA356分项系数法为基础,引入高振型和R值的影响,对顶点目标位移的计算公式提出初步的改进建议。
With the continuous research on structural seismic response and the proposing of performance-based seismic design notion, people are more and more aware the important role of the indicator-displacement in earthquake engineering design and evaluation. Nowadays, displacement-based seismic design is the most convenient and effective way to achieve performance-based design and it is expected to become practical seismic design method and a future trend of seismic design.
Displacement-based seismic design takes displacement (deformation) of structure as the parameter controlling structural performance. The first step is to determine the target displacement of structure according to the seismic performance level, then in turn to determine the equivalent mass, equivalent damping ratio, equivalent stiffness and earthquake force of the equivalent single degree of freedom system. Finally, complete strength design of components. Therefore, in the displacement-based seismic design, the computation of the target displacement is very important.
There are various methods to determine the target displacement, but all of these methods are based on the assumption that the response of structure is controlled by the fundamental mode and that the mode shape remains unchanged after the structure yields. So they can not consider the effect of higher modes. According to the existing research results, we can see that, the effect of higher modes on structure increases gradually along with the growth of period of structure. So in the design for structures with longer period, the methods considering only the first modal effect will have greater error, even will be failure in the deformation controlling.
Based on the platform-OpenSees, which is a foreign newly developed tool used for structural nonlinear analysis, this paper analyzes two parts: the contribution of each modal to the roof displacement of structure in nonlinear seismic response, and the effect of different values of R on the roof displacement of structure in nonlinear seismic response, to research the method that may consider the effect of higher modals in the computation of target roof displacement. The specific contents include as follows:
First, with two frames designed according to Chinese 7 degree, 0.15g area for example, which are 5 layers and 11 layers, respectively, the paper introduces a method of decomposing roof displacement to each modal in elastic response. Further depth to the nonlinear seismic response of structure, the paper introduces three methods to decompose roof displacement to each modal, which are the uncoupled modal response history analysis method proposed by Chopra, the method using the characteristic values at the time of maximum roof displacement appearing, and the method considering reduction of rigid of beams and columns. Based on these methods, this paper decomposes roof displacement to each modal of the structures to research the effect of higher modes other than the first mode on roof displacement of structure. The main conclusions include as follows:
①The maximum roof displacement of structure in nonlinear seismic response increased with the growth of height of structure and the earthquake level.
②In the same earthquake level, with the growth of structure height and period, the participation ratio of the second and third modal increased significantly; and for the same structure in different earthquake levels, the participation ratio of the second and third modal have no obvious rule.
③For the structure with short period, the effect of earthquake levels for participation ratio of higher modes is obvious, and the rule is that, higher the earthquake level is, larger the participation ratio of higher modes are.
Second, with three frames which seismic force reduction factor Rd were respectively taken 2.5, 3.25 and 4.0 for example, input 10 ground motion acceleration records for the nonlinear dynamic response analysis, a statistics of the maximum roof displacements is done and conclusions are as follows:
With the value of Rd increasing, the roof displacement of structure in nonlinear response increases, and larger the Rd is, more obviously the roof displacement increases.
It shows that, in displacement-based seismic design, we also should improve the target roof displacement computing method based on the value of R.
Third, in view of these two conclusions, this paper propose a preliminary suggest on the improving of the target roof displacement computing method based on the subentry coefficient method in FEMA356, which can consider effect of higher modes and the value of R.
引文
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[2]欧洲-国际混凝土协会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:重庆大学土木工程学院, 2004.
[3] Mao Jianmeng, Zhai Changhai and Xie Lili. An improved modal pushover analysis procedure for estimating seismic demands of structures[J]. Earthquake Engineering and Engineering Vibration, 2008, 7: 25-31.
[4]陈建兴,姜文伟,穆为. Pushover分析在性能化抗震设计中的应用[J].结构工程师, 2008, 24(3): 81-86.
[5] Freeman SA, Nicoletti JP, Tyrdl JV. Evaluation of existing buildings for seismic risk-A case study of pugel sound naval shipyard. Proceedings of 1st U:S. National Conference on Earthquake Engineering, EERI, Berkeley, 1975: 113-122.
[6] Fajfar P. Capacity spectrum method based on inelastic demand spectra[J]. Earthquake Engineering and Structural Dynamics, 1999, 28(9): 979-993.
[7] ATC. Seismic evaluation and retrofit of concrete buildings[R] Report. ATC-40, Applied Technology Council, Redwood City, California, 1996.
[8]秦家长,罗奇峰.应用ATC-40能力谱法评估结构目标位移[J].地震工程与工程振动, 2006, 26(6):64~70.
[9] Building Seismic Safety Council, Prestandard and Commentary for the Seismic Rehabilitation of Buildings[M]. FEMA356, Developed for the Federal Emergency Management Agency, Washington DC, 2000.
[10]尹华伟,易伟建.结构地震反应Pushover位移形状向量的选取[J].湖南大学学报(自然科学版), 2004, 31(5):88~93.
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