利用多弹簧模型研究底框架房屋的变轴力影响
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摘要
房屋建筑中,由水平地震引起的倾覆力矩作用,是引起下部框架柱附加轴力的主要原因。该附加轴力一般随时变化,且在结构的非线性阶段与水平作用力之间并不存在比例关系,它一方面使构件的抗弯、抗剪等强度以及变形能力等发生变化,另一方面,也使构件的滞回特性发生改变。因此,在结构的非线性动力分析中,如何合理考虑该变轴力的影响,是当前结构抗震分析的关注点之一。
本论文以底框砌体房屋为例,对框架柱的变轴力影响问题进行研究。
(1)介绍和采用多弹簧模型,并编制动力分析程序。通过文献试验对比验证了该模型具有较高的精度,所编制的程序是可靠、有效的；
(2)对一栋6层底框架房屋在4种不同水平地震强度下进行动力分析,得到各底框柱的最大轴力随地震动增加均有一定幅度的提高,其提高幅度随地震动强度的增大而增大,边柱的增长幅度明显高于中柱,在不同地震动输入下中底框柱轴力变化幅度约为边柱的37%-55%。结构进入屈服状态时,中柱在正反两个方向上的屈服强度值基本接近,而边柱在其正反两个方向上的屈服强度由于受变轴力影响存在明显不同,相差接近30%。故变轴力影响不可忽略；
(3)底框架结构在变轴力影响下,其底层框架的最大位移和最大剪力均比层间模型的结果小,二者的差别随水平地震强度的增加而增大；
(4)对4层、6层、8层底框架结构进行动力分析,得到随结构层数的增加,各底框柱的轴力变化幅度有增大趋势,中柱轴力相对于边柱的变化缓慢。结构进入屈服状态时,随结构层数的增加,左、右边柱正反两向的屈服强度差别增大；
(5)对6层底框架房屋在水平地震作用和水平、竖直(av=2/3ah)地震同时作用下的动力响应进行对比,得到水平、竖直地震同时作用下的各柱轴力变化幅度随地震强度的增大呈增大趋势,但中柱的轴力变化幅度相对于仅水平地震作用时大于左、右边柱,即竖向地震作用对中柱的影响大于边柱,中柱最大轴力变化为15.4%。因此,竖向地震对结构内力响应的影响不可忽略。但结构处于大震时底层最大位移差别仅为3.0%(ah=0.45gav=0.29g),故其对结构的侧移影响可忽略不计。
In building constructions the overturning moment caused by horizontal earthquake is the main source for the additional axial force of the bottom frame columns. Generally, the additional axial force is changing all the time and is not proportional to the horizontal seismic shear when the structure is in nonlinear stage. The variable axial force not only changes the bending capacity, shear strength and deformability of members, but also the hysteretic behaviors. Therefore, how to consider the effects of the variable axial force reasonably is one of the concerned issues in the nonlinear dynamic seismic analysis.
Taking the frame-supported masonry buildings as examples, the effects of variable axial force in frame columns were studied in this paper.
(1) The multi-spring model was introduced and a dynamic analysis program was coded using the model. Comparisons to some literature experimental results showed the multi-spring model was accurate relatively and the program was reliable and effective.
(2) Dynamic analysis for a six-storey frame-supported masonry building was performed in four different levels of horizontal earthquake intensity. It showed the peak axial force at all bottom frame columns had a certain increase according to the increase of the ground motion, and the increase rate improved with the ground motion's increasing. The increase at side columns was obviously larger than that at the middle column, the increase of variable axial force at middle frame column was about37%-55%to the increase at side frame columns in different seismic intensity. The yielding strength of middle frame column at yielding stage was close in both positive and negative direction, but the strength of side columns were obviously different in the opposite directions because of the variable axial force effect, the difference was nearly30%. Therefore, the influence of variable axial force could not be ignored.
(3) The maximum displacement and maximum shear at bottom story of frame supported building were smaller than the storey-model's results due to the effect of the variable axial force. The difference increased with the horizontal seismic intensity increasing.
(4) The dynamic analysis was conducted for frame supported buildings with four-storey, six-storey, and eight-storey. It indicated the changing rate of the variable axial force of each column had an increasing trend to the increase of building stories. The middle column's changing rate was smaller relatively than the side columns'. After the structure's yielding, the difference of3d elding strength of side columns in positive direction to negative direction increased with the story's increasing.
(5) Comparison of dynamic response of six-storey structure was done between in horizontal shock and that with vertical shock (av=2/3ah). It showed the peak axial force at all bottom frame columns under horizontal and vertical excitations increased according to the increase of the ground motion, and the increase rate improved with the ground motion's increasing. But the increase rate at middle column was greater than the side columns relatively to horizontal excitations only. That is, the effect of vertical shock was greater on middle column than on side columns. The relative changing rate of peak axial force of middle column was15.4%. So the vertical excitation could not be ignored for the structure's internal force response. However, the relative difference of peak displacement at bottom storey was only3.0%in the large intensity (ah=0.45g, av=0.29g). Therefore, the effect of vertical excitation could be ignored for the lateral displacement.
本论文以底框砌体房屋为例,对框架柱的变轴力影响问题进行研究。
(1)介绍和采用多弹簧模型,并编制动力分析程序。通过文献试验对比验证了该模型具有较高的精度,所编制的程序是可靠、有效的；
(2)对一栋6层底框架房屋在4种不同水平地震强度下进行动力分析,得到各底框柱的最大轴力随地震动增加均有一定幅度的提高,其提高幅度随地震动强度的增大而增大,边柱的增长幅度明显高于中柱,在不同地震动输入下中底框柱轴力变化幅度约为边柱的37%-55%。结构进入屈服状态时,中柱在正反两个方向上的屈服强度值基本接近,而边柱在其正反两个方向上的屈服强度由于受变轴力影响存在明显不同,相差接近30%。故变轴力影响不可忽略；
(3)底框架结构在变轴力影响下,其底层框架的最大位移和最大剪力均比层间模型的结果小,二者的差别随水平地震强度的增加而增大；
(4)对4层、6层、8层底框架结构进行动力分析,得到随结构层数的增加,各底框柱的轴力变化幅度有增大趋势,中柱轴力相对于边柱的变化缓慢。结构进入屈服状态时,随结构层数的增加,左、右边柱正反两向的屈服强度差别增大；
(5)对6层底框架房屋在水平地震作用和水平、竖直(av=2/3ah)地震同时作用下的动力响应进行对比,得到水平、竖直地震同时作用下的各柱轴力变化幅度随地震强度的增大呈增大趋势,但中柱的轴力变化幅度相对于仅水平地震作用时大于左、右边柱,即竖向地震作用对中柱的影响大于边柱,中柱最大轴力变化为15.4%。因此,竖向地震对结构内力响应的影响不可忽略。但结构处于大震时底层最大位移差别仅为3.0%(ah=0.45gav=0.29g),故其对结构的侧移影响可忽略不计。
In building constructions the overturning moment caused by horizontal earthquake is the main source for the additional axial force of the bottom frame columns. Generally, the additional axial force is changing all the time and is not proportional to the horizontal seismic shear when the structure is in nonlinear stage. The variable axial force not only changes the bending capacity, shear strength and deformability of members, but also the hysteretic behaviors. Therefore, how to consider the effects of the variable axial force reasonably is one of the concerned issues in the nonlinear dynamic seismic analysis.
Taking the frame-supported masonry buildings as examples, the effects of variable axial force in frame columns were studied in this paper.
(1) The multi-spring model was introduced and a dynamic analysis program was coded using the model. Comparisons to some literature experimental results showed the multi-spring model was accurate relatively and the program was reliable and effective.
(2) Dynamic analysis for a six-storey frame-supported masonry building was performed in four different levels of horizontal earthquake intensity. It showed the peak axial force at all bottom frame columns had a certain increase according to the increase of the ground motion, and the increase rate improved with the ground motion's increasing. The increase at side columns was obviously larger than that at the middle column, the increase of variable axial force at middle frame column was about37%-55%to the increase at side frame columns in different seismic intensity. The yielding strength of middle frame column at yielding stage was close in both positive and negative direction, but the strength of side columns were obviously different in the opposite directions because of the variable axial force effect, the difference was nearly30%. Therefore, the influence of variable axial force could not be ignored.
(3) The maximum displacement and maximum shear at bottom story of frame supported building were smaller than the storey-model's results due to the effect of the variable axial force. The difference increased with the horizontal seismic intensity increasing.
(4) The dynamic analysis was conducted for frame supported buildings with four-storey, six-storey, and eight-storey. It indicated the changing rate of the variable axial force of each column had an increasing trend to the increase of building stories. The middle column's changing rate was smaller relatively than the side columns'. After the structure's yielding, the difference of3d elding strength of side columns in positive direction to negative direction increased with the story's increasing.
(5) Comparison of dynamic response of six-storey structure was done between in horizontal shock and that with vertical shock (av=2/3ah). It showed the peak axial force at all bottom frame columns under horizontal and vertical excitations increased according to the increase of the ground motion, and the increase rate improved with the ground motion's increasing. But the increase rate at middle column was greater than the side columns relatively to horizontal excitations only. That is, the effect of vertical shock was greater on middle column than on side columns. The relative changing rate of peak axial force of middle column was15.4%. So the vertical excitation could not be ignored for the structure's internal force response. However, the relative difference of peak displacement at bottom storey was only3.0%in the large intensity (ah=0.45g, av=0.29g). Therefore, the effect of vertical excitation could be ignored for the lateral displacement.
引文
[1]张之立,李钦祖,谷继成,靳雅敏,杨懋源,刘万琴.唐山地震的破裂过程及其力学分析[J].地震学报,1980,2(2):111-129.
[2]李翔;吕西林;李建中.汶川地震中广元市底层框架结构房屋震害调查与分析[J].结构工程师,2008,24(3)：12-15.
[3]薛素铎,赵均,高向宇.建筑抗震设计(第二版)[M].科学出版社,2007.
[4]王光远.建筑物所受地震力的计算方法[J].土木工程学报,1958,5(2)：107-122.
[5]刘俊玲.静力弹塑性分析方法的研究与应用[J].低温建筑技术,2005,2：39-40.
[6]陈功.静力弹塑性Pushover分析方法在高层建筑结构中的应用[D].成都：西南交通大学,2008.
[7]陈爱君.时程分析中计算结构动力响应的小波分析方法[D].西安：西安建筑科技大学,2008.
[8]黄尚安.底部框剪配筋砌块砌体房屋抗震设计研究[D].长沙：湖南大学,2005.
[9]Gu Jianhua. Inelastic earthquake response analysis of RC frames with shear walls under two ground motion components in horizontal and vertical direction[D]. Sendai:Tohuku University,1998.
[10]M. Al. Saadeghvziri. Nonlinear response and modeling of RC columns subjected to varying axial load[J], Engineering Structures,1997,19 (6):417-424.
[11]杨红,白绍良.基于结构弹塑性地震反应的柱变轴力加载方法研究[J].世界地震工程,2002,18(2)：80-84.
[12]杨红,白绍良.基于变轴力和定轴力试验对比的钢筋混凝土柱恢复力滞回特性研究[J].工程力学,2003,20(6)：58-64.
[13]王建平.考虑变轴力影响的钢筋混凝土柱滞回特性研究[J].山西建筑,2008,34(27)107-108.
[14]钮忠华.考虑变化轴力的钢筋混凝十截面非线性分析[D].重庆：重庆大学,2004.
[15]陈以一,刘永明,岳吕智.基于变轴力柱恢复力模型的钢框筒地震反应分析[J].时间界地震工程,2000,16(4)：47-52.
[16]汪训流,陆新征,叶列平.变轴力下钢筋混凝土柱的抗震性能分析[J].工业建筑,2007,37(12)：71-75.
[17]江近仁,康慨,张令心.钢筋混凝土柱的双轴弯曲特性[J].世界地震工程,1998,14(4)23-29.
[18]黄翔.规则变轴力下钢筋硂框架柱的抗震性能研究[J].福建建筑,2003,3:46-48.
[19]耿继国,李力.钢筋混凝土构件变轴力恢复力模型[J].四川建筑,2005,25(6)：106-108.
[20]刑秋顺,继耀东,陈肇元.变轴力下钢筋硂受弯截面的性能[J].建筑结构学报,1987,5:52-61.
[21]党育,霍凯成.多层隔震结构的竖向地震作用研究[J].地震工程与工程振动,2010,30(4)：139-145.
[22]王涛.竖向地震的若干问题研究[J].河南城建学院学报,2010,19(2)：21-26.
[23]辛娅云.竖向地震作用的重要性[J].工程抗震与加固改造,2005,27:48-50.
[24]陈念英,从日本阪神地震再谈竖向地震作用的重要性[J],成都大学学报(自然科学版)1996,15(1)：56-59.
[25]李宏男,王强,李兵.钢筋混凝土框架柱多维恢复力特性的试验研究[J].东南大学学报,2002,32(5)：728-732.
[26]邱法维,李文峰,潘鹏.钢筋混凝士柱的双向拟静力实验研究[J].建筑结构学报,2001,22(5)：26-31.
[27]彭成军.钢管混凝土底框架砌体建筑的抗震性能[J].辽宁建材,2004,2：66-69.
[28]赵世春,黄雄军,路湛沁.劲性钢筋混凝土柱基本抗震行为的试验研究[J].建筑结构学报,1996,17(3)：43-51.
[29]徐亚丰,王连广,陈兆才,等.钢骨高强混凝土框架节点恢复力模型的研究[J].兰州理工大学学报,2004,30(5)：462-464.
[30]钱培风.竖向地震力和抗震砌块建筑[M].中国大地出版社,1997.唐成欢.带高位二次转换层建筑结构弹塑性分析[D].长沙：中南大学,2008.
[2]李翔;吕西林;李建中.汶川地震中广元市底层框架结构房屋震害调查与分析[J].结构工程师,2008,24(3)：12-15.
[3]薛素铎,赵均,高向宇.建筑抗震设计(第二版)[M].科学出版社,2007.
[4]王光远.建筑物所受地震力的计算方法[J].土木工程学报,1958,5(2)：107-122.
[5]刘俊玲.静力弹塑性分析方法的研究与应用[J].低温建筑技术,2005,2：39-40.
[6]陈功.静力弹塑性Pushover分析方法在高层建筑结构中的应用[D].成都：西南交通大学,2008.
[7]陈爱君.时程分析中计算结构动力响应的小波分析方法[D].西安：西安建筑科技大学,2008.
[8]黄尚安.底部框剪配筋砌块砌体房屋抗震设计研究[D].长沙：湖南大学,2005.
[9]Gu Jianhua. Inelastic earthquake response analysis of RC frames with shear walls under two ground motion components in horizontal and vertical direction[D]. Sendai:Tohuku University,1998.
[10]M. Al. Saadeghvziri. Nonlinear response and modeling of RC columns subjected to varying axial load[J], Engineering Structures,1997,19 (6):417-424.
[11]杨红,白绍良.基于结构弹塑性地震反应的柱变轴力加载方法研究[J].世界地震工程,2002,18(2)：80-84.
[12]杨红,白绍良.基于变轴力和定轴力试验对比的钢筋混凝土柱恢复力滞回特性研究[J].工程力学,2003,20(6)：58-64.
[13]王建平.考虑变轴力影响的钢筋混凝土柱滞回特性研究[J].山西建筑,2008,34(27)107-108.
[14]钮忠华.考虑变化轴力的钢筋混凝十截面非线性分析[D].重庆：重庆大学,2004.
[15]陈以一,刘永明,岳吕智.基于变轴力柱恢复力模型的钢框筒地震反应分析[J].时间界地震工程,2000,16(4)：47-52.
[16]汪训流,陆新征,叶列平.变轴力下钢筋混凝土柱的抗震性能分析[J].工业建筑,2007,37(12)：71-75.
[17]江近仁,康慨,张令心.钢筋混凝土柱的双轴弯曲特性[J].世界地震工程,1998,14(4)23-29.
[18]黄翔.规则变轴力下钢筋硂框架柱的抗震性能研究[J].福建建筑,2003,3:46-48.
[19]耿继国,李力.钢筋混凝土构件变轴力恢复力模型[J].四川建筑,2005,25(6)：106-108.
[20]刑秋顺,继耀东,陈肇元.变轴力下钢筋硂受弯截面的性能[J].建筑结构学报,1987,5:52-61.
[21]党育,霍凯成.多层隔震结构的竖向地震作用研究[J].地震工程与工程振动,2010,30(4)：139-145.
[22]王涛.竖向地震的若干问题研究[J].河南城建学院学报,2010,19(2)：21-26.
[23]辛娅云.竖向地震作用的重要性[J].工程抗震与加固改造,2005,27:48-50.
[24]陈念英,从日本阪神地震再谈竖向地震作用的重要性[J],成都大学学报(自然科学版)1996,15(1)：56-59.
[25]李宏男,王强,李兵.钢筋混凝土框架柱多维恢复力特性的试验研究[J].东南大学学报,2002,32(5)：728-732.
[26]邱法维,李文峰,潘鹏.钢筋混凝士柱的双向拟静力实验研究[J].建筑结构学报,2001,22(5)：26-31.
[27]彭成军.钢管混凝土底框架砌体建筑的抗震性能[J].辽宁建材,2004,2：66-69.
[28]赵世春,黄雄军,路湛沁.劲性钢筋混凝土柱基本抗震行为的试验研究[J].建筑结构学报,1996,17(3)：43-51.
[29]徐亚丰,王连广,陈兆才,等.钢骨高强混凝土框架节点恢复力模型的研究[J].兰州理工大学学报,2004,30(5)：462-464.
[30]钱培风.竖向地震力和抗震砌块建筑[M].中国大地出版社,1997.唐成欢.带高位二次转换层建筑结构弹塑性分析[D].长沙：中南大学,2008.