钢筋混凝土矩形桥墩开裂刚度理论初探
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摘要
地震是人类面临的最严重自然灾害之一。地震发生后,公路路网作为抗震救灾的生命线,对运送救灾物资、设备起着至关重要的作用,而公路桥梁往往占据路网中的咽喉部位,同时也是地震中极易遭到破坏的部分。因此,桥梁的抗震设计就显得格外重要。对一般桥梁而言,桥墩的抗震性能对全桥的抗震性能起着控制作用。地震荷载作用下,钢筋混凝土桥墩通常处于带裂缝工作状态,其刚度分布特性对研究桥梁的总体受力与变形有着重要影响。本论文以桥梁墩柱构件为研究对象,初步分析了墩柱构件在地震力作用下各截面抗弯刚度的分布情况以及其开裂刚度的计算方法,为桥梁延性抗震设计及相关研究提供参考。
本论文以双筋矩形混凝土墩柱构件为对象,从基本的力学概念出发,初步讨论了构件在弹性范围内,构件受弯开裂时的各截面受压区高度与刚度的分布特性。并以此为基础,首次提出了混凝土受弯构件开裂刚度的“三段式”刚度分析法,并给出了相应的计算方法与计算步骤。
通过使用“三段式”刚度分析法对墩柱构件各截面进行等效抗弯刚度分析后,本论文得出如下几点结论:
(1)对于无轴向力的受弯构件,各截面中性轴关于墩高方向呈直线分布,其开裂刚度可通过截面特性求解,且各个截面的抗弯刚度为只与构件的材料与截面特性有关,而与外力的大小无关的常数;而对于压弯构件,各截面的中性轴关于墩高方向的分布函数不再是一条直线,如果不对中性轴分布曲线进行一定的简化,求解各截面的抗弯刚度较为困难。同时,对于受弯构件,增大其纵筋率和适当增大轴向压力,会使构件的开裂刚度增加,反之则减小。
(2)对于压弯构件,其中性轴分布曲线c = f(z)有z = 0与c = c0两条渐近线。通过压弯构件中性轴分布曲线与截面抗弯刚度的性质,提出“三段式”刚度分析法的计算理念,即将压弯构件分为全截面刚度段、开裂刚度段与最小刚度段三部分,分别对各段刚度进行计算。
(3)三个刚度段的抗弯刚度的计算方法为:第I段,其抗弯刚度为全截面抗弯刚度;第II段,使用一条或多条割线模拟中性轴的分布曲线,再通过各截面的中性轴位置计算其抗弯刚度;第III段,将各截面的抗弯刚度看作定值,认为该段各截面的受压区高度为该墩在无轴压时的受压区高度的两倍,即c = 2c0,再根据其截面形式计算其开裂刚度。
(4)三个刚度段的分界截面的计算方法为:I、II段的分界点z0截面的确定方法比较简单,只需找到构件中受拉区应力为0的截面即可解出z0;而II、III段的分界截面z1的确定,本论文推荐的方法为在构件中受压区高度c = 2c0的截面为z1截面。
(5)对于低配筋率或高轴压比的墩柱构件,当墩底截面达到屈服弯矩My时,以c = 2c0的标准划分构件中的第II、III段,也有可能不出现第III段最小刚度段。
(6)针对“三段式”刚度分析法的计算特点所编制的力-位移曲线的计算程序,能有效地反应压弯墩柱构件在弹性范围内逐步加载的刚度变化过程。
“三段式”刚度分析法的提出与相关的研究工作,对研究压弯构件的受力性能分析与延性能力计算提供了一个新的计算思路,部分弥补了现今的刚度计算理论中理论基础薄弱的缺点。同时,对钢筋混凝土墩柱构件等效刚度的相关理论研究及试验研究工作也具有一定的参考价值。
The earthquake is one of the most serious natural disasters in the world. And the highway network, as a lifeline of relief work, plays a very important role in the transportation of materials and equipments. The highway bridge is critical position among the network as well as the part that is easily broken when the earthquake comes. Therefore, the seismic design of bridge is important for the highway network especially.
The seismic design of the pier governs the whole bridge’s seismic performance. Under the action of seismic load, the reinforced concrete works in the state of cracks, and its stiffness distribution has influenced the stress and deformation of the bridge. In this paper, based on the concrete column members, the flexural stiffness distribution of them and the algorithmic method of cracked section stiffness by the action of the earthquake were analyzed. Hence, this paper can provide a reference for the seismic ductile design and relative researches.
Based on the concepts of the mechanics and the dimensionless analysis, this paper, targeting at the bi-reinforced rectangular concrete column, discusses the depth of compression zone and properties of the rigidity distribution in the elastic range. And then, an analogue method called "three-phase method" which is studied on the post-cracking flexural stiffness of concrete flexural members, is theoretically presented forward in the paper for the first time, as well as its algorithmic method and procedure are introduced.
With the analysis of the“three-phase method”, conclusions are in this paper as follows:
1. For the bending members without axial force, the cracking stiffness is only relative to the materials and sectional characteristics, but has nothing to do with the external force degree. To increase the ratio of longitudinal reinforcement or the axial pressure properly to the compression-bending member, the cracking stiffness will also increase; on the contrary, it will decrease.
2. For the compression-bending member, its neutral axis distribution curve c = f (z) includes two asymptotes: z = 0 and c = c0. Based on the neutral axis distribution and properties of flexural stiffness, the concept of“three-phase method”is proposed in this paper. That is, the compression-bending member is separated to three parts: full section stiffness, cracked section stiffness and minimum stiffness, and, by the“three-phase method”, which are calculated respectively.
3. The three segment of algorithmic method of flexural stiffness are as following: I: the flexural stiffness of total cross section; II: to use one or more than one secants as the distribution curve of the neutral axis, then to calculate the flexural stiffness by deciding the position of neutral axises of these sections; III: regarding the different sections’flexural rigidity as a constant. To take the depth of compression of the different sections should be twice as high as it is pressed without axial force. that is , c = 2c0, and then to calculate the cracked section stiffness according to the sectional types.
4. The demarcation section of the three parts: it is indeed easy to define the demarcation point section of I and II part. However, the demarcation point section between II and III seems a little difficult to find. The paper recommends the section of c = 2c0 is section z1.
5. for the low reinforcement ratio or high axial compression ratio pier column, when section reaches a certain yield moment My, the II and III part is divided by c = 2c0 (it is also possible that the minimums part won’t be presented).
6. The computational procedure of force-displacement curve can efficiently reflect the changing process of stiffness of pier column members with loading steps.
The proposition and study of the "three-phase method" provide a totally new calculation idea of the analysis of mechanical behavior and ductile capacity, and compensate for the disadvantages of theory of stiffness calculation. Meanwhile, it is of a great reference value in the study of effective stiffness of reinforced concrete column members.
本论文以双筋矩形混凝土墩柱构件为对象,从基本的力学概念出发,初步讨论了构件在弹性范围内,构件受弯开裂时的各截面受压区高度与刚度的分布特性。并以此为基础,首次提出了混凝土受弯构件开裂刚度的“三段式”刚度分析法,并给出了相应的计算方法与计算步骤。
通过使用“三段式”刚度分析法对墩柱构件各截面进行等效抗弯刚度分析后,本论文得出如下几点结论:
(1)对于无轴向力的受弯构件,各截面中性轴关于墩高方向呈直线分布,其开裂刚度可通过截面特性求解,且各个截面的抗弯刚度为只与构件的材料与截面特性有关,而与外力的大小无关的常数;而对于压弯构件,各截面的中性轴关于墩高方向的分布函数不再是一条直线,如果不对中性轴分布曲线进行一定的简化,求解各截面的抗弯刚度较为困难。同时,对于受弯构件,增大其纵筋率和适当增大轴向压力,会使构件的开裂刚度增加,反之则减小。
(2)对于压弯构件,其中性轴分布曲线c = f(z)有z = 0与c = c0两条渐近线。通过压弯构件中性轴分布曲线与截面抗弯刚度的性质,提出“三段式”刚度分析法的计算理念,即将压弯构件分为全截面刚度段、开裂刚度段与最小刚度段三部分,分别对各段刚度进行计算。
(3)三个刚度段的抗弯刚度的计算方法为:第I段,其抗弯刚度为全截面抗弯刚度;第II段,使用一条或多条割线模拟中性轴的分布曲线,再通过各截面的中性轴位置计算其抗弯刚度;第III段,将各截面的抗弯刚度看作定值,认为该段各截面的受压区高度为该墩在无轴压时的受压区高度的两倍,即c = 2c0,再根据其截面形式计算其开裂刚度。
(4)三个刚度段的分界截面的计算方法为:I、II段的分界点z0截面的确定方法比较简单,只需找到构件中受拉区应力为0的截面即可解出z0;而II、III段的分界截面z1的确定,本论文推荐的方法为在构件中受压区高度c = 2c0的截面为z1截面。
(5)对于低配筋率或高轴压比的墩柱构件,当墩底截面达到屈服弯矩My时,以c = 2c0的标准划分构件中的第II、III段,也有可能不出现第III段最小刚度段。
(6)针对“三段式”刚度分析法的计算特点所编制的力-位移曲线的计算程序,能有效地反应压弯墩柱构件在弹性范围内逐步加载的刚度变化过程。
“三段式”刚度分析法的提出与相关的研究工作,对研究压弯构件的受力性能分析与延性能力计算提供了一个新的计算思路,部分弥补了现今的刚度计算理论中理论基础薄弱的缺点。同时,对钢筋混凝土墩柱构件等效刚度的相关理论研究及试验研究工作也具有一定的参考价值。
The earthquake is one of the most serious natural disasters in the world. And the highway network, as a lifeline of relief work, plays a very important role in the transportation of materials and equipments. The highway bridge is critical position among the network as well as the part that is easily broken when the earthquake comes. Therefore, the seismic design of bridge is important for the highway network especially.
The seismic design of the pier governs the whole bridge’s seismic performance. Under the action of seismic load, the reinforced concrete works in the state of cracks, and its stiffness distribution has influenced the stress and deformation of the bridge. In this paper, based on the concrete column members, the flexural stiffness distribution of them and the algorithmic method of cracked section stiffness by the action of the earthquake were analyzed. Hence, this paper can provide a reference for the seismic ductile design and relative researches.
Based on the concepts of the mechanics and the dimensionless analysis, this paper, targeting at the bi-reinforced rectangular concrete column, discusses the depth of compression zone and properties of the rigidity distribution in the elastic range. And then, an analogue method called "three-phase method" which is studied on the post-cracking flexural stiffness of concrete flexural members, is theoretically presented forward in the paper for the first time, as well as its algorithmic method and procedure are introduced.
With the analysis of the“three-phase method”, conclusions are in this paper as follows:
1. For the bending members without axial force, the cracking stiffness is only relative to the materials and sectional characteristics, but has nothing to do with the external force degree. To increase the ratio of longitudinal reinforcement or the axial pressure properly to the compression-bending member, the cracking stiffness will also increase; on the contrary, it will decrease.
2. For the compression-bending member, its neutral axis distribution curve c = f (z) includes two asymptotes: z = 0 and c = c0. Based on the neutral axis distribution and properties of flexural stiffness, the concept of“three-phase method”is proposed in this paper. That is, the compression-bending member is separated to three parts: full section stiffness, cracked section stiffness and minimum stiffness, and, by the“three-phase method”, which are calculated respectively.
3. The three segment of algorithmic method of flexural stiffness are as following: I: the flexural stiffness of total cross section; II: to use one or more than one secants as the distribution curve of the neutral axis, then to calculate the flexural stiffness by deciding the position of neutral axises of these sections; III: regarding the different sections’flexural rigidity as a constant. To take the depth of compression of the different sections should be twice as high as it is pressed without axial force. that is , c = 2c0, and then to calculate the cracked section stiffness according to the sectional types.
4. The demarcation section of the three parts: it is indeed easy to define the demarcation point section of I and II part. However, the demarcation point section between II and III seems a little difficult to find. The paper recommends the section of c = 2c0 is section z1.
5. for the low reinforcement ratio or high axial compression ratio pier column, when section reaches a certain yield moment My, the II and III part is divided by c = 2c0 (it is also possible that the minimums part won’t be presented).
6. The computational procedure of force-displacement curve can efficiently reflect the changing process of stiffness of pier column members with loading steps.
The proposition and study of the "three-phase method" provide a totally new calculation idea of the analysis of mechanical behavior and ductile capacity, and compensate for the disadvantages of theory of stiffness calculation. Meanwhile, it is of a great reference value in the study of effective stiffness of reinforced concrete column members.
引文
[1]卢寿德,李小军.汶川8.0级地震未校正加速度记录:中国强震记录汇报.地震出版社.2008
[2]中华人民共和国交通运输部.汶川地震公路震害调查图集.人民交通出版社.2009
[3]交通部公路规划设计院. JTJ 021-89.公路桥涵设计通用规范.北京.人民交通出版社. 1989
[4]郭磊,李建中,范立础.桥梁结构抗震设计中截面刚度的取值分析.同济大学学报(自然科学版) .2004.32(11) .1423-1427
[5]范立础,卓卫东.桥梁延性抗震设计.人民交通出版社.2001
[6]范立础.桥梁抗震.同济大学出版社.1996
[7] CEN.Eurcode8-Design Provisions for Earthquake Resistance of Structures, Part2: Bridges. Committee European De Normalization(CEN) .1998
[8] California Department of Transportation (CALTRANS). Seismic Design Criteria,Version1.4. California.2006
[9]日本道路协会.道路桥示方书?同解说,V耐震设计篇.东京.平成14年3月
[10]重庆交通科研设计院. JTG/T B02-01-2008.公路桥梁抗震设计细则.北京.人民交通出版社.2008
[11]钢筋混凝土小偏心受压构件的曲率、刚度和杆端转角.同济大学科学技术情报组编印.1973-4
[12]南京工学院工民建专业刚度裂缝科研小组.钢筋混凝土构件刚度和裂缝的计算.南京工学院学报土木工程专集. 1979
[13]南京工学院第五系.钢筋混凝土偏心受力构件刚度计算初探(初稿).1977
[14]丁大钧等.钢筋混凝土矩形截面偏心受压构件刚度裂缝的试验研究.南京工学院.1979-9
[15]四川省建筑科学研究所.钢筋混凝土屋架考虑非弹性的试验分析及刚度计算.1979-12
[16] Mehanny,S.S.F.Modeling and Assessment of Seismic Performance of Composite Frames with Reinforced Concrete Columns and Steel Beams. Dissertation. Department of Civil and Environmental Engineering, Stanford University.1999
[17] Panagiotakos, T. B. and Fardis, M. N.Deformations of Reinforced Concrete at Yielding and Ultimate.ACI Structural Journal.2001.Vol. 98, No. 2.135-147
[18] K.J. Elwood,M.O. Eberhard. Effective Stiffness of Reinforced Concrete Columns.PEER Research Digest 2006-1.2006
[19] Curt B. Haselton, Abbie B. Liel, Sarah Taylor Lange, and Gregory g.Beam-Column Element Model Calibrated for Predicting Flexural Response Leading to Global Collapse of RC Frame Buildings.PEER Research Report.University of California-Berkeley.May 2008
[20] Micheal P.Berry, Dawn E.Lehman, Laura N.Lowes.Lumped-Plasticity Models for Performance Simulation of bridge columns.ACI Structure Journal.2008.V.105,No.3.270-279
[21] American Society of Civil Engineers.FEMA 356: Prestandard and Commentary for the Seismic Rehabilitation of Buildings.Federal Emergency Management Agency.Washington.2000
[22] http://www.usc.edu/dept/civil_eng/structure_lab/asad/usc_rc.htm
[23] http://opensees.berkeley.edu
[24] R.帕克,T.波利.秦文钺译.钢筋混凝土结构.重庆大学出版社.1986
[25] S.P.铁摩辛柯,J.M.格尔.李春亮译.材料力学.第二版.晓园出版社.1985
[26] WAI-FAN CHEN. Theory of Beam-Columns,VOLUME 1:In-Plane Behavior and Design. McGraw-Hill. 1976
[27]李丽,王振领. MATLAB工程计算及应用.人民邮电出版社.2001
[28] http://www.mathworks.com
[29] Robert L. Taylor.FEAP - A Finite Element Analysis Program.Version 8.2 User Manual. University of California-Berkeley.2008
[30]中交公路规划设计院.JTJ D62-2004.公路钢筋混凝土及预应力混凝土桥涵设计规范.北京.人民交通出版社.2004
[2]中华人民共和国交通运输部.汶川地震公路震害调查图集.人民交通出版社.2009
[3]交通部公路规划设计院. JTJ 021-89.公路桥涵设计通用规范.北京.人民交通出版社. 1989
[4]郭磊,李建中,范立础.桥梁结构抗震设计中截面刚度的取值分析.同济大学学报(自然科学版) .2004.32(11) .1423-1427
[5]范立础,卓卫东.桥梁延性抗震设计.人民交通出版社.2001
[6]范立础.桥梁抗震.同济大学出版社.1996
[7] CEN.Eurcode8-Design Provisions for Earthquake Resistance of Structures, Part2: Bridges. Committee European De Normalization(CEN) .1998
[8] California Department of Transportation (CALTRANS). Seismic Design Criteria,Version1.4. California.2006
[9]日本道路协会.道路桥示方书?同解说,V耐震设计篇.东京.平成14年3月
[10]重庆交通科研设计院. JTG/T B02-01-2008.公路桥梁抗震设计细则.北京.人民交通出版社.2008
[11]钢筋混凝土小偏心受压构件的曲率、刚度和杆端转角.同济大学科学技术情报组编印.1973-4
[12]南京工学院工民建专业刚度裂缝科研小组.钢筋混凝土构件刚度和裂缝的计算.南京工学院学报土木工程专集. 1979
[13]南京工学院第五系.钢筋混凝土偏心受力构件刚度计算初探(初稿).1977
[14]丁大钧等.钢筋混凝土矩形截面偏心受压构件刚度裂缝的试验研究.南京工学院.1979-9
[15]四川省建筑科学研究所.钢筋混凝土屋架考虑非弹性的试验分析及刚度计算.1979-12
[16] Mehanny,S.S.F.Modeling and Assessment of Seismic Performance of Composite Frames with Reinforced Concrete Columns and Steel Beams. Dissertation. Department of Civil and Environmental Engineering, Stanford University.1999
[17] Panagiotakos, T. B. and Fardis, M. N.Deformations of Reinforced Concrete at Yielding and Ultimate.ACI Structural Journal.2001.Vol. 98, No. 2.135-147
[18] K.J. Elwood,M.O. Eberhard. Effective Stiffness of Reinforced Concrete Columns.PEER Research Digest 2006-1.2006
[19] Curt B. Haselton, Abbie B. Liel, Sarah Taylor Lange, and Gregory g.Beam-Column Element Model Calibrated for Predicting Flexural Response Leading to Global Collapse of RC Frame Buildings.PEER Research Report.University of California-Berkeley.May 2008
[20] Micheal P.Berry, Dawn E.Lehman, Laura N.Lowes.Lumped-Plasticity Models for Performance Simulation of bridge columns.ACI Structure Journal.2008.V.105,No.3.270-279
[21] American Society of Civil Engineers.FEMA 356: Prestandard and Commentary for the Seismic Rehabilitation of Buildings.Federal Emergency Management Agency.Washington.2000
[22] http://www.usc.edu/dept/civil_eng/structure_lab/asad/usc_rc.htm
[23] http://opensees.berkeley.edu
[24] R.帕克,T.波利.秦文钺译.钢筋混凝土结构.重庆大学出版社.1986
[25] S.P.铁摩辛柯,J.M.格尔.李春亮译.材料力学.第二版.晓园出版社.1985
[26] WAI-FAN CHEN. Theory of Beam-Columns,VOLUME 1:In-Plane Behavior and Design. McGraw-Hill. 1976
[27]李丽,王振领. MATLAB工程计算及应用.人民邮电出版社.2001
[28] http://www.mathworks.com
[29] Robert L. Taylor.FEAP - A Finite Element Analysis Program.Version 8.2 User Manual. University of California-Berkeley.2008
[30]中交公路规划设计院.JTJ D62-2004.公路钢筋混凝土及预应力混凝土桥涵设计规范.北京.人民交通出版社.2004