非均布荷载作用下钢筋混凝土板力学性能分析
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摘要
板上直接承受集中荷载和线荷载越来越多的出现在工程实际中,但可供工程设计直接采用的资料却不多。所以对板在线荷载和集中荷载作用下力学性能的分析具有重要理论意义和工程参考价值。
本文在传统板壳理论的基础上,以四边固支的钢筋混凝土薄板为研究对象,运用有限元分析方法,对正常使用阶段,承受集中荷载和线荷载的钢筋混凝土四边固支薄板进行受力性能分析。本论文的主要工作如下:
(1)在理论的基础上,建立了钢筋混凝土板在线荷载和集中荷载下的有限元分析模型,并将有限元计算结果与SlabCAD的计算结果进行对比,发现两者的变化趋势一致,且吻合较好。研究表明,将隔墙荷载简化成线荷载是满足工程要求的,本文所建立的有限元模型是正确的。
(2)运用有限元软件分析了板的几何尺寸对弯矩和挠度的影响,得出板的弯矩系数和挠度系数与板的边长及边长比的关系,板的弯矩和挠度与板厚的关系;分析了弹性模量、泊松比等因素对弯矩和挠度的影响,这与均布荷载作用下结论相同;分析线荷载和集中荷载作用在不同位置时板的变形,寻找出荷载的最不利位置。
由变形图得出在线荷载和集中荷载作用下板薄弱部位,依据大量的数据进行回归分析得线荷载作用下弯矩和挠度的计算表格;得出线荷载和集中荷载下的板都是双向受力的,线荷载作用下的正方形板纵横弯矩不等,这与均布荷载作用下的板有区别;根据本文的结果,可以快速计算出非均布荷载下的弯矩和挠度,并进行挠度验证。本文的研究成果具有一定的理论意义和工程参考价值。
It is more and more common that slabs bear the force of concentrated or linear load directly, but there are no materials which can be adopted directly by engineering design at present. Therefore, it is of great theoretical importance and engineering value to analyze the physical function of slabs under the effect of linear load and concentrated load.
Based on traditional theory of plate and shell, with reinforced concrete slabs fixed at four sides as research subjects, this thesis has analyzed the loaded property of reinforced concrete slabs fixed at four sides in the stage of normal use with a method of finite element analysis. The thesis includes:
(1) Under the guide of the theory, the thesis has set up a model of finite element analysis which studies reinforced concrete slabs forced by linear or concentrated load, and made a comparison between the results of finite element data analysis and SlabCAD calculation, concluding that both change in the same direction and match well with each other. The study shows that to simplify partition wall load as linear load complies with the requirement of project and the finite element model set up in this thesis is correct.
(2) The thesis has analyzed the influence that the physical dimension of slabs has on bending moment and deflection and come up with the relationships between coefficient of bending moment or deflection and the ratio of sides, and the relationships between bending moment or deflection and thickness of slabs .Besides, this thesis has analyzed the influence of elements such as elastic modulus, Poisson ratio on bending moment and deflection, which is nearly the same as the conclusion drawn from the study on uniform load. Furthermore, it has analyzed the deformation of slabs in different position under the force of linear load and concentrated load and found out the most unfavorable position of load.
The weak points of slabs under the force of linear load and concentrated load are found out by deformation chart; the calculation form of bending moment and deflection under the force of linear load is set by regression analysis according to large numbers of data; the conclusion that both linear load and concentrated load are two-way slabs, and the bending moment of square slab under the force of linear load is not the same in length and width, which are different from that of uniform load, is drawn in this thesis. According to this thesis, the bending moment and deflection under the force of non-uniform load can be calculated quickly and the deflection can be verified. This thesis is of theoretical importance and reference value of engineering.
本文在传统板壳理论的基础上,以四边固支的钢筋混凝土薄板为研究对象,运用有限元分析方法,对正常使用阶段,承受集中荷载和线荷载的钢筋混凝土四边固支薄板进行受力性能分析。本论文的主要工作如下:
(1)在理论的基础上,建立了钢筋混凝土板在线荷载和集中荷载下的有限元分析模型,并将有限元计算结果与SlabCAD的计算结果进行对比,发现两者的变化趋势一致,且吻合较好。研究表明,将隔墙荷载简化成线荷载是满足工程要求的,本文所建立的有限元模型是正确的。
(2)运用有限元软件分析了板的几何尺寸对弯矩和挠度的影响,得出板的弯矩系数和挠度系数与板的边长及边长比的关系,板的弯矩和挠度与板厚的关系;分析了弹性模量、泊松比等因素对弯矩和挠度的影响,这与均布荷载作用下结论相同;分析线荷载和集中荷载作用在不同位置时板的变形,寻找出荷载的最不利位置。
由变形图得出在线荷载和集中荷载作用下板薄弱部位,依据大量的数据进行回归分析得线荷载作用下弯矩和挠度的计算表格;得出线荷载和集中荷载下的板都是双向受力的,线荷载作用下的正方形板纵横弯矩不等,这与均布荷载作用下的板有区别;根据本文的结果,可以快速计算出非均布荷载下的弯矩和挠度,并进行挠度验证。本文的研究成果具有一定的理论意义和工程参考价值。
It is more and more common that slabs bear the force of concentrated or linear load directly, but there are no materials which can be adopted directly by engineering design at present. Therefore, it is of great theoretical importance and engineering value to analyze the physical function of slabs under the effect of linear load and concentrated load.
Based on traditional theory of plate and shell, with reinforced concrete slabs fixed at four sides as research subjects, this thesis has analyzed the loaded property of reinforced concrete slabs fixed at four sides in the stage of normal use with a method of finite element analysis. The thesis includes:
(1) Under the guide of the theory, the thesis has set up a model of finite element analysis which studies reinforced concrete slabs forced by linear or concentrated load, and made a comparison between the results of finite element data analysis and SlabCAD calculation, concluding that both change in the same direction and match well with each other. The study shows that to simplify partition wall load as linear load complies with the requirement of project and the finite element model set up in this thesis is correct.
(2) The thesis has analyzed the influence that the physical dimension of slabs has on bending moment and deflection and come up with the relationships between coefficient of bending moment or deflection and the ratio of sides, and the relationships between bending moment or deflection and thickness of slabs .Besides, this thesis has analyzed the influence of elements such as elastic modulus, Poisson ratio on bending moment and deflection, which is nearly the same as the conclusion drawn from the study on uniform load. Furthermore, it has analyzed the deformation of slabs in different position under the force of linear load and concentrated load and found out the most unfavorable position of load.
The weak points of slabs under the force of linear load and concentrated load are found out by deformation chart; the calculation form of bending moment and deflection under the force of linear load is set by regression analysis according to large numbers of data; the conclusion that both linear load and concentrated load are two-way slabs, and the bending moment of square slab under the force of linear load is not the same in length and width, which are different from that of uniform load, is drawn in this thesis. According to this thesis, the bending moment and deflection under the force of non-uniform load can be calculated quickly and the deflection can be verified. This thesis is of theoretical importance and reference value of engineering.
引文
[01]哈尔滨工业大学,大连理工大学,北京建筑工程学院等.混凝土及砌体结构[M].北京:中国建筑工业出版社,2002
[02]阿加雷A C.板壳应力[M].范钦珊译.北京:中国建筑工业出版社,1986
[03]唐锦春,郭鼎康.简明建筑结构设计手册(第二版)[M].北京:中国建筑工业出版社,1992
[04]GB50010-2002,混凝土结构设计规范[S].北京:中国建筑工业出版社,2002
[05]陈基发,沙志国.建筑结构荷载设计手册[M].北京:中国建筑工业出版社,2004
[06]《建筑结构静力计算手册》编写组.建筑结构静力计算手册[M].北京:中国建筑工业出版社,1998
[07]丁大钧.现代混凝土结构学[M].北京:中国建筑工业出版社,2000
[08]天津大学等主编.混凝土结构(上册)[M].北京:中国建筑工业出版社,1998
[09]天津大学等主编.混凝土结构(下册)[M].北京:中国建筑工业出版社,1998
[10]R·派克,W·L·根勃尔著.钢筋混凝土板[M].黄国祯,成源华译.上海:同济大学出版社,1992
[11]Park R.Reinforeed Conerete Slab[M].NewYork:Johnwiley and Sons,Inc,1980
[12][美]A.H.尼尔逊等.混凝土结构设计(第十一版).北京:中国建筑工业出版社,1991
[13]丁大钧,结构机理学—双向板的结构机理[J].工业建筑,1994.8:47-53
[14](美)R.Szilard.板的理论和分析[M].陈太平,戈鹤翔,周孝贤译.北京:中国铁道出版社,1984
[15]成祥生,应用板壳理论[M].上海:山东科学技术出版社,1989
[16]黄与宏,板结构[M].北京:人民交通出版社,1992
[I7]Timoshenko S P and woinowsky-Krieger S.Theory of Plates and Shells.New York.McGraw-Hill,1959
[18]何福保,沈亚鹏,板壳理论(第一版)[M].西安:西安交通大学出版社,1993
[19]Qian,W.Z.(钱伟长).The intrinsic theory of thin shells and plates.Quart Appl Math.1(1944),297-327;2(1994),43-59,120-135
[20]Ye Kai-yuan(叶开沅).The development of investigation of flexible structural elements in China.Proceedings of the International Conferences on Nonlinear Mechanics.Science Press.Shanghai,1985.
[21]张福范.弹性薄板[M].北京:科学出版社,1980
[22]余寿文,黄克智.考虑剪切变形的正交各向异性弹性平板的近似理论[J].力学学报,6卷4期,1963。
[23]曹志远、杨升田.厚板动力学理论及其应用[M].北京:科学出版社,1983
[24]Wang,A.J.(王仁),Hopkins H.G.Mech Phys.Solids 3.1954,22-37
[25]熊祝华,郑泉水.非线性力学场论的几个基本课题[J].力学进展,1991(3),310-332
[26]张盛东.混凝土本构理论研究进展于评述.南京建筑工程学院学报,2002(3):44-53
[27]叶英华,刁波.钢筋混凝土结构非线性分析中的本构关系.哈尔滨建筑大学学报,1995(6),28(3):7-12
[28]江见鲸.关于钢筋混凝土数值分析中的本构关系,力学进展,1992,21(1),117-123
[29]江见鲸.钢筋混凝土结构非线性有限元分析(第一版)[M],西安:陕西科学技术出版社,1994
[30]Elwi A.and Murray,D.W.A 3D.Hypoelastic Conerete Constitutive Relationship.Journal of Engineering Mechanics,ASCE,1979,105(4),623-641
[31]Zienkiewicz O.C.Finite element nonlinear analysis of concrete structure.Proc.Inst.Civil Eng.1976,61,Part2:59-88
[32]Ottosen,N.S.Constitutive model for short time loading.of concrete.Journal of Engineering Mechanics ASCE,1979,105(1):127-141
[33]Bhzant,Z.P.and Bhat P.D.Endochronic Theory for Concrete.Journal of Engineering Mechanics ASCE,1976,102(3):515-530
[34]Bazant,Z.P.and Kim,S.Plastic-Fractuing Theory for Concrete.Journal of Engineering Mechanics ASCE,1979,105(3):407-428
[35]熊猛,李冈.简析混凝土本构关系模型.广西大学学报,2002(6),170-172
[36]过镇海.混凝土的强度和变形试验基础和本构关系(第一版)[M].北京:清华大学出版社,1997
[37]吴勇明,钢筋砼双向板设计的计算机方法[J].华南理工大学学报,1996(6):138-142
[38]曲庆璋主编.弹性板理论[M].北京:人民交通出版社,1999
[39]王伟.楼板上有砌体墙时的设计计算与运用[J].广东土木与建筑.2004(3):14-15
[40]徐有邻等.混凝土结构设计规范理解与应用[M].北京:中国建筑工业出版社,2002
[41]徐芝纶.弹性力学(下册)[M].北京:高等教育出版社,1990
[42]徐芝纶.弹性力学简明教程[M].北京:高等教育出版社,1983
[43]美国ANSYS公司北京办事处,ANSYS用户手册,2006
[44]GB5009-2001.建筑结构荷载规范[S].北京:中国建筑工业出版社,2002
[45]GB50011-2001.建筑抗震设计规范[S].北京:中国建筑工业出版社,2001
[46]何仁斌,MATLAB 6工程计算及应用[M].重庆大学出版社,2001
[02]阿加雷A C.板壳应力[M].范钦珊译.北京:中国建筑工业出版社,1986
[03]唐锦春,郭鼎康.简明建筑结构设计手册(第二版)[M].北京:中国建筑工业出版社,1992
[04]GB50010-2002,混凝土结构设计规范[S].北京:中国建筑工业出版社,2002
[05]陈基发,沙志国.建筑结构荷载设计手册[M].北京:中国建筑工业出版社,2004
[06]《建筑结构静力计算手册》编写组.建筑结构静力计算手册[M].北京:中国建筑工业出版社,1998
[07]丁大钧.现代混凝土结构学[M].北京:中国建筑工业出版社,2000
[08]天津大学等主编.混凝土结构(上册)[M].北京:中国建筑工业出版社,1998
[09]天津大学等主编.混凝土结构(下册)[M].北京:中国建筑工业出版社,1998
[10]R·派克,W·L·根勃尔著.钢筋混凝土板[M].黄国祯,成源华译.上海:同济大学出版社,1992
[11]Park R.Reinforeed Conerete Slab[M].NewYork:Johnwiley and Sons,Inc,1980
[12][美]A.H.尼尔逊等.混凝土结构设计(第十一版).北京:中国建筑工业出版社,1991
[13]丁大钧,结构机理学—双向板的结构机理[J].工业建筑,1994.8:47-53
[14](美)R.Szilard.板的理论和分析[M].陈太平,戈鹤翔,周孝贤译.北京:中国铁道出版社,1984
[15]成祥生,应用板壳理论[M].上海:山东科学技术出版社,1989
[16]黄与宏,板结构[M].北京:人民交通出版社,1992
[I7]Timoshenko S P and woinowsky-Krieger S.Theory of Plates and Shells.New York.McGraw-Hill,1959
[18]何福保,沈亚鹏,板壳理论(第一版)[M].西安:西安交通大学出版社,1993
[19]Qian,W.Z.(钱伟长).The intrinsic theory of thin shells and plates.Quart Appl Math.1(1944),297-327;2(1994),43-59,120-135
[20]Ye Kai-yuan(叶开沅).The development of investigation of flexible structural elements in China.Proceedings of the International Conferences on Nonlinear Mechanics.Science Press.Shanghai,1985.
[21]张福范.弹性薄板[M].北京:科学出版社,1980
[22]余寿文,黄克智.考虑剪切变形的正交各向异性弹性平板的近似理论[J].力学学报,6卷4期,1963。
[23]曹志远、杨升田.厚板动力学理论及其应用[M].北京:科学出版社,1983
[24]Wang,A.J.(王仁),Hopkins H.G.Mech Phys.Solids 3.1954,22-37
[25]熊祝华,郑泉水.非线性力学场论的几个基本课题[J].力学进展,1991(3),310-332
[26]张盛东.混凝土本构理论研究进展于评述.南京建筑工程学院学报,2002(3):44-53
[27]叶英华,刁波.钢筋混凝土结构非线性分析中的本构关系.哈尔滨建筑大学学报,1995(6),28(3):7-12
[28]江见鲸.关于钢筋混凝土数值分析中的本构关系,力学进展,1992,21(1),117-123
[29]江见鲸.钢筋混凝土结构非线性有限元分析(第一版)[M],西安:陕西科学技术出版社,1994
[30]Elwi A.and Murray,D.W.A 3D.Hypoelastic Conerete Constitutive Relationship.Journal of Engineering Mechanics,ASCE,1979,105(4),623-641
[31]Zienkiewicz O.C.Finite element nonlinear analysis of concrete structure.Proc.Inst.Civil Eng.1976,61,Part2:59-88
[32]Ottosen,N.S.Constitutive model for short time loading.of concrete.Journal of Engineering Mechanics ASCE,1979,105(1):127-141
[33]Bhzant,Z.P.and Bhat P.D.Endochronic Theory for Concrete.Journal of Engineering Mechanics ASCE,1976,102(3):515-530
[34]Bazant,Z.P.and Kim,S.Plastic-Fractuing Theory for Concrete.Journal of Engineering Mechanics ASCE,1979,105(3):407-428
[35]熊猛,李冈.简析混凝土本构关系模型.广西大学学报,2002(6),170-172
[36]过镇海.混凝土的强度和变形试验基础和本构关系(第一版)[M].北京:清华大学出版社,1997
[37]吴勇明,钢筋砼双向板设计的计算机方法[J].华南理工大学学报,1996(6):138-142
[38]曲庆璋主编.弹性板理论[M].北京:人民交通出版社,1999
[39]王伟.楼板上有砌体墙时的设计计算与运用[J].广东土木与建筑.2004(3):14-15
[40]徐有邻等.混凝土结构设计规范理解与应用[M].北京:中国建筑工业出版社,2002
[41]徐芝纶.弹性力学(下册)[M].北京:高等教育出版社,1990
[42]徐芝纶.弹性力学简明教程[M].北京:高等教育出版社,1983
[43]美国ANSYS公司北京办事处,ANSYS用户手册,2006
[44]GB5009-2001.建筑结构荷载规范[S].北京:中国建筑工业出版社,2002
[45]GB50011-2001.建筑抗震设计规范[S].北京:中国建筑工业出版社,2001
[46]何仁斌,MATLAB 6工程计算及应用[M].重庆大学出版社,2001