圆端形钢管混凝土受压力学性能与可靠度研究
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摘要
目前国内外关于钢管混凝土的研究主要集中在圆形和矩形钢管混凝土,对异形钢管混凝土的研究还较少。异形截而钢管混凝土具有截而形式灵活、节点构造多样及抗震性能好等优点,在工程中已被逐渐应用。武汉后湖大桥采用单索而非对称独塔圆端形钢管塔柱,是一种创新型结构形式。针对圆端形截而钢管混凝土构件,如何计算其承载力,进行结构设计,最基本、最可靠的研究工作是通过模型试验来研究该类构件的力学行为,结合理论分析对比,校正模型,弥补试验数据不足的缺陷,从而为结构设计提供依据。
本文依托武汉后湖大桥工程实际,通过圆端形钢管混凝土轴压试验、偏压试验及有限元分析,系统研究了圆端形钢管混凝土抗压力学性能,进而基于可靠度理论,利用ANSYS可靠度分析模块,对圆端形钢管混凝塔柱可靠度进行了分析。本文进行的主要工作和取得的成果有：
第一,基于工程实际,进行大尺寸圆端形截而钢管混凝土试件轴心受压试验、偏心受压试验,轴压试验表明：轴向荷载作用下,圆端形钢管混凝土试件具有较好的承载能力,但由于角部应力集中,套箍效应引起的试件强度提高有限；套箍力分布不均匀,其在钢管壁的分布与钢管形状有很大关系；由于本试件套箍系数较小,钢管对核心混凝土的约束不大,试件破坏整体表现出脆性破坏的特征。偏压试验分析表明：偏心率是影响试件偏心受压力学性能的主要因素,随着偏心距的增大,承载力不断降低：在偏心距较大的工况下,试件荷载-横向位移曲线弹性工作阶段较短,承载能力降低较多；极限荷载作用下,圆弧与直线段交接处钢管焊缝首先开裂,试件破坏时,钢管受压区边缘已达到屈服,而另一侧尚处于弹性受拉阶段。
第二,在试验的基础上,对圆端形钢管混凝土轴心受压及偏心受压进行了有限元模拟。研究表明：摩擦系数的变化对圆端形钢管混凝土试件的轴心受压承载力影响很小；核心混凝土的强度对钢管混凝土轴压承载力提高影响不大；钢材强度对轴心受压试件弹塑性影响较大；相同含钢率的情况下,钢材的强度越大,圆端形钢管混凝土轴心受压的承载力越高,试件的延性越强。对于圆端形钢管混凝土偏心受压试件,随着长细比的增加,圆端形钢管混凝土的承载力降低,弹性工作阶段缩短,而弹塑性工作阶段延长；随混凝土强度的增大,相对屈曲系数逐渐变小；随着钢材强度增大,试件承载力不断提高,但承载力提高趋势趋缓；随着钢管壁厚增加,试件的承载力越高,延性增强。
第三,基于统一理论,结合试验及有限元模拟,拟合得到适合于圆端形钢管混凝土轴心受压、偏压试件的承载力计算公式,并将公式计算结果与试验结果及有限元分析结果进行对比,吻合良好。
第四,基于可靠度理论及ANSYS可靠度分析模块,对后湖大桥圆端形钢管混凝土塔柱,采用蒙特卡洛法和响应面法进行可靠度分析。研究表明：对于以应力作为输出控制指标的可靠度计算而言,抗拉强度满足要求的结构可靠度为98.69%,抗压强度满足要求的结构可靠度为98.89%。上述分析表明,有限元理论与可靠度理论的有机结合,可应用于复杂结构的可靠性分析。
对于圆端形这种特殊截面钢管混凝土,本文给出了大量首次发表的研究成果,揭示了圆端形钢管混凝土受压力学特性,系统分析了圆端形钢管混凝土塔柱可靠度,其研究结果为圆端形钢管混凝土的进一步研究和工程应用提供了重要的理论依据。
Research of CFST mainly in square and rectangular sections at home and abroad, specially shaped CFST is less. The advantages of specially shaped Steel Tube-Filled Concrete (CFST) are flexible section form, diverse node constructor and good seismic performance, which have been has been gradually applied in engineering. A large size round-ended CFST tower with single cable plane was used in Houhu Bridge in Wuhan, which is an innovative structure. For round-ended CFST design, how to calculate bearing capacity, the most basic and reliable research work is to study mechanical behavior through model experiment, combined with theoretical analysis to make for experimental data, and thus provide basis for structure design.
Based on Houhu Bridge project, compressive mechanical properties of round-ended CFST are studied through axial compression experiments, eccentric compression experiments and finite element analysis. Based on reliability theory, reliability of round-ended CFST tower is studied by reliability analysis module of ANSYS. The main work and achievements in the article are summarized as following:
Firstly, based on engineering practice, axial compression experiments and eccentric compression experiments of large sized round-ended CFST are carried out to study compressive mechanical behavior of round-ended CFST. Results show that:round-ended CFST under vertical load with good carrying capacity, but because corner stress concentration, bearing capacity improvement by stirrups effect is limited. Circumferential force distribution within the tube is uneven, which has great relation with tube shape. Because stirrups effect of steel tube on core concrete is small, component damage overall demonstrates the obvious fragility characteristic performance. Eccentric compressive experiment shows that eccentricity is major factor to affect bearing capacity. With increasement of eccentricity, bearing capacity will decrease. For large eccentricity conditions, load-lateral displacement curve of elastic stage is short and bearing capacity reduces much. Under ultimate load, steel tubular welded joint dehiscence at circular arc and tangential interface point, steel tublar compression zone have reached yield, while the other side is still in elastic stage.
Secondly, based on experiments, round-ended CFST compressive mechanical properties are studied by finite element simulation. Finite element simulation shows that friction coefficient has little effect on round-end CFST bearing capacity. Core concrete strength has significant influence on component elastic-plastic properties. In the case of the same steel ratio, for round-ended CFST under axial compression, the greater of steel strength, the greater of bearing capacity, the stronger of component ductility. For round-ended CFST under eccentric compression, as the slenderness ratio increases, bearing capacity reduce, elastic stage shortens, but elastic-plastic stage extend. As concrete strength increase, the relative buckling coefficient gradually becomes smaller. As steel strength increase, bearing capacity increase, but rising slope slower gradually. As tube thickness increase, bearing capacity increase.
Thirdly, based on unified theory, combined with experiment and finite element simulation analysis, bearing capacity formula of round-ended CFST under axial compression and eccentric compression are summarized, and the formula results compared with experiment data and finite element simulation results show results are in good agreement.
Fourthly, based on reliability theory and reliability analysis module of ANSYS, round-ended CFST tower reliability of Houhu Bridge is systematically studied by Monte Carlo method and response surface method. Study shows that:for the control indicators of stress as the output reliability calculation, tensile strength to meet the requirements of structural reliability is98.69%, compressive strength to meet the requirements of structural reliability is98.89%. Analysis shows that the integration of finite element theory and reliability theory can be applied to complex structural reliability analysis.
For round-ended CFST, the article gives a large number of first publication research results, which reveal round-ended CFST compressive mechanical properties, and systematic analysis round-ended CFST tower reliability. The research provides theoretical foundation of round-ended CFST further study and engineering application.
本文依托武汉后湖大桥工程实际,通过圆端形钢管混凝土轴压试验、偏压试验及有限元分析,系统研究了圆端形钢管混凝土抗压力学性能,进而基于可靠度理论,利用ANSYS可靠度分析模块,对圆端形钢管混凝塔柱可靠度进行了分析。本文进行的主要工作和取得的成果有：
第一,基于工程实际,进行大尺寸圆端形截而钢管混凝土试件轴心受压试验、偏心受压试验,轴压试验表明：轴向荷载作用下,圆端形钢管混凝土试件具有较好的承载能力,但由于角部应力集中,套箍效应引起的试件强度提高有限；套箍力分布不均匀,其在钢管壁的分布与钢管形状有很大关系；由于本试件套箍系数较小,钢管对核心混凝土的约束不大,试件破坏整体表现出脆性破坏的特征。偏压试验分析表明：偏心率是影响试件偏心受压力学性能的主要因素,随着偏心距的增大,承载力不断降低：在偏心距较大的工况下,试件荷载-横向位移曲线弹性工作阶段较短,承载能力降低较多；极限荷载作用下,圆弧与直线段交接处钢管焊缝首先开裂,试件破坏时,钢管受压区边缘已达到屈服,而另一侧尚处于弹性受拉阶段。
第二,在试验的基础上,对圆端形钢管混凝土轴心受压及偏心受压进行了有限元模拟。研究表明：摩擦系数的变化对圆端形钢管混凝土试件的轴心受压承载力影响很小；核心混凝土的强度对钢管混凝土轴压承载力提高影响不大；钢材强度对轴心受压试件弹塑性影响较大；相同含钢率的情况下,钢材的强度越大,圆端形钢管混凝土轴心受压的承载力越高,试件的延性越强。对于圆端形钢管混凝土偏心受压试件,随着长细比的增加,圆端形钢管混凝土的承载力降低,弹性工作阶段缩短,而弹塑性工作阶段延长；随混凝土强度的增大,相对屈曲系数逐渐变小；随着钢材强度增大,试件承载力不断提高,但承载力提高趋势趋缓；随着钢管壁厚增加,试件的承载力越高,延性增强。
第三,基于统一理论,结合试验及有限元模拟,拟合得到适合于圆端形钢管混凝土轴心受压、偏压试件的承载力计算公式,并将公式计算结果与试验结果及有限元分析结果进行对比,吻合良好。
第四,基于可靠度理论及ANSYS可靠度分析模块,对后湖大桥圆端形钢管混凝土塔柱,采用蒙特卡洛法和响应面法进行可靠度分析。研究表明：对于以应力作为输出控制指标的可靠度计算而言,抗拉强度满足要求的结构可靠度为98.69%,抗压强度满足要求的结构可靠度为98.89%。上述分析表明,有限元理论与可靠度理论的有机结合,可应用于复杂结构的可靠性分析。
对于圆端形这种特殊截面钢管混凝土,本文给出了大量首次发表的研究成果,揭示了圆端形钢管混凝土受压力学特性,系统分析了圆端形钢管混凝土塔柱可靠度,其研究结果为圆端形钢管混凝土的进一步研究和工程应用提供了重要的理论依据。
Research of CFST mainly in square and rectangular sections at home and abroad, specially shaped CFST is less. The advantages of specially shaped Steel Tube-Filled Concrete (CFST) are flexible section form, diverse node constructor and good seismic performance, which have been has been gradually applied in engineering. A large size round-ended CFST tower with single cable plane was used in Houhu Bridge in Wuhan, which is an innovative structure. For round-ended CFST design, how to calculate bearing capacity, the most basic and reliable research work is to study mechanical behavior through model experiment, combined with theoretical analysis to make for experimental data, and thus provide basis for structure design.
Based on Houhu Bridge project, compressive mechanical properties of round-ended CFST are studied through axial compression experiments, eccentric compression experiments and finite element analysis. Based on reliability theory, reliability of round-ended CFST tower is studied by reliability analysis module of ANSYS. The main work and achievements in the article are summarized as following:
Firstly, based on engineering practice, axial compression experiments and eccentric compression experiments of large sized round-ended CFST are carried out to study compressive mechanical behavior of round-ended CFST. Results show that:round-ended CFST under vertical load with good carrying capacity, but because corner stress concentration, bearing capacity improvement by stirrups effect is limited. Circumferential force distribution within the tube is uneven, which has great relation with tube shape. Because stirrups effect of steel tube on core concrete is small, component damage overall demonstrates the obvious fragility characteristic performance. Eccentric compressive experiment shows that eccentricity is major factor to affect bearing capacity. With increasement of eccentricity, bearing capacity will decrease. For large eccentricity conditions, load-lateral displacement curve of elastic stage is short and bearing capacity reduces much. Under ultimate load, steel tubular welded joint dehiscence at circular arc and tangential interface point, steel tublar compression zone have reached yield, while the other side is still in elastic stage.
Secondly, based on experiments, round-ended CFST compressive mechanical properties are studied by finite element simulation. Finite element simulation shows that friction coefficient has little effect on round-end CFST bearing capacity. Core concrete strength has significant influence on component elastic-plastic properties. In the case of the same steel ratio, for round-ended CFST under axial compression, the greater of steel strength, the greater of bearing capacity, the stronger of component ductility. For round-ended CFST under eccentric compression, as the slenderness ratio increases, bearing capacity reduce, elastic stage shortens, but elastic-plastic stage extend. As concrete strength increase, the relative buckling coefficient gradually becomes smaller. As steel strength increase, bearing capacity increase, but rising slope slower gradually. As tube thickness increase, bearing capacity increase.
Thirdly, based on unified theory, combined with experiment and finite element simulation analysis, bearing capacity formula of round-ended CFST under axial compression and eccentric compression are summarized, and the formula results compared with experiment data and finite element simulation results show results are in good agreement.
Fourthly, based on reliability theory and reliability analysis module of ANSYS, round-ended CFST tower reliability of Houhu Bridge is systematically studied by Monte Carlo method and response surface method. Study shows that:for the control indicators of stress as the output reliability calculation, tensile strength to meet the requirements of structural reliability is98.69%, compressive strength to meet the requirements of structural reliability is98.89%. Analysis shows that the integration of finite element theory and reliability theory can be applied to complex structural reliability analysis.
For round-ended CFST, the article gives a large number of first publication research results, which reveal round-ended CFST compressive mechanical properties, and systematic analysis round-ended CFST tower reliability. The research provides theoretical foundation of round-ended CFST further study and engineering application.
引文
[1]Lally Handbook of Lally Column construction (steel columns-concrete filled) tenth edition. New York:Lally column companies,1926:85.
[2]KloPpel V.K., Goder W.An investigation of the load carrying capacity of concrete-filled Steel tubes and development of design formula [J]. Der Stahlbau,1957a,26(1):1-10.
[3]KloPpel V.K., Goder W.An investigation of the load carrying capacity of concrete-filled Steel tubes and development of design formula [J]. Der Stahlbau,1957b,26(2):44-50.
[4]Furlong R W. Strength of steel-encased concrete beam-columns [J]. Journal of Structural Division, ASCE,1967,93(ST5):113-124.
[5]Gardner J, Jacobson E R.Structural behaviour of concrete filled steel tubes [J]. ACI Structural Journal,1967,64(7):404-413.
[6]Knowles P.R.and Park R. Strength of concrete-filled steel tubular columns [J]. Journal of the Structural Division.1969,95(12):2565-2587.
[7]Tomii M, Yoshimaro K, Morishita Y.Experimental studies on concrete filled steel tubular stub column under concentric loading [J]. Proceedings of the International Colloquium on Stability of Structures under Static and Dynamic loads. Washington,USA,1977:718-741.
[8]Luksha L.K., NesteroviehA.P.Strength testing of larger-diameter conerete filled steel tubular members [J]. Proceedings of the Third International Conference on Steel-Conerete Composite Struetures, ASCCS, Fukuoka, JaPan,1991:67-70.
[9]Grauers M,1993.Composite columns of hollow steel sections filled with high strength concrete[J]. Division of Concrete Structure, Chalmers University of Technology, Goteborg, SWEDEN,140.
[10]Johansson M.Structural behaviour of circular steel-concrete composite columns:Non-linear finite element analyses and experiments[J]. Licentiate thesis, Chalmers University of Technology, Div of Concrete Struct..Goteborg, Sweden,2000.
[11]Johansson M, Gylltoft K. Structural behaviour of slender circular steel-concrete composite columns under various means of load application [J]. Steel and Composite Structures, 2001,1(4):393-410.
[12]Johansson M, Gylltoft K. Mechanical behaviour of circular steel-concrete composite[J]. Journal of Structural Engineering,2002,128(8):1073-1081.
[13]Fam A, Qie F S, Rizkalla S.Concrete-filled steel tubes subjected to axial compression and lateral cyclicloads [J]. Journal of Structural Engineering,2004,130(4):631-640.
[14]汤关柞,招炳泉,竺惠仙,等.钢管混凝土基本力学性能的研究[J].建筑结构学报.1982,3(1)：13-31.
[15]蔡绍怀,邸小坛.钢管混凝土偏压柱的性能和强度计算的研究[J].建筑结构学报.1985,04：32-42.
[16]蔡绍怀,焦占栓.钢管混凝土短柱的基本性能和强度计算的研究[J].中国建筑科学研究院结构所,1984.4.
[17]蔡绍怀.钢管混凝土结构的计算与应用[M].北京：中国建筑工业出版社,1988.3.
[18]李继读.钢管混凝土轴压承载力的研究[J].工业建筑,1985,(2)：25-31.
[19]顾维平,蔡绍怀,冯文林.钢管高强混凝土长柱性能和承载能力的研究[J].建筑科学,1991(3)：3-8.
[20]顾维平,蔡绍怀,冯文林.钢管高强混凝土偏压柱性能与承载能力的研究[J].建筑科学,1993(3)：8-12.
[21]张素梅,周明.方钢管约束下混凝土的抗压强度[A].中国钢协钢-混凝土组合结构协会第七次年会论文集.1999,(3)：14-18.
[22]吕西林,余勇,陈冠一,Tanak K, Sasaki轴心受压方钢管混凝土短柱的性能研究[J].建筑结构.1999(10)：41-43.
[23]余勇,吕西林,Tanaka K,Sasaki S.2000轴心受压方钢管混凝土短柱的性能研究[J].建筑结构,2000,30(2)：43-46.
[24]余志武,丁发兴,林松.钢管高性能混凝土短柱受力性能研究[J].建筑结构学报,2002,23(2)：41-47.
[25]韩林海.钢管混凝土结构[M].北京：科学出版社,2004：93-97.
[26]陈宝春,欧智著,王来永.钢管混凝十偏心受压承载力试验分析[J].福州大学学报,2002,30(6),838-844.
[27]陈宝春,王来永,欧智著.钢管混凝土偏心受压应力-应变试验研究[J]工程力学,2003,20(6),154-159.
[28]陈宝春,陈友杰,王来永.钢管混凝土偏心受压应力-应变关系模型研究[J].中国公路学报,2004,17(1),24-28.
[29]张耀春,曹宝珠.轴心受压溥壁圆钢管混凝土柱临界径厚比的确定[J].工程力学,2005,22(1)：170-174.
[30]江枣,钱稼茹.钢管混凝土短柱轴心受压承载力与钢管作用研究[J].建筑结构,2010,40(8)：94-98.
[31]Shakir Khalil H,AI Rawadan A. Experimental behaviour and numerical modelling of concrete-filled rectangular hollow section tubular columns[J].Proceedings of the Engineering Foundation Conference 1997,ASCE,NewYork,USA,1997:222-235.
[32]Schneider S P.Axially concrete-filled steel tubes[J]. Journal of Structural Engineering,1998,124(10):1125-1138.
[33]Johansson M, Gylltoft K. Structural behaviour of slender circular steel-concrete composite columns under various means of load application[J].Steel and Composite Structures,2001,1(4):393-410.
[34]Varma A H.Seismic behavior, analysis, tube(CFT)columns[R].Doctoral Dissertation and design of high strength square concrete filled steel of Lehigh University,2000.
[35]Varma A H.Ricles J M Sause R.et al.Seimsic behavior and modeling of high-strength composite concrete-filled steel tube(CFT)beam columns[J].Journal of Structural Engineering,2002,58(5-8):725-758.
[36]Roeder C W,Cameron B,Brown C B.Composite action in concrete filled tubes[J].Journal of Structural Engineering,1999,125(5):477-484.
[37]Susantha K A S, Ge H B,Usami T.Confinement evaluation of concrete-filled box-shaped Steel columins[J].Steel and Composite Struetures,2001,1(3):313-328.
[38]Hu H T,Huang C S,Wu M H,Wu Y M.Nonlinear analysis of axially loaded conerete-filled tube columns with confinement effect[J].Journal of Structural Engineering,2003,129(10): 1322-1329.
[39]韩林海.钢管混凝土压弯扭试件工作机理研究[D].哈尔滨：哈尔滨建筑工程学院博士学位论文,1993.
[40]韩林海.钢管混凝土统一设计理论研究.博士后研究工作报告[R].黑龙江：国家地震局工程力学研究所,1995.
[41]韩林海,钟善桐.钢管混凝土力学[M].大连：大连理工大学出版社,1996.
[42]陈洪涛.各种截面钢管混凝土轴压短柱基本性能连续性的理论研究[D].哈尔滨工业大学博士学位论文,2001.
[43]余勇,吕西林.方钢管混凝土柱的三维非线性分析[J].地震工程与工程震动.1999,1(1)：57-64.
[44]刘威.钢管混凝土局部受压时的工作机理研究[D].福州：福州大学博士学位论文,2005.
[45]韩林海.钢管混凝土结构[M].北京：科学出版社,2001：35-47
[46]李振宇.十字形截而方钢管混凝土组合异形柱承载力研究[D].天津：天津大学硕士学位论文,2005.
[47]陈之毅.矩形钢管混凝土结构施工工艺及异形柱承载力的研究[D].同济大学硕士学位论文.2003.
[48]乔景.T形方钢管混凝土组合异形柱轴心受压承载力研究[D].天津：天津大学硕士学位论文,2005.
[49]荣彬.方钢管混凝土柱和L形截而方钢管混凝土组合异形柱研究[D].天津：天津大学硕士学位论文,2005.
[50]杜国锋,徐礼华,温芳,等.钢管混凝土组合T形短柱轴压力学性能试验[J].西安建筑科技大学学报(自然科学版),2008,40(4)：549-555.
[51]赵毅.异形钢管混凝土短柱轴压性能研究[D].哈尔滨：哈尔滨工业大学硕士学位论文.2007.
[52]王丹.T形、L形钢管混凝土柱抗震性能研究[D].上海：同济大学博十后学位论文,2005.
[53]赵国藩,曹居易,张宽权.工程结构可靠度[M].北京：水利电力出版社,1984.
[54]Freudenthal A M. The safety of structures[J].Transaction,ASCE,1947:112.
[55]Basler,S.E.Analysis of structural safety [J].ASCE Annual Convention, Boston,Mass,tune.1960.
[56]Freudenthai A M,GarreltsJ.The analysis of structural sarety[J].Journal of struetural Division ASCE,1966,22(1).
[57]Comnell C A.A probability-based structural code[J].ACIJ.1969,66(12):974-985.
[58]Lind N C.Consistent Partial safety factors.[J].J.Struct.Div,ASCE.1971,97(ST6):1651-1699.
[59]Hasofer A M,Lind N C. An exact and invariant first order reliability format [J].J.Eng.Meeh.Div,ASCE.1974,100(1):111-121.
[60]Liu p,Der K.Multivariate distribution model swith prescribed marginals and covariances[J].Probabilistic Engineering Mechanies.1986,1(2):105-112.
[61]Der K A,Liu P L.Structural Reliability Under incomplete Probability information[J].Journal of Engineering Mechanies,ASCE.1986,112(1):85-104.
[62]Fiessler B,Neumann H, Raekwitz R. Quadratic limit states in structural reliability [J]. J.Eng.Meeh.Div,ASCE.1979,105(EM4):661-676.
[63]Tvedt L. The distribution of quadratic forms in the normal space an application to structural reliability[J].J.Eng.Meeh.1990,116(6):1183-1197.
[64]Kiureghian A D, Lin H, Hwang S J. Second order reliability approximation [J].J.Eng.Meeh.,ASCE.1987,113(8):1208-1225.
[65]CaiGQ,Elishakoff I. Refined Second-order reliability analysis[J].StructuralSafety.1994, 14(4):267-276.
[66]Gu P.S.,Manohar C.S. An improved response surface method of the ination of failure probability and importance measures [J].Structural,2004,26:123-139.
[67]Kaymaz I.,McMahon C.A. A response surface method based on weighted regression of structural reliability analysis[J].Probabilistic Engineering Mechanics,2005,20(1):11-17.
[68]Su C.,Luo X.F.,Yun T.Q. Aerostatic reliability analysis of long-span bridges[J].Safety Journal of Bridge Engineering,2010,15:260-268.
[69]秦权,林道锦,梅刚.结构可靠度随机有限-理论及工程应用[M].北京：清华大学出版社,2006.
[70]肖国涛,廖绍怀.基于Matlab的Monte-Carlo法对钢管混凝土试件的可靠度分析[J].建筑技术开发,2004,31(9).
[71]陶忠,韩林海,杨华.钢管混凝土试件设计计算及可靠度分析[J].工业建筑,2000,30(6)：1-6.
[72]陈静,陈梦成,蔡小萍.基于Matlab优化工具箱对钢管混凝土轴压短柱的可靠度分析[J].南昌大学学报,2006,28(3)：303-306.
[73]余志武,贺飒飒.钢管混凝土短柱极限承载力可靠度分析[J].工程力学,2006,23(11)：139-144.
[74]覃亚伟,李惠强.钢管混凝土轴心受压柱的可靠性研究[J].华中科技大学学报,2003,20(1)：62-64.
[75]张彦玲,戴运良,李运生.钢管混凝土拱肋体系可靠度的研究[J].石家庄铁道学院学报.1998,11(2)：67-71.
[76]许富友,张健仁,郝海霞.钢管混凝土拱桥的拱肋稳定性可靠度分析[J].长沙交通学院学报.2004,20(1)：6-10.
[77]周圣斌.钢管混凝土柱极限承载力可靠度校准分析[J].建筑科学.2009,25(3)：79-81.
[78]陶忠,韩林海,杨华.钢管混凝土试件设计计算及可靠度分析[J].工业建筑.2000,30(6)：1-6.
[79]余志武,贺飒飒.钢管混凝土短柱极限承载力可靠度分析[J].工程力学.2006,23(11)：139-144.
[80]滕启杰,张哲,李生勇.大跨度钢管混凝土窄拱桥稳定性可靠度分析[J].大连理工大学学报.46(增刊)：144-150.
[81]余大胜.钢管混凝土拱桥体系可靠度的探索[D].大连：大连理工大学硕士学位论文,2005.
[82]王哲.基于响应而法的钢管混凝土拱桥可靠度分析[D].西安：长安大学硕十学位论文,2010.
[83]李飞.钢管混凝土柱的可靠度与优化分析[D].西安：西安理工大学硕士学位论文,2008.
[84]郑舟军.桥梁中不确定因素对可靠度的影响分析[D].武汉：武汉理工大学硕士学位论文,2005.
[85]陈猛.后湖斜拉桥钢管混凝土塔柱受力性能分析[D].武汉：武汉理工大学大学硕十学位论文,2008.
[86]李彬.圆端形钢管混凝土塔柱钢管与混凝土相互作用研究[D].武汉：武汉理工大学大学硕十学位论文,2008.
[87]冯涛华.后湖斜拉桥钢管混凝土转换区应力分析[D].武汉：武汉理工大学大学硕士学位论文,2008.
[88]谢建雄.大尺寸双肢圆端形钢管混凝土斜拉桥设计与施工关键技术研究[D].武汉：武汉理工大学博士学位论文,2011.
[89]《工程结构可靠性设计统一标准》GB50153-2008[S].北京：中国建筑工业出版社,2009.
[90]ABAQUS,Inc.ABAQUS Theory Manual[M].2003:12-167.
[91]Holland J H.Adaptiye of nature and artifici al systems[M].Annarbor:the university of miehegan Press,1975.
[92]Chow C L, Wang J.A finite element analysis of continuum damage mechanies for duetile fracture[J].Int Jof fracture,1998,38:83-102.
[93]Halm D,Dragon A.A model of anisotropic damage by micro crack growth[J].Unilateral effeet.Int J of damage mech,1996,5:401-402.
[94]LemaitreJ.A continuous damage mechanics model for ductile tractrue[J].Jof Engg Mater and Teeh,1985,107:83-89.
[95]MurakemiS.Notion of continuum damage mechanicas and its sapPlieation to anisotropic creep damage theory[J].Jof Engg Mater and Teeh,1982,107:83-85.
[96]程文瀼,康谷贻,颜德姮.混凝土结构设计原理(第二版)[M].中国建筑工业出版社.2002.
[97]《混凝土结构设计规范》GB50010-2010[S].北京：中国建筑工业出版社,2010.
[98]关虓,冯仲奇.基于ABAQUS的混凝土材料非线性本构模型的研究[J].安徽建筑,2010.01：89-90.
[99]钟善桐.钢管混凝土结构[M].哈尔滨：黑龙江科学技术出版社,1994.
[100]景悦.钢管混凝土轴压短柱非线性有限元分析[D].保定：河北农业大学硕士学位论文,2008：21-22.
[101]Baltay P, Gjelsvik A. Coefficient of friction for steel on concrete at high normal stress [J]. Journal of Materials in Civil Engineering,1990,2(1):46-49.
[102]Boverket, Byggavdelningen, Karlskrona.Boverket's Handbook for Concrete Structures, BBK 94, Vol.1, Design. In Swedish [M]. Sweden,1994.185.
[103]Using a Servo Hydraulic Tension-Torsion Machine for Measurement of Friction at Low Sliding Speed[M]. Swedish National Testing and Research Institute, Boras, Sweden,1992. 13.
[104]王勖成,邵敏编著.有限单元法基本原理和数值方法[M].北京：清华大学出版社,2001.
[105]朱伯芳.有限单元法原理与应用(第二版)[M].北京：中国水利水电出版社,1998.
[106]刘威.钢管混凝土局部受压时的作机理研究[D].福州：福州大学博士学位论文,2005：71-73.
[107]钟善桐.钢管混凝土中钢管与混凝土的共同工作[J].黑龙江：哈尔滨建筑大学学报,2001,1(1)：6-10
[108]王玉银,张素梅,郭兰慧.受荷方式对钢管混凝土轴压短柱力学性能影响[J].哈尔滨工业大学学报,2005,37(1)：40-44.
[109]《钢管混凝土结构设计与施工规程》CECS 28：90[S].北京：中国计划出版社,1992.
[110]《高强混凝土结构技术规程》CECS 104：99[S].北京：中国建筑工业出版社,1999.
[111]M.Nisnevih, G.Sirotin, B.Belostozky, et. Stressed state of composite structural components in CFT under axial loading [C]. Proceedings of 8th international conference on steel-concrete composite and hybrid structures,2006.
[112]陈志华,李黎明,李树海等.矩形钢管混凝土柱的超声波式研究[M],建筑结构,2005,Vo1.35,No.9：34-38.
[113]Li Xueping, Lu Xilin and Wang Dan. Modeling and experimentalverification for concrete-filled steel tubular columns with L or Tsection [C].Proceedings of 8th international conference on steel-concrete composite and hybrid structures,2006.
[114]钟善桐.钢管混凝上偏心受压试件承载力计算的研究[J].建筑结构学报.1985(4)21-30.
[115]周广师.钢管混凝土偏心受压试件稳定承载力的研究[J].哈尔滨建筑工程学院学报,1982,15(4)：29-46.
[116]蔡绍怀.现代钢管混凝土结构[M].北京：人民交通出版社,2003.
[117]汤关祚,招炳泉.钢管混凝土基本力学性能的研究[J].建筑结构学报,1982,3(1)：13-31.
[118]侯晓英,李天,王华.钢管混凝土柱偏心受压承载力计算方法探讨[J].郑州大学学报(理学版),2002,34(3)：91-94.
[119]Min Yu,Xiaoxiong Zha,Jianqiao Ye,Chunyan She.A unified formulation for hollow and solid concrete-filled steel tube columns under axial compression[J].Engineering structure,2010,32(4):1046-1053.
[120]Mander JB, Priestley MJN,Park R. Theoretical Stress-strain Model for Confined Concrete [J]. Struct Engng ASCE V 1988,114(8):1804-1826
[121]于戈.离心钢管混凝土结构在组合作用下的承载力性能研究[D].杭州：浙江大学硕：士学位论文.2003
[122]钟善桐.钢管混凝土结构(第三版)[M].北京：清华大学出版社.2003
[123]刘习超.椭圆形钢管混凝土基本性能的研究[D].哈尔滨：哈尔滨工业大学硕士学位论文,2010：26-28.
[124]武庆玺.结构可靠性分析及随机有限元分析[M].北京：机械工业出版社,2005.2：1-8,45-96.
[125]赵国藩.工程结构可靠性理论与应用[M].大连：大连理工大学出版社,1996.
[126]Schneider, S.P. Axially Loaded Concrete-Filled Steel Tubes Journal of Structural Engineering [J].ASCE,1998 Vol.124,N0.10:1125-1138
[127]Alredo H-S,Ang Wilson H. Tang. Probability concept in engineering planning and design [J].John Wiley &Sons, Volume 1,1975.
[128]董聪.结构系统可靠性理论与模拟算法[J].强度与环境,1997(4)：51-61.
[129]周宁APDL高级工程应用实例分析与二次开发[M].北京：中国水利水电出版社,2007.
[130]谢建雄,蔡崇华,卢哲安.微膨胀钢管混凝土双肢柱试验研究与数值模拟[J].武汉大学学报,2010,43(4)：485-489.
[131]沈惠中,高峰.斜拉桥索塔的可靠性分析[J].中国公路学报,1994,7(4)：40-43.
[132]谢建雄,蔡崇华,卢哲安,任志刚.基于子模型法的CFST塔柱变截而区有限元分析[J].武汉理工大学学报,2010,32(13)：62-66.
[133]李帼昌,刘之洋.自应力钢管轻骨料混凝上结构[M].沈阳：东北大学出版社,2001：39-81.
[134]《工程结构可靠度设计统一标准》GB 50153-2008[S].北京：中国计划出版社,2009.
[135]《钢结构工程施工质量验收规范》GB50205-2001[S].北京：中国计划出版社,2009.
[136]覃亚伟,李惠强.钢管混凝土受压柱的可靠性研究[J].华中科技大学学报(城市科学版),2003,20(1)：62-64.
[137]施贤真.预应力混凝土斜拉桥施工过程内力测量概率分布[D].广州：华南理工大学硕士学位论文,2011.
[138]杨跃,彭君义.基于健康监测的斜拉索荷载效应分析[J].施工技术,2009,38(6)：25-28.
[139]朱劲松,肖汝诚.桥梁损伤识别的实用模型修正方法研究[J].工业建筑,2006,36：219-224.
[2]KloPpel V.K., Goder W.An investigation of the load carrying capacity of concrete-filled Steel tubes and development of design formula [J]. Der Stahlbau,1957a,26(1):1-10.
[3]KloPpel V.K., Goder W.An investigation of the load carrying capacity of concrete-filled Steel tubes and development of design formula [J]. Der Stahlbau,1957b,26(2):44-50.
[4]Furlong R W. Strength of steel-encased concrete beam-columns [J]. Journal of Structural Division, ASCE,1967,93(ST5):113-124.
[5]Gardner J, Jacobson E R.Structural behaviour of concrete filled steel tubes [J]. ACI Structural Journal,1967,64(7):404-413.
[6]Knowles P.R.and Park R. Strength of concrete-filled steel tubular columns [J]. Journal of the Structural Division.1969,95(12):2565-2587.
[7]Tomii M, Yoshimaro K, Morishita Y.Experimental studies on concrete filled steel tubular stub column under concentric loading [J]. Proceedings of the International Colloquium on Stability of Structures under Static and Dynamic loads. Washington,USA,1977:718-741.
[8]Luksha L.K., NesteroviehA.P.Strength testing of larger-diameter conerete filled steel tubular members [J]. Proceedings of the Third International Conference on Steel-Conerete Composite Struetures, ASCCS, Fukuoka, JaPan,1991:67-70.
[9]Grauers M,1993.Composite columns of hollow steel sections filled with high strength concrete[J]. Division of Concrete Structure, Chalmers University of Technology, Goteborg, SWEDEN,140.
[10]Johansson M.Structural behaviour of circular steel-concrete composite columns:Non-linear finite element analyses and experiments[J]. Licentiate thesis, Chalmers University of Technology, Div of Concrete Struct..Goteborg, Sweden,2000.
[11]Johansson M, Gylltoft K. Structural behaviour of slender circular steel-concrete composite columns under various means of load application [J]. Steel and Composite Structures, 2001,1(4):393-410.
[12]Johansson M, Gylltoft K. Mechanical behaviour of circular steel-concrete composite[J]. Journal of Structural Engineering,2002,128(8):1073-1081.
[13]Fam A, Qie F S, Rizkalla S.Concrete-filled steel tubes subjected to axial compression and lateral cyclicloads [J]. Journal of Structural Engineering,2004,130(4):631-640.
[14]汤关柞,招炳泉,竺惠仙,等.钢管混凝土基本力学性能的研究[J].建筑结构学报.1982,3(1)：13-31.
[15]蔡绍怀,邸小坛.钢管混凝土偏压柱的性能和强度计算的研究[J].建筑结构学报.1985,04：32-42.
[16]蔡绍怀,焦占栓.钢管混凝土短柱的基本性能和强度计算的研究[J].中国建筑科学研究院结构所,1984.4.
[17]蔡绍怀.钢管混凝土结构的计算与应用[M].北京：中国建筑工业出版社,1988.3.
[18]李继读.钢管混凝土轴压承载力的研究[J].工业建筑,1985,(2)：25-31.
[19]顾维平,蔡绍怀,冯文林.钢管高强混凝土长柱性能和承载能力的研究[J].建筑科学,1991(3)：3-8.
[20]顾维平,蔡绍怀,冯文林.钢管高强混凝土偏压柱性能与承载能力的研究[J].建筑科学,1993(3)：8-12.
[21]张素梅,周明.方钢管约束下混凝土的抗压强度[A].中国钢协钢-混凝土组合结构协会第七次年会论文集.1999,(3)：14-18.
[22]吕西林,余勇,陈冠一,Tanak K, Sasaki轴心受压方钢管混凝土短柱的性能研究[J].建筑结构.1999(10)：41-43.
[23]余勇,吕西林,Tanaka K,Sasaki S.2000轴心受压方钢管混凝土短柱的性能研究[J].建筑结构,2000,30(2)：43-46.
[24]余志武,丁发兴,林松.钢管高性能混凝土短柱受力性能研究[J].建筑结构学报,2002,23(2)：41-47.
[25]韩林海.钢管混凝土结构[M].北京：科学出版社,2004：93-97.
[26]陈宝春,欧智著,王来永.钢管混凝十偏心受压承载力试验分析[J].福州大学学报,2002,30(6),838-844.
[27]陈宝春,王来永,欧智著.钢管混凝土偏心受压应力-应变试验研究[J]工程力学,2003,20(6),154-159.
[28]陈宝春,陈友杰,王来永.钢管混凝土偏心受压应力-应变关系模型研究[J].中国公路学报,2004,17(1),24-28.
[29]张耀春,曹宝珠.轴心受压溥壁圆钢管混凝土柱临界径厚比的确定[J].工程力学,2005,22(1)：170-174.
[30]江枣,钱稼茹.钢管混凝土短柱轴心受压承载力与钢管作用研究[J].建筑结构,2010,40(8)：94-98.
[31]Shakir Khalil H,AI Rawadan A. Experimental behaviour and numerical modelling of concrete-filled rectangular hollow section tubular columns[J].Proceedings of the Engineering Foundation Conference 1997,ASCE,NewYork,USA,1997:222-235.
[32]Schneider S P.Axially concrete-filled steel tubes[J]. Journal of Structural Engineering,1998,124(10):1125-1138.
[33]Johansson M, Gylltoft K. Structural behaviour of slender circular steel-concrete composite columns under various means of load application[J].Steel and Composite Structures,2001,1(4):393-410.
[34]Varma A H.Seismic behavior, analysis, tube(CFT)columns[R].Doctoral Dissertation and design of high strength square concrete filled steel of Lehigh University,2000.
[35]Varma A H.Ricles J M Sause R.et al.Seimsic behavior and modeling of high-strength composite concrete-filled steel tube(CFT)beam columns[J].Journal of Structural Engineering,2002,58(5-8):725-758.
[36]Roeder C W,Cameron B,Brown C B.Composite action in concrete filled tubes[J].Journal of Structural Engineering,1999,125(5):477-484.
[37]Susantha K A S, Ge H B,Usami T.Confinement evaluation of concrete-filled box-shaped Steel columins[J].Steel and Composite Struetures,2001,1(3):313-328.
[38]Hu H T,Huang C S,Wu M H,Wu Y M.Nonlinear analysis of axially loaded conerete-filled tube columns with confinement effect[J].Journal of Structural Engineering,2003,129(10): 1322-1329.
[39]韩林海.钢管混凝土压弯扭试件工作机理研究[D].哈尔滨：哈尔滨建筑工程学院博士学位论文,1993.
[40]韩林海.钢管混凝土统一设计理论研究.博士后研究工作报告[R].黑龙江：国家地震局工程力学研究所,1995.
[41]韩林海,钟善桐.钢管混凝土力学[M].大连：大连理工大学出版社,1996.
[42]陈洪涛.各种截面钢管混凝土轴压短柱基本性能连续性的理论研究[D].哈尔滨工业大学博士学位论文,2001.
[43]余勇,吕西林.方钢管混凝土柱的三维非线性分析[J].地震工程与工程震动.1999,1(1)：57-64.
[44]刘威.钢管混凝土局部受压时的工作机理研究[D].福州：福州大学博士学位论文,2005.
[45]韩林海.钢管混凝土结构[M].北京：科学出版社,2001：35-47
[46]李振宇.十字形截而方钢管混凝土组合异形柱承载力研究[D].天津：天津大学硕士学位论文,2005.
[47]陈之毅.矩形钢管混凝土结构施工工艺及异形柱承载力的研究[D].同济大学硕士学位论文.2003.
[48]乔景.T形方钢管混凝土组合异形柱轴心受压承载力研究[D].天津：天津大学硕士学位论文,2005.
[49]荣彬.方钢管混凝土柱和L形截而方钢管混凝土组合异形柱研究[D].天津：天津大学硕士学位论文,2005.
[50]杜国锋,徐礼华,温芳,等.钢管混凝土组合T形短柱轴压力学性能试验[J].西安建筑科技大学学报(自然科学版),2008,40(4)：549-555.
[51]赵毅.异形钢管混凝土短柱轴压性能研究[D].哈尔滨：哈尔滨工业大学硕士学位论文.2007.
[52]王丹.T形、L形钢管混凝土柱抗震性能研究[D].上海：同济大学博十后学位论文,2005.
[53]赵国藩,曹居易,张宽权.工程结构可靠度[M].北京：水利电力出版社,1984.
[54]Freudenthal A M. The safety of structures[J].Transaction,ASCE,1947:112.
[55]Basler,S.E.Analysis of structural safety [J].ASCE Annual Convention, Boston,Mass,tune.1960.
[56]Freudenthai A M,GarreltsJ.The analysis of structural sarety[J].Journal of struetural Division ASCE,1966,22(1).
[57]Comnell C A.A probability-based structural code[J].ACIJ.1969,66(12):974-985.
[58]Lind N C.Consistent Partial safety factors.[J].J.Struct.Div,ASCE.1971,97(ST6):1651-1699.
[59]Hasofer A M,Lind N C. An exact and invariant first order reliability format [J].J.Eng.Meeh.Div,ASCE.1974,100(1):111-121.
[60]Liu p,Der K.Multivariate distribution model swith prescribed marginals and covariances[J].Probabilistic Engineering Mechanies.1986,1(2):105-112.
[61]Der K A,Liu P L.Structural Reliability Under incomplete Probability information[J].Journal of Engineering Mechanies,ASCE.1986,112(1):85-104.
[62]Fiessler B,Neumann H, Raekwitz R. Quadratic limit states in structural reliability [J]. J.Eng.Meeh.Div,ASCE.1979,105(EM4):661-676.
[63]Tvedt L. The distribution of quadratic forms in the normal space an application to structural reliability[J].J.Eng.Meeh.1990,116(6):1183-1197.
[64]Kiureghian A D, Lin H, Hwang S J. Second order reliability approximation [J].J.Eng.Meeh.,ASCE.1987,113(8):1208-1225.
[65]CaiGQ,Elishakoff I. Refined Second-order reliability analysis[J].StructuralSafety.1994, 14(4):267-276.
[66]Gu P.S.,Manohar C.S. An improved response surface method of the ination of failure probability and importance measures [J].Structural,2004,26:123-139.
[67]Kaymaz I.,McMahon C.A. A response surface method based on weighted regression of structural reliability analysis[J].Probabilistic Engineering Mechanics,2005,20(1):11-17.
[68]Su C.,Luo X.F.,Yun T.Q. Aerostatic reliability analysis of long-span bridges[J].Safety Journal of Bridge Engineering,2010,15:260-268.
[69]秦权,林道锦,梅刚.结构可靠度随机有限-理论及工程应用[M].北京：清华大学出版社,2006.
[70]肖国涛,廖绍怀.基于Matlab的Monte-Carlo法对钢管混凝土试件的可靠度分析[J].建筑技术开发,2004,31(9).
[71]陶忠,韩林海,杨华.钢管混凝土试件设计计算及可靠度分析[J].工业建筑,2000,30(6)：1-6.
[72]陈静,陈梦成,蔡小萍.基于Matlab优化工具箱对钢管混凝土轴压短柱的可靠度分析[J].南昌大学学报,2006,28(3)：303-306.
[73]余志武,贺飒飒.钢管混凝土短柱极限承载力可靠度分析[J].工程力学,2006,23(11)：139-144.
[74]覃亚伟,李惠强.钢管混凝土轴心受压柱的可靠性研究[J].华中科技大学学报,2003,20(1)：62-64.
[75]张彦玲,戴运良,李运生.钢管混凝土拱肋体系可靠度的研究[J].石家庄铁道学院学报.1998,11(2)：67-71.
[76]许富友,张健仁,郝海霞.钢管混凝土拱桥的拱肋稳定性可靠度分析[J].长沙交通学院学报.2004,20(1)：6-10.
[77]周圣斌.钢管混凝土柱极限承载力可靠度校准分析[J].建筑科学.2009,25(3)：79-81.
[78]陶忠,韩林海,杨华.钢管混凝土试件设计计算及可靠度分析[J].工业建筑.2000,30(6)：1-6.
[79]余志武,贺飒飒.钢管混凝土短柱极限承载力可靠度分析[J].工程力学.2006,23(11)：139-144.
[80]滕启杰,张哲,李生勇.大跨度钢管混凝土窄拱桥稳定性可靠度分析[J].大连理工大学学报.46(增刊)：144-150.
[81]余大胜.钢管混凝土拱桥体系可靠度的探索[D].大连：大连理工大学硕士学位论文,2005.
[82]王哲.基于响应而法的钢管混凝土拱桥可靠度分析[D].西安：长安大学硕十学位论文,2010.
[83]李飞.钢管混凝土柱的可靠度与优化分析[D].西安：西安理工大学硕士学位论文,2008.
[84]郑舟军.桥梁中不确定因素对可靠度的影响分析[D].武汉：武汉理工大学硕士学位论文,2005.
[85]陈猛.后湖斜拉桥钢管混凝土塔柱受力性能分析[D].武汉：武汉理工大学大学硕十学位论文,2008.
[86]李彬.圆端形钢管混凝土塔柱钢管与混凝土相互作用研究[D].武汉：武汉理工大学大学硕十学位论文,2008.
[87]冯涛华.后湖斜拉桥钢管混凝土转换区应力分析[D].武汉：武汉理工大学大学硕士学位论文,2008.
[88]谢建雄.大尺寸双肢圆端形钢管混凝土斜拉桥设计与施工关键技术研究[D].武汉：武汉理工大学博士学位论文,2011.
[89]《工程结构可靠性设计统一标准》GB50153-2008[S].北京：中国建筑工业出版社,2009.
[90]ABAQUS,Inc.ABAQUS Theory Manual[M].2003:12-167.
[91]Holland J H.Adaptiye of nature and artifici al systems[M].Annarbor:the university of miehegan Press,1975.
[92]Chow C L, Wang J.A finite element analysis of continuum damage mechanies for duetile fracture[J].Int Jof fracture,1998,38:83-102.
[93]Halm D,Dragon A.A model of anisotropic damage by micro crack growth[J].Unilateral effeet.Int J of damage mech,1996,5:401-402.
[94]LemaitreJ.A continuous damage mechanics model for ductile tractrue[J].Jof Engg Mater and Teeh,1985,107:83-89.
[95]MurakemiS.Notion of continuum damage mechanicas and its sapPlieation to anisotropic creep damage theory[J].Jof Engg Mater and Teeh,1982,107:83-85.
[96]程文瀼,康谷贻,颜德姮.混凝土结构设计原理(第二版)[M].中国建筑工业出版社.2002.
[97]《混凝土结构设计规范》GB50010-2010[S].北京：中国建筑工业出版社,2010.
[98]关虓,冯仲奇.基于ABAQUS的混凝土材料非线性本构模型的研究[J].安徽建筑,2010.01：89-90.
[99]钟善桐.钢管混凝土结构[M].哈尔滨：黑龙江科学技术出版社,1994.
[100]景悦.钢管混凝土轴压短柱非线性有限元分析[D].保定：河北农业大学硕士学位论文,2008：21-22.
[101]Baltay P, Gjelsvik A. Coefficient of friction for steel on concrete at high normal stress [J]. Journal of Materials in Civil Engineering,1990,2(1):46-49.
[102]Boverket, Byggavdelningen, Karlskrona.Boverket's Handbook for Concrete Structures, BBK 94, Vol.1, Design. In Swedish [M]. Sweden,1994.185.
[103]Using a Servo Hydraulic Tension-Torsion Machine for Measurement of Friction at Low Sliding Speed[M]. Swedish National Testing and Research Institute, Boras, Sweden,1992. 13.
[104]王勖成,邵敏编著.有限单元法基本原理和数值方法[M].北京：清华大学出版社,2001.
[105]朱伯芳.有限单元法原理与应用(第二版)[M].北京：中国水利水电出版社,1998.
[106]刘威.钢管混凝土局部受压时的作机理研究[D].福州：福州大学博士学位论文,2005：71-73.
[107]钟善桐.钢管混凝土中钢管与混凝土的共同工作[J].黑龙江：哈尔滨建筑大学学报,2001,1(1)：6-10
[108]王玉银,张素梅,郭兰慧.受荷方式对钢管混凝土轴压短柱力学性能影响[J].哈尔滨工业大学学报,2005,37(1)：40-44.
[109]《钢管混凝土结构设计与施工规程》CECS 28：90[S].北京：中国计划出版社,1992.
[110]《高强混凝土结构技术规程》CECS 104：99[S].北京：中国建筑工业出版社,1999.
[111]M.Nisnevih, G.Sirotin, B.Belostozky, et. Stressed state of composite structural components in CFT under axial loading [C]. Proceedings of 8th international conference on steel-concrete composite and hybrid structures,2006.
[112]陈志华,李黎明,李树海等.矩形钢管混凝土柱的超声波式研究[M],建筑结构,2005,Vo1.35,No.9：34-38.
[113]Li Xueping, Lu Xilin and Wang Dan. Modeling and experimentalverification for concrete-filled steel tubular columns with L or Tsection [C].Proceedings of 8th international conference on steel-concrete composite and hybrid structures,2006.
[114]钟善桐.钢管混凝上偏心受压试件承载力计算的研究[J].建筑结构学报.1985(4)21-30.
[115]周广师.钢管混凝土偏心受压试件稳定承载力的研究[J].哈尔滨建筑工程学院学报,1982,15(4)：29-46.
[116]蔡绍怀.现代钢管混凝土结构[M].北京：人民交通出版社,2003.
[117]汤关祚,招炳泉.钢管混凝土基本力学性能的研究[J].建筑结构学报,1982,3(1)：13-31.
[118]侯晓英,李天,王华.钢管混凝土柱偏心受压承载力计算方法探讨[J].郑州大学学报(理学版),2002,34(3)：91-94.
[119]Min Yu,Xiaoxiong Zha,Jianqiao Ye,Chunyan She.A unified formulation for hollow and solid concrete-filled steel tube columns under axial compression[J].Engineering structure,2010,32(4):1046-1053.
[120]Mander JB, Priestley MJN,Park R. Theoretical Stress-strain Model for Confined Concrete [J]. Struct Engng ASCE V 1988,114(8):1804-1826
[121]于戈.离心钢管混凝土结构在组合作用下的承载力性能研究[D].杭州：浙江大学硕：士学位论文.2003
[122]钟善桐.钢管混凝土结构(第三版)[M].北京：清华大学出版社.2003
[123]刘习超.椭圆形钢管混凝土基本性能的研究[D].哈尔滨：哈尔滨工业大学硕士学位论文,2010：26-28.
[124]武庆玺.结构可靠性分析及随机有限元分析[M].北京：机械工业出版社,2005.2：1-8,45-96.
[125]赵国藩.工程结构可靠性理论与应用[M].大连：大连理工大学出版社,1996.
[126]Schneider, S.P. Axially Loaded Concrete-Filled Steel Tubes Journal of Structural Engineering [J].ASCE,1998 Vol.124,N0.10:1125-1138
[127]Alredo H-S,Ang Wilson H. Tang. Probability concept in engineering planning and design [J].John Wiley &Sons, Volume 1,1975.
[128]董聪.结构系统可靠性理论与模拟算法[J].强度与环境,1997(4)：51-61.
[129]周宁APDL高级工程应用实例分析与二次开发[M].北京：中国水利水电出版社,2007.
[130]谢建雄,蔡崇华,卢哲安.微膨胀钢管混凝土双肢柱试验研究与数值模拟[J].武汉大学学报,2010,43(4)：485-489.
[131]沈惠中,高峰.斜拉桥索塔的可靠性分析[J].中国公路学报,1994,7(4)：40-43.
[132]谢建雄,蔡崇华,卢哲安,任志刚.基于子模型法的CFST塔柱变截而区有限元分析[J].武汉理工大学学报,2010,32(13)：62-66.
[133]李帼昌,刘之洋.自应力钢管轻骨料混凝上结构[M].沈阳：东北大学出版社,2001：39-81.
[134]《工程结构可靠度设计统一标准》GB 50153-2008[S].北京：中国计划出版社,2009.
[135]《钢结构工程施工质量验收规范》GB50205-2001[S].北京：中国计划出版社,2009.
[136]覃亚伟,李惠强.钢管混凝土受压柱的可靠性研究[J].华中科技大学学报(城市科学版),2003,20(1)：62-64.
[137]施贤真.预应力混凝土斜拉桥施工过程内力测量概率分布[D].广州：华南理工大学硕士学位论文,2011.
[138]杨跃,彭君义.基于健康监测的斜拉索荷载效应分析[J].施工技术,2009,38(6)：25-28.
[139]朱劲松,肖汝诚.桥梁损伤识别的实用模型修正方法研究[J].工业建筑,2006,36：219-224.