摘要
在役钢筋混凝土箱梁桥一般都处于弯剪扭共同作用的复合受力状态。本文结合国家自然科学基金项目“在役混凝土箱梁桥时变承载力的分析理论及试验研究(51178416)”,以独柱式钢筋混凝土连续箱梁桥为背景,从理论、试验和数值分析的角度对钢筋混凝土箱梁的复合受力特性进行探索。主要研究内容及成果如下：
(1)提出了基于桁架模型的复合受力钢筋混凝土箱梁构件迭代配筋设计方法,并给出了详细的计算流程。
(2)设计制作并完成了4个不同设计参数的独柱式钢筋混凝土双跨连续箱梁复合受力模型试验研究工作。研究探讨了不同边界及加载方式下箱梁的纵应力沿横向的分布规律；对比给出了不同设计参数下箱梁的裂缝扩展特征及破坏模式；讨论了不同配筋和宽跨比对箱梁强度、刚度等力学特性的影响。试验结果验证了提出的配筋设计方法的合理性。
(3)基于有限元软件MSC.Marc的弹塑性+断裂混凝土模型,同时考虑支座接触效应和Rots裂缝面剪切模型,建立了试验构件的有限元模型。与试验对比结果表明,该模型可以较好的模拟试验的加载过程,构件抗弯和抗扭刚度的变化规律及开裂模式均与试验结果吻合良好。
(4)对独柱式钢筋混凝土连续箱梁的横向倾覆稳定性进行了探讨。分析认为,箱梁抗倾覆安全性验算时应综合考虑跨径、截面形式、配筋等因素；设置抗拉支座可以显著提高箱梁的抗倾覆能力,但墩梁固结对于改善箱梁横向稳定性的效果并不明显。
(5)基于正截面抗弯承载能力计算方法,引入剪扭钢筋混凝土构件的桁架理论,导出了复合受力混凝土箱梁的弯剪扭强度关系表达式,并提出了简化计算公式。计算结果表明,对于弯扭构件,用所提出的简化计算公式得到的弯扭强度关系曲线与试验和数值结果均吻合较好；与本文4个弯剪扭箱梁构件的试验结果相比,其计算结果整体偏于保守。
(6)提出了适用于钢筋混凝土箱梁复合受力全过程分析的改进板-桁模型。该模型考虑了等效剪切厚度沿腹板的变化情况,可以进行复杂截面箱梁的复合受力全过程分析。与试验对比结果表明,该模型可以较好地预测复合受力钢筋混凝土箱梁构件的荷载-变形曲线和荷载-钢筋应变曲线等力学响应；同时,还能进一步预测给出构件各箱壁的主应力(裂缝)倾角。
(7)提出了基于改进板-桁模型的复合受力钢筋混凝土箱梁裂缝评估方法及流程。结合剪力墙等平面受力钢筋混凝土构件裂缝控制问题的研究成果,通过提取非线性全过程分析过程中的主压应变、主拉应变、等效剪切厚度等参数,计算得到裂缝宽度和平均裂缝间距等特征参数。结果表明,不同加载等级下箱梁构件加载侧腹板的平均裂缝间距计算结果与试验观测统计值吻合较好；在裂缝扩展阶段,荷载-裂缝宽度的变化曲线与试验观测值基本一致。
(8)提出了综合考虑粘结滑移效应及正交配筋效应的钢筋修正本构模型；并进一步引入钢筋和混凝土材料劣化模型,研究给出了基于改进板-桁模型的复合受力钢筋混凝土箱梁时变承载力的计算流程。算例结果表明,对纯扭和弯剪扭混凝土构件,考虑粘结滑移的钢筋修正本构可以更好的模拟构件裂后抗扭刚度的退化情况。L1构件在寿命期内抗扭强度将经历“提高-稳定-下降”的过程,在给定的一般大气环境和扭弯比受力条件下,100年后该构件抗扭强度会出现约15%的损失。
In-service reinforced concrete (RC) box-girder bridges are generally subjected to the combined actions of bending, shear and torsion. According to the National Natural Science Foundation of China (51178416), the main objective of this study is to explore the mechanical characteristics of RC box girder subjected to bending, shear and torsion. Details of this study are mainly summarized as follows:
(1) Based on the truss model, an iterative reinforcement design approach of RC box girder subjected to combined actions was presented. The detailed calculation flowchart was given.
(2) Experimental study of four RC continuous box girders with single-column support was conducted by considering different design parameters, in which the proposed reinforcement design approach was used. The elastic mechanical properties of test model under different condition boundaries and loading cases were analyzed. The crack patterns and failure modes of four test models were observed and compared. Also, the effect of different design parameters on the strength and rigidity of box girders were discussed. Finally, the proposed reinforcement design approach was verified by the test results.
(3) Based on the elastic-plastic and fracture concrete model in the software of MSC. Marc, finite element (FE) models of the test models were developed, in which the bearing contact simulation and Rots shear crack model were considered. The results show that the whole loading process can be effectively simulated using the presented FE model. The crack patterns and the degradation curve of flexural (torsional) rigidity are in good agreement with the test results.
(4) The transverse stability of RC box-girder bridge using single-column support was discussed. Theoretical analysis result shows that the factors of span, cross section and reinforcement arrangement should be considered when checking the transverse stability of RC box-girder bridge with single-column support. Parameter analysis by FE method shows that tensile bearing can obviously improve the stability performance. However, the supporting way of fixed pier and girder has little effect on overturning-resistance performance.
(5) Based on the calculation method of flexural bearing capacity, the formula of bending-shear-torsion strength interaction of RC box girder was derived by introducing the truss model and shear-torsion strength interaction curve of RC member. The applicability of the proposed formula was discussed. Then a simplified formula was fitted and given by considering the parameters of height-width ratio, top slab width, reinforcement ratio in top and bottom slabs, concrete strength, and stirrup ratio. The results show that, for coupled bending and torsion member, the proposed simplified formula can be well verified when comprising with literature and FE results. Comparing with model tests of RC box girder subjected to combined bending, shear, and torsion, the predicted interaction curves are conservative.
(6) A modified plate-truss model used for the nonlinear whole-process analysis of RC box girder subjected to bending, shear and torsion was proposed. In the proposed model, the truss theory was satisfied in the top and bottom slabs of box girder, the flange slabs were assumed to be non-crack compressive slabs with varying thickness, and the webs were considered to be several truss elements with different equivalent shearing thickness. The result shows that the torque-twist curves, bending moment-curvature curves, and even the load-reinforcement strain curves can be well predicted by the proposed model. The angles of principal stress in different walls of box girder are also well agreement with the test results.
(7) Based on the modified plate-truss model, a crack estimation approach of RC box girder subjected to bending, shear and torsion was presented. After introducing the achievements of crack estimation for plane-stress RC member (e.g. shear wall), the parameters of principal strain and equivalent shear thickness were extracted in the whole-process nonlinear analysis. The concrete average crack spacing and width of RC box girder were then analyzed. Comparing with previous model tests of RC box girder, the results show that the predicted average crack spacing for the web of the loading side is in good agreement with the observed value. The load-crack width curves in crack propagation stage by the proposed method conform well to the test results.
(8) Based on the modified plate-truss model, the time-varying ultimate capacity of RC box girder subjected to bending, shear and torsion were studied. An average constitutional relationship of steel bar was developed by considering both the bonding-slipping effect and corrosion ratio of steel bars. The calculation flowchart of time-varying bearing capacity was given by the introducing material degradation models in general environment. It is concluded that the predicted mechanical behavior conforms well to the test result for pure torsional and coupled torsional RC members. The torsional strength will decrease by15%after100years in the assumed environment and loading conditions.
引文
[1-1]http://bbs.chinabridge.org.cn/thread-827-1-1.html
[1-2]JTG D62-2004,公路钢筋混凝土及预应力混凝土桥涵设计规范[S].北京：人民交通出版社,2004.
[1-3]AASHTO LFRD-2010, AASHTO LFRD bridge design specifications [S]. Washington D. C.: American Association of State Highway and Transportation Officials,2010.
[1-4]http://society.people.com.cn/GB/41158/6426470.html
[1-5]http://news.163.com/09/0715/09/5E8M114C0001124J.html
[1-6]http://news.qq.com/a/20110222/000346.htm
[1-7]http://news.qq.com/zt2012/ymttq/
[1-8]项贻强,唐国斌.混凝土箱梁桥开裂机理及控制[M].北京：中国水利水电出版社,2010.
[1-9]王国亮,谢峻,傅宇方.在用大跨度预应力混凝土箱梁桥裂缝调查研究[J].公路交通科技.2008(8)：52-56.
[1-10]项贻强,徐建武,唐国斌等.钢筋混凝土构件裂缝宽度计算的修正方法及其实桥试验[J].公路交通科技,201 1,28(2)：45-51.
[1-11]Kundsen A, Jensen F M. Klinghoffer O et al. Cost effective enhancement of durability of concrete structures by intelligent use of stainless steel reinforcement[A]. Conference on Corrosion and Rehabilitation of Reinforced Concrete Structures[C]. Florida,1998.
[1-12]Yunovich M, Thompson N G, Balvanyos T, Lave L. Corrosion cost and preventive strategies in the United States:Appendix D:Highway Bridges[R].2001.
[1-13]金伟良,赵羽习.混凝土结构耐久性[M].北京：科学出版社,2002.
[1-14]http://npd.nsfc.gov.cn/anywordSearch!search.action
[1-15]http://www.glzx.gov.cn/xiangmucg/baogaojb/qiaolianggch/
[1-16]赵羽习,金伟良.锈蚀箍筋混凝土梁的抗剪承载力分析[J].浙江大学学报(工学版),2008,01：19-24.
[1-17]金伟良,赵羽习.锈蚀钢筋混凝土梁抗弯强度的试验研究[J].工业建筑,2001,05：9-11.
[1-18]孙彬,牛荻涛,王庆霖.锈蚀钢筋混凝土梁抗弯承载力计算方法[J].土木工程学报,2008,11：1-6.
[1-19]张建仁,张克波,彭晖,桂成.锈蚀钢筋混凝土矩形梁正截面抗弯承载力计算方法[J].中国公路学报,2009,03：45-51.
[1-20]唐国斌.基于全寿命设计的混凝土箱梁桥若干理论问题研究[D].杭州：浙江大学博士学位论文,2011.
[1-21]Ritter W. Die Bauweise Hennebique, Schweizerische Bauzeitung.1899,33(5-7):41-43,49-52, 59-61.
[1-22]Morsch E. Der Eisenbetonbau. seine Anwendung und Theorie, Wayss and Freytag, A.G, Im Selbstverlag der Firma, Neustadt, A.D. Haardt.1902:118.
[1-23]Vecchio F, Collins M P. Stress-strain characteristics of reinforced concrete in pure shear [J]. Final report,1981:211-225.
[1-24]Hsu T T C. Stresses and crack angles in concrete membrane elements [J]. Journal of Structural Engineering,1998,124(12):1476-1484.
[1-25]Belarbi A, Hsu T T C. Constitutive laws of concrete in tension and reinforcing bars stiffened by concrete[J]. ACI Structural Journal,1994,91(4):465-474.
[1-26]Pang X B D, Hsu T T C. Behavior of reinforced concrete membrane elements in shear [J]. ACI Structural Journal,1995,92(6):665-679.
[1-27]Hsu T T C, Zhang L X. Tension stiffening in reinforced concrete membrane elements [J]. ACI Structural Journal,1996,93(1):108-115.
[1-28]Pang X B D, Hsu T T C. Fixed angle softened truss model for reinforced concrete [J]. ACI Structural Journal,1996,93(2):197-207.
[1-29]Hsu T T C. Nonlinear analysis of membrane elements by fixed-angle softened-truss model [J]. ACI Structural Journal,1997,94(5):483-492.
[1-30]Zhu R R H, Hsu T T C, Lee J Y. Rational shear modulus for smeared-crack analysis of reinforced concrete [J]. ACI Structural Journal,2001,98(4):443-450.
[1-31]Zhu R R H, Hsu T T C. Poisson effect in reinforced concrete membrane elements [J]. ACI Structural Journal,2002,99(5):631-640
[1-32]Vecchio F J. Disturbed stress field model for reinforced concrete:formulation [J]. Journal of Structural Engineering,2000,126(9):1070-1077.
[1-33]Vecchio F J. Disturbed stress field model for reinforced concrete:implementation [J]. Journal of Structural Engineering,2001,127(1):12-20.
[1-34]Vecchio F J, Lai D, Shim W, et al. Disturbed stress field model for reinforced concrete:validation [J]. Journal of Structural Engineering,2001,127(4):350-358.
[1-35]雷俊卿,谢幼藩.复合外力作用下箱梁的应力计算与分析[J].西安公路交通大学学报,1994,2：27-33.
[1-36]季韬,郑建岚.固定角软化桁架模型的新计算方法[J].中国公路学报,2003,16(1)：48-50.
[1-37]Jeng C H, Hsu T T C. A softened membrane model for torsion in reinforced concrete members [J]. Engineering Structures,2009,31(9):1944-1954.
[1-38]Mitchell D, Collins M P. Diagonal compression field theory-a rational model for structural concrete in pure torsion[C]//ACI Journal Proceedings. ACI,1974,71(8):396-408.
[1-39]Hsu T T C. Torsion of structural concrete-behavior of reinforced concrete rectangular members [J]. ACI Special Publication,1968,18:261-306.
[1-40]聂建国,唐亮.波形钢腹板PC组合箱梁纯扭性能的非线性分析[J].中国公路学报,2007,05：71-77.
[1-41]聂建国,唐亮,胡少伟,等.钢-混凝土组合箱梁的抗扭强度[J].土木工程学报,2008,41(1)：1-11.
[1-42]祝明桥,方志,胡秀兰,等.配筋钢纤维高强混凝土薄壁箱梁纯扭试验研究[J].中国公路学报,2005,18(3)：43-47.
[1-43]徐艳秋,许克宾.钢筋混凝土构件纯扭极限强度计算[J].北方交通大学学报,1999,23(1)：42-46.
[1-44]项贻强,程坤.基于转动角软化桁架模型的锈蚀钢筋混凝土纯扭构件非线性分析[J].建筑结构学报,2013,34(5)：139-144.
[1-45]苏幼坡,康谷贻.钢筋砼T形纯扭构件出裂后工作性能全过程分析[J].天津大学学报,1989,03：58-66.
[1-46]Elfgren L, Karlsson I, Losberg A. Nodal forces in the analysis of the ultimate torsional moment for rectangular beams [J]. Magazine of Concrete Research,1974,26(86):21-28.
[1-47]Rabbat B, Collins M P. A variable angle space truss model for structural concrete members subjected complex loading [C]//BRESLER B. Douglas McHenry International Symposium on Concrete and Concrete Structures. Farmington Hills, Michigan:ACI Special Publication,1978: 547-588.
[1-48]Mullapudi T R S. Seismic analysis of reinforced concrete structures subjected to combined axial, flexure, shear and torsion loads [D]. Houston:University of Houston,2010.
[1-49]Onsongo W M. the diagonal compression field theory for reinforced concrete beams subjected to combined torsion, flexure and axial load [D]. Toronto:University of Toronto,1978.
[1-50]Leung M B, Schnobrich W C. Reinforced concrete beams subjected to bending and torsion [J]. Journal of Structural Engineering,1987,113(2):307-321.
[1-51]Cocchi G M, Volpi M. Inelastic analysis of RC beams subjected to combined torsion, flexural and axial loads [J]. Computers & Structures,1996,61(3):479-494.
[1-52]Rahal K N, Collins M P. Analysis of sections subjected to combined shear and torsion-a theoretical model [J]. ACI Structural Journal,1995,92(4):459-469.
[1-53]Rahal K. N, Collins M P. Combined torsion and bending in reinforced and prestressed beams [J]. ACI Structural Journal,2003,100(2):157-165.
[1-54]Gary G J, Abdeldjelil B. Model for reinforced concrete members under torsion, bending and shear: theory [J]. Journal of Engineering Mechanics,2009,135(9):961-969.
[1-55]Gary G J, Abdeldjelil B. Model for reinforced concrete members under torsion, bending and shear: model application and validation [J]. Journal of Engineering Mechanics,2009,135(9):970-977.
[1-56]刘凤奎,许克宾.弯剪扭共同作用下钢筋混凝土构件的板-桁模型理论[J].土木工程学报,1996,29(3)：3-15.
[1-57]Nielsen J S. Theoretical and experimental study of concrete beams-especially over-reinforced beams-subjected to torsion. Part Ⅱ. Experiments.[J].1983, (171):56-62.
[1-58]Rahal K N, Collins M P. Effect of thickness of concrete cover on shear-torsion interaction-an experimental investigation [J]. ACI Structural Journal.1995,92(3):334-342.
[1-59]Chiu H, Fang 1, Young W, et al. Behavior of reinforced concrete beams with minimum torsional reinforcement [J]. Engineering Structures,2007,29(9):2193-2205.
[1-60]房贞政,郭金琼.变截面连续箱梁模型试验研究[J].中国公路学报,1995,4：59-63.
[1-61]Kurian B, Menon D. Estimation of collapse load of single-cell concrete box-girder bridges [J]. Journal of Bridge Engineering,2007,12(4):518-526.
[1-62]Galal K, Yang Q. Experimental and analytical behavior of haunched thin-walled RC girders and box girders [J]. Thin-Walled Structures.2009,47(2):202-218.
[1-63]雷俊卿,谢幼藩.预应力混凝土箱梁在弯剪扭复合作用下的试验研究[C]//中国土木工程学会桥梁及结构工程学会第八届年会论文集,1988.
[1-64]徐艳秋,许克宾,刘凤奎.复合受力下混凝土箱梁抗扭承载力计算方法与试验研究[J].中国公路学报,2000,3：38-42.
[1-65]胡少伟,陈亮.复合弯扭作用下预应力钢箱高强混凝土组合梁受力性能试验研究[J].建筑结构学报,2010,1：379-384.
[1-66]胡少伟,陈亮.预.应力钢箱高强混凝土组合梁受扭性能试验[J].中国公路学报,2010,23(6)：66-72.
[1-67]李忠献,景萌.在弯矩、剪力和反复扭矩复合作用下的碳纤维布加固RC箱梁抗扭性能试验 研究[J].土木工程学报,2006,39(11)：77-83.
[1-68]李忠献,景萌,苏标,等.碳纤维布加固弯剪扭复合受力的钢筋混凝土箱梁抗扭性能的模型试验[J].土木工程学报,2005,(12)：38-44.
[1-69]Mo Y L, Jeng C H, Chang Y S. Torsional behavior of prestressed concrete box-girder bridges with corrugated steel webs [J]. ACI Structural Journal,2000,97(6):849-859.
[1-70]Mo Y L, Jeng C H, Krawinkler H. Experimental and analytical studies of innovative prestressed concrete box-girder bridges [J]. Materials and Structures,2003,36(2):99-107.
[1-71]任红伟.波纹钢腹板预应力混凝土组合箱梁设计理论与试验研究[D].北京：北京交通大学博士学位论文,2011.
[1-72]李宏江,叶见曙,万水,等.波形钢腹板预应力混凝土箱梁的试验研究[J].中国公路学报,2004,04：34-39.
[1-73]李立峰,刘志才,王芳.波形钢腹板PC组合箱梁抗弯承载力的理论与试验研究[J].工程力学,2009,7：89-96.
[1-74]狄谨,周绪红,孔祥福,等.波形钢腹板预应力混凝土组合箱梁试验[J].长安大学学报(自然科学版),2009,05：64-70.
[1-75]刘成熹.钢筋混凝土独柱桥墩的设计理论及试验研究[D].杭州：浙江大学硕士学位论文,2012.
[1-76]祝明桥.混凝土薄壁箱梁受力性能的试验研究与分析[D].长沙：湖南大学博士学位论文,2004.
[1-77]曹国辉,方志.钢筋混凝土连续宽箱梁受力性能试验[J].中国公路学报,2006,19(5)：46-52.
[1-78]方志,张志田.钢筋混凝土箱梁横向受力有效分布宽度的试验研究[J].中国公路学报,2001,01：37-40.
[1-79]Luo Q Z, Wu Y M, Tang J, et al. Experimental studies on shear lag of box girders [J]. Engineering Structures,2002,24(4):469-477.
[1-80]Klaiber F W, Sanders Jr W W, Elleby H A. Ultimate load test of a high-truss bridge [J]. Transportation Research Record,1976, (607):75-80.
[1-81]Jorgensen J L, Larson W. Field testing of a reinforced concrete highway bridge to collapse [J]. Transportation Research Record, Transportation Research Board,1976(607):66-80.
[1-82]Bakht Baidar, Jaeger Leslie G. Ultimate load test of slab-on-girder bridge [J]. Journal of Structural Engineering,1992,118(6):1608-1624.
[1-83]Aktan A E, Lee K L, Naghavi R. Destructive testing of two 80-year-old truss bridges [J]. Transportation Research Record,1994(1460):62-72.
[1-84]Allbright K, Parekh K, Miller R, et al. Modal verification of a destructive test of a damaged prestressed concrete beam [J]. Experimental Mechanics,1994,34(4):389-396.
[1-85]Miller R A. Destructive testing of decommissioned concrete slab bridge [J]. Journal of Structural Engineering.1994,120(7):2176-2198.
[1-86]StorΦy H, SEther J, Johannessen K. Fiber optic condition monitoring during a full scale destructive bridge test [J]. Journal of Intelligent Material Systems and Structures,1997,8(8): 633-643.
[1-87]Alkhrdaji T. Destructive testing of a highway bridge strengthened with FRP systems [D]. Missouri: University of Missouri-Rolla,2001.
[1-88]Kim J, Chung W, Jay Kim J H. Experimental investigation on behavior of a spliced PSC girder with precast box segments [J]. Engineering Structures,2008,30(11):3295-3304.
[1-89]Takebayashi T, Deeprasertwong K, Leung Y W. A full-scale destructive test of a precast segmental box girder bridge with dry joints and external tendons [C]. Proceedings of the ICE-Structures and Buildings,1994,104(3):297-315.
[1-90]Zhang Jianren, Li Chuanxi, Xu Feihong. Test and analysis for ultimate load-carrying capacity of existing reinforced concrete arch ribs [J]. Journal of Bridge Engineering,2007,12(1):4-12.
[1-91]张建仁,彭晖,张克波,等.锈蚀钢筋混凝土旧桥超限及极限荷载作用的现场破坏性试验研究[J].工程力学,2009：212-213.
[1-92]徐文平.既有预应力混凝土梁桥承载能力实桥试验及分析研究[D].南京：东南大学博士学位论文,2006.
[1-93]张健飞,张宇峰.预应力混凝土连续箱梁桥破坏性试验研究[J].公路交通科技,2008(10)：63-68.
[1-94]夏叶飞.预应力混凝土简支T梁桥的承载能力实桥试验分析研究[D].南京：东南大学硕士学位论文,2006.
[1-95]余波,李勇,孙晓红,等.左家堡大桥实桥承载力破坏试验及分析[J].公路交通科技,2011,07：100-105.
[1-96]康省桢.预应力混凝土空心板梁桥破坏机理试验研究[D].郑州：郑州大学博士学位论文,2010.
[1-97]GB50010-201 0,混凝土结构设计规范[S].
[1-98]ACI 318-08, Building Code Requirements for Structure Concrete and Commentary [S].
[1-99]BS 5400-2:1900, Steel, Concrete and Composite Bridges-Part 4:Code of Practice for Design of Concrete Bridges [S].
[1-100]程远兵,康谷贻.钢筋砼弯扭构件出裂后工作性能的全过程分析[J].天津大学学报,1988,(4)：35-45.
[1-101]Leu L J, Lee Y S. Torsion design charts for reinforced concrete rectangular members [J]. Journal of Structural Engineering,2000,126(2):201-218.
[1-102]Cladera A, Mari A R. Shear design procedure for reinforced normal and high-strength concrete beams using artificial neural networks. Part Ⅰ:beams without stirrups [J]. Engineering Structures, 2004,26(7):917-926.
[1-103]Cladera A, Mari A R. Shear design procedure for reinforced normal and high-strength concrete beams using artificial neural networks. Part Ⅱ:beams with stirrups [J]. Engineering Structures,2004, 26(7):927-936
[1-104]Mo Y L, Fan Y L. Torsional design of hybrid concrete box girders [J]. Journal of Bridge Engineering,2006,11(3):329-339.
[1-105]周履.用软化桁架模型设计在扭矩作用下的混凝土多室箱梁桥[J].世界桥梁,2002,(3)：26-31.
[1-106]王骞,张哲,李文武,等.复合受力下钢筋混凝土单箱多室箱梁抗剪分析[J].武汉理工大学学报,2010,32(1)：115-118.
[1-107]Hsu T T C. Torsion of structural concrete-interaction surface for combined torsion, shear, and bending in beams without stirrups[C]//ACI Journal Proceedings,1968,65(1):51-60.
[1-108]Collins M P, Walsh P F, Archer F E, et al. Ultimate strength of reinforced concrete beams subjected to combined torsion and bending [J]. ACI Special Publication,1968,18(1):379-402.
[1-109]Kirk D W, Lash S D. T-beams subject to combined bending and torsion[C]//ACI Journal Proceedings. ACI,1971,68(2):150-159.
[1-110]Syamal P K, Mirza M S, Ray D P. Plain and reinforced concrete L-beams under combined flexure, shear, and torsion[C]//ACI Journal Proceedings. ACI,1971,68(11):848-860.
[1-111]张泽霖.钢筋混凝土弯扭构件的强度研究[J].福州大学学报,1985,25(3)：115-134.
[1-112]鲁懿虬,黄靓,徐紫鹏.对钢筋混凝土弯扭构件承载力计算公式的修正[J].工程力学,2012,29(7)：130-135.
[1-113]Elfgren L, Karlsson I, Losberg A. Torsion-bending-shear interaction for concrete beams [J]. Journal of Structural Division,1974,100(8):1657-1676.
[1-114]康谷贻,王士琴.弯剪扭共同作用下钢筋混凝土构件的强度[J].天津大学学报,1986,(1)：21-31.
[1-115]黄道凤,李建中.预应力混凝土箱梁在弯剪扭作用下破坏模式的判别及强度计算[J].石家庄铁道学院学报,1994,7(3)：31-37.
[1-116]陈溪,刘西拉.钢筋混凝土矩形梁受弯扭作用的极限分析[J].上海交通大学学报,2012,46(10)：1573-1580.
[1-117]徐艳秋,季文玉.弯剪扭共同作用下预应力混凝土箱梁抗扭极限强度的理论计算[J].北方交通大学学报,1998,22(1)：101-106.
[1-118]吕西林,金国芳,吴晓涵.钢筋混凝土结构非线性有限元理论与应用[M].上海：同济大学出版社,1997.
[1-119]凌道盛,徐兴.非线性有限元及程序[M].杭州：浙江大学出版社,2004.
[1-120]江见鲸,陆新征.混凝土结构有限元分析(第2版)[M].北京：清华大学工业出版社,2013.
[1-121]Moaveni S. Finite element analysis:theory and application with ANSYS[M]. Pearson Education India,2003.
[1-122]Hibbitt, Karlsson, Sorensen. ABAQUS/Standard user's manual[M]. Hibbitt, Karlsson & Sorensen, 2001.
[1-123]MSC.Marc User's Manual, Volume A (Theory and User Information), MSC. Software Corporation,2010.
[1-124]Seif S P, Dilger W H. Nonlinear analysis and collapse load of P.C. cable-Stayed bridges [J]. Journal of Structural Engineering,1990,116(3):829-849.
[1-125]周世军,朱晞.钢筋混凝土箱梁的非线性有限元分析及模型试验研究[J].土木工程学报,1996,29(4)：21-30.
[1-126]夏桂云.预应力混凝土箱梁承载力与裂缝研究[D].长沙：中南大学博士学位论文,2006.
[1-127]陆新征,张炎圣,黄盛楠,等.基于非线性有限元和快速建模的桥梁承载力预测[J].兰州交通大学学报,2009,28(4)：12-16.
[1-128]Broo H, Plos M, Lundgren K, et al. Non-linear finite-element analysis of the shear response in prestressed concrete bridges [J]. Magazine of Concrete Research,2009,61(8):591-608.
[1-129]许镇,任爱珠,陆新征.基于Marc和OSG的桥梁垮塌场景模拟研究[C]//第十五届全国工程设计计算机应用学术会议论文集,哈尔滨.2010.
[1-130]徐兴,凌道盛.实体退化单元系列[J].固体力学学报,2001,22：1-12.
[1-131]吴光宇.大跨P.C.桥梁非线性行为的分析理论及其极限承载力计算研究[D].杭州：浙江大学博士学位论文,2006.
[1-132]汪劲丰.预应力混凝土斜拉桥施工控制的关键技术研究[D].杭州：浙江大学博士学位论文, 2003.
[1-133]程晓东.大跨度钢管混凝土拱桥的三维非线性层合元分析研究[D].杭州：浙江大学博士学位论文,2004.
[1-134]蔡金标.大跨度悬索桥空间分析的组合单元法[D].杭州：浙江大学博士学位论文,2002.
[1-135]肖盛燮.桥梁承载力演变理论及其应用技术[M].北京：科学出版社,2009.
[1-136]牛荻涛.混凝土结构耐久性与寿命预测[M].北京：科学出版社,2003.
[1-137]Saad-Eldeen S, Garbatov Y, Soares C G. Corrosion-dependent ultimate strength assessment of aged box girders based on experimental results [J]. Journal of Ship Research,2011,55(4):289-300.
[1-138]赵新.锈蚀钢筋混凝土梁工作性能的试验研究[D].长沙：湖南大学博士学位论文,2006.
[1-139]吴庆,袁迎曙.锈蚀钢筋力学性能退化规律试验研究[J].土木工程学报,2008,12：42-47.
[1-140]Almusallam A A, Al-Gahtani A S, Aziz A R, et al. Effect of reinforcement corrosion on flexural behavior of concrete slabs [J]. Journal of Materials in Civil Engineering,1996,8(3):123-127.
[1-141]金伟良,夏晋,蒋遨宇,等.锈蚀钢筋混凝土梁受弯承载力计算模型[J].土木工程学报,2009,11：64-70.
[1-142]孙彬,牛荻涛,王庆霖.锈蚀钢筋混凝土梁抗弯承载力计算方法[J].土木工程学报,2008,11：1-6.
[1-143]王小惠,刘西拉.锈蚀钢筋混凝土梁的斜截面抗剪承载能力[J].上海交通大学学报,2007,6：944-949.
[1-144]Nakai T, Matsushita H, Yamamoto N. Effect of pitting corrosion on ultimate strength of web plates subjected to shear loading [J]. Key Engineering Materials,2007,340:489-494.
[1-145]郭冬梅.沿海地区在役钢筋混凝土桥梁性能退化机理及剩余使用寿命预测[D].杭州：浙江大学博士学位论文,2014.
[1-146]Thoft Christensen P, Baker M J. Sturctural reliability theory and it's application [M]. Berlin: Springer-verlag,1982.
[1-147]Enright M P, Framgopol D M. Service life prediction of deterioration concrete bridges [J] Journal of Structure Engineering,1998,124(4):309-317.
[1-148]薛鹏飞.预应力混凝土连续刚构桥结构性能退化预测评估研究[D].杭州：浙江大学博士学位论文,2009.
[1-149]Hutchinson T C, Wang T. Evaluation of crack spacing in reinforced concrete shear walls [J]. Journal of Structural Engineering,2009,135(5):499-508.
[2-1]李盼到,马利君.独柱支撑匝道桥抗倾覆验算汽车荷载研究[J].桥梁建设,2012,42(3)：14-18.
[2-2]Galal k, Yang Q. Experimental and analytical behavior of haunched thin-walled RC girders and box girders [J]. Thin-Walled Structures,2009,47(2):202-218.
[2-3]李忠献,景萌,苏标,等.碳纤维布加固弯剪扭复合受力的钢筋混凝土箱梁抗扭性能的模型试验[J].土木工程学报,2005,38(12)：38-44.
[2-4]祝明桥.混凝土薄壁箱梁受力性能的试验研究与分析[D].长沙：湖南大学博士学位论文,2004.
[2-5]曹国辉,方志.钢筋混凝土连续宽箱梁受力性能试验[J].中国公路学报,2006,19(5)：46-52.
[2-6]GB 50010-2010.混凝土结构设计规范[S].
[2-7]JTG D62-2004.公路钢筋混凝土及预应力混凝土桥涵设计规范[S].
[2-8]ACI 318-08, Building code requirements for structure concrete and commentary [S].
[2-9]AASHTO LFRD-2010, AASHTO LFRD bridge design specifications [S].
[2-10]BS 5400-2:1900, Steel, Concrete and Composite Bridges-Part 4:Code of practice for design of concrete bridges [S].
[2-11]徐艳秋,季文玉,许克宾,弯剪扭共同作用下预应力混凝土箱梁抗扭极限强度的理论计算方法[J].北方交通大学学报,1998,22(1)：101-106.
[2-12]Hsc T T C. Shear flow zone in torsion of reinforced concrete [J]. Journal of Structural Engineering,1988,116(11):3206-3226.
[2-13]Collins M P, Mitchell D. Prestressed concrete structures [M]. Englewood Cliffs, New Jersey:Prentice Hall,1991.
[2-14]Hsu T T C. Unified approach to shear analysis and design [J]. Cement and Composite Structures,1998,20(6):419-435.
[2-15]Vlazov V Z. Thin-walled elastic beams [M]. OTS61-11400, National Science Foundation, Washington, D.C.1965.
[2-16]Maisel B I, Roll F. Methods of analysis and design of concrete box beams with side cantilevers [R]. Tech. Rep No.42, Cement and Concrete Association, London.1974.
[2-17]Swann R A. A feature survey of concrete spin-beam bridges [R]. Tech. Rep. No.42-469, Cement and Concrete Association, London.1972.
[2-18]Rasmussen L J, Baker G. Large-scale experimental investigation of deformable RC box sections [J]. Journal of Structural Engineering,1999,125(3):227-235.
[2-19]GB/T 50152-2012.混凝土结构试验方法标准[S].
[2-20]GB/T 50081-2002.普通混凝土力学性能试验方法标准[S].
[2-21]GB/T 228.1-2010.金属材料拉伸试验第1部分：室温试验方法[S].
[3-1]GB/T 50152-2012.混凝土结构试验方法标准[s].
[3-2]GB/T 228.1-2010.金属材料拉伸试验第1部分：室温试验方法[S].
[3-3]JTG D62-2004.公路钢筋混凝土及预应力混凝土桥涵设计规范[S].
[3-4]曹国辉,方志.钢筋混凝土连续宽箱梁受力性能试验[J].中国公路学报,2006,19(5)：46-52.
[3-5]刘凤奎,许克宾.弯剪扭共同作用下钢筋混凝土构件的板-桁模型理论[J].土木工程学报,1996,29(3)：3-15.
[3-6]GB 50010-2010.混凝土结构设计规范[S].
[3-7]ACI 318-08, Building code requirements for structure concrete and commentary [S]. Farmington Hills:American Concrete Institute,2008.
[3-8]AASHTO LFRD-2010, AASHTO LFRD bridge design specifications [S]. Washington D. C.: American Association of State Highway and Transportation Officials,2010.
[3-9]MSC.Marc User's Manual, Volume A (Theory and User Information), MSC. Software Corporation,2010:448-449.
[3-10]江见鲸,陆新征.混凝土结构有限元分析(第2版)[M].北京：清华大学出版社,2013.
[3-11]陆新征,叶列平,缪志伟.建筑抗震弹塑性分析[M].北京：中国建筑工业出版社,2009.
[3-12]陈火红,杨剑,薛小香,等.新编Marc有限元实例教程[M].北京：机械工业出版社,2007.
[3-13]Buyukozturk O. Nonlinear analysis of reinforced concrete structures [J]. Computers and Structures,1977,7:149-156.
[3-14]Hognestad E. A study of combined bending and axial load in reinforced concrete members [R]. University of Illinois Engineering Experiment Station, Bulletin Series No.399, Bulletin No.l,1951.
[3-15]Rots J G, Kusters G. M A, Nauta P. Variable reduction factor for the shear resistance of cracked concrete [R]. TNO-report BI-84-33/68.8.2001, Rijswijk, the Netherlands,1984.
[3-16]Walraven J C, Reinhardt H W. Theory and experiments on the mechanical behaviour of cracks in plain and reinforced concrete subject to shear load [R], HERON.1981.26 (1): 56-62.
[3-17]左晓明,叶献国,杨启龙.钢筋混凝土非线性有限元中剪力传递系数及其数值试验[J].建筑结构,2009,39(3)：14-16.
[4-1]黄国勇,兰长青.墩梁固结独柱墩桥梁抗倾覆分析及加固设计方法[J].公路交通科技：应用技术版,2012(12)：87-89.
[4-2]李盼到,马利君.独柱支撑匝道桥抗倾覆验算汽车荷载研究[J].桥梁建设,2012(3)：14-18.
[4-3]JTG D62-2004,公路钢筋混凝土及预应力混凝土桥涵设计规范[S].
[4-4]张健,肖文杰.独柱墩桥梁抗倾覆稳定性分析[J].公路工程,2013,38(4)：170-173.
[4-5]刘成熹.钢筋混凝土独柱桥墩的设计理论及试验研究[D].杭州：浙江大学硕士学位论文,2012.
[4-6]刘飞,刘世忠,张慧,等.独柱曲线刚构匝道桥抗倾覆稳定试验研究[J].兰州交通大学学报,2012,31(4)：26-30.
[5-1]刘西拉,陈溪.关于建立拉/压弯剪扭统一计算公式的讨论[J].四川建筑科学研究,2012,38(1)：1-5.
[5-2]GB50010-2010.混凝土结构设计规范[S].
[5-3]JTGD62-2004.公路钢筋混凝土及预应力混凝土桥涵设计规范[S].
[5-4]钢筋混凝土抗扭专题组.钢筋混凝土纯扭构件抗扭强度的试验研究和计算方法[J].建筑结构学报,1987,04：1-11.
[5-5]Elfgren L, Karlsson I, Losberg A. Torsion-bending-shear interaction for concrete beams [J]. Journal of Structural Division,1974,100(8):1657-1676.
[5-6]康谷贻,王士琴.弯剪扭共同作用下钢筋混凝土构件的强度[J].天津大学学报,1986,(1)：21-31.
[5-7]黄道凤,李建中.预应力混凝土箱梁在弯剪扭作用下破坏模式的判别及强度计算[J].石家庄铁道学院学报,1994,7(3)：31-37.
[5-8]Hsu T T C. Softening truss model theory for shear and torsion [J]. ACI Journal,1988,85(6):625-635.
[5-9]Rahal K N, Collins M P. Combined torsion and bending in reinforced and prestressed beams [J]. ACI Structural Journal,2003,100(2):157-165.
[5-10]Hsu T T C. Shear flow zone in torsion of reinforced concrete [J]. Journal of Structural Engineering, 1988,116(11):3206-3226.
[5-11]刘凤奎,许克宾.弯剪扭共同作用下钢筋混凝土构件的板-桁模型理论[J].土木工程学报,1996,29(3)：3-15.
[5-12]ACI 318-08, Building code requirements for structure concrete and commentary [S]. Farmington Hills:American Concrete Institute,2008.
[5-13]张泽霖.钢筋混凝土弯扭构件强度研究[J].福州大学学报,1985,3：115-135.
[5-14]鲁懿虬,黄靓,徐紫鹏.对钢筋混凝土弯扭构件承载力计算公式的修正[J].工程力学,2012,29(7)：130-135.
[5-15]Onsongo W M. The diagonal compression field theory for reinforced concrete beams subjected to combined torsion, flexure and axial load [D]. Toronto:PhD Dissertation of University of Toronto, 1978.
[5-16]Rots J G., Kusters G M A, Nauta P, Variable reduction factor for the shear resistance of cracked concrete [R], in:TNO-report BI-85-33/68.8.2001, Rijswijk, the Netherlands,1985.
[5-17]Kyungsik K, Chai H Y. Ultimate strengths of steel rectangular box beams subjected to combined action of bending and torsion [J]. Engineering Structures,2008,30:1677-1687.
[6-1]刘凤奎,许克宾.弯剪扭共同作用下钢筋混凝土构件的板-桁模型理论[J].土木工程学报,1996,29(3)：3-15.
[6-2]Hsu T T C. Softening truss model theory for shear and torsion [J]. ACI Journal,1988,85(6): 624-635.
[6-3]Onsongo W M. The diagonal compression field theory for reinforced concrete beams subjected to combined torsion, flexure and axial load [D]. Toronto:University of Toronto, 1978.
[6-4]Leung M B, Schnobrich W C. Reinforced concrete beams subjected to bending and torsion [J]. Journal of Structural Engineering,1987,113(2):307-321.
[6-5]Cocchi G M, Volpi M. Inelastic analysis of RC beams subjected to combined torsion, flexural and axial loads [J]. Computers & Structures,1996,61(3):479-494.
[6-6]Gary G J, Abdeldjelil B. Model for reinforced concrete members under torsion, bending and shear:theory [J]. Journal of Engineering Mechanics,2009,135(9):961-969.
[6-7]Rahal K N, Collins M P. Analysis of sections subjected to combined shear and torsion-a theoretical model [J]. ACI Structural Journal,1995,92(4):459-469.
[6-8]Rahal K N, Collins M P. Combined torsion and bending in reinforced and prestressed beams [J]. ACI Structural Journal,2003,100(2):157-165.
[6-9]Hsc T T C. Shear flow zone in torsion of reinforced concrete [J]. Journal of Structural Engineering,1988,116(11):3206-3226.
[6-10]Collins M P, Mitchell D. Prestressed concrete structures [M]. Englewood Cliffs, New Jersey:Prentice Hall,1991.
[6-11]Hognestad E. A study of combined bending and axial load in reinforced concrete members [R]. University of Illinois Engineering Experiment Station, Bulletin Series No.399, Bulletin No.1,1951.
[7-1]Chi M, Kirstein A F. Flexural cracks in reinforced concrete beams [J]. ACI Journal,1958,29 (10):865-878.
[7-2]Broms B B, Lutz L A. Effects of arrangement of reinforcement on crack width and spacing of reinforced concrete members [J]. ACI Journal,1965,62(11):1395-1410.
[7-3]GB50010-2010.混凝土结构设计规范[S].
[7-4]ACI 318-08, Building code requirements for structure concrete and commentary [S].
[7-5]Bazant Z P, Oh B H. Spacing of cracks in reinforced concrete [J]. Journal of Structure Engineering,1983,109(9):2066-2085.
[7-6]Hsc T T C. Shear flow zone in torsion of reinforced concrete [J]. Journal of Structural Engineering,1988,116(11):3206-3226.
[7-7]Hutchinson T C, Wang T. Evaluation of crack spacing in reinforced concrete shear walls [J]. Journal of Structural Engineering,2009,135(5):499-508.
[7-8]Vincenzo C, Giuseppe S. An analytical model for crack control in reinforced concrete elements under combined forces [J]. Cement & Concrete Composites,2005,27:503-514.
[8-1]施锦杰,孙伟.混凝土中钢筋锈蚀研究现状与热点问题分析[J].硅酸盐学报,2010,9：1753-1764.
[8-2]张伟平,顾祥林,金贤玉,等.混凝土中钢筋锈蚀机理及锈蚀钢筋力学性能研究[J].建筑结构学报,2010,S1：327-332.
[8-3]赵羽习.钢筋锈蚀引起混凝土结构锈裂综述[J].东南大学学报(自然科学版),2013,5：1122-1134.
[8-4]Khan I, Francois R, Castel A. Prediction of reinforcement corrosion using corrosion induced cracks width in corroded reinforced concrete beams [J]. Cement and Concrete Research, 2014,56:84-96.
[8-5]Bo Yu, LuFeng Yang, Ming Wu, et al. Practical model for predicting corrosion rate of steel reinforcement in concrete structures [J]. Construction and Building Materials,2014,54(15): 385-401.
[8-6]陆春华,赵羽习,金伟良.锈蚀钢筋混凝土保护层锈胀开裂时间的预测模型[J].建筑结构学报,2010,2：85-92.
[8-7]项贻强,程坤,郭冬梅,等.基于热力耦合的钢筋混凝土锈胀开裂分析[J].浙江大学学报(工学版),2012,8：1444-1449.
[8-8]林刚,向志海,刘应华.钢筋混凝土保护层锈胀开裂时间预测模型[J].清华大学学报(自然科学版),2010,7：1125-1129.
[8-9]Saad-Eldeen S, Garbatov Y, Soares C G Corrosion-dependent ultimate strength assessment of aged box girders based on experimental results [J]. Journal of Ship Research,2011,55(4): 289-300.
[8-10]Almusallam A A, Al-Gahtani A S, Aziz A R, et al. Effect of reinforcement corrosion on flexural behavior of concrete slabs [J]. Journal of Materials in Civil Engineering,1996,8(3.): 123-127.
[8-11]金伟良,夏晋,蒋遨宇,等.锈蚀钢筋混凝土梁受弯承载力计算模型[J].土木工程学报,2009,11：64-70.
[8-12]孙彬,牛荻涛,王庆霖.锈蚀钢筋混凝土梁抗弯承载力计算方法[J].土木工程学报,2008,11：1-6.
[8-13]王小惠,刘西拉.锈蚀钢筋混凝土梁的斜截面抗剪承载能力[J].上海交通大学学报,2007，6：944-949.
[8-14]项贻强,程坤.基于转动角软化桁架模型的锈蚀钢筋混凝土纯扭构件非线性分析[J].建筑结构学报,2013,5：139-144.
[8-15]Almusallam A A, Al-Gahtani A S, Aziz A R. Effect of reinforcement corrosion on bond strength [J]. Construction and building materials,1996,10(2):123-129.
[8-16]Almusallam A A. Effect of corrosion on the properties of reinforcing steel bars [J]. Construction and Building Materials,2001,15:361-368.
[8-17]张伟平,商登峰,顾祥林.锈蚀钢筋应力-应变关系研究[J].同济大学学报(自然科学版),2006,5：586-592.
[8-18]吴庆,袁迎曙.锈蚀钢筋力学性能退化规律试验研究[J].土木工程学报,2008,12：42-47.
[8-19]柏洁,王志军,高巧玲,等.考虑黏结滑移的RC非锚固区段平均本构关系[J].土木建筑与环境工程,2009,31(2)：38-44.
[8-20]Hsu T T C. Shear flow zone in torsion of reinforced concrete [J]. Journal of Structural Engineering,1990,116(11):3206-3226.
[8-21]Eligehausen R, Popov E P, Bertero V V. Local bond stress-slip relationships of deformed bars under generalized excitations [R]. EERC Report 83/23. Berkeley:University of California,1983.
[8-22]赵羽习,金伟良.钢筋与混凝土粘结本构关系的试验研究[J].建筑结构学报,2002,23(1)：32-37.
[8-23]Hutchinson T C, Wang T. Evaluation of crack spacing in reinforced concrete shear walls [J]. Journal of Structural Engineering,2009,135(5):499-508.
[8-24]Belarbi A, Hsu T T C. Constitutive laws of concrete in tension and reinforcing bars stiffened by concrete [J]. Structural Journal of ACI,1994,91(4):465-474.
[8-25]王凤池,张霓,刘统广,等.锈蚀钢筋混凝土梁的抗扭承载力[J].沈阳建筑大学学报(自然科学版),2009,25(6)：1074-1076.
[8-26]郭冬梅.沿海地区在役钢筋混凝土桥梁性能退化机理及剩余使用寿命预测[D].杭州：浙江大学博士学位论文,2014.
[8-27]牛荻涛,王庆霖.一般大气环境下混凝土强度经时变化模型[J].工业建筑,1995,6：36-38.
[8-28]唐国斌.基于全寿命设计的混凝土箱梁桥若干理论问题研究[D].杭州：浙江大学博士学位论文,2011.
[8-29]Vu K A T, Stewart M G. Structural reliability of concrete bridges including improved chloride-induced corrosion models [J]. Structural Safety,2000,22(4):313-333.
[8-30]董振平,牛荻涛,刘西芳,等.一般大气环境下钢筋开始锈蚀时间的计算方法[J].西安建筑科技大学学报(自然科学版),2006,2：204-209.