考虑动力效应的钢筋混凝土柱抗震性能研究
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摘要
钢筋混凝土结构在地震作用下的动力响应通常会受到荷载速率的影响,而钢筋混凝土柱作为主要的承重构件,其在不同加载速率下的抗震性能研究尚且较少,同时,目前的结构抗震设计规范并未涉及由荷载速率引起的钢筋混凝土构件力学性能和变形性能变化方面的条款。本文基于试验研究和数值计算相结合的方法,分析了地震荷载速率作用下钢筋混凝土柱的率敏感性对其力学特性的影响,主要内容归结如下：
(1)试验研究了加载速率对钢筋混凝土柱力学性能和变形性能的影响。主要考虑的因素有：剪跨比、轴压比、混凝土强度、纵筋强度等级、纵向配筋率、体积配箍率、加载模式(单向加载、双向加载和变轴力加载)和加载速率。试验结果表明,随着加载速率的提高,构件的屈服承载力和极限承载力均有所增加,且屈服承载力增加的程度更为显著；加载速率的提高导致构件的强度退化、刚度退化和损伤加剧,延性略有降低,耗能则有所增加；轴力变化加剧了构件的率敏感性,使构件在加载后期提前失稳；双向加载过程中存在的耦联作用则进一步加剧了柱强度退化和刚度退化的进程。另外,基于理论分析发现,在快速加载条件下柱的截面受压区高度略有减小,加载速率导致柱的抗弯承载力的增长水平远高于抗剪承载力,同时,加载速率的提高致使构件的破坏机理也发生明显改变。
(2)试验研究了钢筋混凝土柱在不同加载路径下的动力特性,主要考虑的加载路径有：单向循环加载、十字形加载、菱形加载和圆形加载路径。试验结果表明,加载路径和加载速率的综合作用使柱的强度退化、刚度退化、延性降低程度均明显提高；通过双向加载条件下的等效阻尼比计算结果,可以看到,圆形加载路径下柱的耗能能力最强;加载速率使柱的荷载-位移骨架曲线在加载后期斜率下降更为迅速,这种现象在菱形加载路径下表现更为显著；经过回归分析给出了不同加载路径下静力和动力加载的等效阻尼比计算的经验公式。
(3)基于OpenSees中的分布塑性铰模型,数值计算给出了不同材料应变率下柱单调加载条件下的荷载-位移关系曲线和地震作用下柱的动力响应,并通过回归分析给出了不同材料应变率下柱极限承载力的动力增长因子经验公式。另外,基于OpenSees中的BeamwithHingesElement单元,引入钢筋和混凝土材料的应变率效应,考虑了构件的双向弯曲、轴力的耦联作用及剪切、粘结滑移效应,编制了钢筋混凝土柱的Tcl程序,对不同加载路径下的钢筋混凝土柱进行了数值模拟,并与试验结果进行了对比。
As the main bearing component of RC structure, the seismic behavior of reinforced concrete column will be influenced by loading rate. However, there are very few studies on the dynamic properties of the RC members subjected to earthquake loading, and the current seismic design code for buildings hasn't considered the effect of loading rate on the RC members. In this paper, the effects of loading rate on the RC columns are investigated by using the methods of experimental research and numerical calculation. The main sections of the research work are listed as follows:
(1) The effects of loading rate on the dynamic properties of RC columns are experimentally studied with different parameters, including shear span ratio, axial compression ratio, concrete strength, steel strength, longitudinal steel ratio, volume-stirrup ratio, loading mode (uniaxial loading, biaxial loading and variable axial force) and loading rate. The test results show that as the loading rate increases, the yield load and ultimate load increase, and the growth of yield load is higher; the strength degradation, stiffness degradation and damage are faster; the ductility of RC columns decreases; the energy absorption increases slightly. The variable axial force enhances the sensitivity of loading rate of RC columns, and leads to buckling in advance, At the same time, the coupling behavior of the biaxial loading worsens both stiffness and strength degradation. In addition, based on theoretical analysis, as the loading increases, the relative depth of compression zone of RC columns decreases; the growth on the flexural bearing capacity of RC column is far higher than that of the shear bearing capacity; and the failure mechanism has also changed.
(2) The effects of loading pattern (uniaxial cyclic loading, cross loading path, rhombus loading path and circular loading path) on the dynamic properties of RC columns are studied experimentally. The test results show that the combination of loading path and loading rate leads to enhancement of strength degradation, stiffness strength and the decrease level of ductility. Based on the calculation of equivalent damping, it is observed that the strongest energy dissipation occurs in the circular loading path. As the loading rate increases, the slope of skeleton curve decreases more quickly in the later stage of loading, especially in the rhombus loading path. Moreover, the empirical formulas of equivalent damping under static and dynamic loading are proposed by regression analysis of test results.
(3) Based on the force-based beam-column element with distributed plasticity in OpenSees, the loading processes under monotonic and earthquake loading are simulated with different strain rate of materials, and the empirical formulas of ultimate bearing capacity are proposed according to the simulation results. Furthermore, in order to simulate the dynamic properties of RC column subjected to earthquake loading, based on the Beam with Hinges Element in OpenSees, considering the influence of different factors (strain rate effects of materials, the interaction between biaxial bending and axial force, the shear effect, the bond-slip effect), a Tcl program is compiled, and the dynamic behavior of RC columns under different loading paths are simulated. The results show that the Tcl program can simulate the hysteretic behavior of RC columns well.
(1)试验研究了加载速率对钢筋混凝土柱力学性能和变形性能的影响。主要考虑的因素有：剪跨比、轴压比、混凝土强度、纵筋强度等级、纵向配筋率、体积配箍率、加载模式(单向加载、双向加载和变轴力加载)和加载速率。试验结果表明,随着加载速率的提高,构件的屈服承载力和极限承载力均有所增加,且屈服承载力增加的程度更为显著；加载速率的提高导致构件的强度退化、刚度退化和损伤加剧,延性略有降低,耗能则有所增加；轴力变化加剧了构件的率敏感性,使构件在加载后期提前失稳；双向加载过程中存在的耦联作用则进一步加剧了柱强度退化和刚度退化的进程。另外,基于理论分析发现,在快速加载条件下柱的截面受压区高度略有减小,加载速率导致柱的抗弯承载力的增长水平远高于抗剪承载力,同时,加载速率的提高致使构件的破坏机理也发生明显改变。
(2)试验研究了钢筋混凝土柱在不同加载路径下的动力特性,主要考虑的加载路径有：单向循环加载、十字形加载、菱形加载和圆形加载路径。试验结果表明,加载路径和加载速率的综合作用使柱的强度退化、刚度退化、延性降低程度均明显提高；通过双向加载条件下的等效阻尼比计算结果,可以看到,圆形加载路径下柱的耗能能力最强;加载速率使柱的荷载-位移骨架曲线在加载后期斜率下降更为迅速,这种现象在菱形加载路径下表现更为显著；经过回归分析给出了不同加载路径下静力和动力加载的等效阻尼比计算的经验公式。
(3)基于OpenSees中的分布塑性铰模型,数值计算给出了不同材料应变率下柱单调加载条件下的荷载-位移关系曲线和地震作用下柱的动力响应,并通过回归分析给出了不同材料应变率下柱极限承载力的动力增长因子经验公式。另外,基于OpenSees中的BeamwithHingesElement单元,引入钢筋和混凝土材料的应变率效应,考虑了构件的双向弯曲、轴力的耦联作用及剪切、粘结滑移效应,编制了钢筋混凝土柱的Tcl程序,对不同加载路径下的钢筋混凝土柱进行了数值模拟,并与试验结果进行了对比。
As the main bearing component of RC structure, the seismic behavior of reinforced concrete column will be influenced by loading rate. However, there are very few studies on the dynamic properties of the RC members subjected to earthquake loading, and the current seismic design code for buildings hasn't considered the effect of loading rate on the RC members. In this paper, the effects of loading rate on the RC columns are investigated by using the methods of experimental research and numerical calculation. The main sections of the research work are listed as follows:
(1) The effects of loading rate on the dynamic properties of RC columns are experimentally studied with different parameters, including shear span ratio, axial compression ratio, concrete strength, steel strength, longitudinal steel ratio, volume-stirrup ratio, loading mode (uniaxial loading, biaxial loading and variable axial force) and loading rate. The test results show that as the loading rate increases, the yield load and ultimate load increase, and the growth of yield load is higher; the strength degradation, stiffness degradation and damage are faster; the ductility of RC columns decreases; the energy absorption increases slightly. The variable axial force enhances the sensitivity of loading rate of RC columns, and leads to buckling in advance, At the same time, the coupling behavior of the biaxial loading worsens both stiffness and strength degradation. In addition, based on theoretical analysis, as the loading increases, the relative depth of compression zone of RC columns decreases; the growth on the flexural bearing capacity of RC column is far higher than that of the shear bearing capacity; and the failure mechanism has also changed.
(2) The effects of loading pattern (uniaxial cyclic loading, cross loading path, rhombus loading path and circular loading path) on the dynamic properties of RC columns are studied experimentally. The test results show that the combination of loading path and loading rate leads to enhancement of strength degradation, stiffness strength and the decrease level of ductility. Based on the calculation of equivalent damping, it is observed that the strongest energy dissipation occurs in the circular loading path. As the loading rate increases, the slope of skeleton curve decreases more quickly in the later stage of loading, especially in the rhombus loading path. Moreover, the empirical formulas of equivalent damping under static and dynamic loading are proposed by regression analysis of test results.
(3) Based on the force-based beam-column element with distributed plasticity in OpenSees, the loading processes under monotonic and earthquake loading are simulated with different strain rate of materials, and the empirical formulas of ultimate bearing capacity are proposed according to the simulation results. Furthermore, in order to simulate the dynamic properties of RC column subjected to earthquake loading, based on the Beam with Hinges Element in OpenSees, considering the influence of different factors (strain rate effects of materials, the interaction between biaxial bending and axial force, the shear effect, the bond-slip effect), a Tcl program is compiled, and the dynamic behavior of RC columns under different loading paths are simulated. The results show that the Tcl program can simulate the hysteretic behavior of RC columns well.
引文
[1]胡聿贤.地震工程学[M].地震出版社,1988.
[2]Soroushian P, Obaseki K. Strain rate-dependent interaction diagrams for reinforced concrete sections [C]. ACI Journal Proceedings. ACI,1986,83(1).
[3]李宏男.结构多维抗震理论[M].科学出版社,2006.
[4]Watstein D. Effect of straining rate on the compressive strength and elastic properties of concrete [C]. ACI Journal Procedings, ACI,1953,49(4).
[5]Sparks P R, Menzies J B. The effect of rate of loading upon the static and fatigue strengths of plain concrete in compression [J]. Magazine of Concrete Research,1973, 25(83):73-80.
[6]Hughes B P, Watson A J. Compressive strength and ultimate strain of concrete under impact loading [J]. Magazine of Concrete Research,1978,30(105):189-199.
[7]尚仁杰.混凝土动态本构行为研究[D].大连：大连理工大学,1994.
[8]肖诗云.混凝土率型本构模型及其在拱坝动力分析中的应用[D].大连：大连理工大学,2002.
[9]李杰,任晓丹.混凝土静力与动力损伤本构模型研究进展评述[J].力学进展,2010,40(3)：284-297.
[10]Mellinger F M,Birkimer D L. Measurement of stress and strain on cylindrical test specimens of rock and concrete under impact loading [R]. Ohio River Div Labs Cincinnati, 1966.
[11]Birkimer D L, Lindemann R. The impact strength of concrete materials [J]. American Concrete Institute,1971,68:47-49.
[12]Yon J H, Hawkins N M, Kobayashi A S. Strain rate sensitivity concrete mechanical properties [J]. ACI Material Journal,1992,89(2):146-153.
[13]闫东明,林皋,王哲,等.不同应变速率下混凝土直接拉伸试验研究[J].土木工程学报,2005,38(6)：97-103.
[14]Mlakar P F, Vitaya-Udom K P, Cole R A. Dynamic tensile-compressive behavior of concrete [J]. ACI Journal Proceedings. ACI,1985,82(4).
[15]Zielinski A J. Concrete under biaxial compressive-impact tensile loading [J]. Fracture Toughness and Fracture Energy of Concrete.1986,489.
[16]Weerheijm J. Concrete under impact tensile loading and lateral compression [D]. Delft: Delft University of Technology,1992.
[17]鞠庆海,吴绵拔.岩石材料三轴压缩动力特性的试验研究[J].岩土工程学报,1993,15(3)：73-80.
[18]闫东明.混凝土动态力学性能试验与理论研究[D].大连：大连理工大学,2006.
[19]Scott B D, Park R, Priestley M J N. Stress-strain behavior of concrete confined by overlapping hoops at low and high strain rates [J]. ACI Journal Proceedings. ACI, 1982,79(1):13-27.
[20]Kent D C, Park R. Flexural members with confined concrete [J]. Journal of the Structural Division,1971,97(7):1969-1990.
[21]Dilger W H, Koch R, Kowalczyk R. Ductility of plain and confined concrete under different strain rates [J]. ACI Journal Proceedings. ACI,1984,81(1):73-81.
[22]Sargin M, Ghosh S K, Handa V K. Effects of lateral reinforcement upon the strength and deformation properties of concrete [J]. Magazine of Concrete Resesearch, 1971,23(75/76):99-118.
[23]Soroushian P, Choi K, Alhamad A. Dynamic constitutive behavior of concrete [J]. ACI Journal Proceedings. ACI,1986,83(2):251-258.
[24]Mander J B, Priestley J N, Park R. Observed stress-strain behavior of confined concrete [J]. Journal of Structural Engineering,1988,114(8):1827-1849.
[25]Mander J B, Priestley J N, Park R. Theoretical stress-strain model for confined concrete [J]. Journal of Structural Engineering,1988,114(8):1804-1826,
[26]Ahmad S H, Shah S P. Behavior of hoop confined concrete under high strain rates [J]. ACI Journal Proceedings. ACI,1985,82(5):634-647.
[27]CEB. Concrete structures under impact and implosive loading [R]. Synthesis Report. Lausanne:Committee Euro-International du Beton,1998,187.
[28]Gebbeken N, Ruppert M. A new material model for concrete in high-dynamic hydrocode simulations [J]. Archive of Applied Mechanics,2000,70(7):463-478.
[29]Malvar L J, John E C. Dynamic increase factors for steel reinforcing bars [C]. 1st ed. Florida:Twenty-Eighth DDESB (Department of Defense Explosives Safety Board) Seminar, 1998.
[30]Malvar L J, Ross C A. Review of strain rate effects for concrete in tension [J]. ACI Materials Journal,1998,95(6):735-739.
[31]Tedesco J W, Ross C A. Strain-rate-dependent constitutive equation for concrete [J]. Journal of Pressure Vessel Technology,1998, (120):398-405.
[32]Bischoff P H, Perry S H. Compressive behavior of concrete at high strain rates [J]. Materials and Structures,1991,24:425-450.
[33]董毓利,谢和平,赵鹏.不同应变率下混凝土受压全过程的实验研究及其本构模型[J].水利学报,1997,(7)：72-77.
[34]Soroushian P, Choi K, Kowalczak R. Ductility of plain and confined concrete under different strain rates [J]. ACI Journal Proceedings. ACI,1984:73-81.
[35]Lu Y, Xu K. Modeling of dynamic behavior of concrete materials under blast loading [J]. International Journal of Solids and Structures,2004,41(1):131-143.
[36]Grote D L, Park S W, Zhou M. Dynamic behavior of concrete at high strain-rates and pressures:I. Experimental characterization[J]. International Journal of Impact Engineering,2001,25(9):869-886.
[37]Ross P, Van Mier J G M, Boulay C. The dynamic behavior of concrete:The influence of free water [J]. Materials and Structures,1992,25:509-514.
[38]Ross P, Toutlemonde F. Effect of loading rate on the tensile behavior of concrete: description of physical mechanisms [J]. Materials and Structures,1996,29(2): 116-118.
[39]Tang T, Malvern L E, Jenkins D A. Rate effects in uniaxial dynamic compression of concrete [J]. Journal of Engineering Mechanics,1992,118(1):108-124.
[40]Holmquist T J, Johnson G R,. Cook W H. A computational constitutive model for concrete subjected to large strains, high strain rates and high pressures[C]. The 14th International Symposium on Ballistics, Quebec, Canada,1993.
[41]陈书宇.一种混凝土损伤本构模型和数值方法[J].爆炸与冲击,1998,18(4)：349-357.
[42]陈书宇,陈成光.混凝土本构模型及其动态有限元算法研究[J].上海力学,1998,19(2)：109-116.
[43]唐志平,田兰桥,朱兆祥,等.高应变率下环氧树脂的力学性能[C].第二届爆炸力学会议文集,扬州,1981,53：88-166.
[44]唐志平.高应变率下环氧树脂的动态力学性能[D].合肥：中国科学技术大学,1981.
[45]刘文彦.水泥基复合材料在冲击载荷下的力学响应和纤维的桥联行为研究[D].合肥：中国科学技术大学,2001.
[46]王礼立,余同希,李永池.冲击动力学进展[M].合肥：中国科学技术大学出版社,1992.
[47]Duvaut G, Lions J L. Les inequations en mecanique et en physique [M]. Paris:Dunod, 1972.
[48]Wang W M. Stationary and propagative instabilities in metals:a computational point of view[M]. Delft University Press,1997.
[49]Lemaitre J, Plumtree A. Application of damage concepts to predict creep-fatigue failures[J]. Journal of Engineering Materials and Technology,1979,101:284.
[50]李兆霞.一个综合模糊裂纹和损伤的混凝土应变软化本构模型[J].固体力学学报,1995,16(1)：22-30.
[51]Suaris W, Shah S P. Rate-sensitive damage theory for brittle solids[J]. Journal of engineering mechanics,1984,110(6):985-997.
[52]Bui H D, Ehrlacher A. Propagation of damage in elastic and plastic solids [J]. Advances in Fracture Research,1981, (2):533-551.
[53]Burlion N, Gatuingt F, Pijaudier C G. Compaction and tensile damage in concrete constitutive modeling and application to dynamics [J]. Computer Methods in Applied Mechanics and Engineering,2000,183(3):291-308.
[54]Sukontasukkul P, Ninityongskul P, Mindess S. Effect of loading rate on damage of concrete [J]. Cement and Concrete Research,2004,34(11):2127-2134.
[55]Cervera M, Oliver J, Manzoli 0. A rate-dependent isotropic damage model for the seismic analysis of concrete dams [J]. Earthquake Engineering and Structure Dynamics,1996, 25(9):987-1010.
[56]Faria R, Olivella J 0. A rate dependent plastic-damage constitutive model for large scale computations in concrete structures[M]. Centro Internacional de Metodos Numericos en Ingenieria,1993.
[57]Faria R, Oliver J, Cervera M. A strain-based plastic viscous-damage model for massive concrete structures[J]. International Journal of Solids Structures,1998,35(14): 1533-1558.
[58]李庆斌,邓宗才,张立翔.考虑初始弹性模量变化的混凝土动力损伤本构模型[J].清华大学学报,2003,43(8)：1088-1091.
[59]邓宗才.单轴状态下混凝土的静力、动力损伤本构模型[J].山东建材学院学报,1999,13(4)：334-337.
[60]杜荣强,林皋.混凝土动力损伤本构关系的基础理论及应用[J].哈尔滨工业大学学报,2006,38(5)：746-751.
[61]胡时胜,王道荣.冲击荷载下混凝土材料的动态本构关系[J].爆炸与冲击,2002,22(3)：242-246.
[62]吴建营,李杰.考虑应变率效应的混凝土动力弹塑性损伤本构模型[J].同济大学学报(自然科学版),2006,34(11)：1427-1430.
[63]吴建营,李杰.反映阻尼影响的混凝土弹塑性损伤本构模型[J].工程力学,2006,23(11)：116-121.
[64]肖诗云,田子坤.混凝土单轴动态受拉损伤试验研究[J],土木工程学报,2008,41(7)：14-20.
[65]Eibl J. Concrete structures under impact and impulsive loading (CEB-Bulletind' information, NO.187) [R] Dubrovnik:Comite Euro-International du Beton,1988.
[66]Restrepo-Posada J I, Dodd L L, Park R, et al. Variables affecting cyclic behavior of reinforcing steel [J]. Journal of Structural Engineering,1994,120(11):3178-3196.
[67]Cadoni E, Fenu L, Forni D. Strain rate behavior in tension of austenitic stainless steel used for reinforcing bars [J]. Construction and Building Materials,2012,35: 399-407.
[68]陈肇元,曹炽康,李庆标.建筑钢筋在快速变形下的力学性能[R].抗爆结构研究报告第一集：结构材料的动力性能及其计算强度.北京：清华大学,1971.
[69]林峰,顾祥林,匡昕昕,等.高应变率下建筑钢筋的本构模型[J].建筑材料学报,2008,11(1)：14-20.
[70]李敏,李宏男.建筑钢筋动态试验及本构模型[J].土木工程学报,2010,43(4)：70-75.
[71]Manjoine M J. Influence of rate of strain and temperature on yield stress of mild steel [J]. Journal of Applied Mechanics,1944,11:211-218.
[72]Cowper G R, Symonds P S. Strain hardening and strain rate effect in the impact loading of cantilever beams [R]. Brown University, Division of Applied Mathematics report, 1957, p.28.
[73]Johnson G R, Cook W H. A constitutive model and data for metals subjected to large strains, high strain rate, and temperatures [C]. Proceedings of the 7th International Symposium on Ballistics. The Hague, Netherlands:International Ballistics Committee, 1983,21:541-547.
[74]Soroushian P, Choi K B. Steel mechanical properties at different strain rates [J]. Journal of Structural Engineering,1987,113(4):663-672.
[75]Malvar L J. Review of static and dynamic properties of steel reinforcing bars [J]. ACI Material Journal,1998,95(5):609-616.
[76]Vos E, Reinhardt H W. Influence of loading rate on bond behaviour of reinforcing steel and prestressing strands[J]. Materiaux et Construction,1982,15(1):3-10.
[77]Takeda J. Strain Rate Effects on Concrete and Reinforcements, and their Contributions to Structures[C]. MRS Proceedings. Cambridge University Press,1985,64(1).
[78]Mindess S. Effects of dynamic loading on bond[R]. ACI Committee 446:State of the Art Report, Section 4.2.3,1989.
[79]Banthia N P, Mindess S, Bentur A. Impact behavior of concrete beams [J]. Materials and Structures,1987,20(118):293-302.
[80]Yan C. Bond between reinforcing bars and concrete under impact loading [D]. The University of British Columbia,1992.
[81]洪小健,赵鸣.加载速率对锈蚀钢筋与混凝土粘结性能的影响[J].同济大学学报,2002,30(7)：792-796.
[82]Mahin S A, Bertero V V, Atalay M B, Rea D. Rate of loading effects on uncracked and repaired reinforced concrete members [C]. Proceedings, Fifth World Conference on Earthquake Engineering, Rome.1973,1:1461-1470.
[83]Bertero V V, Rea D, Mahin S, et al. Rate of loading effects on uncracked and repaired reinforced concrete members [C]. Proceeding of fifth world conference on earthquake engineering, Rome,1973(1):1461-1471.
[84]Mutsuyoshi H, Machida A. Properties and failure of reinforced concrete members subjected to dynamic loading [J]. Transactions of the Japan Concrete Institute,61 521-528.
[85]Mutsuyoshi H, Machida A. Dynamic properties of reinforced concrete piers [C]. Proceeding of eighth world conference on earthquake engineering, San Francisco, 1984(6):299-306.
[86]Kulkarni S M, Shah S P. Response of reinforced concrete beams at high strain rates [J]. ACI Structural Journal,1998,95(6):705-715.
[87]Chung L, Shah S P. Effect of loading rate on anchorage bond and beam-column joints [J]. ACI Structural Journal,1989,86(2):132-142.
[88]Al-Haddad M S.Curvature ductility of reinforced concrete beams under low and high strain rates [J]. ACI Structural Journal,1995,92(5):526-534.
[89]Otani S, Kaneko T, Shiohara H. Strain rate effect on performance of reinforced concrete members [C]. Concrete structures in seismic regions:FiB,2003.
[90]Ozbolt J, Sharma A. Numerical simulation of reinforced concrete beams with different shear reinforcements under dynamic impact loads [J]. International Journal of Impact Engineering,2011,38:940-950.
[91]Adhikary S D, Li B, Fujikake K. Dynamic behavior of reinforced concrete beams under varying rates of concentrated loading [J]. International Journal of Impact Engineering,2012,47:24-38.
[92]陈肇元,施岚青.钢筋混凝土梁在静速和快速变形下的弯曲性能[R].科学研究报告第四集：钢筋混凝土结构构件在冲击荷载下的性能。北京：清华大学出版社,1986.
[93]陈俊名.钢筋混凝土剪力墙动力加载试验及考虑应变率效应的有限元模拟[D].长沙：湖南大学,2010.
[94]肖诗云,曹闻博,潘浩浩.不同加载速率下钢筋混凝土梁力学性能试验研究[J].建筑结构学报,2012,33(12)：142-146.
[95]许斌,龙业平.基于纤维模型的钢筋混凝土柱应变率效应研究[J].工程力学,2011,28(7)：103-108.
[96]Li M, Li H N. Effects of strain rate on reinforced beam [J]. Advanced Materials Research, 2011,243:4033-4036.
[97]邹笃建,刘铁军,滕军,严桂兰.混凝土梁式构件弹性模量的应变率效应研究[J].振动工程学报,2011,24(2)：170-174.
[98]Kreger M E, Linbeck L. Behavior of reinforced concrete columns subjected to lateral axial load reversals [C]. The 3rd U. S. National Conference on earthquake Engineering, Charleston, South Carolina,1986,2:24-28.
[99]Abrams D P. Influence of axial force variations on flexural behavior of reinforced concrete columns [J]. ACI Structural Journal,1987,84(3):246-254.
[100]Kuramoto H, Kabeyasawa T, Shen F H. Influence of axial deformation on ductility of high-strength reinforced concrete columns under varying tri-axial force [J]. ACI Structural Journal,1995,92(9):610-618.
[101]Saadeghvaziri M A. Nonlinear response and modeling of RC columns subjected to varying axial load [J]. Engineering Structures,1997,19(6):417-424.
[102]EIMandooh Galal K, Ghobarah A. Flexural and shear hysteretic behavior of reinforced concrete columns with variable axial load [J]. Engineering Structure,2003,25(11): 1353-1367.
[104]邢秋顺,季耀东,陈肇元.变轴力下钢筋混凝土受弯截面的性能[J].建筑结构学报,1987,(5)：52-61.
[106]黄翔.规则变轴力作用下钢筋混凝土框架柱的抗震性能研究[D].重庆：重庆建筑大学,1995.
[107]钟树生.水平及竖向荷载地震作用下钢筋混凝土柱抗震性能的试验研究[D].重庆：重庆大学,1999.
[108]顾祥林,蔡茂,林峰.地震作用下钢筋混凝土柱受力性能研究[J].工程力学,2010,27(11)：160-166.
[109]Takizawa H, Aoyama M. Biaxial effects in modeling earthquake response of RC structures [J]. Earthquake Engineering and Structure Dynamics,1976,4(6):523-552.
[110]Lachance L. Ultimate strength of biaxially loaded composite sections[J]. Journal of the Structural Division,1982,108(10):2313-2329.
[111]ZahnFA, Park R, Priestly M J N. Strength and ductility of square reinforced concrete column sections subjected to biaxial bending [J]. ACI Structural Journal,1989,56(2): 123-131.
[112]Bousias S N, VerzelletiG, FardisMN, MagonetteG. RC columns in cyclic biaxial bending and axial load [C]. Proceedings of the 10th World Conference on Earthquake Engineering, Madrid.1992:3041-3046.
[113]Munoz P R, Hsu C T. Biaxially loaded concrete-encased composite columns:Design equation [J].Journal of Structural Engineering,1997,123(12):1576-1585.
[114]Kim J K, Lee S S. The behavior of reinforced concrete columns subjected to axial force and biaxial bending [J]. Engineering Structures,2000,22(11):1518-1528.
[115]Hong H P. Strength of slender reinforced concrete columns under biaxial bending [J]. Journal of Structural Engineering,2001,127(7):758-762.
[116]Tsuno K, Park R. Experimental study of reinforced concrete bridge piers subjected to bi-directional quasi-static loading[J]. Structural Engineering Earthquake Engineering,2004,21(1):11s-26s.
[117]Hsu H L, Jan F J, Juang J L. Performance of composite members subjected to axial load and bi-axial bending [J]. Journal of Constructional Steel Research,2009,65:869-878.
[118]Chang S Y. Experimental studies of reinforced concrete bridge columns under axial load plus biaxial bending [J]. Journal of Structural Engineering,2010,136(1):12-25.
[119]Otani S, Cheung V W T, Lai S S. Behavior and analytical models of reinforced concrete columns under biaxial earthquake loads [C]. Third Canadian Conference on Earthquake Engineering, Canadian National Committee for Earthquake Engineering et al, Montreal, 1979, (2):1141-1167.
[120]Ogawa J et al. Damage behavior of reinforced concrete columns under uniaxial and biaxial lateral loading [J]. Journal of Structural and Construction Engineering, 1991, (419):87-98.
[121]Ogawa J et al. Earthquake damage evaluation of reinforced concrete columns [C]. Proceedings of the Tenth World Conference on Earthquake Engineering, A. A. Balkema, Rotterdam,1992, (5):3053-3058.
[122]Ogawa J et al. Flexural behavior of precast and reinforced concrete columns under biaxial loadings [C]. Proceedings,10th European Conference on Earthquake Engineering, A. A. Balkema, Rotterdam,1995, (3):2383-2388.
[123]Saatcioglu M, Ozcebe G. Response of reinforced concrete columns to simulated seismic loading [J]. ACI Structural Journal,1989,86(1):3-12.
[124]Sato T, Kobayashi H. A study on reinforced concrete columns under cyclic biaxial moment [J]. Memoirs of the Faculty of Engineering, Osaka City University,2004, (45):29-36.
[125]Rodrigues H, Arede A, Varum H, et al. Experimental evaluation of rectangular reinforced concrete column behavior under biaxial cyclic loading [J]. Earthquake Engineering & Structural Dynamics,2013,42(2):239-259.
[126]Qiu F W, Li W F, Pan P, Qian J. Experimental tests on reinforced concrete columns under biaxial quasi-static loading [J].2002,24:419-428.
[127]康洪震,江见鲸.不同加载路径下钢筋混凝土框架柱抗震性能的试验研究[J].土木工程学报,2003,36(5)：71-75.
[128]Kogoma I, Hayashida T, Minowa C. Experimental studies on the collapse of RC columns during strong earthquake motions [C]. Proceedings of the Tenth World Conference on Earthquake Engineering, A. A. Balkema, Rotterdam,1992, (5):3013-3017.
[129]Kitajima K et al. Response characteristics of reinforced concrete columns under bi-directional earthquake motions [C]. Proceedings of the Tenth World Conference on Earthquake Engineering, A. A. Balkema, Rotterdam,1992,(5):3019-3024.
[130]Kitajima K, Adachi H, Nakanishi M. Response characteristics of reinforced concrete structures under bi-directional earthquake motions [C]. Eleventh World Conference on Earthquake Engineering, Pergamon, Elsevier Science Ltd, (Oxford, England),1996,Disc 1, Paper No.566.
[131]Nakeyama T et al. Shaking table tests of reinforced concrete structures under bi-directional earthquake motions [C]. Eleventh World Conference on Earthquake Engineering, Oxford, England,1996, Paper No.1001.
[132]Inoue N et al. Shaking table tests of reinforced concrete columns subjected to simulated input motions with different time durations [C]. Proceedings of the 12th World Conference on Earthquake Engineering, New Zealand,2000, Paper No.1734.
[133]Ogimoto H, Kawashima K, Watanabe G, Nagata S. Effect of bilateral excitation on the seismic performance of reinforced concrete bridge columns based on hybrid loading test [J]. Journal of Structure Mechanic Earthquake Engineering JSCE,2005,801: 33-50.
[134]Sakai J, Unjoh S. Shake table experiment on circular reinforced concrete bridge column under multidirectional seismic excitation [J]. Structural Engineering Research Frontiers,2007:1-12.
[135]陈肇元.高强钢筋在快速变形下的性能及其在抗爆结构中的应用[R].科学研究报告第四集：钢筋混凝土结构构件在冲击荷载下的性能.北京：清华大学出版社.1986.
[136]宋军.应变率敏感材料物理参量的研究及其工程应用[D].北京：清华大学,1990.
[137]Zech B, and Wittmann F H. Variability and mean value of strength of concrete as a function of load [C]. ACI Journal Proceedings,1980,77(5).
[138]Zielinski A J. Reinhardt H W. Stress-strain behavior of concrete and mortar at high rates of tensile loading [J]. Cement and concrete research,1982,12(3):309-319.
[139]Ghabossi J, Millavee W A, Isenberg J. RC structures under impulsive loading [J]. Journal of Structural Engineering, ASCE,1984,110(3):505-522.
[140]Karauthammer T. Shallow-buried RC box-type structures [J]. Journal of Structural Engineering, ASCE,1984,110(3):637-651.
[141]Krauthammer T, Bazeos N, Hohmquist T J. Modeified SDOF analysis of RC box-type structures [J]. Journal of Structural Engineering, ASCE,1986,112(4):726-744.
[142]Kunnath S K, Reinhorn A M. Model for inelastic biaxial.bending interaction of reinforced concrete beam-columns [J]. ACI Structural Journal,1990,87(3):284-291.
[143]Sziveri J, Topping B H V, Ivanyi P. Parallel transient dynamic non-linear analysis of reinforced concrete plates [J]. Advances in Engineering Software,1999,87(3): 867-882.
[144]方秦,柳锦春,张亚栋,钱七虎.爆炸荷载作用下钢筋混凝土梁破坏形态有限元分析[J].工程力学,2001,18(2)：1-8.
[145]王利恒,周锡元,闫维明,等.钢筋混凝土梁非线性动力特性试验研究[J].地震研究,2006,29(1)：65-71.
[146]Pozzo E. The influence of axial load and rate of loading on experimental post-elastic behavior and ductility of reinforced concrete members [J]. Materials and Structures, 1987,20(4):303-314.
[147]Kulkarni S M, Shah S P. Response of reinforced concrete beams at high strain rates [J]. ACI Structural Journal,1998,95(6).
[148]Park Y J, Ang H S. Mechanistic seismic damage model for reinforced concrete [J]. Journal of Structure Engineering, ASCE,1985,111(4):722-739.
[149]Park Y J, Ang A H S, Wen Y K. Seismic damage analysis of reinforced concrete buildings [J]. Journal of Structural Engineering,1985,111(4):740-757.
[150]EIBL J. Concrete structures under impact and impulsive loading (CEB-Bulletind' information, No.187) [R]. Dubrovnik:Comite Euro-International du Beton,1988.
[151]中华人民共和国建设部.GB 50010-2010,混凝土结构设计规范[S].北京：中国建筑工业出版社,2010.
[152]Panagiotakos T B, Fardis M N. Deformations of reinforced concrete members at yielding and ultimate [J]. ACI Structural Journal,2001,98(2):135-148.
[153]Kobayashi K, Kokusho S, Takiguchi K, et al. Study on the restoring force characteristics of RC column to bi-directional deflection history [C]//Proc. of the 8th World Conference on Earthquake Engineering, San Francisco,1984:537-544.
[154]Studies on Earthquake Engineering, Digests of Project Research Activities [R]. The Institute of Industrial Science, University of Tokyo, March 1986, (5):106-107.
[155]Low S S, Moehle J P. Experimental study of reinforced concrete columns subjected to multi-axial cyclic loading [M]. Earthquake Engineering Research Center, University of California,1987.
[156]Bousias S N, Verzeletti G, Fardis M N, et al. Load-path effects in column biaxial bending with axial force [J]. Journal of Engineering Mechanics,1995,121(5): 596-605.
[157]江近仁,康慨,张令心.钢筋混凝土柱的双轴弯曲特性[J].世界地震工程,1998,14(4)：23-29.
[158]陈滔.基于单元柔度法的钢筋混凝土框架三维非线性地震反应分析[D].重庆：重庆大学,2003.
[159]Rodrigues H, Varum H, Arede A, Costa A. A comparative analysis of energy dissipation and equivalent viscous damping of RC columns subjected to uniaxial and biaxial loading[J]. EngStruct 2012; 35:149-164.
[160]Gulkan P, Sozen M A. Inelastic response of reinforced concrete structure to earthquake motions[J]. ACI Journal Proceedings.1974,71(12).
[161]Stojadinovic B, Thewalt C R. Energy balanced hysteresis models[C]. Eleventh World Conference on Earthquake Engineering, Earthquake Engineering Research at Berkeley, College of Engineering, University of California at Berkeley,1996.
[162]Lu Y, Hao H, Carydis P G, et al. Seismic performance of RC frames designed for three different ductility levels[J]. Engineering Structures,2001,23(5):537-547.
[163]Priestley M J N, Calvi G M, Kowalsky M J. Direct displacement-based seismic design of structures[C]. The 5th NZSEE Conference,2007.
[164]Mazzoni S, McKennaF, Scott MH, FenvesGL. OpenSees Users Manual [R]. PEER, University of California, Berkeley.2004.
[165]ABAQUS V6.8. ABAQUS/Standard user's manual.2008.
[166]Mazzoni S, McKenna F, Scott M H, Fenves G L. OpenSees Example Manual [R]. PEER, University of California, Berkeley.2003.
[167]陈学伟.剪力墙结构构件变形指标的研究及计算平台开发[D].广州：华南理工大学,2011.
[168]Karsan I D, Jirsa J 0. Behavior of concrete under compressive loadings [J]. Journal of the structural division, ASCE,1969,95(12),2543-2563.
[169]Menegotto M, Pinto P E. Method of analysis for cyclically loaded reinforced concrete plane frames including changes in geometry and non-elastic behavior of elements under combined normal force and bending[C]./ABSE Symposium on the resistance and ultimate deformability of structures acted on by well-defined repeated loads, Lisbon.1973.
[170]Mo Y L, Wang S J. Seismic behavior of RC columns with various tie configurations [J]. Journal of Structural Engineering,2000,126(10):1122-1130.
[171]Martinelli P, Filippou F C. Simulation of the shaking table test of a seven-story shear wall building[J]. Earthquake Engineering & Structural Dynamics,2009, 38(5):587-607.
[172]Meng C, Lu X. Application of flexibility-based fiber-model beam-column element in simulation analysis of CFRT columns[J]. Journal of Earthquake Engineering and Engineering Vibration,2009,4:009.
[173]张强,周德源,伍永飞,等.钢筋混凝土框架结构非线性分析纤维模型研究[J].土木工程师,2008,24(1)：15-25.
[174]Priestley M J N, Calvi G M and Kowalsky M J. Displacement based seismic design of structure[J]. IUSS Press, Italy,2007,721.
[175]Zhao J, Sritharan S. Modelling of strain penetration effects in fibre-based analysis of reinforced concrete structures[J]. ACI Structure Journal,2007,104(2):133-141.
[176]Priestley M J N, Verna R, Xiao Y. Seismic Shear Strength of Reinforced Concrete Columns [J]. Journal of Structural Engineering,ASCE,1994,120 (8):2310-2329.
[177]Kunnath S K, Heo Y A, Mohle J F. Nonlinear uniaxial material model for reinforcing steel bars [J]. Journal of structural engineering,2009,135:335.
[178]Chang G, Mander J B. Seismic energy based fatigue damage analysis of bridge columns Part Ⅰ:Evaluation of seismic capacity [R]. NCEER Report 94-0006,1997.
[179]Gomes A, Appleton J. Nonlinear cyclic stress-strain relationship of reinforcing bars including buckling [J]. Engineering Structures,1997,19(10):822-826.
[180]Dhakal R P, Maekawa K. Modeling for postyield buckling of reinforcement [J]. Journal of Structural Engineering,2002,128(9):1139-1147.
[2]Soroushian P, Obaseki K. Strain rate-dependent interaction diagrams for reinforced concrete sections [C]. ACI Journal Proceedings. ACI,1986,83(1).
[3]李宏男.结构多维抗震理论[M].科学出版社,2006.
[4]Watstein D. Effect of straining rate on the compressive strength and elastic properties of concrete [C]. ACI Journal Procedings, ACI,1953,49(4).
[5]Sparks P R, Menzies J B. The effect of rate of loading upon the static and fatigue strengths of plain concrete in compression [J]. Magazine of Concrete Research,1973, 25(83):73-80.
[6]Hughes B P, Watson A J. Compressive strength and ultimate strain of concrete under impact loading [J]. Magazine of Concrete Research,1978,30(105):189-199.
[7]尚仁杰.混凝土动态本构行为研究[D].大连：大连理工大学,1994.
[8]肖诗云.混凝土率型本构模型及其在拱坝动力分析中的应用[D].大连：大连理工大学,2002.
[9]李杰,任晓丹.混凝土静力与动力损伤本构模型研究进展评述[J].力学进展,2010,40(3)：284-297.
[10]Mellinger F M,Birkimer D L. Measurement of stress and strain on cylindrical test specimens of rock and concrete under impact loading [R]. Ohio River Div Labs Cincinnati, 1966.
[11]Birkimer D L, Lindemann R. The impact strength of concrete materials [J]. American Concrete Institute,1971,68:47-49.
[12]Yon J H, Hawkins N M, Kobayashi A S. Strain rate sensitivity concrete mechanical properties [J]. ACI Material Journal,1992,89(2):146-153.
[13]闫东明,林皋,王哲,等.不同应变速率下混凝土直接拉伸试验研究[J].土木工程学报,2005,38(6)：97-103.
[14]Mlakar P F, Vitaya-Udom K P, Cole R A. Dynamic tensile-compressive behavior of concrete [J]. ACI Journal Proceedings. ACI,1985,82(4).
[15]Zielinski A J. Concrete under biaxial compressive-impact tensile loading [J]. Fracture Toughness and Fracture Energy of Concrete.1986,489.
[16]Weerheijm J. Concrete under impact tensile loading and lateral compression [D]. Delft: Delft University of Technology,1992.
[17]鞠庆海,吴绵拔.岩石材料三轴压缩动力特性的试验研究[J].岩土工程学报,1993,15(3)：73-80.
[18]闫东明.混凝土动态力学性能试验与理论研究[D].大连：大连理工大学,2006.
[19]Scott B D, Park R, Priestley M J N. Stress-strain behavior of concrete confined by overlapping hoops at low and high strain rates [J]. ACI Journal Proceedings. ACI, 1982,79(1):13-27.
[20]Kent D C, Park R. Flexural members with confined concrete [J]. Journal of the Structural Division,1971,97(7):1969-1990.
[21]Dilger W H, Koch R, Kowalczyk R. Ductility of plain and confined concrete under different strain rates [J]. ACI Journal Proceedings. ACI,1984,81(1):73-81.
[22]Sargin M, Ghosh S K, Handa V K. Effects of lateral reinforcement upon the strength and deformation properties of concrete [J]. Magazine of Concrete Resesearch, 1971,23(75/76):99-118.
[23]Soroushian P, Choi K, Alhamad A. Dynamic constitutive behavior of concrete [J]. ACI Journal Proceedings. ACI,1986,83(2):251-258.
[24]Mander J B, Priestley J N, Park R. Observed stress-strain behavior of confined concrete [J]. Journal of Structural Engineering,1988,114(8):1827-1849.
[25]Mander J B, Priestley J N, Park R. Theoretical stress-strain model for confined concrete [J]. Journal of Structural Engineering,1988,114(8):1804-1826,
[26]Ahmad S H, Shah S P. Behavior of hoop confined concrete under high strain rates [J]. ACI Journal Proceedings. ACI,1985,82(5):634-647.
[27]CEB. Concrete structures under impact and implosive loading [R]. Synthesis Report. Lausanne:Committee Euro-International du Beton,1998,187.
[28]Gebbeken N, Ruppert M. A new material model for concrete in high-dynamic hydrocode simulations [J]. Archive of Applied Mechanics,2000,70(7):463-478.
[29]Malvar L J, John E C. Dynamic increase factors for steel reinforcing bars [C]. 1st ed. Florida:Twenty-Eighth DDESB (Department of Defense Explosives Safety Board) Seminar, 1998.
[30]Malvar L J, Ross C A. Review of strain rate effects for concrete in tension [J]. ACI Materials Journal,1998,95(6):735-739.
[31]Tedesco J W, Ross C A. Strain-rate-dependent constitutive equation for concrete [J]. Journal of Pressure Vessel Technology,1998, (120):398-405.
[32]Bischoff P H, Perry S H. Compressive behavior of concrete at high strain rates [J]. Materials and Structures,1991,24:425-450.
[33]董毓利,谢和平,赵鹏.不同应变率下混凝土受压全过程的实验研究及其本构模型[J].水利学报,1997,(7)：72-77.
[34]Soroushian P, Choi K, Kowalczak R. Ductility of plain and confined concrete under different strain rates [J]. ACI Journal Proceedings. ACI,1984:73-81.
[35]Lu Y, Xu K. Modeling of dynamic behavior of concrete materials under blast loading [J]. International Journal of Solids and Structures,2004,41(1):131-143.
[36]Grote D L, Park S W, Zhou M. Dynamic behavior of concrete at high strain-rates and pressures:I. Experimental characterization[J]. International Journal of Impact Engineering,2001,25(9):869-886.
[37]Ross P, Van Mier J G M, Boulay C. The dynamic behavior of concrete:The influence of free water [J]. Materials and Structures,1992,25:509-514.
[38]Ross P, Toutlemonde F. Effect of loading rate on the tensile behavior of concrete: description of physical mechanisms [J]. Materials and Structures,1996,29(2): 116-118.
[39]Tang T, Malvern L E, Jenkins D A. Rate effects in uniaxial dynamic compression of concrete [J]. Journal of Engineering Mechanics,1992,118(1):108-124.
[40]Holmquist T J, Johnson G R,. Cook W H. A computational constitutive model for concrete subjected to large strains, high strain rates and high pressures[C]. The 14th International Symposium on Ballistics, Quebec, Canada,1993.
[41]陈书宇.一种混凝土损伤本构模型和数值方法[J].爆炸与冲击,1998,18(4)：349-357.
[42]陈书宇,陈成光.混凝土本构模型及其动态有限元算法研究[J].上海力学,1998,19(2)：109-116.
[43]唐志平,田兰桥,朱兆祥,等.高应变率下环氧树脂的力学性能[C].第二届爆炸力学会议文集,扬州,1981,53：88-166.
[44]唐志平.高应变率下环氧树脂的动态力学性能[D].合肥：中国科学技术大学,1981.
[45]刘文彦.水泥基复合材料在冲击载荷下的力学响应和纤维的桥联行为研究[D].合肥：中国科学技术大学,2001.
[46]王礼立,余同希,李永池.冲击动力学进展[M].合肥：中国科学技术大学出版社,1992.
[47]Duvaut G, Lions J L. Les inequations en mecanique et en physique [M]. Paris:Dunod, 1972.
[48]Wang W M. Stationary and propagative instabilities in metals:a computational point of view[M]. Delft University Press,1997.
[49]Lemaitre J, Plumtree A. Application of damage concepts to predict creep-fatigue failures[J]. Journal of Engineering Materials and Technology,1979,101:284.
[50]李兆霞.一个综合模糊裂纹和损伤的混凝土应变软化本构模型[J].固体力学学报,1995,16(1)：22-30.
[51]Suaris W, Shah S P. Rate-sensitive damage theory for brittle solids[J]. Journal of engineering mechanics,1984,110(6):985-997.
[52]Bui H D, Ehrlacher A. Propagation of damage in elastic and plastic solids [J]. Advances in Fracture Research,1981, (2):533-551.
[53]Burlion N, Gatuingt F, Pijaudier C G. Compaction and tensile damage in concrete constitutive modeling and application to dynamics [J]. Computer Methods in Applied Mechanics and Engineering,2000,183(3):291-308.
[54]Sukontasukkul P, Ninityongskul P, Mindess S. Effect of loading rate on damage of concrete [J]. Cement and Concrete Research,2004,34(11):2127-2134.
[55]Cervera M, Oliver J, Manzoli 0. A rate-dependent isotropic damage model for the seismic analysis of concrete dams [J]. Earthquake Engineering and Structure Dynamics,1996, 25(9):987-1010.
[56]Faria R, Olivella J 0. A rate dependent plastic-damage constitutive model for large scale computations in concrete structures[M]. Centro Internacional de Metodos Numericos en Ingenieria,1993.
[57]Faria R, Oliver J, Cervera M. A strain-based plastic viscous-damage model for massive concrete structures[J]. International Journal of Solids Structures,1998,35(14): 1533-1558.
[58]李庆斌,邓宗才,张立翔.考虑初始弹性模量变化的混凝土动力损伤本构模型[J].清华大学学报,2003,43(8)：1088-1091.
[59]邓宗才.单轴状态下混凝土的静力、动力损伤本构模型[J].山东建材学院学报,1999,13(4)：334-337.
[60]杜荣强,林皋.混凝土动力损伤本构关系的基础理论及应用[J].哈尔滨工业大学学报,2006,38(5)：746-751.
[61]胡时胜,王道荣.冲击荷载下混凝土材料的动态本构关系[J].爆炸与冲击,2002,22(3)：242-246.
[62]吴建营,李杰.考虑应变率效应的混凝土动力弹塑性损伤本构模型[J].同济大学学报(自然科学版),2006,34(11)：1427-1430.
[63]吴建营,李杰.反映阻尼影响的混凝土弹塑性损伤本构模型[J].工程力学,2006,23(11)：116-121.
[64]肖诗云,田子坤.混凝土单轴动态受拉损伤试验研究[J],土木工程学报,2008,41(7)：14-20.
[65]Eibl J. Concrete structures under impact and impulsive loading (CEB-Bulletind' information, NO.187) [R] Dubrovnik:Comite Euro-International du Beton,1988.
[66]Restrepo-Posada J I, Dodd L L, Park R, et al. Variables affecting cyclic behavior of reinforcing steel [J]. Journal of Structural Engineering,1994,120(11):3178-3196.
[67]Cadoni E, Fenu L, Forni D. Strain rate behavior in tension of austenitic stainless steel used for reinforcing bars [J]. Construction and Building Materials,2012,35: 399-407.
[68]陈肇元,曹炽康,李庆标.建筑钢筋在快速变形下的力学性能[R].抗爆结构研究报告第一集：结构材料的动力性能及其计算强度.北京：清华大学,1971.
[69]林峰,顾祥林,匡昕昕,等.高应变率下建筑钢筋的本构模型[J].建筑材料学报,2008,11(1)：14-20.
[70]李敏,李宏男.建筑钢筋动态试验及本构模型[J].土木工程学报,2010,43(4)：70-75.
[71]Manjoine M J. Influence of rate of strain and temperature on yield stress of mild steel [J]. Journal of Applied Mechanics,1944,11:211-218.
[72]Cowper G R, Symonds P S. Strain hardening and strain rate effect in the impact loading of cantilever beams [R]. Brown University, Division of Applied Mathematics report, 1957, p.28.
[73]Johnson G R, Cook W H. A constitutive model and data for metals subjected to large strains, high strain rate, and temperatures [C]. Proceedings of the 7th International Symposium on Ballistics. The Hague, Netherlands:International Ballistics Committee, 1983,21:541-547.
[74]Soroushian P, Choi K B. Steel mechanical properties at different strain rates [J]. Journal of Structural Engineering,1987,113(4):663-672.
[75]Malvar L J. Review of static and dynamic properties of steel reinforcing bars [J]. ACI Material Journal,1998,95(5):609-616.
[76]Vos E, Reinhardt H W. Influence of loading rate on bond behaviour of reinforcing steel and prestressing strands[J]. Materiaux et Construction,1982,15(1):3-10.
[77]Takeda J. Strain Rate Effects on Concrete and Reinforcements, and their Contributions to Structures[C]. MRS Proceedings. Cambridge University Press,1985,64(1).
[78]Mindess S. Effects of dynamic loading on bond[R]. ACI Committee 446:State of the Art Report, Section 4.2.3,1989.
[79]Banthia N P, Mindess S, Bentur A. Impact behavior of concrete beams [J]. Materials and Structures,1987,20(118):293-302.
[80]Yan C. Bond between reinforcing bars and concrete under impact loading [D]. The University of British Columbia,1992.
[81]洪小健,赵鸣.加载速率对锈蚀钢筋与混凝土粘结性能的影响[J].同济大学学报,2002,30(7)：792-796.
[82]Mahin S A, Bertero V V, Atalay M B, Rea D. Rate of loading effects on uncracked and repaired reinforced concrete members [C]. Proceedings, Fifth World Conference on Earthquake Engineering, Rome.1973,1:1461-1470.
[83]Bertero V V, Rea D, Mahin S, et al. Rate of loading effects on uncracked and repaired reinforced concrete members [C]. Proceeding of fifth world conference on earthquake engineering, Rome,1973(1):1461-1471.
[84]Mutsuyoshi H, Machida A. Properties and failure of reinforced concrete members subjected to dynamic loading [J]. Transactions of the Japan Concrete Institute,61 521-528.
[85]Mutsuyoshi H, Machida A. Dynamic properties of reinforced concrete piers [C]. Proceeding of eighth world conference on earthquake engineering, San Francisco, 1984(6):299-306.
[86]Kulkarni S M, Shah S P. Response of reinforced concrete beams at high strain rates [J]. ACI Structural Journal,1998,95(6):705-715.
[87]Chung L, Shah S P. Effect of loading rate on anchorage bond and beam-column joints [J]. ACI Structural Journal,1989,86(2):132-142.
[88]Al-Haddad M S.Curvature ductility of reinforced concrete beams under low and high strain rates [J]. ACI Structural Journal,1995,92(5):526-534.
[89]Otani S, Kaneko T, Shiohara H. Strain rate effect on performance of reinforced concrete members [C]. Concrete structures in seismic regions:FiB,2003.
[90]Ozbolt J, Sharma A. Numerical simulation of reinforced concrete beams with different shear reinforcements under dynamic impact loads [J]. International Journal of Impact Engineering,2011,38:940-950.
[91]Adhikary S D, Li B, Fujikake K. Dynamic behavior of reinforced concrete beams under varying rates of concentrated loading [J]. International Journal of Impact Engineering,2012,47:24-38.
[92]陈肇元,施岚青.钢筋混凝土梁在静速和快速变形下的弯曲性能[R].科学研究报告第四集：钢筋混凝土结构构件在冲击荷载下的性能。北京：清华大学出版社,1986.
[93]陈俊名.钢筋混凝土剪力墙动力加载试验及考虑应变率效应的有限元模拟[D].长沙：湖南大学,2010.
[94]肖诗云,曹闻博,潘浩浩.不同加载速率下钢筋混凝土梁力学性能试验研究[J].建筑结构学报,2012,33(12)：142-146.
[95]许斌,龙业平.基于纤维模型的钢筋混凝土柱应变率效应研究[J].工程力学,2011,28(7)：103-108.
[96]Li M, Li H N. Effects of strain rate on reinforced beam [J]. Advanced Materials Research, 2011,243:4033-4036.
[97]邹笃建,刘铁军,滕军,严桂兰.混凝土梁式构件弹性模量的应变率效应研究[J].振动工程学报,2011,24(2)：170-174.
[98]Kreger M E, Linbeck L. Behavior of reinforced concrete columns subjected to lateral axial load reversals [C]. The 3rd U. S. National Conference on earthquake Engineering, Charleston, South Carolina,1986,2:24-28.
[99]Abrams D P. Influence of axial force variations on flexural behavior of reinforced concrete columns [J]. ACI Structural Journal,1987,84(3):246-254.
[100]Kuramoto H, Kabeyasawa T, Shen F H. Influence of axial deformation on ductility of high-strength reinforced concrete columns under varying tri-axial force [J]. ACI Structural Journal,1995,92(9):610-618.
[101]Saadeghvaziri M A. Nonlinear response and modeling of RC columns subjected to varying axial load [J]. Engineering Structures,1997,19(6):417-424.
[102]EIMandooh Galal K, Ghobarah A. Flexural and shear hysteretic behavior of reinforced concrete columns with variable axial load [J]. Engineering Structure,2003,25(11): 1353-1367.
[104]邢秋顺,季耀东,陈肇元.变轴力下钢筋混凝土受弯截面的性能[J].建筑结构学报,1987,(5)：52-61.
[106]黄翔.规则变轴力作用下钢筋混凝土框架柱的抗震性能研究[D].重庆：重庆建筑大学,1995.
[107]钟树生.水平及竖向荷载地震作用下钢筋混凝土柱抗震性能的试验研究[D].重庆：重庆大学,1999.
[108]顾祥林,蔡茂,林峰.地震作用下钢筋混凝土柱受力性能研究[J].工程力学,2010,27(11)：160-166.
[109]Takizawa H, Aoyama M. Biaxial effects in modeling earthquake response of RC structures [J]. Earthquake Engineering and Structure Dynamics,1976,4(6):523-552.
[110]Lachance L. Ultimate strength of biaxially loaded composite sections[J]. Journal of the Structural Division,1982,108(10):2313-2329.
[111]ZahnFA, Park R, Priestly M J N. Strength and ductility of square reinforced concrete column sections subjected to biaxial bending [J]. ACI Structural Journal,1989,56(2): 123-131.
[112]Bousias S N, VerzelletiG, FardisMN, MagonetteG. RC columns in cyclic biaxial bending and axial load [C]. Proceedings of the 10th World Conference on Earthquake Engineering, Madrid.1992:3041-3046.
[113]Munoz P R, Hsu C T. Biaxially loaded concrete-encased composite columns:Design equation [J].Journal of Structural Engineering,1997,123(12):1576-1585.
[114]Kim J K, Lee S S. The behavior of reinforced concrete columns subjected to axial force and biaxial bending [J]. Engineering Structures,2000,22(11):1518-1528.
[115]Hong H P. Strength of slender reinforced concrete columns under biaxial bending [J]. Journal of Structural Engineering,2001,127(7):758-762.
[116]Tsuno K, Park R. Experimental study of reinforced concrete bridge piers subjected to bi-directional quasi-static loading[J]. Structural Engineering Earthquake Engineering,2004,21(1):11s-26s.
[117]Hsu H L, Jan F J, Juang J L. Performance of composite members subjected to axial load and bi-axial bending [J]. Journal of Constructional Steel Research,2009,65:869-878.
[118]Chang S Y. Experimental studies of reinforced concrete bridge columns under axial load plus biaxial bending [J]. Journal of Structural Engineering,2010,136(1):12-25.
[119]Otani S, Cheung V W T, Lai S S. Behavior and analytical models of reinforced concrete columns under biaxial earthquake loads [C]. Third Canadian Conference on Earthquake Engineering, Canadian National Committee for Earthquake Engineering et al, Montreal, 1979, (2):1141-1167.
[120]Ogawa J et al. Damage behavior of reinforced concrete columns under uniaxial and biaxial lateral loading [J]. Journal of Structural and Construction Engineering, 1991, (419):87-98.
[121]Ogawa J et al. Earthquake damage evaluation of reinforced concrete columns [C]. Proceedings of the Tenth World Conference on Earthquake Engineering, A. A. Balkema, Rotterdam,1992, (5):3053-3058.
[122]Ogawa J et al. Flexural behavior of precast and reinforced concrete columns under biaxial loadings [C]. Proceedings,10th European Conference on Earthquake Engineering, A. A. Balkema, Rotterdam,1995, (3):2383-2388.
[123]Saatcioglu M, Ozcebe G. Response of reinforced concrete columns to simulated seismic loading [J]. ACI Structural Journal,1989,86(1):3-12.
[124]Sato T, Kobayashi H. A study on reinforced concrete columns under cyclic biaxial moment [J]. Memoirs of the Faculty of Engineering, Osaka City University,2004, (45):29-36.
[125]Rodrigues H, Arede A, Varum H, et al. Experimental evaluation of rectangular reinforced concrete column behavior under biaxial cyclic loading [J]. Earthquake Engineering & Structural Dynamics,2013,42(2):239-259.
[126]Qiu F W, Li W F, Pan P, Qian J. Experimental tests on reinforced concrete columns under biaxial quasi-static loading [J].2002,24:419-428.
[127]康洪震,江见鲸.不同加载路径下钢筋混凝土框架柱抗震性能的试验研究[J].土木工程学报,2003,36(5)：71-75.
[128]Kogoma I, Hayashida T, Minowa C. Experimental studies on the collapse of RC columns during strong earthquake motions [C]. Proceedings of the Tenth World Conference on Earthquake Engineering, A. A. Balkema, Rotterdam,1992, (5):3013-3017.
[129]Kitajima K et al. Response characteristics of reinforced concrete columns under bi-directional earthquake motions [C]. Proceedings of the Tenth World Conference on Earthquake Engineering, A. A. Balkema, Rotterdam,1992,(5):3019-3024.
[130]Kitajima K, Adachi H, Nakanishi M. Response characteristics of reinforced concrete structures under bi-directional earthquake motions [C]. Eleventh World Conference on Earthquake Engineering, Pergamon, Elsevier Science Ltd, (Oxford, England),1996,Disc 1, Paper No.566.
[131]Nakeyama T et al. Shaking table tests of reinforced concrete structures under bi-directional earthquake motions [C]. Eleventh World Conference on Earthquake Engineering, Oxford, England,1996, Paper No.1001.
[132]Inoue N et al. Shaking table tests of reinforced concrete columns subjected to simulated input motions with different time durations [C]. Proceedings of the 12th World Conference on Earthquake Engineering, New Zealand,2000, Paper No.1734.
[133]Ogimoto H, Kawashima K, Watanabe G, Nagata S. Effect of bilateral excitation on the seismic performance of reinforced concrete bridge columns based on hybrid loading test [J]. Journal of Structure Mechanic Earthquake Engineering JSCE,2005,801: 33-50.
[134]Sakai J, Unjoh S. Shake table experiment on circular reinforced concrete bridge column under multidirectional seismic excitation [J]. Structural Engineering Research Frontiers,2007:1-12.
[135]陈肇元.高强钢筋在快速变形下的性能及其在抗爆结构中的应用[R].科学研究报告第四集：钢筋混凝土结构构件在冲击荷载下的性能.北京：清华大学出版社.1986.
[136]宋军.应变率敏感材料物理参量的研究及其工程应用[D].北京：清华大学,1990.
[137]Zech B, and Wittmann F H. Variability and mean value of strength of concrete as a function of load [C]. ACI Journal Proceedings,1980,77(5).
[138]Zielinski A J. Reinhardt H W. Stress-strain behavior of concrete and mortar at high rates of tensile loading [J]. Cement and concrete research,1982,12(3):309-319.
[139]Ghabossi J, Millavee W A, Isenberg J. RC structures under impulsive loading [J]. Journal of Structural Engineering, ASCE,1984,110(3):505-522.
[140]Karauthammer T. Shallow-buried RC box-type structures [J]. Journal of Structural Engineering, ASCE,1984,110(3):637-651.
[141]Krauthammer T, Bazeos N, Hohmquist T J. Modeified SDOF analysis of RC box-type structures [J]. Journal of Structural Engineering, ASCE,1986,112(4):726-744.
[142]Kunnath S K, Reinhorn A M. Model for inelastic biaxial.bending interaction of reinforced concrete beam-columns [J]. ACI Structural Journal,1990,87(3):284-291.
[143]Sziveri J, Topping B H V, Ivanyi P. Parallel transient dynamic non-linear analysis of reinforced concrete plates [J]. Advances in Engineering Software,1999,87(3): 867-882.
[144]方秦,柳锦春,张亚栋,钱七虎.爆炸荷载作用下钢筋混凝土梁破坏形态有限元分析[J].工程力学,2001,18(2)：1-8.
[145]王利恒,周锡元,闫维明,等.钢筋混凝土梁非线性动力特性试验研究[J].地震研究,2006,29(1)：65-71.
[146]Pozzo E. The influence of axial load and rate of loading on experimental post-elastic behavior and ductility of reinforced concrete members [J]. Materials and Structures, 1987,20(4):303-314.
[147]Kulkarni S M, Shah S P. Response of reinforced concrete beams at high strain rates [J]. ACI Structural Journal,1998,95(6).
[148]Park Y J, Ang H S. Mechanistic seismic damage model for reinforced concrete [J]. Journal of Structure Engineering, ASCE,1985,111(4):722-739.
[149]Park Y J, Ang A H S, Wen Y K. Seismic damage analysis of reinforced concrete buildings [J]. Journal of Structural Engineering,1985,111(4):740-757.
[150]EIBL J. Concrete structures under impact and impulsive loading (CEB-Bulletind' information, No.187) [R]. Dubrovnik:Comite Euro-International du Beton,1988.
[151]中华人民共和国建设部.GB 50010-2010,混凝土结构设计规范[S].北京：中国建筑工业出版社,2010.
[152]Panagiotakos T B, Fardis M N. Deformations of reinforced concrete members at yielding and ultimate [J]. ACI Structural Journal,2001,98(2):135-148.
[153]Kobayashi K, Kokusho S, Takiguchi K, et al. Study on the restoring force characteristics of RC column to bi-directional deflection history [C]//Proc. of the 8th World Conference on Earthquake Engineering, San Francisco,1984:537-544.
[154]Studies on Earthquake Engineering, Digests of Project Research Activities [R]. The Institute of Industrial Science, University of Tokyo, March 1986, (5):106-107.
[155]Low S S, Moehle J P. Experimental study of reinforced concrete columns subjected to multi-axial cyclic loading [M]. Earthquake Engineering Research Center, University of California,1987.
[156]Bousias S N, Verzeletti G, Fardis M N, et al. Load-path effects in column biaxial bending with axial force [J]. Journal of Engineering Mechanics,1995,121(5): 596-605.
[157]江近仁,康慨,张令心.钢筋混凝土柱的双轴弯曲特性[J].世界地震工程,1998,14(4)：23-29.
[158]陈滔.基于单元柔度法的钢筋混凝土框架三维非线性地震反应分析[D].重庆：重庆大学,2003.
[159]Rodrigues H, Varum H, Arede A, Costa A. A comparative analysis of energy dissipation and equivalent viscous damping of RC columns subjected to uniaxial and biaxial loading[J]. EngStruct 2012; 35:149-164.
[160]Gulkan P, Sozen M A. Inelastic response of reinforced concrete structure to earthquake motions[J]. ACI Journal Proceedings.1974,71(12).
[161]Stojadinovic B, Thewalt C R. Energy balanced hysteresis models[C]. Eleventh World Conference on Earthquake Engineering, Earthquake Engineering Research at Berkeley, College of Engineering, University of California at Berkeley,1996.
[162]Lu Y, Hao H, Carydis P G, et al. Seismic performance of RC frames designed for three different ductility levels[J]. Engineering Structures,2001,23(5):537-547.
[163]Priestley M J N, Calvi G M, Kowalsky M J. Direct displacement-based seismic design of structures[C]. The 5th NZSEE Conference,2007.
[164]Mazzoni S, McKennaF, Scott MH, FenvesGL. OpenSees Users Manual [R]. PEER, University of California, Berkeley.2004.
[165]ABAQUS V6.8. ABAQUS/Standard user's manual.2008.
[166]Mazzoni S, McKenna F, Scott M H, Fenves G L. OpenSees Example Manual [R]. PEER, University of California, Berkeley.2003.
[167]陈学伟.剪力墙结构构件变形指标的研究及计算平台开发[D].广州：华南理工大学,2011.
[168]Karsan I D, Jirsa J 0. Behavior of concrete under compressive loadings [J]. Journal of the structural division, ASCE,1969,95(12),2543-2563.
[169]Menegotto M, Pinto P E. Method of analysis for cyclically loaded reinforced concrete plane frames including changes in geometry and non-elastic behavior of elements under combined normal force and bending[C]./ABSE Symposium on the resistance and ultimate deformability of structures acted on by well-defined repeated loads, Lisbon.1973.
[170]Mo Y L, Wang S J. Seismic behavior of RC columns with various tie configurations [J]. Journal of Structural Engineering,2000,126(10):1122-1130.
[171]Martinelli P, Filippou F C. Simulation of the shaking table test of a seven-story shear wall building[J]. Earthquake Engineering & Structural Dynamics,2009, 38(5):587-607.
[172]Meng C, Lu X. Application of flexibility-based fiber-model beam-column element in simulation analysis of CFRT columns[J]. Journal of Earthquake Engineering and Engineering Vibration,2009,4:009.
[173]张强,周德源,伍永飞,等.钢筋混凝土框架结构非线性分析纤维模型研究[J].土木工程师,2008,24(1)：15-25.
[174]Priestley M J N, Calvi G M and Kowalsky M J. Displacement based seismic design of structure[J]. IUSS Press, Italy,2007,721.
[175]Zhao J, Sritharan S. Modelling of strain penetration effects in fibre-based analysis of reinforced concrete structures[J]. ACI Structure Journal,2007,104(2):133-141.
[176]Priestley M J N, Verna R, Xiao Y. Seismic Shear Strength of Reinforced Concrete Columns [J]. Journal of Structural Engineering,ASCE,1994,120 (8):2310-2329.
[177]Kunnath S K, Heo Y A, Mohle J F. Nonlinear uniaxial material model for reinforcing steel bars [J]. Journal of structural engineering,2009,135:335.
[178]Chang G, Mander J B. Seismic energy based fatigue damage analysis of bridge columns Part Ⅰ:Evaluation of seismic capacity [R]. NCEER Report 94-0006,1997.
[179]Gomes A, Appleton J. Nonlinear cyclic stress-strain relationship of reinforcing bars including buckling [J]. Engineering Structures,1997,19(10):822-826.
[180]Dhakal R P, Maekawa K. Modeling for postyield buckling of reinforcement [J]. Journal of Structural Engineering,2002,128(9):1139-1147.