摘要
近年来地壳运动活跃，地震已成为危害人类生命财产安全的最大的自然灾害。如何提高结构抗震性能，更好的实现抗震设防目标，改进结构设计方法一直是结构工程科研关注的重点和热点。钢框架在低、多层建筑中应用普遍，但该类结构刚度较小，二阶效应成为影响其抗震性能的重要因素，尤其在中、大震下影响较为明显，在工程设计中如何正确的考虑二阶效应是目前研究的热点之一。
本文针对二阶效应，对以下几个方面内容进行研究：国内外关于二阶效应和抗震设计方法的最新研究进展；钢框架弹性抗震抗侧需求刚度与弹性稳定分类的相关关系；整体和初始缺陷对结构抗侧刚度的影响；钢框架弹塑性抗侧刚度的影响因素；最后根据分析计算成果，给出考虑二阶效应的抗震设计建议和对策。具体研究内容如下：
目前《钢结构设计规范》是通过弹性稳定来考虑结构整体二阶效应，采用该法在地震工况设计钢框架时，存在物理意义不清晰，与抗震设计方法不匹配等问题。基于此，本文总结国内外关于钢框架考虑二阶效应的抗震设计研究的最新进展以及目前国内外抗震设计方法，为研究提供相应基础。
依据轴力负刚度的概念，分析钢框架弹性稳定设计实质，并得出钢框架弹性抗震设防需求刚度和弹性稳定分类相关关系，探讨分析钢框架、支撑钢框架结构的抗侧刚度需求和计算长度系数等参数之间相互关系。研究得出：弹性抗震设防需求刚度可能大于静力荷载稳定需求刚度；根据分析结果，在目前设计方法的基础上，推导得出考虑层抗侧刚度的弱支撑、纯框架计算长度系数修正公式，以造粒塔为工程背景，给出该类异型钢框架结构的稳定设计建议和方法，并应用于陕西兴平、广西柳州、福建邵武等三地的化肥厂造粒塔建设，加快了塔桅的建造速度，取得了良好的经济效果。
钢框架结构的初始缺陷和影响稳定的因素主要有结构整体初始侧倾、构件初始弯曲、残余应力、结构整体几何P-Δ效应。将Vogel标准框架作为有限元分析参数校正基础，对大量不同几何、荷载参数的钢框架进行数值模拟，包括不同轴压比、不同层数、不同截面钢柱和长细比的钢框架。采用归纳法总结各个稳定因素和初始缺陷对钢框架结构的抗侧能力影响，并研究钢框架结构在侧向地震荷载下的塑性、位移、应力状态。最后得出：焊接H型、热轧H型钢、焊接箱型柱钢框架的初始缺陷和重力下几何大变形对结构的抗侧能力影响均很小，只有残余应力影响相对较大。
在以上数值分析基础之上，进一步研究钢框架弹塑性抗侧刚度和弹性稳定系数取值的影响因素。研究得出：弹塑性抗侧刚度和稳定系数的最主要因素是钢柱轴压比，随着轴压比的增大，抗侧刚度减小，即影响弹塑性抗侧刚度的主要因素是材料非线性而非几何大变形；同时研究发现，梁端约束刚度、非均匀荷载对弹塑性抗侧刚度影响较小；随着钢柱长细比的减小，弹性稳定系数的极限取值减小。
最后，在总结数值计算结果的基础上，给出考虑二阶效应的设计对策和建议。提出以地震力计算为基础的钢框架计算长度系数修正方法；相比结构弹性稳定系数，按层轴压比控制结构弹塑性抗侧刚度更加合理；并给出支撑框架结构的剪力分配设计建议；为考虑二阶效应，分析了将高等分析应用于钢框架抗震设计的合理性，并给出加载模式和初步的评估方法；最后以造粒塔为工程背景，给出了将高等分析应用于实际工程抗震设计的具体建议，并应用于陕西兴平化肥厂造粒塔抗震性能评估。
In recent years, crustal movement come into the active phase.Earthquake has becomethe biggest disasters to human life and property. Improve the seismic performance ofbuildings has become research focus and hotspot. Steel frame structure has a good seismicperformance, but structure stiffness is flexible. Second-order effects become one of themost important factors of structure seismic performance. In engineering design, includingsecond-order effect design method is a currently hot research.
In this paper, the following points will be studied: First summarizes the studies aboutsecond-order effects; the relationship between steel frame stability demand andclassification of elastic stability will be studied; the effect of structural defects andcomponent defects on steel frame lateral stiffness; the elastic-plastic lateral stiffness factors;according to the calculation results, consider the second-order effect given the seismicdesign recommendations.
Currently,"Code for seismic design of buildings" and "Code for design of steelstructures" considering second order effects by elastic stability. The steel frame is designedaccording to the above suggestions, the physical concept is not clear. Summary the latestresearch about steel frame seismic performance consider second-order effects. This papersummarizes the current domestic and foreign seismic design method, then providefoundation for this study.
According to the concept of load negative stiffness, pointed out the nature of steelframe elastic stability. Give the relationship between steel frame stiffness that earthquakedemand for and elastic stability classification.Analyse the coefficient function betweensteel frame structural stiffness requirement and calculation length. Study concludes that the steel frame structure in high-intensity seismic area stiffness requirement is greater thanload negative stiffness. Finally, according to results of the analysis and the current designmethod, the design recommendations are given.
The initial defects of mainly includes structure steel frame structure: structure initialdisplacement, member initial curvature, residual stress. The geometry of P-Δ effect is oneof steel frame stable factors.Take Vogel frame calculation results as the finite elementanalysis parameters correction foundation. Analyse different parameters steel frame,including the different axial compression ratio, different layers, different cross-section steelcolukNs and different slenderness ratio.Induction influence of different initial defects andstudy displacement plastic state of steel frame under lateral seismic loads. The initialdefects and geometric large deformation has has little effect on steel frame lateral bearingcapacity in addition to residual stress.
Based on a large number of numerical analysis, summarize factors of steel frameelastic lateral stiffness and stability coefficient. Study concludes that the main factor is theaxial compression ratio of the steel colukNs, with the axial compression ratio increases, thelateral stiffness decreases; main factor is the material nonlinearity. At the same time studyconcluded that beam end restraint stiffness on elastic-plastic lateral stiffness influence issmall; with steel colukN slenderness ratio decreases, the extremes of elastic stabilitycoefficient decreases.
Finally, in summarizing the results of numerical analysis, the design countermeasuresand suggestions considering the two order effects is given. According to the seismic forceto fix steel frame calculation length coefficient method is recommended; Compared withthe structure stability coefficient, story axial compression ratio that control structureelastic-plastic lateral stiffness is more reasonable index; and gives the braced framestructures shear distribution design recommendations; The way that advanced analysis isused for steel frame seismic design is reasonable, but also gives load models andassessment methods.
引文
[1]中华人民共和国国家标准：建筑抗震设计规范(GB50011-2010)[S]．北京：中国建筑工业出版社,2010
[2]中华人民共和国国家标准：钢结构设计规范设计(GB50017-2003)[S]．北京：中国计划出版社,2003
[3]童根树，赵永峰．动力P-Δ效应对地震力调整系数的影响[J]．浙江大学学报,2007,41(1)：120-125
[4]李琪．基于位移模式结构抗震设计方法研究[D]．南京：河海大学,2005
[5]白晓红，白国良．基于性能的抗震设计理论的研究现状及展望[J]．河南科技大学学报,2005,26(6)：74-77
[6]中华人民共和国国家标准：高层建筑混凝土结构技术规程(JGJ3-2010)[S]．北京：中国建筑工业出版社,2010
[7] Federal Emergency Management Agency (FEMA)[S]．NEHRP Recommended Provisios for theDevelopment of Seismic Regulations for New Buildings,1991
[8] European Prestandard Eurocode [S]． Design Provisios for Earthquake Resistance ofStructure,1998
[9] Bertero R., Bertero, V., V.,et al. Peroformance-based earthquke-resistant design based oncomprehensive philosophy and energy concepts [C]．Proceedings of the11th World Conference onEarthquake Engineering,Elservier Science Ltd,1996
[10] ATC-40. Seismic evaluation and retrofit of concrete buildings[R]．Applied Technology Council.Red Wood City,Cailfornia,1996
[11] FEMA273. NEHRP guidelines for the rehabilitation of buildings[R]． Federal EmergencyManagement Agency, Washington,D.C.September,1996
[12] FEMA274. NEHRP guidelines for the rehabilitation of buildings[R]． Federal EmergencyManagement Agency, Washington,D.C.September,1996
[13]中华人民共和国国家标准：建筑结构可靠度设计统一标准(GB50068-2001)[S]．北京：中国建筑工业出版社,2003
[14]陈骥．钢结构稳定理论与设计[M]．第二版．北京：科学出版社,2003
[15]中华人民共和国国家标准：建筑工程抗震形性态设计准则(CECS160-2004)[S]．北京：中国计划出版社,2004
[16]童根树．钢结构设计方法[M]．北京：中国建筑工业出版社,2007:50-87
[17]日本建筑学会．钢筋混凝土造建物的韧性保证型耐震设计指针i同解说(Design Guidelines forEarthquake Resistant Reinforced Buildings Based on Inelastic Displacement Concept),1999
[18] International Code Council．Uniform Building Code1997[S]．California: Interational Conferenceof Building Officials,1997
[19]赵永峰．精致化延性抗震设计理论[D]．浙江：浙江大学,2008
[20]童根树，施祖元，李志飚．计算长度系数的物理意义及对各种钢框架稳定设计方法的评论[J]．建筑钢结构进展,2004,6(4)：1-8
[21]饶之英，童根树．钢结构稳定性的新诠释[J]．建筑结构,2002,32(5)：12-14
[22]叶列平，陆新征，马千里．屈服后刚度对建筑结构地震响应影响的研究[J]．建筑结构学报,2002,32(5)：12-14
[23]缪志伟，陆新征，叶列平．高强配筋剪力墙框剪结构的地震行为研究[J]．华中科技大学学报,2007,24(4)：17-25
[24]叶列平，曲哲，陆新征．提高建筑结构抗地震倒塌能力的设计思想与方法[J]．建筑结构学报,2008,29(4)：42-50
[25]叶列平，程光煜，齐玉军．体系能力设计法在消能减震结构设计中的应用[J]．工程抗震与加固改造,2008,30(2)：1-5
[26] Beral D.(1987). Amplification factors for inelastic dynamic P Δ effects in earthquake analysis.Earthquake Engineering and Strucural, Elservier,25:635-551
[27] Beral D.(1992). Instability of buildings subjected to earthquakes. Journal of StructuralEngineering, ASCE,118(8):2239-2260
[28] Beral D.(1998). Instability of buildings during seismic response. Engineering Structures,20:496-502
[29] Gupta A., Krawinkler H.(2000). Dynamic P-Delta Effects for Flexibile Inelastic Steel Structures.Journal of Structural Engineering, ASCE,126(1):145-154
[30] Han S.W., Kwon O.S. and Lee L.H.(2001). Investigating of dynamic P Δ effect on ductilityfactor, Structures Engineering and Mechanics,12(3):249-266
[31] Jennings PC, Husid R. Collapse of yielding structures during earthquakes. Journal of theEngineering Mechanics Division (ASCE)1968;94:1045–1065
[32] Sun CK, Berg GV, Hanson RD. Gravity effect on single degree inelastic system. Journal ofEngineering Mechanics Division (ASCE)1973;99:183–200
[33] Faella C, Mazzarela O, Piluso V. L’ influenza della non-linearit′a geometrica sul danneggiamentostrutturale. Proceedings of VI Convegno Nazionale l’Ingegneria Sismica in Italia, Perougia,13–15Ottobre1993
[34] Mac Rae GA. P–Δeffects on single-degree-of-freedom structures in earthquakes. EarthquakeSpectra1994;10:539–568
[35] Tremblay R, Duval C, L′eger P. Effects of viscous damping models, hysteretic models and groundmotion characteristics on seismic P–delta strength amplification factors. In Stability and Ductilityof Steel Structures, Usami T, Itoh Y (eds). Elsevier: Amsterdam,1998;103–108
[36] Williamson EB. Evaluation of damage and P–Δ effects for systems under earthquake excitation.Journal of Structural Engineering (ASCE)2003;129:1036–1046
[37] Ascheim M, Montes EH. The representation of P–Δeffects using yield point spectra. EngineeringStructures2003;25:1387–1396
[38] Miranda E, Akkar SD. Dynamic Instability of simple structural systems. Journal of StructuralEngineering (ASCE)2003;129:1722–1726
[39] Vian D, Bruneau M. Tests to structural collapse of single degree of freedom frames subjected toearthquake excitations. Journal of Structural Engineering (ASCE)2003;129:1676–1685
[40] Goel SC. P–Δand axial colukN deformation in aseismic frames. Journal of the Structural Division(ASCE)1969;95:1693–1711
[41] Takizawa H, Jennings PC. Collapse of a model for ductile reinforced concrete frames underextreme earthquake motions. Earthquake Engineering and Structural Dynamics1980;8:117–144
[42] Roeder CW, Schneider SP, Carpenter JE. Seismic behavior of moment-resisting steel frames:analytical studies. Journal of Structural Engineering (ASCE)1993;119:1866–1884
[43] Murty Challa VR, Hall JF. Earthquake collapse analysis of steel frames. Earthquake Engineeringand Structural Dynamics1994;23:1199–1218
[44] Park CH, Lee DG, Kim JK. Effect of gravity load on seismic response of steel-framed structures.Engineering Structures1997;19:439–451
[45] Della Corte G, Landolfo R. Global stability of MR steel frames under seismic actions. Proceedingsof the12th European Conference on Earthquake Engineering, London,9–13September2002.Elsevier: London,2002, CD Rom paper no.307
[46] Paulay T. A consideration of P–delta effects in ductile reinforced concrete frames. Bulletin of theNew Zealand National Society for Earthquake Engineering1978;11:151–160
[47] Montgomery CJ. Influence of P–delta effects on seismic design. Canadian Journal of CivilEngineering1981;8:31–42.22. Neuss CF, Maison BF. Analysis for P–Δeffects in seismicresponse of buildings. Computers and Structures1984;19:369–380
[48] Guerra CA, Mazzolani FM, Piluso V. Overall stability effects in steel structures under seismicloads. Proceedings of the9th European Conference on Earthquake Engineering, Moscow,11–16September1990
[49] Mazzolani FM, Piluso V. Theory and Design of Seismic Resistant Steel Frames. E&FN Spon,Chapman&Hall: London,1996
[50] Bernal D. Instability of buildings subjected to earthquakes. Journal of Structural Engineering(ASCE)1992;118:2239–2260
[51] Bernal D. Instability of buildings during seismic response. Engineering Structures1998;20:496–502
[52] Davidson BJ, Fenwick RC, Chung BT. P–delta effects in multi-storey structural design.Proceedings of the10th World Conference on Earthquake Engineering, vol.7, Madrid, Spain,19–24July1992, A.A. Balkema: Rotterdam,1992;3847–3852
[53] Tremblay R, C ot′e B, L′eger P. An evaluation of P–Δ amplification factors in multistorey steelmoment resisting frames. Canadian Journal of Civil Engineering1999;26:535–548
[54] Krawinkler H, Gupta A. Seismic design issues for steel moment-resisting frame structures. InProceedings of the4th National (Greek) Conference on Steel Structures, Patras, Greece,24–25May2002, Beskos DE, Karabalis DL, Kounadis AN (eds), vol.1. Typorama Press: Patras2002;60–71
[55] Aydinoglu kN. Inelastic seismic response analysis based on storey pushover curves includingP–delta effects. Report No.2001/1, KOERI, Department of Earthquake Engineering, BogaziciUniversity, Istanbul, Turkey, June2001
[56] Adam C, Ibbara LF, Krawinkler H. Evaluation of P–delta effects in non-deteriorating MDOFstructures from equivalent SDOF systems. Proceedings of the13th World Conference onEarthquake Engineering, Vancouver, BC, Canada,1–6August2004, CD Rom paper no.3407
[57] Aritisdis V., Dimitiris L.. Inclusion of P–Δ effect in displacement-based seismic design of steelmoment resisting frames, Earthquake Engineering and Structural Dynamics,2007;36:2171–2188
[58]刘大海，杨翠如．高楼钢结构设计[M]．北京：中国建筑工业出版社,2003:161-162
[59]李国强．关于多高层钢结构柱计算长度(I):理论解释[J]．建筑钢结构进展,2009,11(2)：1-7
[60]王翼，李国强．关于多高层钢结构柱计算长度(II):数例说明[J]．建筑钢结构进展,2009,11(2)：8-11
[61]侯和涛，李国强．初始缺陷对钢框架柱性能的影响(II):参数分析[J]．建筑钢结构进展,2009,11(2)：20-26
[62]陈骥．关于《钢结构设计规范》(GB50017-2003)修订的建议[J]．建筑钢结构进展,2010,12(3)：1-6
[63]徐建．建筑结构设计常见疑难问题解析[M]．北京：中国建筑工业出版社,2007:38-100
[64] Vogel,U.Calibrating Frames.Stahlbau,Germany,10,1985,pp.295~301
[65]沈世钊，陈昕．网壳结构稳定性[M]．北京：科学技术出版社,1999:1-10
[66]童根树．钢结构平面内稳定[M]．北京：中国建筑工业出版社,2004:93-105
[67]童根树．钢结构设计方法[M]．北京：中国建筑工业出版社,2007:1-15
[68]梁兴文，史庆轩，童岳生．钢筋混凝土结构设计[M]．北京：科学技术出版社,1999:206-210
[69]童根树，施祖元．非完全支撑的框架结构的稳定性[J]．土木工程学报,1998,31(4)：31-37
[70]童根树．按照整层模式失稳的框架稳定性计算[J]．西安建筑科科技大学学报,2006,38(3)：297-301
[71]梁启智.高层建筑结构分析与设[M]．广州：华南理工大学出版社,1989
[72]陈绍蕃．钢结构稳定设计的新进展[J]．建筑钢结构进展,2004,6(2)：1-13
[73]陈绍蕃．钢结构稳定设计指南[M]．北京：中国建筑工业出版社
[74]梁兴文，黄雅捷，杨其伟．钢筋混凝土框架结构基于位移的抗震设计研究[J]．土木工程学报，2005,38(9):53-60
[75]罗文斌，钱稼茹．钢筋混凝土框架基于位移的抗震设计[J]．土木工程学报，2003,36(5):22-29
[76]罗文斌，钱稼茹．RC框架弹塑性位移的解构规则与构件的目标侧移角[J]．工程力学，2003,20(5):32-36
[77]刘清山，梁兴文，黄雅捷．对结构静力弹塑性分析方法的几点改进[J]．建筑科学，2005,21(5):28-33
[78]杨志勇，何若全．高层钢结构弹塑性抗震分析静动力综合法[J]．建筑结构学报，2003,24(3):25-32
[79]吕西林，王亚勇，郭子雄．建筑结构抗震变形验算[J]．建筑科学，2002,28(1):11-15
[80]程耿东，李刚．基于功能的结构抗震设计的一些问题的探讨[J]．建筑结构学报，2000,21(1)5-11
[81]马宏旺，吕西林．建筑结构基于性能抗震设计的几个问题[J]．同济大学学报，2002,30(12):1429-1434
[82]程斌，薛伟辰．基于性能的框架结构抗震设计研究[J]．地震工程与工程振动，2003,23(4):50-55
[83]白国良，刘林，李晓文．冷支架结构基于内容物的性能设计方法研究[J]．建筑结构学报，2008,29(5):107~113
[84]范立础，卓卫东．桥梁延性抗震设计[M]．北京：人民交通出版社，2001：104-112
[85]李晓莉，吴敏哲．基于功能的建筑结构抗震设计研究[J]．世界地震工程，2004,20(1)153-156
[86]徐培福，戴国莹．超高层建筑结构基于性能的设计抗震设计研究[J]．土木工程学报，2005，38(1):1~10
[87]钱家茹，纪晓东．国家体育场大跨钢结构罕遇地震性能分析[J]．建筑结构学报，2007,28(2):17~25
[88]白国良，楚留声．型钢混凝土框架静力非线性分析塑性铰参数研究[J]．西安建筑科技大学学报,2007,39(6):757~761
[89]谢礼立，马玉宏．现代抗震设计理论的发展过程[J]．国际地震动态，2003,10:1~8
[90]童根树，季渊．多高层—弯剪型支撑结构的稳定性研究[J]．土木工程学报,2005,38(5)：28~33
[91]刑国然．纯框架和支撑框架弹塑性稳定分析[D]．浙江：浙江大学,2007
[92]黄金桥．钢结构弹塑性动力学及抗震设计理论研究[D]．浙江：浙江大学,2005
[93]童根树，王金鹏．考虑层与层支援的框架计算长度系数[J]．建筑钢结构进展,2004,6(4)：9-14
[94]吕西林，周定松．考虑场地类别与设计分组的延性需求谱和弹塑性位移反应谱[J]．地震工程与工程振动,2004,24(1)：39-48
[95]童根树．与抗震设计有关的结构和构件分类及结构影响系数[J]．建筑科学与工程学报,2007,24(3)：65~75
[96]周奎，宋启根．钢结构几何缺陷的直接分析法[J]．建筑钢结构进展,2007,9(1)：57-62
[97]薛强，郝际平，王迎春．钢管混凝土造粒塔结构基于内容物性能的抗震设计方法研究．哈尔滨工业大学学报．2010.42(1):205-208
[98]施刚，石永久，王元清．运用ANSYS分析超高强度钢材钢柱整体稳定特性[J]．吉林大学学报,2009,39(1)：113~118
[99]张俊峰，郝际平，王连坤．基于ANSYS的某拱形刚架极限承载力研究[J]．西安建筑科技大学学报,2008,40(1):71~75
[100]张俊峰，郝际平，王连坤．基于数据文件的ANSYS二次开发[J]．钢结构,2007,22(6):85~87
[101]陈绍蕃．钢结构设计原理[M]．第三版．北京：科学出版社,2005
[102]薛强，郝际平，王迎春．基于性能的钢管混凝土空间筒体结构抗震设计研究．世界地震工程．2011.27(4):116-120
[103]A.A. Vasilopoulos,D.E.Beskos. Seismic design of plane steel frames using advanced methods ofanalysis. Soil Dynamics and Earthquake Engineering,2006;26:1077–1100
[104]N. Bazeos. Comparison of three seismic design methods for plane steel frames. Soil Dynamics andEarthquake Engineering,2009;29:553–562
[105]A.A. Vasilopoulos,D.E.Beskos. Seismic design of space steel frames using advanced methods ofanalysis. Soil Dynamics and Earthquake Engineering,2009;29:194–218
[106]童根树，高宇．两个弯剪型抗侧力体系的线性相互作用[J]．建筑钢结构进展,2008,10(5)：28-34
[107]蒋丽忠，汤裕坤．钢-混凝土组合框架柱的稳定设计方法[J]．建筑科学与工程学报,2008,25(3)：12~16
[108]薛强，郝际平，王迎春．化肥工业造粒塔结构稳定设计方法研究．工业建筑2011.41(4):107-111
[109]郝际平，王迎春．钢结构造粒塔的设计．石油与化工设备，2007，04：36~38
[110]殷有泉，固体力学非线性有限元引论，北京：北京大学出版社，1986
[111]黄羽立，陆新征，叶列平．基于多点位移控制的推覆分析算法[J]．工程力学，2011,28(2):18-23
