摘要
破坏性地震会给国家经济建设和人民生命财产安全造成巨大的危害与损失,故强震作用下结构的抗震分析理论和设计方法一直是地震工程界所关注的重要研究课题,也是目前的研究热点之一。一般的抗震设计主要考虑结构的抗震承载力,而基于性能设计方法采用的性能目标一般和结构最大位移或延性相关,但在地震地面运动作用下结构产生破坏的因素除了最大非线性位移外,大量非线性滞回循环引起的塑性累积破坏也是重要的影响因素。基于能量抗震设计方法具有概念清晰、计算简单的优点,较好地反映地震动强度、频谱特性和强震持续时间对结构破坏的影响。目前能量方法中主要采用滞回耗能值来评估结构的破坏程度,本论文在总结前人研究成果的基础上,通过系统的理论研究和大量的计算,分别求得结构在强震作用下的滞回耗能需求值和能力值,初步建立了基于滞回耗能的抗震性能评价方法,并以钢结构和钢筋混凝土框架为算例进行了设计与复核。论文的主要内容如下:
1、以单自由度弹塑性体系振动理论为基础,编制结构的能量反应时程分析Matlab程序;按场地类别和强震持时对302条美国Northridge地震和339条台湾ChiChi地震的水平向地震加速度记录进行分类,由非线性程序计算得到结构的平均滞回耗能需求谱;研究了地震动工程特性和结构动力特性对滞回耗能值的影响,分析结果表明屈服强度系数和刚度折减系数对结构的滞回耗能值影响都较小,滞回耗能峰值和地震动加速度峰值的平方大致成正比。
2、由等效输入能谱速度峰值放大因子的不同,可分别得到Vidic-Fajfar和Chai-Fajar模式双折线滞回耗能需求谱的数学表达式;由能量反应时程分析结果,可统计分析建立与场地类别和强震持时相关的滞回耗能谱的简化计算公式。比较分析了由以上三种方法求得到的滞回耗能需求谱曲线,结果表明双折线滞回耗能需求谱计算结果偏保守,尤其当结构周期较大时,和时程计算值的差异性较大。
3、由修正的Park-Ang损伤模型和低周疲劳破坏模型可分别推导出对应于结构破坏时的滞回耗能能力值。在滞回耗能能力值的计算公式中,除了相应的经验系数外,单调位移延性系数由结构非线性静力推覆分析得到,循环位移延性系数由结构的强度折减系数得到。
4、归纳整理了12种不同的等效体系方案(ESS),求解结构的滞回耗能需求值时可避免做复杂繁琐的多自由度体系(MDOF)非线性时程分析。为分析不同ESS的等效效果,首先采用经验公式或非线性推覆分析方法可求得实际多自由度体系的层剪计算模型,再由自编Matlab程序计算结构MDOF和等效单自由度体系(ESDOF)的能量反应,得到ESS的耗能比值。结果分析表明,场地特征和滞回耗能标准值对ESS的耗能比值有重要的影响,对所有典型地震波的耗能比值做非线性回归分析,便可分别得到与场地a/v值和耗能标准值S_E相关的耗能比值Rh的数学表达式。
5、实际多自由度结构对应于不同恢复力模型,本论文分别选用了适合于钢结构、砌体结构和钢筋混凝土结构的双线型、半退化三线型和退化三线型三种恢复力模型,编制相应Matlab计算程序,准确求得对应的滞回耗能需求谱和耗能比值。相比较于双线型模型,三线型模型可考虑刚度退化现象,更真实地反应了钢筋混凝土和砌体结构的受力特性。
6、由结构能量平衡思想,建立基于滞回耗能的结构能量反应判别式,从而可判断在强震作用下结构是否发生破坏。修正Park-Ang损伤模型的损伤指数可表征结构的破坏程度,则业主要求的结构性能水平对应于特定的损伤指数,故可得到对应于特定性能目标的结构滞回耗能能力值,从而初步建立考虑滞回耗能的基于性能抗震设计与复核过程。
7、为将以上分析成果应用于实际结构的抗震评价与设计中,分别以钢结构和钢筋混凝土框架为例,计算其在强震作用下的滞回耗能需求值和能力值,便可判断结构是否会出现倒塌或预定性能目标,通过二次设计得到合适的构件和钢筋配置等参数。
Ruinous earthquake will cause great destruction and damage on the national economy and property, even lead to death. Therefore the seismic analysis and design of structure under strong earthquake is the significant research subject and hotspot on seismic engineering. Normal seismic design mainly considers the carrying capacity of structure. The performance target of performance-based design mostly is concerned with ultimate displacement or ductility. Ultimate displacement contributes to the destruction of buildings basically, so does cumulative damage which is caused by nonlinear hysteretic cycles. Performance-based seismic design procedure possesses several advantages, such as clear in conception and simple in computation, which can preferably represent the influence of earthquake intensity, frequency character and ground motion duration on the structural destruction. At present energy-based design procedure mainly adopt hysteretic energy to evaluate structural damage degree. The dissertation computes hysteretic energy demand and capacity of structures under severe earthquake respectively by the means of sum-up of former research fruits, systemic academic investigation and large numbers of computation. Therefore hysteretic energy-based seismic evaluating procedure is built primarily, and uses steel frame and concrete frame as example in design and check. The main contents of this dissertation are described as follows:
1. On the basis of vibrational theory of single degree of freedom elastic-plastic system, a Matlab time-history analysis program is made to compute the structural energy response. 302 Northridge in USA and 339 ChiChi in Taiwan earthquake ground motion records are classified according to soil condition and duration of strong ground motion, and their mean hysteretic energy demand spectra is computed by means of nonlinear program. The result shows that force reduction factor and stiffness reduction factor have little influence on the hysteretic energy values, and peak hysteretic energy is proportional to the square of peak ground motion acceleration approximately.
2. The bilinear hysteretic energy demand spectrum mathematical equations of Vidic-Fajfar and Chai-Fajar model are developed because of different velocity peak amplification factor of equivalent seismic input energy spectrum. Through the energy response result of time-history analysis, a simple formulation of hysteretic energy is proposed by means of nonlinear regression analysis, in which site character and duration of strong ground motion are considered. Former three kinds of demand spectrum are compared, and bilinear hysteretic energy demand spectrum is conservative. Especially for large structural period, bilinear hysteretic energy demand values are much larger than the time-history response values.
3. The hysteretic energy capacity which corresponds to structural collapse state can be calculated from modified Park-Ang damage model and low-cycles fatigue model. The monotonic displacement ductility factor can be calculated through nonlinear static Push-over, and the cyclic displacement ductility factor can be calculated through the structural force-reduction factor too.
4. The structural hysteretic energy demand can be calculated through 12 kinds of different equivalent system scheme(ESS), which can avoid of complicated and time-consuming nonlinear time-history analysis of multi degree of freedom(MDOF) system. In order to analyze equivalent effect of different ESS, the floor-shear model should be built by experiential formulae or nonlinear Push-over firstly. The energy response of MDOF and equivalent single degree of freedom (ESDOF)systems can be computed by self-compiling Matlab programs. Therefore it is convenient to acquire hysteretic energy ratios of ESS. The result indicates that site characters and normal hysteretic energy have significant influence on the hysteretic energy ratios. Consequently the hysteretic energy ratios expressed by site characters(value a/v) and normal hysteretic energy(S_E) can be calculated by means of nonlinear regression analysis of the hysteretic energy ratios produced by typical earthquake waves.
5. Real multi degree of freedom structures correspond to different hysteretic models. This dissertation uses bilinear, semi-degraded trilinear and degraded trilinear hysteretic models which can represent the steel frame, brickwork and concrete structures respectively well. By means of Matlab program, corresponding hysteretic energy demand and energy ratio is calculated precisely. Compared to bilinear model, trilinear models can consider stiffness degradation which reflects the mechanical characters of reinforce concrete and brickwork structures more truly.
6. Hysteretic energy-based design checking equation is built via energy equilibrium ideology to judge whether the building will collapse. The damage index of modified Park-Ang damage model quantifying structural damage can mark the structural performance target which is required by owners. Then the hysteretic energy capacity can be computed to create the elementary performance-base seismic designing and checking procedure considering hysteretic energy.
7. In order to make use of former analysis in the seismic evaluation and design of real structure, steel frame and concrete frame are chosen as examples. Their hysteretic energy demand and capacity values under strong earthquake are calculated to judge whether the collapse or target performance will happen. Via second design we can obtain suitable components and reinforcing steel bar etc.
引文
[1]Housner GW.Limit Design of Structures to Resist Earthquakes[J].Proceedings of the First World Conference on Earthquake Engineering.EERI,Berkeley,CA,1956.
[2]Housner GW.Behavior of Structures during Earthquake[J].Journal of Engineering Mechanics(ASCE),1959,85(14):109-129.
[3]Newmark NM,Hall WJ.Seismic Design Criteria for Nuclear Reactor Facilities[M].Proceedings of the fourth World Conference on Earthquake Engineering,1969.
[4]Newmark NM,Hall WJ.A Rational Approach of Seismic Design Standards for Structures[M].Proceedings of the fifth World Conference on Earthquake Engineering,1975.
[5]Applied Technology Council.A critical review of current approaches to earthquake-resistance design.ATC-34,1995.
[6]Applied Technology Council.Seismic evaluation and retrofit of concrete buildings.ATC-40Redwood City(CA),1996.
[7]Federal Emergency Management Agency.NEHRP guidelines for the rehabilitation of buildings.FEMA273.FEMA274.Commentary Washington(DC),1996.
[8]SEAOC Vision2000 Committee.Performance-based seismic engineering.Vol.Ⅰ and Ⅱ:Conceptual Framework.Sacramento(CA),1995.
[9]中国工程建设标准化协会.建筑工程抗震性态设计通则(试用).中国计划出版社,2004.
[10]Moehle JP.Displacement-Based Design Procedure of RC Structures Subjected to Earthquakes[J].Earthquake Spectra,EERI,1992,8(3):403-428.
[11]郭磊,李建中,范立础.直接基于位移的结构抗震设计理论研究进展[J].世界地震工程,2005,21(4):157-164.
[12]Freeman SA.Prediction of response of concrete buildings to severe earthquake motion[J].Publication SP-55,Detroit,Michigan.American Concrete Institute,1978,589-605.
[13]Freeman SA.Development and use of capacity spectrum method.Proceedings of the sixth U.S.National Conference on Earthquake Engineering.Seattle.Oakland,California:EERI,1998.
[14]Goel RK,Chopra AK.Capacity-demand-diagram methods for estimating seismic deformation of inelastic structures:SDOF system.Report NO.PEER-1999/02.Pacific Earthquake Engineering Research Center.University of California at Berkeley,1999.
[15]Peter Fajfar.Capacity spectrum method based on inelastic demand spectra[J].Journal of Earthquake Engineering and Structural Dynamics,1999,28(9):979-993.
[16]Park YJ,Ang AHS.Mechanistic seismic damage model for reinforced concrete[J].Journal of Structural Engineering(ASCE),1985,111(4):722-739.
[17]Benioff Hugo.The physical destructiveness of earthquakes.The bulletin of the seismological society of America,1934.
[18]Biot MA.A mechanical analyzer for the prediction of earthquake stresses.The bulletin of the seismological society of America,1940.
[19]Fajfar,Krawinkler.Nonlinear seismic analysis and design of reinforced concrete buildings[Z].London and New York:Elsevier Applied Science,1992.
[20]Zahrah TF,Hall WJ.Earthquake energy absorption in SDOF structures[J].Journal of Structural Engineering,ASCE,1984,110(8):1757-1772.
[21]Uang CM,Bertero W.Use of energy as a design criterion in earthquake-resistant design.Report No.UCB/EERC-88/18.University of California at Berkeley(CA),1988.
[22]Chou CC,Uang CM.Establishing absorbed energy spectra-an attenuation approach.Earthquake Engineering and Structural Dynamics,2000,29(10):1441-1455.
[23]Manfredi G.Evaluation of seismic energy demand.Earthquake Engineering and Structural Dynamics,2001,30(4):485-499.
[24]Fajfar P.Equivalent ductility factors,taking into account low-cycle fatigue[J].Earthquake Engineering and Structural Dynamics,1992,21(10):837-848.
[25]Cornell CA,Jalayer F,Hamburger RO,Foutch DA.Probabilistic basis for the 2000 SAC FEMA steel moment frame guidelines[J].Journal of Structural Engincering,ASCE,2002,128(4):526-533.
[26]Vamvatsikos D,Cornell CA.Incremental dynamic analysis[J].Earthquake Engineering and Structural Dynamics,2002,31(3):491-514.
[27]Ann Gilbert Sardo.Damage calibrated seismic design spectra[D].University of Califomia.Davis,1999.
[28]Akiyama H.Earthquake-Resistant Limit-state Design for Buildings[M].University of Tokyo Press,1985.
[29]Amador Teran.Performance-based earthquake-resistant design of framed buildings using energy concepts[D].University of California at Berkeley,1996.
[30]Liu Hong.Seismic design and damage evaluation of buildings with steel moment resisting frames[D].Clemson university,1996.
[31]Bulent Akbas.Energy-based earthquake resistant design of steel moment resisting framses[D].Illinois institute of technology,1997.
[32]Hao Tzong-Ying.Investigation of energy flow in earthquake response of structures[D].University of southern California,2002.
[33]Thomas Louis Attard.Modeling of higher mode effects in various frame structures using a pushover analysis[D].Arizona state university,2003.
[34]Siddhartha Ghosh.Two alternatives for implementing performance-based seismic design of buildings—life cycle cost and seismic energy demand[D].Michigan university,2003.
[35]Leelataviwat S,Goel SC,and Stojadinovic B.Toward performance based seismic design of structures[J].Earthquake Spectra,EERI,1999(3),15:435-461.
[36]Leelataviwat S,Goel SC,and Stojadinovic B.Energy-based seismic design of structures using yield mechanism and target drift[J].Journal of structural engineering.Earthquake Spectra,2002,128(8):1046-1054.
[37]Chou CC,Uang CM.Evaluation of site-specific energy demand for building structures.Proccedings of the seventh U.S.National Conference on Earthquake Engineering,2002.
[38]Chou Chung-Che.An energy-based seismic evaluation procedure for moment-resisting frames[D].University of California.San Diego,2001.
[39]Kent Richard Estes.An energy method for seismic design[D].University of Southern California,2003.
[40]裴星洙,张立,任正权.高层建筑结构地震响应的时程分析法[M].中国水利水电出版 社,2006.
[41]东南大学编著.建筑结构抗震设计[M].中国建筑工业出版社,2000.
[42]贺国京,阎奇武,袁锦根.工程结构弹塑性地震反应[M].中国铁道出版社,2005.
[43]凌复华,殷学纲,何治奇.常微分方程数值方法及其在力学中的应用[M].重庆大学出版社,1990.
[44]朱镜清.结构抗震分析原理[M].地震出版社,2002.
[45]赵岩,林家浩,唐光武.复杂结构局部非线性地震反应精细时程分析[J].大连理工大学学报,2004,44(2):190-194.
[46]Hilber HM,Hughes TJR.1978.Collocation,dissipation and overshoot for time integration schemes in structural dynamics[J].Journal of Earthquake Engineering and Structural Dynamics,6(1):99-117.
[47]肖明葵,刘纲,白绍良.恢复力模型中求折点的一种方法[J].重庆大学学报,2002,25(1):13-16.
[48]史庆轩,杨文星,门进杰.单自由度体系非线性地震能量反应的计算[J].建筑科学与工程学报,2005,22(2):25-29.
[49]杨文星,罗少锋.单自由度体系能量反应的计算[J].西安科技大学学报,2006,26(1):40-43.
[50]肖明葵,刘纲,白绍良等.抗震结构的滞回耗能谱[J].世界地震工程,2002,18(3):110-115.
[51]肖明葵,白绍良,赖明等.基于滞回耗能的抗震结构最大位移反应[J].重庆大学学报,2003,26(3):133-137.
[52]翟长海,谢礼立,吴知丰.基于台湾集集地震的结构滞回耗能影响分析[J].哈尔滨工业大学学报,2002,38(1):59-62.
[53]公茂盛,翟长海,谢礼立等.地震动滞回能量谱衰减规律研究[J].地震工程与工程振动,2004,24(2):9-14.
[54]童根树,黄金桥.不同滞回模型下单自由度系统的位移和能量反应[J].浙江大学学报,2005,39(1):123-130.
[55]Chai YH,Fajfar P,Romstad KM.Formulation of duration-dependent inelastic seismic design spectrum[J].Journal of Structural Engineering(ASCE),1998,124(8):913-921.
[56]Iunio Iervolino,Gaetano Manfredi,Edoardo Cosenza.Ground motion duration effects on nonlinear seismic response[J].Earthquake Engineering and Structural Dynamics,2006,35(1):21-38.
[57]罗奇峰,盛明强,万召侗.结构设计基准期与设防标准的讨论[J].国际地震动态(增刊),中国地震学会第11次学术大会论文摘要集,2006,334:83.
[58]盛明强,刘颖.浅析不同设计使用期建筑结构抗震设防烈度的选取[J].江西水利科技,2005,31(4):209-211.
[59]Vidic T,Fajfar P,Fischinger M.Consistent inelastic design spectra:Strength and displacement[J].Earthquake Engineering and Structural Dynamics,1994,23(5):507-521.
[60]Trifunac MD,Brady AG.A study on the duration of strong earthquake ground motion[J].Bulletin of the Seismological Society of America,1975,65(3):58-626.
[61]Michel Bruneau,Niandi Wang.Some aspects of energy methods for the inelastic seismic response of ductile SDOF structures[J].Engineering Structures,1996,18(1):1-12.
[62]Yazdani Motlagh AR,Ala Saadeghvaziri M.Nonlinear seismic response of stiffening SDOF systems[J].Engineering Structures,2001,23(10):1269-1280.
[63]Chopra AK,Chatpan Chintanapakdee.Comparing response of SDF systems to near-fault and far-fault earthquake motions in the context of spectral regions[J].Earthquake Engineering and Structural Dynamics,2001,30(12):1769-1789.
[64]Constantin Christopoulos,Andre Filiatrault,Bryan Folz.Seismic response of self-centring hysteretic SDOF system[J].Earthquake Engineering and Structural Dynamics,2002,31(5):1131-1150.
[65]Akkar S,Ozen O.Effect of peak ground velocity on deformation demands for SDOF Systems[J].Earthquake Engineering and Structural Dynamics,2005,34(13):1551-1571.
[66]Danny Arroyo,Mario Ordaz.On the estimation of hysteretic energy demands for SDOF systems[J].Earthquake Engineering and Structural Dynamics,2007,36(15):2365-2382.
[67]Ioannis Politopoulos,Cyril Feau.Some aspects of floor spectra of 1DOF nonlinear primary structures[J].Earthquake Engineering and Structural Dynamics,2007,36(8):975-993.
[68]Park YJ,Ang AHS,Wen YK.Seismic damage analysis of reinforced concrete buildings [J].Journal of Structure Engineering,1985,111(4):740-757.
[69]Park YJ,Ang AHS,Wen YK.Damage-limiting a seismic design of buildings[J].Earthquake Spectra,1987,3(1):1-26.
[70]Kevin KF Wong,Yuemei Wang.Energy-based damage assessment on structures during earthquakes[J].The structural design of tall buildings,2001,10(2):135-154.
[71]A.Benavent-Climent.An energy-based damage model for seismic response of steel structures[J].Earthquake Engineering and Structural Dynamics,2007,36:1049-1064.
[72]Chai YH,Romstad KM,Bird SM.Energy-based linear damage model for high-intensity seismic loading[J].Journal of Structure Engineering,1995,121(5):857-864.
[73]王东升,司炳君,艾庆华等.改进的Park-Ang地震损伤模型及其比较[J].工程抗震与加固改造,2005,27(增刊):138-143.
[74]Chai YH,Romstad KM.Correlation between strain-based low-cycle fatigue and energy-based linear damage models[J].Earthquake spectra,1997,13(2):191-209.
[75]Chai YH.Incorporating low-cycle fatigue model into duration-dependent inelastic design spectra[J].Earthquake Engineering and Structure Dynamics,2005,34(1):83-96.
[76]Kunnath SK,Chai YH.Cumulative damage-based inelastic cycle demand spectrum[J].Earthquake Engineering and Structure Dynamics,2004,33(4):499-520.
[77]Zahrah T F,Hall W J.Earthquake energy absorption in SDOF structures[J].Journal of Structure Engineering,1983,110(8):1722-1757.
[78]Kuwamura H,Galambos T V.Seismic load for structure reliability[J].Journal of Structure Engineering,1989,115(6):1446-1462.
[79]糜永红.建筑结构在地震作用下的能量反应分析及应用研究[D].湖南大学,2003.
[80]Fajfar P,Vidic T,Fischinger M.Seismic demand in medium and long period structures[J].Earthquake Engineering and Structure Dynamics,1989,18(8):1133-1144.
[81]Kuwamura H,Kirino Y,Akiyama H.Prediction of earthquake energy input from smoothed Fourier amplitude spectrum[J].Earthquake Engineering and Structure Dynamics,1994,23(10):1125-1137.
[82]Vidic T,Fajfar P.Behavior factors taking into account cumulative damage[J].Proc.,10th Eur.Conf.on Earthquake Engineering and Structure Dynamics,1994,23:507-521.
[83]熊仲明,史庆轩,王社良.结构能量分析非线性地震反应的理论研究[J].西安建筑科技大学学报,2005,37(2):204-209.
[84]杨晓明,史庆轩,丰定国.抗震结构能量设计方法中阻尼耗能的研究[J].西安建筑科技大学学报,2006,38(2):189-193.
[85]Fajfar P,Vidic T.Consistent inelastic design spectra:Hysteretic and input energy [J].Earthquake Engineering and Structure Dynamics,1994,23:523-537.
[86]Chai YH,Fajfar P.A procedure for estimating input energy spectra for seismic design [J].Journal of Earthquake Engineering,2000,4(4):539-561.
[87]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,2005,24(1):39-48.
[88]刘哲锋,沈蒲生.地震动输入能量谱的研究[J].工程抗震与加固改造,2006,28(4):1-5.
[89]盛明强,罗奇峰,刘建成等.考虑场地类别和强震持时的滞回耗能谱的特征分析[J].地震研究,2007,30(2):169-174.
[90]高振世,王宝安,庞同和.低周反复荷载作用下钢筋混凝土框架的延性和强度[J].东南大学学报,1991,21(4):38-44.
[91]Qi X,Moehle JP.Displacement design approach for reinforced concrete structures subjected to earthquakes[J].Report NO.UCB/EERC-91/02,University of California at Berkeley,CA,1991.
[92]Collins KR.Investigation of alternative seismic design procedures for standard buildings[D].University of Illinois at Urbana-Champian,IL,1995.
[93]Chen PT.Investigation of pushover analysis procedure for reliability-based and performance-based seismic design with applications to asymmetric building structures [D].University of Michigan,Ann Arbor,MI,1999.
[94]魏新磊,周云,于敬海等.基于结构能量分析的抗震设计新方法的研究[J].世界地震工程,2003,19(3):62-67.
[95]王丰,李宏男.基于等效单自由度体系的结构滞回耗能估计[J].大连理工大学学报,2007,47(1):85-89.
[96]Peter Fajfar.Capacity spectrum method based on inelastic demand spectra[J].Earthquake engineering and structural dynamics,1999,28(9):979-993.
[97]王威,孙景江.基于改进能力谱方法的位移反应估计[J].地震工程与工程振动,2003,23(6):37-43.
[98]李宏男,何浩祥.利用能力谱方法对结构地震损伤评估简化方法[J].大连理工大学学报,2004,44(2):267-270.
[99]Soon-Sik Lee.Performance-based design of steel moment frames using target drift and yield mechanism[D].University of Michigan,2002.
[100]Jun Hee Kim.Performance-based seismic design of light-frame shearwalls[D].Oregon State University,2004.
[101]李刚,程耿东.基于性能的结构抗震设计—理论、方法与应用[M].科学出版社,2004.
[102]熊向阳,戚振华.建筑结构弹塑性静力分析PUSH-OVER方法的研究[M].同济大学,2001.
[103]汪大绥,贺军利,张凤新.静力弹塑性分析(Pushover Analysis)的基本原理贺计算实例[J].世界地震工程,2004,20(1):45-53.
[104]王振宇,刘晶波.建筑结构地震损伤评估的研究进展[J].世界地震工程,2001, 17(3):43-48.
[105]何政,欧进萍.钢筋混凝土结构基于改进能力谱法的地震损伤性能设计[J].地震工程与工程振动,2000,20(2):31-38.
[106]侯钢领,何政,吴斌等.钢筋混凝土结构的屈服位移Chopra能力谱损伤分析与性能设计[J].地震工程与工程振动,2001,21(3):29-35.
[107]李洪泉,贲庆国,于之绰等.钢结构在地震作用下累积损伤分析及试验研究[J].建筑结构学报,2004,25(3):69-74.
[108]左春仁,左振宇.基于地震损伤性能的抗震设计方法[J].大连大学学报,2000,21(6):1-7.
[109]丁建.钢筋混凝土框架直接基于损伤性能的能力设计理论及方法的研究[D].西安建筑科技大学,2004.