高温下钢梁弯扭屈曲及含裂纹梁自由振动频率分析
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摘要
在火灾高温的作用下，结构钢的性能会发生严重劣化，钢结构建筑及其构件将发生复杂的内力重分布现象，结构和构件的变形也会显著加剧，从而造成结构整体的承载性能大大削弱，危及结构的安全，严重时会导致结构发生整体倒塌或破坏。因此建立合理的钢结构构件的抗火研究分析方法，特别是通过系统的理论研究，分析其在各种温度条件下的受力状态变化，具有重要的理论意义和工程应用价值。
本文在前人的工作基础上，对火灾高温作用下纯弯钢梁的弯扭屈曲受力状态做了进一步的研究，主要研究工作如下：
1.考虑高温对结构钢材料性能的影响，分析了高温下（20°C≤T≤300°C）纯弯钢梁的弹性弯扭屈曲变化，给出了两端简支纯弯钢梁、两端固支纯弯钢梁、悬臂纯弯钢梁在高温下临界屈曲弯矩的计算表达式，并考虑了受弯钢梁屈曲前变形对弯扭屈曲临界弯矩的影响。
2.推导了高温下（20°C≤T≤300°C）横向均布荷载作用下、横向集中荷载作用下的受弯钢梁临界屈曲弯矩和临界弯矩系数的计算表达式以及变截面受弯钢梁临界屈曲弯矩的计算表达式。
3.通过算例分析了钢梁临界屈曲弯矩的变化，由算例分析可知：钢梁截面形式和荷载位置作用点位置的不同，对钢梁在高温下的弹性临界屈曲弯矩的差别也很大，但随着温度的提高，临界屈曲弯矩的下降趋势一致，下降的幅度也比较类似。
4.根据弹塑性理论，对火灾高温作用下简支钢梁在弹塑性阶段的弯扭屈曲和临界屈曲弯矩进行了分析，给出了弹塑性阶段临界屈曲弯矩的计算表达式，通过算例分析了钢梁弹塑性阶段临界屈曲弯矩随温度的变化，并利用Ansys有限元软件模拟了钢梁在火灾燃烧不同时刻的竖向变形。
5.在考虑高温对结构材料性能的影响基础上，对高温下含裂纹简支梁的振动频率变化问题展开分析，建立了含裂纹简支梁在高温下的自由振动频率方程，通过算例对含裂纹简支钢梁和含裂纹简支铝合金梁在高温下的自由振动进行了模拟运算，分析了其振动基频随温度的变化规律，给出了高温下含裂纹简支梁的自振频率与材料弹性模量的变化关系表达式。由分析可知：温度的升高导致了结构材料弹性模量的不断下降，而材料弹性模量的下降又使得梁自振频率随之不断降低，而且在梁中裂纹的相对深度越大，随着温度的不断升高，梁自振频率的下降幅度也越大，而裂纹位置离支座位置越近，对高温下梁自振频率的变化影响就越小。
The material properties of the steel degenerate with temperature increased. Internal forceredistribution and obvious deformation will be appeared in the steel structure. The integralload capacity weakens sharply. Even totally collapse or damage will be happened due to a fire.So it is important to build a reasonable fire resisting method. It is meaningful to analysis theinternal force variation against temperature, especially through theoretical analysis.
The flexural torsional buckling of steel beams in high temperature is discussed in thispaper. The aspects that were studied in this research are as follows:
1. The elastic flexural torsional buckling of steel beams are analysised in hightemperature ranging from20℃to300℃considering the influence of high temperature onmaterial properties. The critical buckling moment equations of simply supported, fixed endedand cantilever beams considering the deformation before buckling are also provided.
2. The buckling critical moment and the corresponding coefficient equations of beamswith constant and varying cross-sections under transverse uniform or concentrated loads aredriven in high temperature ranging from20℃to300℃.
3. The critical buckling moments of steel beams against temperature are analysisedthrough an example. It is can be known from the example that influence of the section formand load point on elastic buckling critical moment in high temperature are observably. Thedowntrend and magnitude of the critical buckling moment against temperature of the twoinfluencing factors are analogously.
4. The flexural torsional and critical buckling moments of simplely supported steelbeams against temperature are analysised based on elastic-plastic theory. The elastic-plasticcritical buckling moment equations are provided. The elastic-plastic critical bucklingmoments of steel beams against temperature are analysised through an example. The verticaldeformations of steel beam at different fire burning moments are simulated by ANSYS.
5. The vibration frequencies of simply supported beam with cracks is analysisedconsidering the influence of temperature on material properties. The free vibration frequencyequation of simply supported beam with cracks in high temperature is provided. The vibration frequency variations of a simply supported steel beam and a aluminum alloy beam withcracks against temperature are obtained through numerical simulation. A series of conclusioncan be obtained. Material Young's modulus decrease with temperature increased, the decreaseof material elasticity modulus will result in the decrease of natural frequency. Deeper crackbring more significant drop of natural frequency against temperature, the influence of crackon natural frequency is small when the crack is near the support. The relational expression ofnatural frequency and Young's modulus of the simply supported beam is also obtained.
本文在前人的工作基础上，对火灾高温作用下纯弯钢梁的弯扭屈曲受力状态做了进一步的研究，主要研究工作如下：
1.考虑高温对结构钢材料性能的影响，分析了高温下（20°C≤T≤300°C）纯弯钢梁的弹性弯扭屈曲变化，给出了两端简支纯弯钢梁、两端固支纯弯钢梁、悬臂纯弯钢梁在高温下临界屈曲弯矩的计算表达式，并考虑了受弯钢梁屈曲前变形对弯扭屈曲临界弯矩的影响。
2.推导了高温下（20°C≤T≤300°C）横向均布荷载作用下、横向集中荷载作用下的受弯钢梁临界屈曲弯矩和临界弯矩系数的计算表达式以及变截面受弯钢梁临界屈曲弯矩的计算表达式。
3.通过算例分析了钢梁临界屈曲弯矩的变化，由算例分析可知：钢梁截面形式和荷载位置作用点位置的不同，对钢梁在高温下的弹性临界屈曲弯矩的差别也很大，但随着温度的提高，临界屈曲弯矩的下降趋势一致，下降的幅度也比较类似。
4.根据弹塑性理论，对火灾高温作用下简支钢梁在弹塑性阶段的弯扭屈曲和临界屈曲弯矩进行了分析，给出了弹塑性阶段临界屈曲弯矩的计算表达式，通过算例分析了钢梁弹塑性阶段临界屈曲弯矩随温度的变化，并利用Ansys有限元软件模拟了钢梁在火灾燃烧不同时刻的竖向变形。
5.在考虑高温对结构材料性能的影响基础上，对高温下含裂纹简支梁的振动频率变化问题展开分析，建立了含裂纹简支梁在高温下的自由振动频率方程，通过算例对含裂纹简支钢梁和含裂纹简支铝合金梁在高温下的自由振动进行了模拟运算，分析了其振动基频随温度的变化规律，给出了高温下含裂纹简支梁的自振频率与材料弹性模量的变化关系表达式。由分析可知：温度的升高导致了结构材料弹性模量的不断下降，而材料弹性模量的下降又使得梁自振频率随之不断降低，而且在梁中裂纹的相对深度越大，随着温度的不断升高，梁自振频率的下降幅度也越大，而裂纹位置离支座位置越近，对高温下梁自振频率的变化影响就越小。
The material properties of the steel degenerate with temperature increased. Internal forceredistribution and obvious deformation will be appeared in the steel structure. The integralload capacity weakens sharply. Even totally collapse or damage will be happened due to a fire.So it is important to build a reasonable fire resisting method. It is meaningful to analysis theinternal force variation against temperature, especially through theoretical analysis.
The flexural torsional buckling of steel beams in high temperature is discussed in thispaper. The aspects that were studied in this research are as follows:
1. The elastic flexural torsional buckling of steel beams are analysised in hightemperature ranging from20℃to300℃considering the influence of high temperature onmaterial properties. The critical buckling moment equations of simply supported, fixed endedand cantilever beams considering the deformation before buckling are also provided.
2. The buckling critical moment and the corresponding coefficient equations of beamswith constant and varying cross-sections under transverse uniform or concentrated loads aredriven in high temperature ranging from20℃to300℃.
3. The critical buckling moments of steel beams against temperature are analysisedthrough an example. It is can be known from the example that influence of the section formand load point on elastic buckling critical moment in high temperature are observably. Thedowntrend and magnitude of the critical buckling moment against temperature of the twoinfluencing factors are analogously.
4. The flexural torsional and critical buckling moments of simplely supported steelbeams against temperature are analysised based on elastic-plastic theory. The elastic-plasticcritical buckling moment equations are provided. The elastic-plastic critical bucklingmoments of steel beams against temperature are analysised through an example. The verticaldeformations of steel beam at different fire burning moments are simulated by ANSYS.
5. The vibration frequencies of simply supported beam with cracks is analysisedconsidering the influence of temperature on material properties. The free vibration frequencyequation of simply supported beam with cracks in high temperature is provided. The vibration frequency variations of a simply supported steel beam and a aluminum alloy beam withcracks against temperature are obtained through numerical simulation. A series of conclusioncan be obtained. Material Young's modulus decrease with temperature increased, the decreaseof material elasticity modulus will result in the decrease of natural frequency. Deeper crackbring more significant drop of natural frequency against temperature, the influence of crackon natural frequency is small when the crack is near the support. The relational expression ofnatural frequency and Young's modulus of the simply supported beam is also obtained.
引文
[1]赵金城.钢结构抗火性能研究中的若干问题．工程力学,1996（增刊）：41-46页
[2]李国强.钢梁抗火设计和计算的实用方法.工业建筑，1994，24（7）：43-46页
[3]李国强，蒋首超，林桂祥.钢结构抗火计算与设计.北京：中国建筑工业出版社，1999：24-49页
[4]李国强，吴波，韩林海.结构抗火研究进展与趋势.建筑钢结构进展，2006，8（1）：1-13页
[5]贺晗，余绍锋.钢结构的抗火研究概述.钢结构，2009，24（11）：80-83页
[6]丁军，李国强，蒋首超.火灾下钢结构构件的温度分析.钢结构，2002，17（2）：53-56页
[7]陈长坤.火灾下钢梁瞬态温度分布数值模拟及实验.中南大学学报-自然科学版，2008，39（5）：1094-1099页
[8]周煜琴，姚斌，胡军等.不均匀防火涂层对火灾条件下某简支钢梁温升和变形特性的影响.火灾科学,2008，17（4）：238-243页
[9] CENDAFTENV1993, Eurocode3: Design of steel structures, British StandardsInstitution，1995，7
[10] BSI，Structural Use of Steelwork in Building, Part8. Code of Practice for FireResistance Design,1990
[11] Lie T T，Irwin R J. Fire resistance of rectangular steel columns filled with bar-reinforced concrete. Journal of Structural Engineering，1995,121（5）:797-805.
[12] ECCS, European Recommendations for the Fire Safety of Steel Structures,1983.
[13] Standards Australia, AS4100, Steel structures, Sydney,1990.
[14]苏娟.火灾作用下钢筋混凝土结构非线性分析.哈尔滨工程大学博士学位论文，2008：16-29页
[15]李国强，陈凯，蒋首超等.高温下Q345钢的材料性能试验研究.建筑结构，2001，31（1）：53-55页
[16]徐彦，赵金城. Q235钢在不同应力—温度路径下材料性能的试验研究和本构关系.上海交通大学学报，2004,38（6）：967-971页
[17]赵金城，沈祖炎.局部火灾下钢框架结构整体性能的非线性分析.建筑结构学报，1997，18（4）：30-36页
[18]李国强，金福安.火灾时钢框架结构的极限状态分析.土木工程学报，1994，27（1）：49-56页.
[19]谭巍.高温火灾条件下钢结构的材料性能及钢框架结构反应的分析研究.同济大学硕士论文，2003：1-92页
[20]李晓东，董毓利，高立堂等.单层单跨钢框架抗火性能的试验研究.建筑结构学报，2006，27（6）：39-47页
[21]董毓利，李晓东．组合钢框架火灾时破坏机理实验研究．实验力学，2007，22（5）：463-471页
[22]王振清，韩玉来，王永军等.局部火灾场钢框架结构等效楼面活荷载分析.海军工程大学学报，2007，19（2）：36-40页
[23]韩玉来.建筑结构抗火性能研究.哈尔滨工程大学博士学位论文，2008：3-20，69-81页
[24]陈骥.钢结构稳定理论与设计.科学出版社,2008：322-372页
[25]赵金城.高温下钢结构压弯构件的整体稳定极限状态.钢结构，1998，13（8）：31-34页
[26]郝淑英，杨秀萍，王鹏林，张敬宇.钢梁火灾下响应的虚拟仿真.天津理工学院学报，2004，20（3）：9-12，32页
[27]李国强，郭士雄．受火约束钢梁在升温段和降温段行为的理论分析（I）．防灾减灾工程学报，2006，26（3）：241-250页
[28]郭士雄，李国强.受火约束钢梁在升温段和降温段行为的理论分析（II）.防灾减灾工程学报，2006，26（4）：359-368页
[29]李国强，郭士雄.约束钢梁高温下大变形状态分析.同济大学学报—自然科学版,2006，34（7）：853-858页
[30]王培军，李国强.弹性轴向约束平面钢梁火灾下非线性分析的弧线坐标法.工程力学,2008，25（1）：137-144页
[31]丛术平，董毓利，梁书亭.柔性连接钢梁火灾行为的试验研究.建筑结构,2008，38（7）：61-63页
[32]孙冬明，夏军武，龙谋识.高温下约束钢梁冷却阶段的性能试验研究.建筑结构,2009，7：85-90页
[33]陆建辉，张谦，李丰亭，李兵.钢梁和钢混凝土组合梁在温度载荷作用下的响应.中国海洋大学学报-自然科学版，2009，6：1325-1329页
[34]李国强，吴波，蒋首超.工程结构抗火研究进展与建议.建筑钢结构进展，2010,12（5）：13-18页
[35]李娟，姚斌，胡军.温升速率对某防火保护简支钢梁耐火时间的影响.火灾科学，2010，1：38-44页
[36]马宏彬，薛启迪，薛启超.火灾作用下钢梁抗弯强度可靠度的计算方法.钢结构，2010，6：72-75，59页
[37]刘东亚，杨秀萍.升降温条件对约束钢梁抗火性能的影响.天津理工大学学报，2010，26（5）：11-15页
[38]吕琳，叶中豹.高温火灾下约束钢梁挠度非线性分析.安徽建筑工业学院学报—自然科学版，2011，19（3）：38-40页
[39]王振清，韩玉来，王永军等.火灾场冲击波荷载作用下简支钢梁动力响应.振动与冲击，2007，26（4）：69-72页
[40]韩玉来，孙柏涛，王永刚等.火灾高温作用下波纹腹板钢梁剪切屈曲系数研究.防灾减灾工程学报，2011，31（34）：384-388页
[41]陈树华，韩玉来，侯纲领.火灾中的波纹腹板钢梁弹性剪切屈曲分析.广西大学学报（自然科学版），2011,36（4）：525-529页
[42]王传慧，席丰.受火侵袭波纹腹板钢梁的侧向弯扭屈曲及其参数分析.防灾减灾工程学报，2012，32（1）：117-123页
[43]吕俊利，董毓利，杨志年.整体结构中两跨钢梁火灾变形性能的试验研究.工程力学，2012，29（3）：110-114页
[44]杨秀萍，刘东亚，姚斌.自然火灾条件下约束钢梁可靠性分析.武汉大学学报—工学版，2012，45（1）：70-74页
[45]孙金香，高伟译.建筑物综合防火设计.天津科技翻译出版公司,1992：682-686页
[46]李引擎，马道贞，徐坚.建筑结构防火设计计算和构造处理.北京：中国建筑工业出版社，1991：234-235页
[47]上海市建设与管理委员会．上海市工程建设规范：建筑钢结构防火技术规程（DG/TJ08008–2000），2000．
[48]施丽彦.钢结构防火.重庆建筑大学学报,2002,24（2）：l5-l8页
[49]李国强，李兆治．钢结构性能化防火设计的初步设想．消防科学与技术，2004（1）：46-48页
[50]姚斌，蔡昕，周煜琴等.热—力耦合作用对建筑结构火灾安全的影响.火灾科学，2007，16（1）：60-66页
[51] Dharma R B，Tan K H.火灾中无约束钢梁的扭转弯曲的设计方法.钢结构，2008，23（2）：81-82页
[52]周煜琴，姚斌.火灾高温下耐火保护钢梁设计荷载的分析.消防科学与技术，2012，31（4）：340-343页
[53] Pope N D, Bailey C G. Quantitative comparison of FDS and parametric fire curveswith post-flashover compartment fire test data. Fire Safety Journal,2006,41（2）:99-110P
[54] Mesquita L M R. Experimental and numerical research on the critical temperature oflaterally unrestrained steel I-beams. Journal of Constructional Steel Research,2005,61（2）:1435-1446P
[55] Gardner L，Ng K T. Temperature development in structural stainless steel sectionsexposed to fire. Fire Safety Journal，2006，41（3）：185-203P
[56] Moinuddin K A M, Al-Menhali J S, Prasannan K,etc. Rise in structural steeltemperatures during ISO9705room fires. Fire Safety Journal,2011,46（8）:480-496P
[57] Buchanan A, Moss P, Seputro J,etc. The effect of stress–strain relationships on the fireperformance of steel beams. Engineering Structures,2004,26（11）:1505-1515P
[58] Chen J, Young B. Stress–strain curves for stainless steel at elevated temperatures.Engineering Structures,2006,28（2）:229-239P
[59] Huang Z F, Tan K H. Rankine approach for fire resistance of axially and flexurallyrestrained steel columns. Journal of Constructional Steel Research,2003,59（12）:1553-1571P
[60] Wong M B. Modelling of axial restraints for limiting temperature calculation of steelmembers in fire. Journal of Constructional Steel Research,2005,61（5）:675-687P
[61] Yang K C，Lee H H，Olen C．Experimental study of fire-resistant steel H-columnsat elevated temperature． Journal of Constructional Steel Research，2006，62（6）：544-553P
[62] Tan K H，Toh W S，Huang Z F，etc. Structural responses of restrained steelcolumns at elevated temperatures，Part I：Experiments．Engineering Structures，2007，29（8）：1641-1652P
[63] Huang Z F，Tan K H，Toh W S，etc. Fire resistance of composite columns withembedded I-section steel–Effects of section size and load level． Journal ofConstructional Steel Research，2008，64（3）：312-325P
[64] Garlock M M, Quiel S E. The behavior of steel perimeter columns in a high-risebuilding under fire. Engineering Journal,2007,44（4）:359-372P
[65] Quiel S E, Garlock M E M. Closed-form prediction of the thermal and structuralresponse of a perimeter column in a fire. Open Construction and Building TechnologyJournal，2010,4:64-78P
[66] Ng K T， Gardner L． Buckling of stainless steel columns and beams infire．Engineering Structures，2007，29（5）：717-730P
[67] Ranawaka T, Mahendran M. Distortional buckling tests of cold-formed steelcompression members at elevated temperatures. Journal of Construction SteelResearch,2009,65（2）:249-259P
[68] Shahbazian A, Wang Y C. Calculating the global buckling resistance of thin-walledsteel members with uniform and non-uniform elevated temperatures under axialcompression. Thin-Walled Structures,2011,49（11）1415-1428P
[69] Strej ek M, ezní ek J, Tan K H, etc. Behaviour of column web component of steelbeam-to-column joints at elevated temperatures. Journal of Constructional SteelResearch,2011,67（12）:1890-1899P
[70] Li G Q, Zhang C. Creep effect on buckling of axially restrained steel columns in realfires. Journal of Constructional Steel Research,2012,71（3）:182-188P
[71] Real P M M V,Cazeli R,Silva L S D,etc. Lateral-torsional buckling of unrestrainedsteel beams under fire conditions: improvement of EC3proposal. Computers&Structures,2004,82（20-21）:1737-1744P
[72] Real P M M V，Cazeli R，Silva L S D，etc. The effect of residual stresses in thelateral-torsional buckling of steel I-beams at elevated temperature. Journal ofConstructional Steel Research，2004，60（3-5）:783-793P
[73] Real P M M V, Lopes N, Silva L S D, etc. Parametric analysis of the lateral–torsionalbuckling resistance of steel beams in case of fire. Fire Safety Journal,2007,42（6-7）:416-424P
[74] Real P M M V, Piloto P A G, Franssen J M. A new proposal of a simple model for thelateral-torsional buckling of unrestrained steel I-beams in case of fire： experimentaland numerical validation. Journal of Constructional Steel Research，2008，59（2）:179-199.
[75] Rebelo C, Lopes N, Silva L S D, etc. Statistical evaluation of the lateral–torsionalbuckling resistance of steel I-beams, Part1: Variability of the Eurocode3resistancemodel. Journal of Constructional Steel Research,2009,65（4）:818-831P
[76] Silva L S D, Rebelo C, Nethercot D, etc. Statistical evaluation of the lateral-torsionalbuckling resistance of steel I-beams, Part2: Variability of steel properties. Journal ofConstructional Steel Research,2009,65（4）:832-849P
[77] Mesquita L M R，Piloto P AG，M A P Vaz，etc. Experimental and numericalresearch on the critical temperature of laterally unrestrained steel I beams. Journal ofConstructional Steel Research，2005，61（10）：1435-1446P
[78] Dwaikat M M S, Kodur V K R, Quiel S E, etc. Experimental behavior of steel beam–columns subjected to fire-induced thermal gradients. Journal of Constructional SteelResearch,2011,67（1）:30-38P
[79] Li G Q，Guo S X．Experiment on restrained steel beams subjected to heating andcooling．Journal of Constructional Steel Research，2008，64（3）：268-274P
[80] Ronny B D，Tan K H．Rotational capacity of steel I-beams under fire conditionsPart I：Experimental study．Engineering Structure．2007，29（9）：2391-2402P
[81] Ronny B D，Tan K H．Rotational capacity of steel I-beams under fire conditionsPart II：Numerical simulations．Engineering Structures，2007，29（9）：2403-2418P
[82] Pi Y L, Bradford M A, Gao W. Interval Thermoelastic Response of ElasticallyRestrained Steel Beams. Procedia Engineering，2011，14:2117-2123P
[83] Yang Y B, Lin T J, Leu L J,etc. Inelastic postbuckling response of steel trusses underthermal loadings. Journal of Constructional Steel Research，2008，64（12）:1394-1407P
[84] Li G Q， Wang P J， Jiang S C. Non-linear finite element analysis of axiallyrestrained steel beams at elevated temperatures in a fire. Journal of ConstructionalSteel Research，2007，63（9）:1175-1183P
[85] Heidarpour A，Bradford M A. Generic nonlinear modelling of restrained steel beamsat elevated temperatures. Engineering Structures，2009，31（11）:2787-2796P
[86] Bradford M A，Luu T K，Heidarpour A． Generic nonlinear modelling of a steelbeam in a frame sub-assembly at elevated temperatures. Journal of ConstructionalSteel Research，2008，64（7-8）：732-736P
[87] Yin Y Z，Wang Y C. Analysis of catenary action in steel beams using a simplifiedhand calculation method, Part2： validation for non-uniform temperature distribution.Journal of Constructional Steel Research，2005,61（2）:213-234P
[88] Ellobody E. Composite slim floor stainless steel beam construction exposed todifferent fires. Engineering Structures,2012,36（3）:1-13P
[89] Ellobody E. Nonlinear behaviour of unprotected composite slim floor steel beamsexposed to different fire conditions. Thin-Walled Structures，2011,49（6）:762-771P
[90] Ding J, Li G Q, Sakumoto Y. Parametric studies on fire resistance of fire-resistant steelmembers. Journal of Constructional Steel Research,2004，60（7）:1007-1027P
[91] Wong M B．Adaptation factor for moment capacity calculation of steel beams subjectto temperature gradient． Journal of Constructional Steel Research，2007，63（8）：1009-1015P
[92] Huang Z F, Tan K H. Structural responses of axially restrained steel beams withsemirigid moment connection in fire. Journal of Structural Engineering,2005,131（4）:541-551P
[93] Kodur V K R, Dwaikat M M S. Response of steel beam-columns exposed to fire.Engineering Structures,2009,31（2）:369-379P
[94] Ndoukouo A N, Nubissie A, Woafo P. On the dynamics of fire-exposed steel beamunder mechanical load. Journal of Constructional Steel Research,2011,67（12）:1864-1871P
[95] Dwaikat M, Kodur V. Effect of restraint force location on the response of steel beamsexposed to fire. Proceedings of the2009Structures Congress-Don't Mess withStructural Engineers: Expanding Our Role,2009:632-641P
[96] Dwaikat M, Kodur V. Effect of location of restraint on fire response of steel beams.Fire Technology,2010,46（1）:109-128P
[97] Gillie M，Usmani A S，Rotter J M．A Structural Analysis Of The First CardingtonTest．Journal of Constructional Steel Research，2001，56（6）：581-601P
[98] Gillie M，Usmani A S，Rotter J M．A Structural Analysis Of The CardingtonBritish Steel Corner Test． Journal of Constructional Steel Researeh，2002，58（4）：427-442P
[99] Lamont S，Usmani A S, Gillie M. Behaviour of a small composite steel framestructure in a "long-cool" and a "short-hot" fire. Fire Safety Journal，2004,39（5）:327-357P
[100] Huang Z F，Tan K H．Fire resistance of compartments within a high-rise steelframe：New sub-frame and isolated member models．Journal of Constructional SteelResearch，2006，62（10）：974-986P
[101] Lamont S, Gillie M, Usmani A S. Composite steel-framed structures in fire withprotected and unprotected edge beams. Journal of Constructional Steel Research,2007,63（8）:1138-1150P
[102] Tan K H，Ting S K，Huang Z F．Visco-elasto-plastic analysis of steel frames infire．Journal of Engineering Structures，2002，128（1）：105-114P
[103] Junior V S， Creus G J． Simplified elastoplastic analysis of general frames onfire．Engineering Structures，2007，9（4）：511-518P
[104] Liew J Y R， Ma K Y. Advanced analysis of3D steel framework exposed tocompartment fire. Fire and Materials,2004,28（2-4）:253-267P
[105] Hozjana T，Turk G，Srpocioc S．Fire analysis of steel frames with the use ofartificial neural networks． Journal of Constructional Steel Research，2007，63（10）：1396-1403P
[106] Aldina S，Lu os S D S，Paulo V R，etc. Numerical study of a steel sub-frame infire．Computers&Structures，2008，86（15-16）：1619-1632P
[107] Richard L J Y． Survivability of steel frame structures subject to blast andfire．Journal of Constructional Steel Research，2008，64（7-8）：854-866P
[108] Ruirui S, Huang Z H, Burgess L W. Progressive collapse analysis of steel structuresunder fire conditions. Engineering Structures,2012,34（1）:400-413P
[109] Usmani A S，Chung Y C，Torero J L．How did the WTC towers collapse： a newtheory．Fire Safety Journal，2003，8（6）：501-533P
[110] Barbara L． A suggested cause of the fire-induced collapse of the World TradeTowers．Fire Safety Journal，2003，38（6）：589-591P
[111] Jabri K S A, Burgess I W, Plank R J. Prediction of the degradation of connectioncharacteristics at elevated temperature. Journal of Constructional Steel Research,2004,60（3-5）:771-781P
[112] James B P L， Young B． Effects of elevated temperatures on bolted moment-connections between cold-formed steel members．Engineering Structures，2007，29（10）：2419-2427P
[113] Mao C J, Chiou Y J, Hsiao P A, etc. Fire response of steel semi-rigid beam–columnmoment connections. Journal of Constructional Steel Research,2009,65（6）:1290-1303P
[114] Mao C J, Chiou Y J，Hsiao P A,etc. The stiffness estimation of steel semi-rigid beam–column moment connections in a fire. Journal of Constructional Steel Research，2010，66（5）:680-694P
[115] Jabri K S A, Davison J B, Burgess I W. Performance of beam-to-column joints in fire-A review. Fire Safety Journal,2008,43（1）:50-62P
[116] Spyrou S, Davison J B, Burgess I W,etc. Experimental and analytical investigation ofthe ‘compression zone’ component within a steel joint at elevated temperatures.Journal of Constructional Steel Research,2004,60（6）:841-865P
[117] Spyrou S, Davison J B, Burgess I W,etc. Experimental and analytical investigation ofthe ‘tension zone’ components within a steel joint at elevated temperatures. Journal ofConstructional Steel Research,2004,60（6）:867-896P
[118] Heidarpour A, Bradford M A. Behaviour of a T-stub assembly in steel beam-to-columnconnections at elevated temperatures. Engineering Structures,2008,30（10）:2893-2899P
[119] Yuan Z, Tan K H, Ting S K. Testing of composite steel top-and-seat-and-web anglejoints at ambient and elevated temperatures: Part1—Elevated-temperature tests.Engineering Structures,2011，33（7）:2093-2109P
[120] Yuan Z, Tan K H, Ting S K. Testing of composite steel top-and-seat-and-web anglejoints at ambient and elevated temperatures: Part2—Ambient tests. EngineeringStructures,2011，33（10）:2727-2743P
[121] Yu W J, Zhao J C, Luo H X，etc. Experimental study on mechanical behavior of animpacted steel tubular T-joint in fire. Journal of Constructional Steel Research,2011,67（9）:1376-1385P
[122] Qian Z H，Tan K H，Burgess L W. Numerical and analytical investigations of steelbeam-to-column joints at elevated temperatures. Journal of Constructional SteelResearch,2009,65（5）:1043-1054P
[123] Yu H X，Burgess I W，Davison J B，etc. Numerical simulation of bolted steelconnections in fire using explicit dynamic analysis．Journal of Constructional SteelResearch，2008，64（5）：515–525P
[124] Lee C H, Chiou Y J, Chung H Y. Numerical modeling of the fire–structure behavior ofsteel beam-to-column connections. Journal of Constructional Steel Research，2011,67（9）:1386-1400P
[125] Lopes N, Real P V, Silva L S D,etc. Numerical analysis of stainless steel beam-columns in case of fire. Fire Safety Journal，2012,50（5）:35-50P
[126] Dai X H, Wang Y C, Bailey C G. Numerical modelling of structural fire behaviour ofrestrained steel beam–column assemblies using typical joint types. EngineeringStructures,2010,32（8）:2337-2351P
[127] Chen L, Wang Y C. Efficient modelling of large deflection behaviour of restrainedsteel structures with realistic endplate beam/column connections in fire. EngineeringStructures,2012,43（10）:194-209P
[128] Chen L, Wang Y C. Methods of improving survivability of steel beam/columnconnections in fire. Journal of Constructional Steel Research，2012,79（12）:127-139P
[129] Heidarpour A, Bradford M A. Local buckling and slenderness limits for steel websunder combined bending，compression and shear at elevated temperatures. Thin-Walled Structures,2008,46（2）:128-146P
[130] Heidarpour A, Bradford M A. Local buckling and slenderness limits for flangeoutstands at elevated temperatures. Journal of Constructional Steel Research,2007,63（5）:591-598P
[131] Han Y L, Sun B T, Ju Z, etc. Critical Load Analysis of Double-hinged Circular SteelArch In-plane under High Temperature of Fire. Advances in Civil Engineering andArchitecture，2011（243-249）:3-6P
[132] Pi Y L, Bradford M A. In-plane thermoelastic behaviour and buckling of pin-endedand fixed circular arches. Engineering Structures，2010,32（1）:250-260P
[133] Heidarpour A, Bradford M A, Othman K A M. Thermoelastic flexural-torsionalbuckling of steel arches. Journal of Constructional Steel Research，2011,67（12）:1806-1820P
[134] Bradford M A. In-plane nonlinear behaviour of circular pinned arches with elasticrestraints under thermal loading. International Journal of Structural Stability andDynamics，2006,6（2）:163-177P
[135] Heidarpour A, Pham T H, Bradford M A. Nonlinear thermoelastic analysis ofcomposite steel-concrete arches including partial interaction and elevated temperatureloading. Engineering Structures，2010,32（10）:3248-3257P
[136] Heidarpour A, Pham T H, Bradford M A. Non-linear inelastic analysis of steel archesat elevated temperatures. Journal of Constructional Steel Research，2010,66（4）:512-519P
[137] Heidarpour A, Abdullah A A，Bradford M A. Non-linear thermoelastic analysis ofsteel arch members subjected to fire. Fire Safety Journal，2010,45（3）:183-192P
[138] Lu C K，Chan S L，Zha X X．Material yielding by both axial and bending springstiffness at elevated temperature．Journal of Constructional Steel Research，2007，63（5）：677-685P
[139] Bradford M A． Elastic analysis of straight members at elevatedtemperature．Advances in Structural Engineering，2006，9（5）：611-618P
[140] Kankanamge N D, Mahendran M. Behaviour and design of cold-formed steel beamssubject to lateral–torsional buckling at elevated temperatures. Thin-Walled Structures,2012,61（12）:213-228P
[141] Dharma R B, Tan K H. Proposed design methods for lateral torsional buckling ofunrestrained steel beams in fire. Journal of Constructional Steel Research,2007,63（8）:1066-1076P
[142] Lopes N, Silva L S D, Real P M M V,etc. New proposals for the design of steel beam-columns in case of fire, including a new approach for the lateral–torsional buckling.Computers&Structures,2004,82（17-19）:1463-1472P
[143] Chen J, Young B． Design of high strength steel columns at elevatedtemperatures．Journal of Constructional Steel Research，2008，64（6）：689-703P
[144] Jeffers A E, Sotelino E D. An efficient fiber element approach for the thermo-structural simulation of non-uniformly heated frames. Fire Safety Journal,2012,51（4）:18-26P
[145] Shahbazian A, Wang Y C. Application of the Direct Strength Method to local bucklingresistance of thin-walled steel members with non-uniform elevated temperatures underaxial compression. Thin-Walled Structures,2011,49（12）:1573-1583P
[146] Takagi J, Deierlein G G. Strength design criteria for steel members at elevatedtemperatures. Journal of Constructional Steel Research,2007,63（8）:1036-1050P
[147] Lien K H, Chiou Y J, Wang R Z,etc. Vector Form Intrinsic Finite Element analysis ofnonlinear behavior of steel structures exposed to fire. Engineering Structures,2010,32（1）:80-92P
[148] Benedetti A. Approximate optimal design of fire-resisting beams and columns. Journalof Constructional Steel Research,2003,59（10）:1251-1266P
[149] Gardner L，Baddoo N R. Fire testing and design of stainless steel structures. Journalof Constructional Steel Research，2006，62（6）：532-543P
[150] Wong M B．Universal design charts for insulation of steel members in fire．Journalof Constructional Steel Research，2005，61（10）：1447-1456P
[151] Kodur V K R, Dwaikat M M S. A performance based methodology for fire design ofrestrained steel beams. Journal of Constructional Steel Research,2011,67（3）:510-524P
[152]吴国荣.含裂纹梁自由振动分析.噪声与振动控制，2008，28（4）：31-34页
[153]程礼，何正嘉，李宁等.裂纹非线性呼吸行为对转子临界转速的影响.振动与冲击，2010，29（4）：44-53页
[154]王宗勇，林伟，闻邦椿.开闭裂纹转轴刚度的解析研究.振动与冲击,2010，29（9）：69-72页
[155]张敬芬，赵德有.工程结构裂纹损伤振动诊断的发展现状和展望.振动与冲击，2002，21（4）：22-25页
[156]郑栋梁，李中付，华宏星.结构早期损伤识别技术的现状和发展趋势.振动与冲击，2002，21（2）：1-10页
[157]胡家顺，冯新，李昕等.裂纹梁振动分析和裂纹识别方法研究进展.振动与冲击，2007，26（11）：146-151页
[158]任宜春，马石城，林琳.移动荷载作用下梁裂缝识别的小波方法研究.振动与冲击，2004，23（2）：82-85页
[159]吴宁祥，吴克勤，由关雁等.裂纹梁的动态特性仿真.工程设计学报，2006，13（4）：236-240页
[160] Rosales M B, Filipich C P, Buezas F S. Crack detection in beam-like structures.Engineering Structures，2009，31（10）：2257-2264P
[161] Rezaee M, Hassannejad R. Free vibration analysis of simply supported beam withbreathing crack using perturbation method. Acta Mechanica Solida Sinica,2010,23（5）:459-470P
[162] Caddemi S，Calio I，Marletta M. The non-linear dynamic response of the Euler–Bernoulli beam with an arbitrary number of switching cracks. International Journal ofNon-Linear Mechanics,2010，45（7）：714-726P
[163] Bikri K E, Benamar R, Bennoua M M. Geometrically non-linear free vibrations ofclamped–clamped beams with an edge crack. Computers&Structures,2006,84（7）：485-502P
[164] Mazanoglu K, Sabuncu M. Vibration analysis of non-uniform beams having multipleedge cracks along the beam's height. International Journal of Mechanical Sciences,2010,52（3）：515-522P
[165] Matjaz S. Elastic beam finite element with an arbitrary number of transversecracks. Finite Elements in Analysis and Design，2009，45（3）：181-189P
[166]孙强，张忠平，柴桥等.航空发动机压气机叶片振动频率与温度的关系.应用力学学报，2004，21（4）：137-139页
[167]王振清，刘兵，韩玉来.高温下含裂纹铝合金梁自由振动频率分析.哈尔滨工程大学学报，2012，33（3）：320-324页
[2]李国强.钢梁抗火设计和计算的实用方法.工业建筑，1994，24（7）：43-46页
[3]李国强，蒋首超，林桂祥.钢结构抗火计算与设计.北京：中国建筑工业出版社，1999：24-49页
[4]李国强，吴波，韩林海.结构抗火研究进展与趋势.建筑钢结构进展，2006，8（1）：1-13页
[5]贺晗，余绍锋.钢结构的抗火研究概述.钢结构，2009，24（11）：80-83页
[6]丁军，李国强，蒋首超.火灾下钢结构构件的温度分析.钢结构，2002，17（2）：53-56页
[7]陈长坤.火灾下钢梁瞬态温度分布数值模拟及实验.中南大学学报-自然科学版，2008，39（5）：1094-1099页
[8]周煜琴，姚斌，胡军等.不均匀防火涂层对火灾条件下某简支钢梁温升和变形特性的影响.火灾科学,2008，17（4）：238-243页
[9] CENDAFTENV1993, Eurocode3: Design of steel structures, British StandardsInstitution，1995，7
[10] BSI，Structural Use of Steelwork in Building, Part8. Code of Practice for FireResistance Design,1990
[11] Lie T T，Irwin R J. Fire resistance of rectangular steel columns filled with bar-reinforced concrete. Journal of Structural Engineering，1995,121（5）:797-805.
[12] ECCS, European Recommendations for the Fire Safety of Steel Structures,1983.
[13] Standards Australia, AS4100, Steel structures, Sydney,1990.
[14]苏娟.火灾作用下钢筋混凝土结构非线性分析.哈尔滨工程大学博士学位论文，2008：16-29页
[15]李国强，陈凯，蒋首超等.高温下Q345钢的材料性能试验研究.建筑结构，2001，31（1）：53-55页
[16]徐彦，赵金城. Q235钢在不同应力—温度路径下材料性能的试验研究和本构关系.上海交通大学学报，2004,38（6）：967-971页
[17]赵金城，沈祖炎.局部火灾下钢框架结构整体性能的非线性分析.建筑结构学报，1997，18（4）：30-36页
[18]李国强，金福安.火灾时钢框架结构的极限状态分析.土木工程学报，1994，27（1）：49-56页.
[19]谭巍.高温火灾条件下钢结构的材料性能及钢框架结构反应的分析研究.同济大学硕士论文，2003：1-92页
[20]李晓东，董毓利，高立堂等.单层单跨钢框架抗火性能的试验研究.建筑结构学报，2006，27（6）：39-47页
[21]董毓利，李晓东．组合钢框架火灾时破坏机理实验研究．实验力学，2007，22（5）：463-471页
[22]王振清，韩玉来，王永军等.局部火灾场钢框架结构等效楼面活荷载分析.海军工程大学学报，2007，19（2）：36-40页
[23]韩玉来.建筑结构抗火性能研究.哈尔滨工程大学博士学位论文，2008：3-20，69-81页
[24]陈骥.钢结构稳定理论与设计.科学出版社,2008：322-372页
[25]赵金城.高温下钢结构压弯构件的整体稳定极限状态.钢结构，1998，13（8）：31-34页
[26]郝淑英，杨秀萍，王鹏林，张敬宇.钢梁火灾下响应的虚拟仿真.天津理工学院学报，2004，20（3）：9-12，32页
[27]李国强，郭士雄．受火约束钢梁在升温段和降温段行为的理论分析（I）．防灾减灾工程学报，2006，26（3）：241-250页
[28]郭士雄，李国强.受火约束钢梁在升温段和降温段行为的理论分析（II）.防灾减灾工程学报，2006，26（4）：359-368页
[29]李国强，郭士雄.约束钢梁高温下大变形状态分析.同济大学学报—自然科学版,2006，34（7）：853-858页
[30]王培军，李国强.弹性轴向约束平面钢梁火灾下非线性分析的弧线坐标法.工程力学,2008，25（1）：137-144页
[31]丛术平，董毓利，梁书亭.柔性连接钢梁火灾行为的试验研究.建筑结构,2008，38（7）：61-63页
[32]孙冬明，夏军武，龙谋识.高温下约束钢梁冷却阶段的性能试验研究.建筑结构,2009，7：85-90页
[33]陆建辉，张谦，李丰亭，李兵.钢梁和钢混凝土组合梁在温度载荷作用下的响应.中国海洋大学学报-自然科学版，2009，6：1325-1329页
[34]李国强，吴波，蒋首超.工程结构抗火研究进展与建议.建筑钢结构进展，2010,12（5）：13-18页
[35]李娟，姚斌，胡军.温升速率对某防火保护简支钢梁耐火时间的影响.火灾科学，2010，1：38-44页
[36]马宏彬，薛启迪，薛启超.火灾作用下钢梁抗弯强度可靠度的计算方法.钢结构，2010，6：72-75，59页
[37]刘东亚，杨秀萍.升降温条件对约束钢梁抗火性能的影响.天津理工大学学报，2010，26（5）：11-15页
[38]吕琳，叶中豹.高温火灾下约束钢梁挠度非线性分析.安徽建筑工业学院学报—自然科学版，2011，19（3）：38-40页
[39]王振清，韩玉来，王永军等.火灾场冲击波荷载作用下简支钢梁动力响应.振动与冲击，2007，26（4）：69-72页
[40]韩玉来，孙柏涛，王永刚等.火灾高温作用下波纹腹板钢梁剪切屈曲系数研究.防灾减灾工程学报，2011，31（34）：384-388页
[41]陈树华，韩玉来，侯纲领.火灾中的波纹腹板钢梁弹性剪切屈曲分析.广西大学学报（自然科学版），2011,36（4）：525-529页
[42]王传慧，席丰.受火侵袭波纹腹板钢梁的侧向弯扭屈曲及其参数分析.防灾减灾工程学报，2012，32（1）：117-123页
[43]吕俊利，董毓利，杨志年.整体结构中两跨钢梁火灾变形性能的试验研究.工程力学，2012，29（3）：110-114页
[44]杨秀萍，刘东亚，姚斌.自然火灾条件下约束钢梁可靠性分析.武汉大学学报—工学版，2012，45（1）：70-74页
[45]孙金香，高伟译.建筑物综合防火设计.天津科技翻译出版公司,1992：682-686页
[46]李引擎，马道贞，徐坚.建筑结构防火设计计算和构造处理.北京：中国建筑工业出版社，1991：234-235页
[47]上海市建设与管理委员会．上海市工程建设规范：建筑钢结构防火技术规程（DG/TJ08008–2000），2000．
[48]施丽彦.钢结构防火.重庆建筑大学学报,2002,24（2）：l5-l8页
[49]李国强，李兆治．钢结构性能化防火设计的初步设想．消防科学与技术，2004（1）：46-48页
[50]姚斌，蔡昕，周煜琴等.热—力耦合作用对建筑结构火灾安全的影响.火灾科学，2007，16（1）：60-66页
[51] Dharma R B，Tan K H.火灾中无约束钢梁的扭转弯曲的设计方法.钢结构，2008，23（2）：81-82页
[52]周煜琴，姚斌.火灾高温下耐火保护钢梁设计荷载的分析.消防科学与技术，2012，31（4）：340-343页
[53] Pope N D, Bailey C G. Quantitative comparison of FDS and parametric fire curveswith post-flashover compartment fire test data. Fire Safety Journal,2006,41（2）:99-110P
[54] Mesquita L M R. Experimental and numerical research on the critical temperature oflaterally unrestrained steel I-beams. Journal of Constructional Steel Research,2005,61（2）:1435-1446P
[55] Gardner L，Ng K T. Temperature development in structural stainless steel sectionsexposed to fire. Fire Safety Journal，2006，41（3）：185-203P
[56] Moinuddin K A M, Al-Menhali J S, Prasannan K,etc. Rise in structural steeltemperatures during ISO9705room fires. Fire Safety Journal,2011,46（8）:480-496P
[57] Buchanan A, Moss P, Seputro J,etc. The effect of stress–strain relationships on the fireperformance of steel beams. Engineering Structures,2004,26（11）:1505-1515P
[58] Chen J, Young B. Stress–strain curves for stainless steel at elevated temperatures.Engineering Structures,2006,28（2）:229-239P
[59] Huang Z F, Tan K H. Rankine approach for fire resistance of axially and flexurallyrestrained steel columns. Journal of Constructional Steel Research,2003,59（12）:1553-1571P
[60] Wong M B. Modelling of axial restraints for limiting temperature calculation of steelmembers in fire. Journal of Constructional Steel Research,2005,61（5）:675-687P
[61] Yang K C，Lee H H，Olen C．Experimental study of fire-resistant steel H-columnsat elevated temperature． Journal of Constructional Steel Research，2006，62（6）：544-553P
[62] Tan K H，Toh W S，Huang Z F，etc. Structural responses of restrained steelcolumns at elevated temperatures，Part I：Experiments．Engineering Structures，2007，29（8）：1641-1652P
[63] Huang Z F，Tan K H，Toh W S，etc. Fire resistance of composite columns withembedded I-section steel–Effects of section size and load level． Journal ofConstructional Steel Research，2008，64（3）：312-325P
[64] Garlock M M, Quiel S E. The behavior of steel perimeter columns in a high-risebuilding under fire. Engineering Journal,2007,44（4）:359-372P
[65] Quiel S E, Garlock M E M. Closed-form prediction of the thermal and structuralresponse of a perimeter column in a fire. Open Construction and Building TechnologyJournal，2010,4:64-78P
[66] Ng K T， Gardner L． Buckling of stainless steel columns and beams infire．Engineering Structures，2007，29（5）：717-730P
[67] Ranawaka T, Mahendran M. Distortional buckling tests of cold-formed steelcompression members at elevated temperatures. Journal of Construction SteelResearch,2009,65（2）:249-259P
[68] Shahbazian A, Wang Y C. Calculating the global buckling resistance of thin-walledsteel members with uniform and non-uniform elevated temperatures under axialcompression. Thin-Walled Structures,2011,49（11）1415-1428P
[69] Strej ek M, ezní ek J, Tan K H, etc. Behaviour of column web component of steelbeam-to-column joints at elevated temperatures. Journal of Constructional SteelResearch,2011,67（12）:1890-1899P
[70] Li G Q, Zhang C. Creep effect on buckling of axially restrained steel columns in realfires. Journal of Constructional Steel Research,2012,71（3）:182-188P
[71] Real P M M V,Cazeli R,Silva L S D,etc. Lateral-torsional buckling of unrestrainedsteel beams under fire conditions: improvement of EC3proposal. Computers&Structures,2004,82（20-21）:1737-1744P
[72] Real P M M V，Cazeli R，Silva L S D，etc. The effect of residual stresses in thelateral-torsional buckling of steel I-beams at elevated temperature. Journal ofConstructional Steel Research，2004，60（3-5）:783-793P
[73] Real P M M V, Lopes N, Silva L S D, etc. Parametric analysis of the lateral–torsionalbuckling resistance of steel beams in case of fire. Fire Safety Journal,2007,42（6-7）:416-424P
[74] Real P M M V, Piloto P A G, Franssen J M. A new proposal of a simple model for thelateral-torsional buckling of unrestrained steel I-beams in case of fire： experimentaland numerical validation. Journal of Constructional Steel Research，2008，59（2）:179-199.
[75] Rebelo C, Lopes N, Silva L S D, etc. Statistical evaluation of the lateral–torsionalbuckling resistance of steel I-beams, Part1: Variability of the Eurocode3resistancemodel. Journal of Constructional Steel Research,2009,65（4）:818-831P
[76] Silva L S D, Rebelo C, Nethercot D, etc. Statistical evaluation of the lateral-torsionalbuckling resistance of steel I-beams, Part2: Variability of steel properties. Journal ofConstructional Steel Research,2009,65（4）:832-849P
[77] Mesquita L M R，Piloto P AG，M A P Vaz，etc. Experimental and numericalresearch on the critical temperature of laterally unrestrained steel I beams. Journal ofConstructional Steel Research，2005，61（10）：1435-1446P
[78] Dwaikat M M S, Kodur V K R, Quiel S E, etc. Experimental behavior of steel beam–columns subjected to fire-induced thermal gradients. Journal of Constructional SteelResearch,2011,67（1）:30-38P
[79] Li G Q，Guo S X．Experiment on restrained steel beams subjected to heating andcooling．Journal of Constructional Steel Research，2008，64（3）：268-274P
[80] Ronny B D，Tan K H．Rotational capacity of steel I-beams under fire conditionsPart I：Experimental study．Engineering Structure．2007，29（9）：2391-2402P
[81] Ronny B D，Tan K H．Rotational capacity of steel I-beams under fire conditionsPart II：Numerical simulations．Engineering Structures，2007，29（9）：2403-2418P
[82] Pi Y L, Bradford M A, Gao W. Interval Thermoelastic Response of ElasticallyRestrained Steel Beams. Procedia Engineering，2011，14:2117-2123P
[83] Yang Y B, Lin T J, Leu L J,etc. Inelastic postbuckling response of steel trusses underthermal loadings. Journal of Constructional Steel Research，2008，64（12）:1394-1407P
[84] Li G Q， Wang P J， Jiang S C. Non-linear finite element analysis of axiallyrestrained steel beams at elevated temperatures in a fire. Journal of ConstructionalSteel Research，2007，63（9）:1175-1183P
[85] Heidarpour A，Bradford M A. Generic nonlinear modelling of restrained steel beamsat elevated temperatures. Engineering Structures，2009，31（11）:2787-2796P
[86] Bradford M A，Luu T K，Heidarpour A． Generic nonlinear modelling of a steelbeam in a frame sub-assembly at elevated temperatures. Journal of ConstructionalSteel Research，2008，64（7-8）：732-736P
[87] Yin Y Z，Wang Y C. Analysis of catenary action in steel beams using a simplifiedhand calculation method, Part2： validation for non-uniform temperature distribution.Journal of Constructional Steel Research，2005,61（2）:213-234P
[88] Ellobody E. Composite slim floor stainless steel beam construction exposed todifferent fires. Engineering Structures,2012,36（3）:1-13P
[89] Ellobody E. Nonlinear behaviour of unprotected composite slim floor steel beamsexposed to different fire conditions. Thin-Walled Structures，2011,49（6）:762-771P
[90] Ding J, Li G Q, Sakumoto Y. Parametric studies on fire resistance of fire-resistant steelmembers. Journal of Constructional Steel Research,2004，60（7）:1007-1027P
[91] Wong M B．Adaptation factor for moment capacity calculation of steel beams subjectto temperature gradient． Journal of Constructional Steel Research，2007，63（8）：1009-1015P
[92] Huang Z F, Tan K H. Structural responses of axially restrained steel beams withsemirigid moment connection in fire. Journal of Structural Engineering,2005,131（4）:541-551P
[93] Kodur V K R, Dwaikat M M S. Response of steel beam-columns exposed to fire.Engineering Structures,2009,31（2）:369-379P
[94] Ndoukouo A N, Nubissie A, Woafo P. On the dynamics of fire-exposed steel beamunder mechanical load. Journal of Constructional Steel Research,2011,67（12）:1864-1871P
[95] Dwaikat M, Kodur V. Effect of restraint force location on the response of steel beamsexposed to fire. Proceedings of the2009Structures Congress-Don't Mess withStructural Engineers: Expanding Our Role,2009:632-641P
[96] Dwaikat M, Kodur V. Effect of location of restraint on fire response of steel beams.Fire Technology,2010,46（1）:109-128P
[97] Gillie M，Usmani A S，Rotter J M．A Structural Analysis Of The First CardingtonTest．Journal of Constructional Steel Research，2001，56（6）：581-601P
[98] Gillie M，Usmani A S，Rotter J M．A Structural Analysis Of The CardingtonBritish Steel Corner Test． Journal of Constructional Steel Researeh，2002，58（4）：427-442P
[99] Lamont S，Usmani A S, Gillie M. Behaviour of a small composite steel framestructure in a "long-cool" and a "short-hot" fire. Fire Safety Journal，2004,39（5）:327-357P
[100] Huang Z F，Tan K H．Fire resistance of compartments within a high-rise steelframe：New sub-frame and isolated member models．Journal of Constructional SteelResearch，2006，62（10）：974-986P
[101] Lamont S, Gillie M, Usmani A S. Composite steel-framed structures in fire withprotected and unprotected edge beams. Journal of Constructional Steel Research,2007,63（8）:1138-1150P
[102] Tan K H，Ting S K，Huang Z F．Visco-elasto-plastic analysis of steel frames infire．Journal of Engineering Structures，2002，128（1）：105-114P
[103] Junior V S， Creus G J． Simplified elastoplastic analysis of general frames onfire．Engineering Structures，2007，9（4）：511-518P
[104] Liew J Y R， Ma K Y. Advanced analysis of3D steel framework exposed tocompartment fire. Fire and Materials,2004,28（2-4）:253-267P
[105] Hozjana T，Turk G，Srpocioc S．Fire analysis of steel frames with the use ofartificial neural networks． Journal of Constructional Steel Research，2007，63（10）：1396-1403P
[106] Aldina S，Lu os S D S，Paulo V R，etc. Numerical study of a steel sub-frame infire．Computers&Structures，2008，86（15-16）：1619-1632P
[107] Richard L J Y． Survivability of steel frame structures subject to blast andfire．Journal of Constructional Steel Research，2008，64（7-8）：854-866P
[108] Ruirui S, Huang Z H, Burgess L W. Progressive collapse analysis of steel structuresunder fire conditions. Engineering Structures,2012,34（1）:400-413P
[109] Usmani A S，Chung Y C，Torero J L．How did the WTC towers collapse： a newtheory．Fire Safety Journal，2003，8（6）：501-533P
[110] Barbara L． A suggested cause of the fire-induced collapse of the World TradeTowers．Fire Safety Journal，2003，38（6）：589-591P
[111] Jabri K S A, Burgess I W, Plank R J. Prediction of the degradation of connectioncharacteristics at elevated temperature. Journal of Constructional Steel Research,2004,60（3-5）:771-781P
[112] James B P L， Young B． Effects of elevated temperatures on bolted moment-connections between cold-formed steel members．Engineering Structures，2007，29（10）：2419-2427P
[113] Mao C J, Chiou Y J, Hsiao P A, etc. Fire response of steel semi-rigid beam–columnmoment connections. Journal of Constructional Steel Research,2009,65（6）:1290-1303P
[114] Mao C J, Chiou Y J，Hsiao P A,etc. The stiffness estimation of steel semi-rigid beam–column moment connections in a fire. Journal of Constructional Steel Research，2010，66（5）:680-694P
[115] Jabri K S A, Davison J B, Burgess I W. Performance of beam-to-column joints in fire-A review. Fire Safety Journal,2008,43（1）:50-62P
[116] Spyrou S, Davison J B, Burgess I W,etc. Experimental and analytical investigation ofthe ‘compression zone’ component within a steel joint at elevated temperatures.Journal of Constructional Steel Research,2004,60（6）:841-865P
[117] Spyrou S, Davison J B, Burgess I W,etc. Experimental and analytical investigation ofthe ‘tension zone’ components within a steel joint at elevated temperatures. Journal ofConstructional Steel Research,2004,60（6）:867-896P
[118] Heidarpour A, Bradford M A. Behaviour of a T-stub assembly in steel beam-to-columnconnections at elevated temperatures. Engineering Structures,2008,30（10）:2893-2899P
[119] Yuan Z, Tan K H, Ting S K. Testing of composite steel top-and-seat-and-web anglejoints at ambient and elevated temperatures: Part1—Elevated-temperature tests.Engineering Structures,2011，33（7）:2093-2109P
[120] Yuan Z, Tan K H, Ting S K. Testing of composite steel top-and-seat-and-web anglejoints at ambient and elevated temperatures: Part2—Ambient tests. EngineeringStructures,2011，33（10）:2727-2743P
[121] Yu W J, Zhao J C, Luo H X，etc. Experimental study on mechanical behavior of animpacted steel tubular T-joint in fire. Journal of Constructional Steel Research,2011,67（9）:1376-1385P
[122] Qian Z H，Tan K H，Burgess L W. Numerical and analytical investigations of steelbeam-to-column joints at elevated temperatures. Journal of Constructional SteelResearch,2009,65（5）:1043-1054P
[123] Yu H X，Burgess I W，Davison J B，etc. Numerical simulation of bolted steelconnections in fire using explicit dynamic analysis．Journal of Constructional SteelResearch，2008，64（5）：515–525P
[124] Lee C H, Chiou Y J, Chung H Y. Numerical modeling of the fire–structure behavior ofsteel beam-to-column connections. Journal of Constructional Steel Research，2011,67（9）:1386-1400P
[125] Lopes N, Real P V, Silva L S D,etc. Numerical analysis of stainless steel beam-columns in case of fire. Fire Safety Journal，2012,50（5）:35-50P
[126] Dai X H, Wang Y C, Bailey C G. Numerical modelling of structural fire behaviour ofrestrained steel beam–column assemblies using typical joint types. EngineeringStructures,2010,32（8）:2337-2351P
[127] Chen L, Wang Y C. Efficient modelling of large deflection behaviour of restrainedsteel structures with realistic endplate beam/column connections in fire. EngineeringStructures,2012,43（10）:194-209P
[128] Chen L, Wang Y C. Methods of improving survivability of steel beam/columnconnections in fire. Journal of Constructional Steel Research，2012,79（12）:127-139P
[129] Heidarpour A, Bradford M A. Local buckling and slenderness limits for steel websunder combined bending，compression and shear at elevated temperatures. Thin-Walled Structures,2008,46（2）:128-146P
[130] Heidarpour A, Bradford M A. Local buckling and slenderness limits for flangeoutstands at elevated temperatures. Journal of Constructional Steel Research,2007,63（5）:591-598P
[131] Han Y L, Sun B T, Ju Z, etc. Critical Load Analysis of Double-hinged Circular SteelArch In-plane under High Temperature of Fire. Advances in Civil Engineering andArchitecture，2011（243-249）:3-6P
[132] Pi Y L, Bradford M A. In-plane thermoelastic behaviour and buckling of pin-endedand fixed circular arches. Engineering Structures，2010,32（1）:250-260P
[133] Heidarpour A, Bradford M A, Othman K A M. Thermoelastic flexural-torsionalbuckling of steel arches. Journal of Constructional Steel Research，2011,67（12）:1806-1820P
[134] Bradford M A. In-plane nonlinear behaviour of circular pinned arches with elasticrestraints under thermal loading. International Journal of Structural Stability andDynamics，2006,6（2）:163-177P
[135] Heidarpour A, Pham T H, Bradford M A. Nonlinear thermoelastic analysis ofcomposite steel-concrete arches including partial interaction and elevated temperatureloading. Engineering Structures，2010,32（10）:3248-3257P
[136] Heidarpour A, Pham T H, Bradford M A. Non-linear inelastic analysis of steel archesat elevated temperatures. Journal of Constructional Steel Research，2010,66（4）:512-519P
[137] Heidarpour A, Abdullah A A，Bradford M A. Non-linear thermoelastic analysis ofsteel arch members subjected to fire. Fire Safety Journal，2010,45（3）:183-192P
[138] Lu C K，Chan S L，Zha X X．Material yielding by both axial and bending springstiffness at elevated temperature．Journal of Constructional Steel Research，2007，63（5）：677-685P
[139] Bradford M A． Elastic analysis of straight members at elevatedtemperature．Advances in Structural Engineering，2006，9（5）：611-618P
[140] Kankanamge N D, Mahendran M. Behaviour and design of cold-formed steel beamssubject to lateral–torsional buckling at elevated temperatures. Thin-Walled Structures,2012,61（12）:213-228P
[141] Dharma R B, Tan K H. Proposed design methods for lateral torsional buckling ofunrestrained steel beams in fire. Journal of Constructional Steel Research,2007,63（8）:1066-1076P
[142] Lopes N, Silva L S D, Real P M M V,etc. New proposals for the design of steel beam-columns in case of fire, including a new approach for the lateral–torsional buckling.Computers&Structures,2004,82（17-19）:1463-1472P
[143] Chen J, Young B． Design of high strength steel columns at elevatedtemperatures．Journal of Constructional Steel Research，2008，64（6）：689-703P
[144] Jeffers A E, Sotelino E D. An efficient fiber element approach for the thermo-structural simulation of non-uniformly heated frames. Fire Safety Journal,2012,51（4）:18-26P
[145] Shahbazian A, Wang Y C. Application of the Direct Strength Method to local bucklingresistance of thin-walled steel members with non-uniform elevated temperatures underaxial compression. Thin-Walled Structures,2011,49（12）:1573-1583P
[146] Takagi J, Deierlein G G. Strength design criteria for steel members at elevatedtemperatures. Journal of Constructional Steel Research,2007,63（8）:1036-1050P
[147] Lien K H, Chiou Y J, Wang R Z,etc. Vector Form Intrinsic Finite Element analysis ofnonlinear behavior of steel structures exposed to fire. Engineering Structures,2010,32（1）:80-92P
[148] Benedetti A. Approximate optimal design of fire-resisting beams and columns. Journalof Constructional Steel Research,2003,59（10）:1251-1266P
[149] Gardner L，Baddoo N R. Fire testing and design of stainless steel structures. Journalof Constructional Steel Research，2006，62（6）：532-543P
[150] Wong M B．Universal design charts for insulation of steel members in fire．Journalof Constructional Steel Research，2005，61（10）：1447-1456P
[151] Kodur V K R, Dwaikat M M S. A performance based methodology for fire design ofrestrained steel beams. Journal of Constructional Steel Research,2011,67（3）:510-524P
[152]吴国荣.含裂纹梁自由振动分析.噪声与振动控制，2008，28（4）：31-34页
[153]程礼，何正嘉，李宁等.裂纹非线性呼吸行为对转子临界转速的影响.振动与冲击，2010，29（4）：44-53页
[154]王宗勇，林伟，闻邦椿.开闭裂纹转轴刚度的解析研究.振动与冲击,2010，29（9）：69-72页
[155]张敬芬，赵德有.工程结构裂纹损伤振动诊断的发展现状和展望.振动与冲击，2002，21（4）：22-25页
[156]郑栋梁，李中付，华宏星.结构早期损伤识别技术的现状和发展趋势.振动与冲击，2002，21（2）：1-10页
[157]胡家顺，冯新，李昕等.裂纹梁振动分析和裂纹识别方法研究进展.振动与冲击，2007，26（11）：146-151页
[158]任宜春，马石城，林琳.移动荷载作用下梁裂缝识别的小波方法研究.振动与冲击，2004，23（2）：82-85页
[159]吴宁祥，吴克勤，由关雁等.裂纹梁的动态特性仿真.工程设计学报，2006，13（4）：236-240页
[160] Rosales M B, Filipich C P, Buezas F S. Crack detection in beam-like structures.Engineering Structures，2009，31（10）：2257-2264P
[161] Rezaee M, Hassannejad R. Free vibration analysis of simply supported beam withbreathing crack using perturbation method. Acta Mechanica Solida Sinica,2010,23（5）:459-470P
[162] Caddemi S，Calio I，Marletta M. The non-linear dynamic response of the Euler–Bernoulli beam with an arbitrary number of switching cracks. International Journal ofNon-Linear Mechanics,2010，45（7）：714-726P
[163] Bikri K E, Benamar R, Bennoua M M. Geometrically non-linear free vibrations ofclamped–clamped beams with an edge crack. Computers&Structures,2006,84（7）：485-502P
[164] Mazanoglu K, Sabuncu M. Vibration analysis of non-uniform beams having multipleedge cracks along the beam's height. International Journal of Mechanical Sciences,2010,52（3）：515-522P
[165] Matjaz S. Elastic beam finite element with an arbitrary number of transversecracks. Finite Elements in Analysis and Design，2009，45（3）：181-189P
[166]孙强，张忠平，柴桥等.航空发动机压气机叶片振动频率与温度的关系.应用力学学报，2004，21（4）：137-139页
[167]王振清，刘兵，韩玉来.高温下含裂纹铝合金梁自由振动频率分析.哈尔滨工程大学学报，2012，33（3）：320-324页