半刚接钢框架考虑几何非线性和材料塑性的有限元分析及性能探讨
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摘要
采用焊接刚性节点的钢框架因节点延性较差容易发生脆性破坏，而半刚接
钢框架因节点具有较强的耗能能力可以抵抗一定的地震荷载，同时还可以减少
斜撑的数量及节点用钢量，这使得半刚接钢框架成为一种经济、可靠的选择。
但由于半刚性连接的复杂性和多样性，在钢框架的分析和设计中，还是将框架
的梁柱连接假设成为完全的刚接或理想的铰接。对连接性能的这种理想化假设
简化了钢框架的分析和设计过程，却不能反映结构工作的实际情况，计算结果
误差很大，有时甚至会得到错误的结论。
我国钢结构设计规范(2001，10送审稿)中提到了半刚性连接的概念，但
规范对进一步如何实现半刚性连接的设计、理论、要求、标准和实施步骤均未
做出说明，因而事实上也无法具体执行。本文的目的就是为半刚性连接钢框架
的设计提供一种既符合工程实际又简便易行的计算方法，供规范使用过程的补
充、延伸或参考；同时，也将促进半刚性连接钢框架设计技术的发展，为提高
结构安全性能、节省工程成本发挥应有的作用。
本文首先介绍了常见的几种应用较为广泛的梁柱连接弯矩转角关系模型，
在分析比较的基础上，选用Richard—Abbott函数模型作为外伸端板连接弯矩转
角关系模型，通过对34个外伸端板连接的实验数据与回归分析得到的参数比较
可知，经回归分析得到的此模型参数与实验数据符合较好。然后用弹簧表征连
接点的转动刚度，根据梁的转角位移方程推导出半刚性连接的刚度矩阵，在单
元刚度矩阵中考虑了节点柔性、几何非线性和剪切变形的影响，并对固端力进
行了修正，最后用增量迭代法编制有限元程序进行计算和分析。
通过对几个例子计算结果的分析表明，半刚接与刚接相比会使钢框架的侧
移、柱脚弯矩增大，而使梁端弯矩减小，对无支撑框架尤为明显，支撑框架能
够有效地减小节点半刚接的影响。同时，半刚接对二阶效应、剪切变形有放大
作用。根据计算结果的统计分析，提出可以不考虑半刚性影响的节点刚度范围，
并对考虑半刚性的钢框架的内力和位移给出修正系数，供工程设计参考。
Steel frame with welding joint easily occur brittle collapse because of having a
low ductility at joints．Then，a semi-rigid connected steel frame has large the energy
absorption capacity which can resist dynamic loads and the using steel qualities of
bracing system and joints are small．So adopting a semi-rigid jointed steel frame is
economical and stable．But for semi-rigid connections are complex and variable，in
conventional analysis and design of steel structures，It is usually assumed that the
connections between columns and beams are either rigid or pinned．The analysis of
steel frames adopting the assumption can simplify the procedure of analysis and
design，but cannot precisely reflect structural practical circumstance and the errors of
calculating results are large，even，get incorrect conclusions．
Semi-rigid connection was referred to in Chinese Code for Design of Steel
Structures(2001，10)，however，it isn’t specified how to apply semi-rigid joints in
design．In fact it cannot be carry out．The purpose of the paper give a calculating
method that accords practical engineering and easily put into effect．Worthwhile it is
going to promote the development of semi-rigid jointed steel frame in design and
heighten structural stability．
In the paper，at first some commonly employed methods for the modeling of
connection behavior are introduced．Richard．Abbott function modeling of connection
is adopted for extended end plate bolted connection．By the 34 test data comparing to
regression analysis indicate Richard-Abbott function modeling of connection
represents an excellent fit to test data．Then after a semi-rigid joint behavior can be
modeled as a finite stiffness rotation spring，base on rotation and displacement
equation derive the element stiffness matrixes with semi-rigid connections where the
effects ofj ointed flexibility geometric non-linearity and shear forces in the connection
deformations have been considered in and fixed-end forces are modified．Finally,a
program for calculating semi-rigid with incremental-iterative method has been
compiled for calculating and analyzing．
By calculating results of several example decade for steel frame in semi-rigid
joints cases the top story deflection and the initial end moment at column is larger,
nevertheless the end moment at beam may be smaller when compared to the rigid
joint case．Affect of the semi-rigid joint Can be reduced by the use of bracing
members．Influences of second order effect and shear forces in the connection
deformations are larger when the semi-rigid j oint case is compared to the rigid j oint
case．Base on static and analysis of calculating results the range of the joint stiffness is
put forward when influence of the semi-rigid joint is irrespective and parameter
modified of inter force and displacement is given when influence of the semi-rigid
joint is considered that offers advice for in actual design
钢框架因节点具有较强的耗能能力可以抵抗一定的地震荷载，同时还可以减少
斜撑的数量及节点用钢量，这使得半刚接钢框架成为一种经济、可靠的选择。
但由于半刚性连接的复杂性和多样性，在钢框架的分析和设计中，还是将框架
的梁柱连接假设成为完全的刚接或理想的铰接。对连接性能的这种理想化假设
简化了钢框架的分析和设计过程，却不能反映结构工作的实际情况，计算结果
误差很大，有时甚至会得到错误的结论。
我国钢结构设计规范(2001，10送审稿)中提到了半刚性连接的概念，但
规范对进一步如何实现半刚性连接的设计、理论、要求、标准和实施步骤均未
做出说明，因而事实上也无法具体执行。本文的目的就是为半刚性连接钢框架
的设计提供一种既符合工程实际又简便易行的计算方法，供规范使用过程的补
充、延伸或参考；同时，也将促进半刚性连接钢框架设计技术的发展，为提高
结构安全性能、节省工程成本发挥应有的作用。
本文首先介绍了常见的几种应用较为广泛的梁柱连接弯矩转角关系模型，
在分析比较的基础上，选用Richard—Abbott函数模型作为外伸端板连接弯矩转
角关系模型，通过对34个外伸端板连接的实验数据与回归分析得到的参数比较
可知，经回归分析得到的此模型参数与实验数据符合较好。然后用弹簧表征连
接点的转动刚度，根据梁的转角位移方程推导出半刚性连接的刚度矩阵，在单
元刚度矩阵中考虑了节点柔性、几何非线性和剪切变形的影响，并对固端力进
行了修正，最后用增量迭代法编制有限元程序进行计算和分析。
通过对几个例子计算结果的分析表明，半刚接与刚接相比会使钢框架的侧
移、柱脚弯矩增大，而使梁端弯矩减小，对无支撑框架尤为明显，支撑框架能
够有效地减小节点半刚接的影响。同时，半刚接对二阶效应、剪切变形有放大
作用。根据计算结果的统计分析，提出可以不考虑半刚性影响的节点刚度范围，
并对考虑半刚性的钢框架的内力和位移给出修正系数，供工程设计参考。
Steel frame with welding joint easily occur brittle collapse because of having a
low ductility at joints．Then，a semi-rigid connected steel frame has large the energy
absorption capacity which can resist dynamic loads and the using steel qualities of
bracing system and joints are small．So adopting a semi-rigid jointed steel frame is
economical and stable．But for semi-rigid connections are complex and variable，in
conventional analysis and design of steel structures，It is usually assumed that the
connections between columns and beams are either rigid or pinned．The analysis of
steel frames adopting the assumption can simplify the procedure of analysis and
design，but cannot precisely reflect structural practical circumstance and the errors of
calculating results are large，even，get incorrect conclusions．
Semi-rigid connection was referred to in Chinese Code for Design of Steel
Structures(2001，10)，however，it isn’t specified how to apply semi-rigid joints in
design．In fact it cannot be carry out．The purpose of the paper give a calculating
method that accords practical engineering and easily put into effect．Worthwhile it is
going to promote the development of semi-rigid jointed steel frame in design and
heighten structural stability．
In the paper，at first some commonly employed methods for the modeling of
connection behavior are introduced．Richard．Abbott function modeling of connection
is adopted for extended end plate bolted connection．By the 34 test data comparing to
regression analysis indicate Richard-Abbott function modeling of connection
represents an excellent fit to test data．Then after a semi-rigid joint behavior can be
modeled as a finite stiffness rotation spring，base on rotation and displacement
equation derive the element stiffness matrixes with semi-rigid connections where the
effects ofj ointed flexibility geometric non-linearity and shear forces in the connection
deformations have been considered in and fixed-end forces are modified．Finally,a
program for calculating semi-rigid with incremental-iterative method has been
compiled for calculating and analyzing．
By calculating results of several example decade for steel frame in semi-rigid
joints cases the top story deflection and the initial end moment at column is larger,
nevertheless the end moment at beam may be smaller when compared to the rigid
joint case．Affect of the semi-rigid joint Can be reduced by the use of bracing
members．Influences of second order effect and shear forces in the connection
deformations are larger when the semi-rigid j oint case is compared to the rigid j oint
case．Base on static and analysis of calculating results the range of the joint stiffness is
put forward when influence of the semi-rigid joint is irrespective and parameter
modified of inter force and displacement is given when influence of the semi-rigid
joint is considered that offers advice for in actual design
引文
[1]AMERICAN INSTITUTE OF STEEL CONSTRUCTION，INC．Load and Resistance Factor
Design Specification for Structural Steel Buildings．ChicagO：December 27，1999．
[2]中华人民共和国国家标准．GB50017(送审稿)．钢结构设计规范．2001，10．
[3]H．Schol2，Plastic Design of Sway Frames with Semi-rigid Connections Using Allowable
Slenderness Ratio，J．Constructurt Steel Research，1991，V19
[4]H．Schol2，Approximate P-delts Method for Sway Frames with Semi-rigid Connection，J．
Construct．Steel Research，1990．V1 5
[5]陈绍番．钢结构设计原理．北京：科学出版社，1998．
[6]丁洁民，沈祖炎．节点半刚性对钢框架结构内力和位移的影响．建筑结构，1991(6)：8-12
[7]Astaneh-Asl A．Seistic performance and Design of Bolted Steel Moment-resisting Frames[J]．
Engineering Journal．American Institute ofSteel Construction，1999，36(3)：105-120
[8]Romstad K M，subramanian C V．Analysis of Frames with Partial Connection Rigidity[J]
．Journal of Structural Division，ASCE，Proceeding papers 7664，1970，100(ST6)2283-2300
[9]Lui EM，Chen W EStrength of．H-columns with Small End Restraints[J]．Journal of Institute
Structural Engineers，61B，1983：17-26
[10]S．L．Chan and EET．Chui．NON-LINEAR STATIC AND CYCLIC ANALYSIS OF STEEL
FRAMES WITH SEMI-RIGID CONNECTIONS．The boulevard，Langford lane
kidlington，oxford：Dr Jame．Milne Publisher，Engineering and Technology Elsevier Science
LTD，2000．96-113
[11]Krishnamurthy H T.et a1．Analytical M-θ Curves for End-plate Connections[J]．Journal
ofStructural Division，ASCE，1979，105(STl)：133-145
[12]Goldberg J E，Richard R M．Analysis of Nonl inear Structures[J].Journal of Structural
Division，ASCE，1963，89(ST4)：333-351
[13]Richard R M，Abbott B J．Versatile Elastic-plastic Stress-strain Formula[J]．Joumal of
Engineering Mechanics Division，ASCE，1975，101(EM4)：511-515
[14]Kishi N，Chen WF．Moment-rotation of Semi-rigid Connection[R]．Structural Engineering
Report No．CE-STR-87-29，School of Civil Engineering，Purdue University,West-Lafayette，
Indiana，USA，1987
[15]Yee YL，Melchers RE．Moment-rotation Curves for Bolted Connections[J]．Journal of
Structural Division，ASCE，1986，112(ST3)：615-634 -
[16]Chung-Bang Yun，Jin-Hak Yi，Eun Young Bahng．Jiont Damage Assessment of Framed
Structures Using a Neural Networks Technique．Engineering Structures 2001，23，425-435
[17] Emmanuel Attiogbe，Glenn Morris．Moment-Rotation Functions For Steel
Connections．Journal ofStructural Engineering，V01.117，No．6，June，1991：1703-1710
[18]R．Hasan，N．Kishi，W．EChen，etc．Evaluation of Rigidity of Extended End-plate Connections．
Journal of Structural Engineering，V01．123，No．12，December，1997：1 595-1602
[19]Archibald N．Sherboume，Mohammed R．Bahaari．Finite Element Prediction of End Plate
Bolted connection Behavior．I：Parametric Study．Journal of Structural Engineering，V01．123，No，2
February,1997：157-164
[20]Mohammed R．Bahaari，Archibald N．Sherbourne．Finite Element of Plate Bolted Connection
Behavior．Journal ofStructural Engineering，V01．123，No．2，February，1997：165-175
[21]沈祖炎，李国强．钢框架结构设计．上海：科学技术出版社，1996．8-14
[22]Balaur S．Dhillon，Fellow,James W．O’Malley．InteractiVe Design of Semirigid Steel Frames．
Journal ofStructural Engineering，V01．125，No．5，May，1999：556—564．
[23]龙驭球，包世华．结构力学．北京：高等教育出版社，1994．266-267
[24]J．Dario Aristizabal-Ocho．Nonlinear Large Deflectzon-Small Strain Elastic Analysis of
Beam-Column with Semirigid Connections．Journal of．Structural Engineering／JanuarY
2001．pp92~96。
[25]陈绍番．钢结构设计原理．北京：科学出版社，1998．
[26]陈骥．钢结构稳定理论与设计．北京：科学出版社，2001．83-84
[27]郭兵，陈爱国:半刚接钢框架的有限元分析及性能探讨．建筑结构学报，2001(10)：48-52
[28]中华人民共和国国家标准．GBJl7-88．钢结构设计规范．1988．
[29]S．L．Chan and P.P.T．Chui．NON-LINEAR STATIC AND CYCLIC ANALYSIS OF STEEL
FRAMES WITH SEMI-RIGID CONNECTIONS．The boulevard，Langford lane
kidlington，oxford：Dr Jame．Milne Publisher，Engineering and Technology Elsevier Science
LTD，2000．129-133
[30]冯东、张志平、刘彦青等．轻型钢结构设计指南.北京：中国建筑工业出版社．2000．107-122
[31]王燕、彭福明．多高层钢框架梁柱半刚性连接性能．建筑结构．2000(9)．18-20
[32]Jenkins et al．Struct．engineer．1986，69A(5)：121-132
[33]Bursi and Jaspart．J．Constr．Steel Res．1997，225-265
[34]Packer and Morris．Struct．Engineer 1977，55(10)：446-458
[35]Douty and Mcguire．J．Struct．Div．ASCE 1965，91(ST2)：101-128
Design Specification for Structural Steel Buildings．ChicagO：December 27，1999．
[2]中华人民共和国国家标准．GB50017(送审稿)．钢结构设计规范．2001，10．
[3]H．Schol2，Plastic Design of Sway Frames with Semi-rigid Connections Using Allowable
Slenderness Ratio，J．Constructurt Steel Research，1991，V19
[4]H．Schol2，Approximate P-delts Method for Sway Frames with Semi-rigid Connection，J．
Construct．Steel Research，1990．V1 5
[5]陈绍番．钢结构设计原理．北京：科学出版社，1998．
[6]丁洁民，沈祖炎．节点半刚性对钢框架结构内力和位移的影响．建筑结构，1991(6)：8-12
[7]Astaneh-Asl A．Seistic performance and Design of Bolted Steel Moment-resisting Frames[J]．
Engineering Journal．American Institute ofSteel Construction，1999，36(3)：105-120
[8]Romstad K M，subramanian C V．Analysis of Frames with Partial Connection Rigidity[J]
．Journal of Structural Division，ASCE，Proceeding papers 7664，1970，100(ST6)2283-2300
[9]Lui EM，Chen W EStrength of．H-columns with Small End Restraints[J]．Journal of Institute
Structural Engineers，61B，1983：17-26
[10]S．L．Chan and EET．Chui．NON-LINEAR STATIC AND CYCLIC ANALYSIS OF STEEL
FRAMES WITH SEMI-RIGID CONNECTIONS．The boulevard，Langford lane
kidlington，oxford：Dr Jame．Milne Publisher，Engineering and Technology Elsevier Science
LTD，2000．96-113
[11]Krishnamurthy H T.et a1．Analytical M-θ Curves for End-plate Connections[J]．Journal
ofStructural Division，ASCE，1979，105(STl)：133-145
[12]Goldberg J E，Richard R M．Analysis of Nonl inear Structures[J].Journal of Structural
Division，ASCE，1963，89(ST4)：333-351
[13]Richard R M，Abbott B J．Versatile Elastic-plastic Stress-strain Formula[J]．Joumal of
Engineering Mechanics Division，ASCE，1975，101(EM4)：511-515
[14]Kishi N，Chen WF．Moment-rotation of Semi-rigid Connection[R]．Structural Engineering
Report No．CE-STR-87-29，School of Civil Engineering，Purdue University,West-Lafayette，
Indiana，USA，1987
[15]Yee YL，Melchers RE．Moment-rotation Curves for Bolted Connections[J]．Journal of
Structural Division，ASCE，1986，112(ST3)：615-634 -
[16]Chung-Bang Yun，Jin-Hak Yi，Eun Young Bahng．Jiont Damage Assessment of Framed
Structures Using a Neural Networks Technique．Engineering Structures 2001，23，425-435
[17] Emmanuel Attiogbe，Glenn Morris．Moment-Rotation Functions For Steel
Connections．Journal ofStructural Engineering，V01.117，No．6，June，1991：1703-1710
[18]R．Hasan，N．Kishi，W．EChen，etc．Evaluation of Rigidity of Extended End-plate Connections．
Journal of Structural Engineering，V01．123，No．12，December，1997：1 595-1602
[19]Archibald N．Sherboume，Mohammed R．Bahaari．Finite Element Prediction of End Plate
Bolted connection Behavior．I：Parametric Study．Journal of Structural Engineering，V01．123，No，2
February,1997：157-164
[20]Mohammed R．Bahaari，Archibald N．Sherbourne．Finite Element of Plate Bolted Connection
Behavior．Journal ofStructural Engineering，V01．123，No．2，February，1997：165-175
[21]沈祖炎，李国强．钢框架结构设计．上海：科学技术出版社，1996．8-14
[22]Balaur S．Dhillon，Fellow,James W．O’Malley．InteractiVe Design of Semirigid Steel Frames．
Journal ofStructural Engineering，V01．125，No．5，May，1999：556—564．
[23]龙驭球，包世华．结构力学．北京：高等教育出版社，1994．266-267
[24]J．Dario Aristizabal-Ocho．Nonlinear Large Deflectzon-Small Strain Elastic Analysis of
Beam-Column with Semirigid Connections．Journal of．Structural Engineering／JanuarY
2001．pp92~96。
[25]陈绍番．钢结构设计原理．北京：科学出版社，1998．
[26]陈骥．钢结构稳定理论与设计．北京：科学出版社，2001．83-84
[27]郭兵，陈爱国:半刚接钢框架的有限元分析及性能探讨．建筑结构学报，2001(10)：48-52
[28]中华人民共和国国家标准．GBJl7-88．钢结构设计规范．1988．
[29]S．L．Chan and P.P.T．Chui．NON-LINEAR STATIC AND CYCLIC ANALYSIS OF STEEL
FRAMES WITH SEMI-RIGID CONNECTIONS．The boulevard，Langford lane
kidlington，oxford：Dr Jame．Milne Publisher，Engineering and Technology Elsevier Science
LTD，2000．129-133
[30]冯东、张志平、刘彦青等．轻型钢结构设计指南.北京：中国建筑工业出版社．2000．107-122
[31]王燕、彭福明．多高层钢框架梁柱半刚性连接性能．建筑结构．2000(9)．18-20
[32]Jenkins et al．Struct．engineer．1986，69A(5)：121-132
[33]Bursi and Jaspart．J．Constr．Steel Res．1997，225-265
[34]Packer and Morris．Struct．Engineer 1977，55(10)：446-458
[35]Douty and Mcguire．J．Struct．Div．ASCE 1965，91(ST2)：101-128
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