冷弯残余应力分布及其影响下的轴压构件整体稳定性研究
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摘要
冷弯薄壁型钢近几十年来在工程中得到广泛应用。冷弯薄壁型钢成型后截面上存在冷弯残余应力，它对冷弯薄壁型钢轴心受压构件的整体稳定性影响很大。由于冷弯薄壁型钢的加工过程复杂，对其进行理论分析难度很大，使得目前有关冷弯残余应力的研究成果极少且存在许多不足之处，以至于设计规范中至今还缺少计及它的影响的整体稳定性设计公式。
本文首先在理论上寻求突破，将冷弯加工过程分解成弯曲(加载)和回弹(卸载)两个过程分别加以分析：利用弹塑性理论求得弯曲过程中应力场的理论解；运用有限元分析软件ANSYS对回弹过程进行模拟计算，得出回弹应力场；最后将两个过程产生的应力场相叠加，得到更合理、更全面的冷弯残余应力分布，即除纵向残余应力外，还包括切向和径向残余应力；除弯曲段外，还有直边段的残余应力分布规律。
然后，根据得到的冷弯残余应力分布规律，编写能够描述这种残余应力的初应力文件，充分考虑冷弯残余应力和初弯曲、初偏心等初始缺陷的影响，运用有限元分析软件ANSYS对槽钢和卷边角钢截面形式的冷弯薄壁型钢轴心受压构件进行稳定分析，得到四种截面形式的λ-φ关系，确定了更能反映实际情况的λ-φ柱子曲线，并与现行规范进行了比较分析，发现不同截面形式和尺寸的λ-φ曲线相当接近；对长细比较大的构件，本文计算得到的稳定系数φ值与规范相当；随着长细比的减小，φ值略低于规范值。
最后，根据所得λ-φ关系拟合出实用的φ值计算公式。
Coldformed thinwa1 steel membersaredely aPPlieed in the engineering in the
last several decades.The eold-forllledsidual stresses are remained in the Coldfonned
thin-wall steel members when they are formed，d it eauses a great Influenee to the
overail stability as the members are subjeeted to the axle eenter Pressure force.The
manufacture Proeess of eoldformed thinwa1 steel members 15 very comPlex，d it，5 too
diffieult to Proeeed to analyze in theoretieally.50 there are few researeh achievemenis
about the coldformed residual stresses Whieh have many faults.And thatleads to the lack
of the design fonnula of the overail stability involving the influence of the eold一fonned
residual stresses.
In this Paper， theoretieal brealhrough 15 exPlored firstly，the eoldfonned Proeess of
the members 15 divided inio0 stages:the being formed(or member’5 loading) stage and
the elastie restoration(or member，5 unloading)stage.The Stresses in the member for each
stage are derived resPeetively:based on the theory of elastiePlastie the stresses for the
being formed stage are obtained，then using the ANSYSfinite element analysis software
imitates the elastie restoration stage as to obtain the ealeulating values of the stresses for
the elastie restoration stage.The sus，aehieved by adding the05ges stresses，arejust
the eoldbended residual stresses Whieh are more reasonable and more comPletc:besides
the longitudinal residual stresses，the tangential residual Stresses and the radial residual
ssses are gained too;ineluding the residual stresses of bent segment，the residual
stresses of straight segment are obtained too.
Then，the initial stresses files whieh ean deseribe residual stfCsses areitten based
on the distribution of residual stresses obtained above.Exhaustively eonsidering all initial
imPerfeetion sueh as eoldbended residual stresses，initial一bending and initial-eecentrieity，
and using the finite element analysis software ANSYS to analyze the stability of axle
eenter Pressure members of eold一formed thin·wall ehannel steel and henuning angle steel，
therelationshiPs for these four kinds of sections are obtained.ComParing the eurve
with the Code，it ean be found thateurves of differeni kinds of seetions and sizes
are very close;the stability coefficientsin thisper are equal to these in Code when
members’ratios to slcndemess are large:but when the ratios of slendeme:5 are small，
eoeffieienisin this PaPer are a little lower than those in Code.
Ai last，ealeulation formula of p 15 gained by fittingrelationshiPs obtained
ab0Ve.
本文首先在理论上寻求突破，将冷弯加工过程分解成弯曲(加载)和回弹(卸载)两个过程分别加以分析：利用弹塑性理论求得弯曲过程中应力场的理论解；运用有限元分析软件ANSYS对回弹过程进行模拟计算，得出回弹应力场；最后将两个过程产生的应力场相叠加，得到更合理、更全面的冷弯残余应力分布，即除纵向残余应力外，还包括切向和径向残余应力；除弯曲段外，还有直边段的残余应力分布规律。
然后，根据得到的冷弯残余应力分布规律，编写能够描述这种残余应力的初应力文件，充分考虑冷弯残余应力和初弯曲、初偏心等初始缺陷的影响，运用有限元分析软件ANSYS对槽钢和卷边角钢截面形式的冷弯薄壁型钢轴心受压构件进行稳定分析，得到四种截面形式的λ-φ关系，确定了更能反映实际情况的λ-φ柱子曲线，并与现行规范进行了比较分析，发现不同截面形式和尺寸的λ-φ曲线相当接近；对长细比较大的构件，本文计算得到的稳定系数φ值与规范相当；随着长细比的减小，φ值略低于规范值。
最后，根据所得λ-φ关系拟合出实用的φ值计算公式。
Coldformed thinwa1 steel membersaredely aPPlieed in the engineering in the
last several decades.The eold-forllledsidual stresses are remained in the Coldfonned
thin-wall steel members when they are formed，d it eauses a great Influenee to the
overail stability as the members are subjeeted to the axle eenter Pressure force.The
manufacture Proeess of eoldformed thinwa1 steel members 15 very comPlex，d it，5 too
diffieult to Proeeed to analyze in theoretieally.50 there are few researeh achievemenis
about the coldformed residual stresses Whieh have many faults.And thatleads to the lack
of the design fonnula of the overail stability involving the influence of the eold一fonned
residual stresses.
In this Paper， theoretieal brealhrough 15 exPlored firstly，the eoldfonned Proeess of
the members 15 divided inio0 stages:the being formed(or member’5 loading) stage and
the elastie restoration(or member，5 unloading)stage.The Stresses in the member for each
stage are derived resPeetively:based on the theory of elastiePlastie the stresses for the
being formed stage are obtained，then using the ANSYSfinite element analysis software
imitates the elastie restoration stage as to obtain the ealeulating values of the stresses for
the elastie restoration stage.The sus，aehieved by adding the05ges stresses，arejust
the eoldbended residual stresses Whieh are more reasonable and more comPletc:besides
the longitudinal residual stresses，the tangential residual Stresses and the radial residual
ssses are gained too;ineluding the residual stresses of bent segment，the residual
stresses of straight segment are obtained too.
Then，the initial stresses files whieh ean deseribe residual stfCsses areitten based
on the distribution of residual stresses obtained above.Exhaustively eonsidering all initial
imPerfeetion sueh as eoldbended residual stresses，initial一bending and initial-eecentrieity，
and using the finite element analysis software ANSYS to analyze the stability of axle
eenter Pressure members of eold一formed thin·wall ehannel steel and henuning angle steel，
therelationshiPs for these four kinds of sections are obtained.ComParing the eurve
with the Code，it ean be found thateurves of differeni kinds of seetions and sizes
are very close;the stability coefficientsin thisper are equal to these in Code when
members’ratios to slcndemess are large:but when the ratios of slendeme:5 are small，
eoeffieienisin this PaPer are a little lower than those in Code.
Ai last，ealeulation formula of p 15 gained by fittingrelationshiPs obtained
ab0Ve.
引文
[1] 王世纪，等译．美国冷弯型钢结构构件设计规范(AISI·1986年版)．冶院科技，1988，特刊
[2] 中华人民共和国国家标准．冷弯薄壁型钢结构技术规范(GB50018—2002)．中国计划出版社，2002
[3] 陈骥．钢结构稳定理论与设计．科学出版社，2001
[4] Fukumoto, Y. and Itoh, Y., Evalution of Multiple Column Curves from the Experimental Data-Base Approach, Journal of constructional Steel Research, Vol.3,1983
[5] Weng C C, Pekoz T, Residual Stress in Cold-Formed Steel Members. Journal of Structural Engineering, Vol.116,No.4,1990: 1161～1165
[6] Kato, B., Cold-formed Welded Steel Tubular Members in Axially Compressed Structures, Stability and Strenth, R. Narayanan ed.,Applied Science Pub., 1982.
[7] 赵峰．冷弯卷边角钢的残余应力对轴心压杆弯扭屈曲的影响：[学位论文]．武汉：武汉水利电力学院建工系，1989
[8] Bjorhovde, R., Deterministic and Probabilistic Approaches to the Strength of Steel Columns, Ph.D. Dissertation, Department of Civil Engineering, Lehi University, Bethlehem, PA, 1972
[9] Gel ambos, T.V. ed., Guide to Stability Design Criteria for Structures,4th Ed., John Wiley and Sons,1988
[10] Beedle, L.S.(Editor-in-chief,Stability of Metal Structures—A World View,2nd.Ed.,U.S.A.,1991
[11] Stinteso, D.ed., European Convention of Constructional Steelworks Manual on the Stability of Steel Structures,2nd.Ed.,ECCS,Paris,1976
[12] 中华人民共和国国家标准．钢结构设计规范(TJ17—74)．中国计划出版社，1974
[13] 中华人民共和国国家标准．冷弯薄壁型钢结构技术规范(TJ18—75)．中国计划出版社，1975
[14] 中华人民共和国国家标准．冷弯薄壁型钢结构技术规范(GBJ18—87)．中国计划出版社，1987
[15] 中华人民共和国国家标准．钢结构设机规范(GBJ17—88)．中国计划出版社，1988
[16] 中华人民共和国国家标准．钢结构设计规范(GB50017—2003，)．中国计划出版社，2003
[17] 王祖唐，等．金属塑性成型理论．机械工业出版社，1989：518～529
[18] 徐秉业．塑性力学．高等教育出版社，1989：308～344
[19] 王仁，黄文彬，塑性力学引论．北京大学出版社
[20] 故世光．板料冷压成型原理．国防工业出版社，1978：23～33
[21] 吕雪山等．薄板成型与制造．中国物资出版社，1993：58～100
[22] 金昌成．冷弯型钢的冷作强化及其利用．建筑结构学报，1994，15(2)：43～51
[23] 王勖成，邵敏．有限单元法基本理论和数值方法．清华大学出版社，2000
[24] 张中权．冷弯薄壁型钢轴心受压构件稳定性的试验研究．钢结构研究论文报告选集(第一册)，1982：152～190
[25] 孙训方，方孝淑，关来泰．材料力学．高等教育出版社，1987：121～176
[26] 夏志斌，潘有昌．钢结构稳定理论．高等教育出版社，1988
[27] 任伟新，曾庆元．钢压杆稳定极限承载力分析．中国铁道出版社，1994
[28] 陈绍蕃．钢结构设计原理．科学出版社，1987
[29] 查杰斯，著．结构稳定理论原理．唐家祥译．甘肃人民出版社，1982
[30] 郭耀杰，郭盛，李昆．钢结构稳定设计．武汉大学出版社，2003
[31] 王国周，瞿履谦．钢结构原理与设计．清华大学出版社，1993
[32] 方山峰，等．冷弯残余应力对卷边角钢柱局部和整体屈曲的影响．93结构稳定与疲劳学术讨论会论文集，中国钢结构协会结构稳定与疲劳协会，1993：159～166
[33] 沈祖炎，等．冷弯型钢柱非线性稳定的研究．93结构稳定与疲劳学术讨论会论文集，1993：159～166
[34] 郭耀杰，李昆，郭盛．压弯构件弯扭屈曲相关公式中弯矩附加系数及其影响分析．武汉大学学报，2002(6)：44～47
[35] 郭盛，郭耀杰．冷弯残余应力场研究．钢结构，2003(5)：42～44
[36] 徐芝纶．弹性力学(第二版)．人民教育出版社，1983
[37] 陈绍蕃．钢结构稳定设计指南．中国建筑工业出版社，1996
[38] 郭耀杰，方山峰．钢结构构件弯扭屈曲问题的计算和分析．建筑结构学报，1990，11(3)：38～44
[39] ECCS, Second International Colloquium on Stability, Introductory Report, 1976
[40] ANSYS基本过程手册．ANSYS公司，2000
[41] 博嘉科技编著．有限元分析软件—ANSYS融会于贯通．中国水利水电出版社，2002
[2] 中华人民共和国国家标准．冷弯薄壁型钢结构技术规范(GB50018—2002)．中国计划出版社，2002
[3] 陈骥．钢结构稳定理论与设计．科学出版社，2001
[4] Fukumoto, Y. and Itoh, Y., Evalution of Multiple Column Curves from the Experimental Data-Base Approach, Journal of constructional Steel Research, Vol.3,1983
[5] Weng C C, Pekoz T, Residual Stress in Cold-Formed Steel Members. Journal of Structural Engineering, Vol.116,No.4,1990: 1161～1165
[6] Kato, B., Cold-formed Welded Steel Tubular Members in Axially Compressed Structures, Stability and Strenth, R. Narayanan ed.,Applied Science Pub., 1982.
[7] 赵峰．冷弯卷边角钢的残余应力对轴心压杆弯扭屈曲的影响：[学位论文]．武汉：武汉水利电力学院建工系，1989
[8] Bjorhovde, R., Deterministic and Probabilistic Approaches to the Strength of Steel Columns, Ph.D. Dissertation, Department of Civil Engineering, Lehi University, Bethlehem, PA, 1972
[9] Gel ambos, T.V. ed., Guide to Stability Design Criteria for Structures,4th Ed., John Wiley and Sons,1988
[10] Beedle, L.S.(Editor-in-chief,Stability of Metal Structures—A World View,2nd.Ed.,U.S.A.,1991
[11] Stinteso, D.ed., European Convention of Constructional Steelworks Manual on the Stability of Steel Structures,2nd.Ed.,ECCS,Paris,1976
[12] 中华人民共和国国家标准．钢结构设计规范(TJ17—74)．中国计划出版社，1974
[13] 中华人民共和国国家标准．冷弯薄壁型钢结构技术规范(TJ18—75)．中国计划出版社，1975
[14] 中华人民共和国国家标准．冷弯薄壁型钢结构技术规范(GBJ18—87)．中国计划出版社，1987
[15] 中华人民共和国国家标准．钢结构设机规范(GBJ17—88)．中国计划出版社，1988
[16] 中华人民共和国国家标准．钢结构设计规范(GB50017—2003，)．中国计划出版社，2003
[17] 王祖唐，等．金属塑性成型理论．机械工业出版社，1989：518～529
[18] 徐秉业．塑性力学．高等教育出版社，1989：308～344
[19] 王仁，黄文彬，塑性力学引论．北京大学出版社
[20] 故世光．板料冷压成型原理．国防工业出版社，1978：23～33
[21] 吕雪山等．薄板成型与制造．中国物资出版社，1993：58～100
[22] 金昌成．冷弯型钢的冷作强化及其利用．建筑结构学报，1994，15(2)：43～51
[23] 王勖成，邵敏．有限单元法基本理论和数值方法．清华大学出版社，2000
[24] 张中权．冷弯薄壁型钢轴心受压构件稳定性的试验研究．钢结构研究论文报告选集(第一册)，1982：152～190
[25] 孙训方，方孝淑，关来泰．材料力学．高等教育出版社，1987：121～176
[26] 夏志斌，潘有昌．钢结构稳定理论．高等教育出版社，1988
[27] 任伟新，曾庆元．钢压杆稳定极限承载力分析．中国铁道出版社，1994
[28] 陈绍蕃．钢结构设计原理．科学出版社，1987
[29] 查杰斯，著．结构稳定理论原理．唐家祥译．甘肃人民出版社，1982
[30] 郭耀杰，郭盛，李昆．钢结构稳定设计．武汉大学出版社，2003
[31] 王国周，瞿履谦．钢结构原理与设计．清华大学出版社，1993
[32] 方山峰，等．冷弯残余应力对卷边角钢柱局部和整体屈曲的影响．93结构稳定与疲劳学术讨论会论文集，中国钢结构协会结构稳定与疲劳协会，1993：159～166
[33] 沈祖炎，等．冷弯型钢柱非线性稳定的研究．93结构稳定与疲劳学术讨论会论文集，1993：159～166
[34] 郭耀杰，李昆，郭盛．压弯构件弯扭屈曲相关公式中弯矩附加系数及其影响分析．武汉大学学报，2002(6)：44～47
[35] 郭盛，郭耀杰．冷弯残余应力场研究．钢结构，2003(5)：42～44
[36] 徐芝纶．弹性力学(第二版)．人民教育出版社，1983
[37] 陈绍蕃．钢结构稳定设计指南．中国建筑工业出版社，1996
[38] 郭耀杰，方山峰．钢结构构件弯扭屈曲问题的计算和分析．建筑结构学报，1990，11(3)：38～44
[39] ECCS, Second International Colloquium on Stability, Introductory Report, 1976
[40] ANSYS基本过程手册．ANSYS公司，2000
[41] 博嘉科技编著．有限元分析软件—ANSYS融会于贯通．中国水利水电出版社，2002