冷弯薄壁斜卷边槽钢弹性畸变屈曲计算研究
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摘要
对于高强度的开口冷弯薄壁型钢而言,畸变屈曲是一种重要的屈曲模式。在一定条件下,畸变屈曲可能成为居主导地位的屈曲模式,并对构件的极限承载力起到决定性的作用。近年来,随着钢材的强度逐步提高,冷弯薄壁型钢的板厚向超薄方向发展,构件的截面形式日趋复杂化,畸变屈曲正越来越受到人们的重视。
国内外对于钢结构的整体屈曲与局部屈曲的研究比较成熟。与整体屈曲、局部屈曲相比,畸变屈曲被世人认识的时间相对较短,各国学者对畸变屈曲的研究也有待深入。我国现行国家标准《冷弯薄壁型钢结构技术规范》(GB50018-2002,简称GB50018)还没有针对畸变屈曲的相应的计算规定。目前针对畸变屈曲的成熟计算方法尚不多见,直接强度法(Direct Strength Method,简称DSM)是一种新的设计方法,DSM的一个特点是可用于畸变屈曲计算,目前已被北美和澳洲地区所采纳。该设计方法首先需要求出构件的弹性畸变屈曲值,然后将其值代入DSM中的设计公式进行设计计算,从而得出畸变屈曲设计值。作为一种发展中的计算方法,DSM值得进一步研究。
弹性畸变屈曲的计算是DSM的关键,亦是本文研究的重要内容。DSM可采用相关计算程序,如CUFSM有限条等软件计算弹性畸变屈曲。有关学者也提出了近似模型计算法计算弹性畸变屈曲,并被有关国外规范采纳。近似模型计算法的不方便之处是计算较复杂,往往需迭代计算。
广义梁理论(Generalized Beam Theory,简称GBT)已被提出二十余年,理论上GBT可用于求解弹性畸变屈曲问题,但计算上的复杂性阻碍了“广义梁理论”在弹性畸变屈曲计算方面的应用。
冷弯薄壁卷边槽钢在实际工程中应用广泛,本文基于GBT和相关资料,对斜卷边冷弯薄壁槽钢弹性畸变屈曲进行重点研究。主要研究内容如下：
(1)针对斜卷边冷弯薄壁槽钢轴压柱,推导出弹性畸变屈曲计算公式。除不考虑翼缘弯曲变形的刚体位移计算模型外,本文提出了两种考虑翼缘弯曲变形的新计算模型：横向弯曲铰支计算模型、横向弯曲固支计算模型。翼缘和卷边的交点在计算中被视为铰支座或者固定支座是横向弯曲铰支计算模型和横向弯曲固支计算模型的区别所在。在横向弯曲铰支计算模型计算中,翼缘和卷边的交点被视为铰支座；在横向弯曲固支计算模型计算中,翼缘和卷边的交点被视为固定支座。并分别推导了三种计算模型下的弹性畸变屈曲计算公式。
与现有资料、其他方法进行计算对比,结果表明本文三种计算模型下的公式均具有较高的工程精度。从安全角度考虑,建议弹性畸变屈曲计算值采用横向弯曲铰支计算模型公式值、刚体位移计算模型公式值二者间的小值。
(2)针对斜卷边冷弯薄壁槽钢绕弱轴纯弯梁,推导出弹性畸变屈曲计算公式。类似于轴压柱,除刚体位移计算模型以外,本文提出了绕弱轴纯弯梁弹性畸变屈曲的两种新计算模型：横向弯曲铰支计算模型和横向弯曲固支计算模型。并分别推导了三种计算模型的弹性畸变屈曲计算公式。
计算对比表明,刚体位移模型公式计算值偏大,横向弯曲铰支模型和横向弯曲固支模型公式计算值比较准确,建议采用横向弯曲铰支计算模型公式计算值。
(3)针对绕弱轴冷弯薄壁斜卷边槽钢压弯构件,推导出弹性畸变屈曲压弯构件计算公式。该计算公式中的弹性畸变屈曲轴压临界应力和纯弯临界应力可由前述相关公式计算得到。计算分析表明,弹性畸变屈曲压弯构件计算公式具有良好的计算精度。
为与国情相符合,本文特意选取GB50018所附录的冷弯薄壁卷边槽钢进行计算,研究结果表明本文的弹性畸变屈曲轴压、纯弯、压弯计算公式均能很好地适用于上述槽钢。
本文公式无需迭代计算,适于手算或简单编程计算。摆脱了对弹性畸变屈曲专用软件的依赖,促进DSM实用化进程。本文的计算思路可为后续研究提供借鉴,也可供工程设计人员和冷弯薄壁型钢设计规范修订作参考。
总之,本文针对冷弯薄壁斜卷边槽钢建立了多种计算模型,推导了相对简便实用的计算公式。多种计算方法的对比,论证了本文计算公式的准确性。
The distortional buckling is one of the important buckling modes for high strength cold-formed thin-walled steel open cross-section members. It may become the dominating buckling mode and control the ultimate load-carrying capacity of members in some conditions. With the cold-formed thin-walled steel members tending to higher strength, thinner thickness and more complicate section shapes, the distortional buckling is receiving more attentions in recent years.
Reseachers worldwide have studied the local buckling and the overall buckling for a long time and reached a significant conclusion. Howerver it is a relatively short period of time since the distortional buckling was recognized. And deeper study of the distortional buckling remains to be made. Mature computation methods for the distortional buckling are of rare occurrence in the present. There are no specific clauses for the calculation of distortional buckling in current Chinese national specification'Technical Code for Cold-Formed Thin-Walled Steel Structures" (GB50018-2002, abbr. GB50018). The Direct Strength Method (DSM) is a new design method of the cold-formed thin-walled steel and has been adopted in North America and Australia region. First the value of elastic distortional buckling of element must be calculated. Then the design value of distortional buckling is solved by introducing the value of elastic distortional buckling into the formulae of DSM. As a kind of computing method to be perfected DSM merits further investigation. Its major feature is to calculate the distortional buckling.
The calculation of the elastic distortional buckling is the key for DSM and is the important subject in this paper. The current good method of calculating the elastic distortional buckling is numerical method such as the finite strip program of CUFSM. Proposed by scholars to calculate the elastic distortional buckling, approximation model method has been adopted by some foreign standards. As the computation process is iterative, approximate model method is inconvenient.
Generalized Beam Theory (GBT) can be used for solving the elastic distortional buckling. But the calculation is a bit complicated, which holdbacks the application of GBT.
The cold-formed thin-walled lipped channel steel has been applied widely in practical engineering.Based on GBT and related research data, this paper studies the elastic distortional buckling of cold-formed thin-walled lipped channels. The main contents are as follows:
(1) The formulae of the elastic distortional buckling for cold-formed thin-walled channel columns with inclined simple edge stiffeners under axial pressure are derived. Except the calculating model of rigid body displacement not including the flange transverse bending,two new kinds of calculating model with the inclusion of the flange transverse bending are given, ie, the calculating model of hinged support and the calculating model of restrained support. The intersection of flange and stiffener is viewed as hinged support in the calculating model of hinged support. The intersection of flange and stiffener is regarded as restrained support in the calculating model of restrained support. Based on the three kinds of calculating model, the calculation formulae for the elastic distortional buckling of cold-formed thin-walled inclined lipped channel columns have been established respectively.
The validity, accuracy and efficiency of the method are demonstrated by comparing the results from the presented formulae and the ones from existing data, other computing methods.It shows that the formulae are accurate and suitable for engineering application. The smaller value obtained from the calculating model of hinged support considering transverse bending and the calculating model of rigid body displacement is proposed in terms of safety.
(2) The formulae of the elastic distortional buckling for cold-formed thin-walled pure bending channel beams with inclined simple edge stiffeners acted by moment in the weak plane are derived. Except the calculating model of rigid body displacement, this paper presents two new kinds of calculating model of elastic distortional buckling of cold-formed thin-walled inclined lipped channel beams, ie, the calculating model of hinged support and the calculating model of restrained support. And the related calculation formulae have been derived respectively.
It is shown through the compared calculation that the value obtained from the calculating model of rigid body displacement is a bit larger than that obtained from other methods. The value obtained from other two calculating models is very close to that obtained from other calculation methods.So it is recommended that the calculating model of hinged support considering transverse bending be applicable for the elastic distortional buckling of pure bending channel beams acted by moment in the weak plane.
(3) The linear formulae of the elastic distortional buckling for cold-formed thin-walled channels with inclined simple edge stiffeners subjected to eccentric loading in the symmetry plane are derived. Based on the formulae described above, the linear formulae are obtained. The calculated results indicate that the linear formulae are higher precision.
The correctness of the above formulae is verified through the channel sections of the Appendix B.1.1-4 of GB50018. The results show that the presented formulae suit China's national conditions.
The simple formulae in this paper are applicable to calculate by hand. The formulae are not only independent on the dedicated computer program but also avoid the redundant calculations. There is no need for the iterative calculation by the formulae. They are easy to apply, graspable easily for the disigner and may be directly used in practical design and incorporated into future design codes and guidelines. Therefore the formulae have the practical significance and will accelerate the utilization of DSM.
Based on GBT and related research data, the corresponding mechanics computational models have been proposed, the practical formulae under different loading states have been developed and analyzed in this paper. Compared with other methods, the calculation method proposed in this paper is proved to be reasonable and verified.
国内外对于钢结构的整体屈曲与局部屈曲的研究比较成熟。与整体屈曲、局部屈曲相比,畸变屈曲被世人认识的时间相对较短,各国学者对畸变屈曲的研究也有待深入。我国现行国家标准《冷弯薄壁型钢结构技术规范》(GB50018-2002,简称GB50018)还没有针对畸变屈曲的相应的计算规定。目前针对畸变屈曲的成熟计算方法尚不多见,直接强度法(Direct Strength Method,简称DSM)是一种新的设计方法,DSM的一个特点是可用于畸变屈曲计算,目前已被北美和澳洲地区所采纳。该设计方法首先需要求出构件的弹性畸变屈曲值,然后将其值代入DSM中的设计公式进行设计计算,从而得出畸变屈曲设计值。作为一种发展中的计算方法,DSM值得进一步研究。
弹性畸变屈曲的计算是DSM的关键,亦是本文研究的重要内容。DSM可采用相关计算程序,如CUFSM有限条等软件计算弹性畸变屈曲。有关学者也提出了近似模型计算法计算弹性畸变屈曲,并被有关国外规范采纳。近似模型计算法的不方便之处是计算较复杂,往往需迭代计算。
广义梁理论(Generalized Beam Theory,简称GBT)已被提出二十余年,理论上GBT可用于求解弹性畸变屈曲问题,但计算上的复杂性阻碍了“广义梁理论”在弹性畸变屈曲计算方面的应用。
冷弯薄壁卷边槽钢在实际工程中应用广泛,本文基于GBT和相关资料,对斜卷边冷弯薄壁槽钢弹性畸变屈曲进行重点研究。主要研究内容如下：
(1)针对斜卷边冷弯薄壁槽钢轴压柱,推导出弹性畸变屈曲计算公式。除不考虑翼缘弯曲变形的刚体位移计算模型外,本文提出了两种考虑翼缘弯曲变形的新计算模型：横向弯曲铰支计算模型、横向弯曲固支计算模型。翼缘和卷边的交点在计算中被视为铰支座或者固定支座是横向弯曲铰支计算模型和横向弯曲固支计算模型的区别所在。在横向弯曲铰支计算模型计算中,翼缘和卷边的交点被视为铰支座；在横向弯曲固支计算模型计算中,翼缘和卷边的交点被视为固定支座。并分别推导了三种计算模型下的弹性畸变屈曲计算公式。
与现有资料、其他方法进行计算对比,结果表明本文三种计算模型下的公式均具有较高的工程精度。从安全角度考虑,建议弹性畸变屈曲计算值采用横向弯曲铰支计算模型公式值、刚体位移计算模型公式值二者间的小值。
(2)针对斜卷边冷弯薄壁槽钢绕弱轴纯弯梁,推导出弹性畸变屈曲计算公式。类似于轴压柱,除刚体位移计算模型以外,本文提出了绕弱轴纯弯梁弹性畸变屈曲的两种新计算模型：横向弯曲铰支计算模型和横向弯曲固支计算模型。并分别推导了三种计算模型的弹性畸变屈曲计算公式。
计算对比表明,刚体位移模型公式计算值偏大,横向弯曲铰支模型和横向弯曲固支模型公式计算值比较准确,建议采用横向弯曲铰支计算模型公式计算值。
(3)针对绕弱轴冷弯薄壁斜卷边槽钢压弯构件,推导出弹性畸变屈曲压弯构件计算公式。该计算公式中的弹性畸变屈曲轴压临界应力和纯弯临界应力可由前述相关公式计算得到。计算分析表明,弹性畸变屈曲压弯构件计算公式具有良好的计算精度。
为与国情相符合,本文特意选取GB50018所附录的冷弯薄壁卷边槽钢进行计算,研究结果表明本文的弹性畸变屈曲轴压、纯弯、压弯计算公式均能很好地适用于上述槽钢。
本文公式无需迭代计算,适于手算或简单编程计算。摆脱了对弹性畸变屈曲专用软件的依赖,促进DSM实用化进程。本文的计算思路可为后续研究提供借鉴,也可供工程设计人员和冷弯薄壁型钢设计规范修订作参考。
总之,本文针对冷弯薄壁斜卷边槽钢建立了多种计算模型,推导了相对简便实用的计算公式。多种计算方法的对比,论证了本文计算公式的准确性。
The distortional buckling is one of the important buckling modes for high strength cold-formed thin-walled steel open cross-section members. It may become the dominating buckling mode and control the ultimate load-carrying capacity of members in some conditions. With the cold-formed thin-walled steel members tending to higher strength, thinner thickness and more complicate section shapes, the distortional buckling is receiving more attentions in recent years.
Reseachers worldwide have studied the local buckling and the overall buckling for a long time and reached a significant conclusion. Howerver it is a relatively short period of time since the distortional buckling was recognized. And deeper study of the distortional buckling remains to be made. Mature computation methods for the distortional buckling are of rare occurrence in the present. There are no specific clauses for the calculation of distortional buckling in current Chinese national specification'Technical Code for Cold-Formed Thin-Walled Steel Structures" (GB50018-2002, abbr. GB50018). The Direct Strength Method (DSM) is a new design method of the cold-formed thin-walled steel and has been adopted in North America and Australia region. First the value of elastic distortional buckling of element must be calculated. Then the design value of distortional buckling is solved by introducing the value of elastic distortional buckling into the formulae of DSM. As a kind of computing method to be perfected DSM merits further investigation. Its major feature is to calculate the distortional buckling.
The calculation of the elastic distortional buckling is the key for DSM and is the important subject in this paper. The current good method of calculating the elastic distortional buckling is numerical method such as the finite strip program of CUFSM. Proposed by scholars to calculate the elastic distortional buckling, approximation model method has been adopted by some foreign standards. As the computation process is iterative, approximate model method is inconvenient.
Generalized Beam Theory (GBT) can be used for solving the elastic distortional buckling. But the calculation is a bit complicated, which holdbacks the application of GBT.
The cold-formed thin-walled lipped channel steel has been applied widely in practical engineering.Based on GBT and related research data, this paper studies the elastic distortional buckling of cold-formed thin-walled lipped channels. The main contents are as follows:
(1) The formulae of the elastic distortional buckling for cold-formed thin-walled channel columns with inclined simple edge stiffeners under axial pressure are derived. Except the calculating model of rigid body displacement not including the flange transverse bending,two new kinds of calculating model with the inclusion of the flange transverse bending are given, ie, the calculating model of hinged support and the calculating model of restrained support. The intersection of flange and stiffener is viewed as hinged support in the calculating model of hinged support. The intersection of flange and stiffener is regarded as restrained support in the calculating model of restrained support. Based on the three kinds of calculating model, the calculation formulae for the elastic distortional buckling of cold-formed thin-walled inclined lipped channel columns have been established respectively.
The validity, accuracy and efficiency of the method are demonstrated by comparing the results from the presented formulae and the ones from existing data, other computing methods.It shows that the formulae are accurate and suitable for engineering application. The smaller value obtained from the calculating model of hinged support considering transverse bending and the calculating model of rigid body displacement is proposed in terms of safety.
(2) The formulae of the elastic distortional buckling for cold-formed thin-walled pure bending channel beams with inclined simple edge stiffeners acted by moment in the weak plane are derived. Except the calculating model of rigid body displacement, this paper presents two new kinds of calculating model of elastic distortional buckling of cold-formed thin-walled inclined lipped channel beams, ie, the calculating model of hinged support and the calculating model of restrained support. And the related calculation formulae have been derived respectively.
It is shown through the compared calculation that the value obtained from the calculating model of rigid body displacement is a bit larger than that obtained from other methods. The value obtained from other two calculating models is very close to that obtained from other calculation methods.So it is recommended that the calculating model of hinged support considering transverse bending be applicable for the elastic distortional buckling of pure bending channel beams acted by moment in the weak plane.
(3) The linear formulae of the elastic distortional buckling for cold-formed thin-walled channels with inclined simple edge stiffeners subjected to eccentric loading in the symmetry plane are derived. Based on the formulae described above, the linear formulae are obtained. The calculated results indicate that the linear formulae are higher precision.
The correctness of the above formulae is verified through the channel sections of the Appendix B.1.1-4 of GB50018. The results show that the presented formulae suit China's national conditions.
The simple formulae in this paper are applicable to calculate by hand. The formulae are not only independent on the dedicated computer program but also avoid the redundant calculations. There is no need for the iterative calculation by the formulae. They are easy to apply, graspable easily for the disigner and may be directly used in practical design and incorporated into future design codes and guidelines. Therefore the formulae have the practical significance and will accelerate the utilization of DSM.
Based on GBT and related research data, the corresponding mechanics computational models have been proposed, the practical formulae under different loading states have been developed and analyzed in this paper. Compared with other methods, the calculation method proposed in this paper is proved to be reasonable and verified.
引文
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