薄壁受压构件的畸变屈曲理论与试验研究

发布时间：2018-04-30 02:37

本文选题：受压构件 + 畸变屈曲　；参考：《兰州大学》2015年博士论文

【摘要】：随着结构钢屈服强度的提高,在结构轻量化的要求下和节约钢材的利益驱动下,冷弯型钢受压构件的横截面逐渐趋于开阔、纤薄,这致使畸变屈曲或畸变相关屈曲可能控制构件的设计。本文在总结前人研究成果和分析前人研究不足的基础上,以C形截面和帽形截面冷弯薄壁型钢受压构件为研究对象,采用试验研究、理论分析和数值模拟相结合的技术路线,主要完成了以下三方面的研究：1.建立了薄壁受压构件畸变屈曲的分析理论进行了4组共36个C形截面受压构件的试验研究,考察了腹板和翼缘的宽度比h/b构件几何长度l对屈曲模式和极限荷载的影响,分析了构件横截面的变形特点、屈曲后强度等内容；在试验研究的基础上并结合前人研究成果,提出了识别屈曲模式的判据。揭示了计算长度的物理意义,提出了畸变屈曲和局部屈曲的计算长度系数的概念,实现了畸变屈曲、整体屈曲和局部屈曲的统一表征。提出了受压构件畸变屈曲的分解分析方法,依据经典的板的屈曲理论推导了局部屈曲计算长度的边界条件影响系数,采用能量法推导了弯扭屈曲的总势能方程和平衡微分方程,进而推导了连续弹性支承构件弯扭屈曲的平衡微分方程。研究表明,本文建立的薄壁受压构件畸变屈曲的分析理论概念明确、条理清晰。统一了屈曲问题的研究对象,解决了长期以来因截面形式、荷载工况或边界约束条件的不同而研究对象不同的问题；突出了影响畸变屈曲的关键因素,为全面建立薄壁受压构件畸变屈曲的计算理论和计算方法奠定了基础。2.建立了系统的薄壁受压构件畸变屈曲的计算理论和计算方法在畸变屈曲的临界荷载方面,首先采用有限条软件CUFSM分析了弹性模量、边界约束条件和尺度参数对畸变屈曲临界荷载的影响；继而依据建立的畸变屈曲的分析理论和Lau和Hancock的分析模型,采用Galerkin法推导了畸变屈曲临界荷载的统一公式,建立了畸变屈曲临界荷载Pcr,D的统一理论,提出了Pcr,D的通用公式,并采用有限条软件CUFSM验证了Pcr,D通用公式的精度并确定了其适用范围,同时还与其他数值软件和现有的简支构件畸变屈曲临界应力的解析解的计算值进行了对比。结果表明,对于简支构件畸变屈曲临界荷载,Pcr,D的通用公式较国际上广泛使用的Lau和Hancock的公式、Schafer的公式精度更高、适用范围更广在畸变屈曲的极限荷载方面,根据结构设计“穷举”和“取小”的特点改写了Schafer的固支受压构件畸变屈曲极限荷载Pu,D的计算公式；在提出简支构件Pu,D计算公式后,建立了畸变屈曲极限荷载Pu,D的统一理论并提出了Pu,D的通用公式。然后通过17个C形和17个帽形固支受压构件的ANSYS计算值进一步验证了Pcr,D通用公式的精度,通过42个C形和42个帽形简支受压构件的ANSYS计算值验证了Pu,D的通用公式具有较高的精度。在畸变屈曲的发生条件和计算公式的本质方面,建立了畸变屈曲与λD和λL的关系,提出了畸变屈曲的判据；对比了形式不同的Pu,D计算公式,揭示了畸变屈曲极限荷载计算理论的本质是把强度问题转化为稳定问题进行求解的,同时也指出以有效宽度法或有效截面法形式给出的Pu,D计算公式与直接强度法的Pu,D计算公式无本质区别。以上建立的薄壁受压构件畸变屈曲的计算理论和计算方法,解决了国内外长期以来缺乏固支构件的Pcr,D解析解的问题,拓展了简支构件Pcr,D计算公式的适用范围,解决了临界荷载Pcr,D和极限荷载Pu.D因边界约束条件不同而无法对接的问题。3.建立了薄壁受压构件极限荷载的计算理论和计算方法基于本文提出的整体屈曲极限荷载Pu,G的实用公式和局部屈曲临界荷载Pcr,L的实用公式以及建立的畸变屈曲的计算理论和计算方法,建立了薄壁受压构件极限荷载的统一化理论,提出了包含不同屈曲模式的3种极限状态ULSⅣ,ULSⅥ和ULSⅧ。采用极限荷载的统一化理论分别计算了196个C形截面和32个帽形截面固支轴压构件以及45个C形截面简支轴压构件的极限荷载Pu,Ⅳ,PuⅥ和pu,Ⅷ,并与试验值Pu,Exp进行了对比。为提高极限荷载的计算精度和提高结构材料的利用率,分别建立了屈曲模式和截面承载效率与λ和五的关系,提出了全面的局部-畸变相关屈曲的判据和极限状态ULS的判据,并根据如上判据确定了极限荷载的数值。最后提出了受压构件横截面选形和构件选材的建议。研究表明,极限荷载的计算精度和结构材料的利用率受λD和λL的影响较大：限制构件的λD≤1.290和(或)λL≤1.130不但可以由极限荷载的统一化理论较为准确地计算其极限荷载,还能获得较高的截面承载效率。而且,局部一畸变相关屈曲的承载效率较低,应限制该屈曲模式的出现；为节约钢材和提高极限荷载的计算精度,薄壁受压构件横截面的尺度参数的选择应与构件材料的选择相协调。本文的创新点有：1.揭示了计算长度系数的物理意义,首次统一了屈曲问题的研究对象——两端简支且几何长度为屈曲半波长的构件或构件段。2.首次给出了简支和固支构件畸变屈曲临界荷载统一计算公式,首次建立了畸变屈曲临界荷载Pcr,D的统一理论和极限荷载Pu,,D的统一理论,提出了Pcr,D的通用公式和Pu,D的通用公式。3.首次建立了畸变屈曲、局部-畸变相关屈曲与λD和λL的关系,提出了全面的局部-畸变相关屈曲判据。
[Abstract]:With the increase of yield strength of structural steel, under the demand of lightweight structure and the benefit of saving steel, the cross section of the compression member of the cold bending steel gradually tends to be open and thin, which may lead to the design of the distortional buckling or distortion related buckling. On the basis of the research object, the C section and the cap shaped section cold bending thin-walled steel compression member are studied. The following three aspects are completed by the experimental research, the theoretical analysis and the numerical simulation. 1. the analysis of the distortion buckling of the thin-walled compression members is established, and 4 groups of 36 members of the compression members are tested. The effect of the width of the web and flange on the buckling mode and the ultimate load of the h/b member L is investigated. The deformation characteristics of the cross section of the component and the post buckling strength are analyzed. The criteria for the identification of the buckling mode are proposed on the basis of the experimental research and the previous research results. The physics of the calculation length is revealed. Meaning, the concept of calculating length coefficient of distortion buckling and local buckling is put forward. The unified characterization of distortion buckling, integral buckling and local buckling is realized. A decomposition analysis method for distorted buckling of compression members is proposed. The influence coefficient of boundary condition of local flexion calculation length is derived based on the classical plate buckling theory. The total potential energy equation and the equilibrium differential equation for flexural and torsional buckling are derived and the equilibrium differential equation of flexural and torsional buckling of continuous elastic supporting members is derived. The study shows that the theoretical concept of the distortion buckling of the thin-walled compression members is clear and the bar is clear. The research object of the buckling problem has been unified and the long term has been solved. The different problems of the object are studied in the form of cross section, load condition or boundary constraint conditions, and the key factors affecting the distortion buckling are highlighted. The foundation.2. is established to establish the calculation theory and calculation method of the distortion buckling of the thin-walled compression members. The calculation theory and calculation of the distorted buckling of the thin-walled compression members are established. In the critical load of distorted buckling, the finite strip software CUFSM is used to analyze the influence of elastic modulus, boundary constraint conditions and scale parameters on the critical load of distortional buckling, and then the critical load of distorted buckling is derived by Galerkin method, based on the analysis theory of distortion buckling and the analysis model of Lau and Hancock. The unified formula of the critical load of the distortion buckling load Pcr, D is established. The general formula of Pcr and D is put forward. The precision of Pcr, D general formula is verified by the finite strip software CUFSM, and its application range is determined. At the same time, the calculation value of the analytical solution of the critical stress of the existing simple supported components and the other numerical software and the existing simple supported components is also given. The results show that the general formula of Pcr and D is more accurate than that of Lau and Hancock, which is widely used in the world. The formula of Schafer is more accurate than the formula of Lau and Hancock, which is widely used in the world. The application range is more widely used in the limit load of distortional buckling, and the Schafer is rewritten according to the characteristics of "poor" and "small" structure design. The calculation formula of the limit load of the flexed buckling load Pu and D for the supported compression members; after putting forward the formula of Pu and D for the simply supported component, the unified theory of Pu, D for the ultimate load of the distorted buckling is established and the universal formula of Pu and D is put forward. Then the Pcr, the essence of the D general formula is further verified by the ANSYS calculation values of the 17 C and 17 cap solid supported compression members. Degree, verified by the ANSYS calculation values of 42 C shaped and 42 cap shaped simply supported compression members, the general formula of Pu and D has high accuracy. In terms of the condition of the distortion buckling and the essence of the formula, the relation between the distortion buckling and lambda D and lambda L is established, the criterion of the distortion buckling is put forward, and the different forms of Pu, D calculation formula are compared. The essence of the theory of the ultimate load calculation is to convert the strength problem to the stability problem, and also points out that the Pu, D formula given by the effective width method or the effective cross section method has no essential difference between the Pu and D formulas of the direct strength method. The calculation theory of the distortion buckling of the thin-walled compression members established above has been found. The theory and calculation method have solved the problem of Pcr and D analytical solution for a long time lack of solid supported components, expanded the scope of application of Pcr and D formula for simply supported components, and solved the calculation theory of critical load of Pcr, D and ultimate load Pu.D which can not be butted because of the different boundary constraints, and established the limit load of the thin-walled compression member. The theory and calculation method based on the proposed integral buckling limit load Pu, G's practical formula and the local buckling critical load Pcr, the practical formula of L and the calculation theory and calculation method established for the distortion buckling, establish the unified theory of the limit load of the thin-walled compression member, and put forward 3 extreme state UL containing different buckling modes. S IV, ULS VI and ULS VIII. Using the unified theory of limit load, the ultimate load of 196 C cross sections and 32 cap shaped cross section solid supported axial compression members and 45 C shaped section simply supported axial compression members are calculated respectively, Pu, IV, Pu VI and Pu, VIII, and are compared with the experimental values Pu and Exp. In order to improve the calculation precision of the limit load and improve the structural material The relation between the buckling mode and the cross section bearing efficiency with lambda and five is established respectively. The criterion of the comprehensive local distortion related buckling and the criterion of the limit state ULS are put forward, and the limit load values are determined according to the above criteria. Finally, the suggestion of the cross section selection and the material selection of the compression members is put forward. The research shows that the limit of the limit is the limit. The calculation accuracy of the load and the utilization of structural materials are greatly influenced by the lambda D and lambda L: the limit of the member's lambda D < 1.290 and (or) lambda L < 1.130 can not only calculate the ultimate load more accurately by the unified theory of the limit load, but also obtain higher cross section bearing efficiency. The emergence of the buckling mode should be limited. In order to save the steel and improve the calculation accuracy of the ultimate load, the selection of the scale parameters of the cross section of the thin-walled compression member should be coordinated with the selection of the component materials. The innovation points of this paper are as follows: 1. the physical meaning of the calculation length coefficient is revealed, and the research object of the buckling problem is first unified. .2. for the first time a member or component section with geometric length as a half wavelength, a unified calculation formula for the critical load of the flexural buckling of simply supported and supported components is given for the first time. For the first time, the unified theory of the critical load of the distorted buckling Pcr, the unified theory of D and the limit load Pu, the unified theory of D, and the general formula of Pcr, D, and the general formula.3. of D are proposed. For the first time, the relationship between distortional buckling, local distortion related buckling and lambda D and lambda L is established for the first time. A comprehensive local distortion correlation buckling criterion is proposed.

【学位授予单位】：兰州大学
【学位级别】：博士
【学位授予年份】：2015
【分类号】：TU392.1

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