【作者】 刘斌；

【导师】 舒兴平；

【作者基本信息】 湖南大学 ， 结构工程， 2013， 硕士

【摘要】 钢材具有高强、轻质、力学性能良好的优点，是建造结构物的一种极好的建筑材料。因为钢材的这些特性，使得钢结构构件的极限承载能力往往不是由材料的强度控制，而是由构件的稳定性决定，构件在材料发生强度破坏之前已经发生失稳破坏。对开口截面薄壁构件的整体稳定性研究，国内外学者已经进行了大量的理论研究及试验工作，并取得丰硕的研究成果；但是，对于钢梁在横向偏心荷载作用下的整体稳定性问题的相关研究工作还比较少，而此类问题又在工程中广泛存在，且我国现行《钢结构设计规范》（GB50017-2003）中也没有相关的验算公式，因此有必要对这一问题进行深入的研究和探讨。本文从钢结构的基本稳定理论出发，介绍工字钢梁整体稳定的传统理论。在此基础上，对横向偏心荷载及端弯矩作用下工字形钢梁的稳定问题进行理论研究，分别运用平衡法和能量法列出其平衡微分方程和总势能方程。运用瑞利-里兹法得到一组非齐次方程组，并针对跨中偏心集中荷载这一种情况，在一系列假定的基础上，得到一个包含两个待定参数的弯扭相关方程。由于无法得到该方程的解析解，因此本文借鉴Lindner公式及我国《冷弯薄壁型钢规范》（GB50018-2002）中荷载偏离钢梁截面剪心但与主轴平行时的整体稳定验算公式的形式，引入一个扭矩影响系数kω，来调整约束扭转产生的翘曲正应力对工字钢梁整体稳定的影响，从而提出工字钢梁在考虑扭矩影响时的整体稳定承载力验算公式。运用有限元软件ANSYS对偏心集中荷载作用下工字钢梁的整体稳定进行非线性屈曲分析，得到其极限承载力。分析时主要考虑偏心距e、钢梁跨度l和受压翼缘宽度b1等截面参数的影响，得到钢梁在偏心集中荷载作用下，考虑不同参数影响的整体稳定极限荷载值，并求出不同取值下的kω值。根据计算结果，分析偏心距e、钢梁跨度l和受压翼缘宽度b1等截面参数对钢梁整体稳定极限荷载的影响，以及扭矩影响系数kω随各参数变化而变化的规律。对影响参数采用T/T0进行无量纲化处理，并利用数据分析软件ORIGIN对扭矩影响系数kω和无量纲变量T/T0进行回归分析，得到扭矩影响系数kω的数值计算公式，从而得出偏心集中荷载作用下工字钢梁的整体稳定承载力验算公式。最后与Lindner公式及其试验结果进行对比分析，验证本文所提出的公式的适用性。更多还原

【Abstract】 Steel has the advantages of high strength, light weight and good mechanicalproperties, so it is an excellent building material of construction structures. Becauseof these characteristics of steel, the limit bearing capacity of the steel structuralelement tends to be controlled by the stability of the elements other than the strengthof the material. For the elements encounter instability failure before the materialoccurs strength failure. Domestic and foreign scholars have carried out a large numberof theoretical studies and experimental works on the overall stability of the opensection thin-walled components, and have achieved fruitful research results; however,the researches on the overall stability of steel beams under lateral eccentric loads arerelatively few, while the problem extensively exists in engineering, and there is noverification formula in the current “Design of Steel Structures”(GB50017-2003)either, thus, it is necessary to conduct in-depth studies and discussions on this project.Starting with the basic stability theory of steel structure, the thesis introduces thetraditional theory of overall stability of steel I-beam. Based on this theory, ittheoretically studies on steel I-beam stability under lateral eccentric loads and endmoments, and lists the balanced differential equation and the total potential energyequation by using the balance method and energy method. Then, based on a series ofassumptions, it gets a bending-torsion correlation equation in this case of eccentricconcentrated load with a system of inhomogeneous equations from Rayleigh-Ritzmethod, which contains two undetermined parameters. Since it is hardly to get theanalytic solution of this equation, the thesis draws lessons from the form of theLindner formula and the overall stability calculation formula for load deviated fromshear center of the bending element but paralleled with the main shaft in “TechnicalCode of Cold-formed Thin-wall Steel Structures”(GB50018-2002) of China, andintroduces a torque influence factor kωto adjust the influence of warping stress forrestraining torsion generation on overall stability bearing capacity of steel I-beam.Accordingly, it puts forward the verification formula for overall stability capacity ofsteel I-beam while the influence of torque is taken into consideration.By using the finite element software ANSYS to do non-linear buckling analysison the overall stability of the steel I-beam under eccentric concentrated loads, thethesis gets the limit bearing capacity of the steel I-beam. During analyzing, the influences of section parameters, such as eccentricity e, span of the steel beam l,the compression flange widthb1, are mainly taken into consideration. And then, theoverall stability limit load of the steel steam under eccentric concentrated load withconsideration of influences of different parameters is obtained and the kωwithdifferent values are worked out. According to the results, the thesis analyzes theinfluence of the section parameters, such as eccentricity e, span of the steel beam land the compression flange widthb1, on the overall stability limit load of the steelbeam and the variation rules of torque influence factor kωaccording to theparameter variation. Those influence parameters are applied with dimensionlessmethod byT/T0. Torque influence factor kωand dimensionless variableT/T0areapplied with regression analyses through the data analysis software ORIGIN, and thenumeric calculation formula for torque influence factor kωis obtained. Thereby, theverification formula for overall stability capacity of steel I-beam under eccentricconcentrated loads is obtained. Finally, it compares with the Lindner formula and thetest results, and verifies the applicability of the proposed formula in this thesis afteranalysis.更多还原