钢楔形柱平面内整体稳定极限承载力研究

【作者】 刘中华；

【导师】 李天；

【作者基本信息】 郑州大学 ， 结构工程， 2002， 硕士

【摘要】 1．绪论 近二十年来，高层建筑钢结构，大跨度钢结构和轻型钢结构建筑在我国获得了前所未有的发展。其中轻型钢结构以其经济、快速、高效等优点在工业厂房、仓库、超市等建筑中倍受青睐。在应用最广的轻型钢结构形式——门式刚架中，设计人员往往根据构件弯矩的变化规律，将门式刚架中的构件设计成变截面的形式。根据需要的不同，可以将腹板高度和翼缘宽度分别或同时设计成沿杆长线性变化的形式，并且上下翼缘的厚度可以根据需要取不同的值。实际工程中使用最多的变截面构件形式是仅构件腹板高度线性变化，翼缘宽度保持不变的形式。 弹性失稳荷载的常用理论求解方法有微分方程平衡法、位移法等。这两种方法只能计算等截面构件的弹性屈曲荷载。研究人员先后提出了便于工程应用的瑞利-里兹法、伽辽金法、有限差分法、有限积分法、有限单元法等数值计算方法。这五种方法中除有限差分法和有限积分法较为适用本文计算需要外，其它几种方法都存在诸多弊端，不宜选用。 我国现行《钢结构设计规范》(GBJ17-88)和《门式刚架轻型房屋钢结构技术规程》(CECS102:98)对构件的稳定计算方法是：先对构件进行整体线弹性内力分析，得到构件的轴力和弯矩；再根据边缘屈服准则对构件分别进行平面内和平面外稳定验算。现行普钢规范和轻钢规程中规定的平面内稳定计算公式存在一些不合理的地方。 国外钢压杆稳定计算的方法除了上面提到的一些计算方法外，还有了一些较为实用的计算方法。常用弹性分析的方法有：梁柱法、虚拟荷载法、虚拟侧向荷载法、迭代重力荷载法和负刚度法。研究人员还提出了便于工程实践应用的放大系数法。考虑弹塑性的分析方法有：弹性-塑性铰法和虚拟荷载法 根据非线性研究分析的需要，研究人员先后提出了：荷载控制法、位移控制法、弧长控制法和做功控制法等控制迭代收敛的非线性计算方法。 2．稳定的基本原理 在静载作用下，结构构件非线性静力失稳的现象是十分丰富多彩的。基于不同理论和针对问题侧重点的不同，常有多种分类方法。根据一般钢结构应用的稳定理论，常按屈曲后性能将失稳分为以下三类：平衡分岔失稳、跃越失稳和极值点失稳。区分结构失稳类型的性质十分重要，否则不可能正确估量结构的稳定承载力。 当所研究构件是在弹塑性阶段失稳时，稳定平衡微分方程变为了非常系数微分方 程，而无法求得真解析解。因此，对于大多数情况都需要采用数值方法进行求解。在构 件分析中常用的数值方法大体上可以分成两类。一类是盲接对微分方程求解。另一类是 用总势能驻值原理或真他类似的有夫能量的方法求解。常用直接求解微分方程的方法 有：数值积分法、差分法、加权残数法和迎辽益法。常根据总势能驻值原理末解的方法 有：里兹（尸／tZ）法以及可从总势能驻值原理导出的有限单元法。 数值积分法的种类很多。本文计算中所采用的是泰勒级数法。这种方法的基本原 理是：先建立沟件任一截面的人d一尸一0矢系，然后通过对于整个构件内外力平衡和变 形协调以及截面内力与变形之间的夫系，求得构件极限荷载。该方法的计算过程可分为 两大步骤：第一步根据截面内力平衡条件建立奎矩、压力和曲率之间的夫系；第二步根 据构件的变形曲线建立挠度、转角和曲率之间的夫系。 3．形柱平面内稳定极限承载力计算分析 一般来说，进行截面分析的应力分布摸式，主要有三种形式，分别称为弹性分布、 单面塑性分布及双面塑性分布。由于矩形截面可以得到吝种模式下。－pop夫系的解析 表达式．通过大量计算，本文中也建立了常用工字形截面吝种摸式下一矽丁关系的近 似计算表达式。 在利用数值积分法计算扦件平面内稳定极限承载力时，即使只是一个简单的构件也 十分费时．有时甚至出现迭代无法收敛的惰况。因此，本文在计算中应用了混台迭代手 段，引入了。－少丁近似计尊公式，修正了初始假定变皇，解决了约束条件改变时原收 敛条件的失效的问题．提高了计算效率，扩大了适用范围。 由于构件在加工、运输、安装等过程中不可避免的存在一定的误差，因此一般等截 面自杆都有一定的初始缺陷。本文利用编制的程序，对常见形式的初始缺陷对楔形构件 平面内稳定极限承力的影响进行了讨论．并给出了相应的计算公式及处理手段。 4．楔形构件平面内极限承载力计算分析 ， 由于楔形构件的截面刚度随杆长是不断变化的．因此，这种构件在超静定惰况下的 内力无法通过等截面构件中常用的求解方法求得，刘于工字型截面楔形构件的内力只能 通过数值积分方法借助计算机进行计算。为了计算楔形构件在横向荷载作用下平面内稳 定极限承载力，本文导出几种常用荷载在不同约束条件下的积分计算公式。对于超静定 结构更多还原

【Abstract】 1. IntroductionThe steel construction of high-rise building, the steel structure of large span and the lightweight steel construction has had rapid development during the past twenty years. The lightweight steel construction is widely used with the industrial factory building, storehouse and supermarket because of its specialty of economic, speediness and high efficiency. The portal frame is the most widely used in the lightweight steel construction. When designing the portal frame, designers usually design the members with the variable cross-section on the base of the variation of the members’ moment. With the different use, the height of the web plate and the width of the flange can be designed to be the form of linear variation respectively or synchronously, as well as the thickness of the flanges can be taken with the different values. The form of variable cross-section, used mostly in the practical projects, just has the change of the linear variation on the height of the web plate while keep the width of the flange changeless.The displacement method and the method of the balance of the differential equation are usually used to get the elastic instability load. While these two methods are appropriate only for the elements of constant section. Researchers suggested many numerical methods convenient for the engineering, such as the Rayleigh-Ritz method, Galerkin method, finite difference method, finite integral method, finite element method ,etc. These methods are improper to be used in this thesis except the finite difference method, finite integral method.In the actual ((Code for steel structure design}) (GBJ 17-88) and for the ((Technical specification for steel structure of light-weight buildings with gabled frames)) (CECS 102 : 98), the calculation method for the stability of the members is: obtaining the axial force through the analysis of the linear-elastic inner force of the whole structrue, then checking the stability inside and outside the plane respectively on the foundation of the yielding rule of the edge. There is much illogicality with the formula for the calculation of internal plane in the actual modes for the normal steel and the lightweight steel.Besides the methods mentioned above, there are some applied methods overseas to calculate the stability of the steel compression bar. The elastic methods are beam-columns method, the pseudo load method, the pseudo lateral load method, the iterative gravity load method and the negative rigidity method. Researchers advanced the magnifying coefficient method easy to the engineering practice. The methods considering the elastoplasticity are the elastic-plastic hinge method and the pseudo load method.Based on the need of non-linear analysis, researchers brought forward nonlinear calculation methods to control the iterative constringency, such as the load controlling method, the displacement controlling method, the arc length controlling method and the pseudo load method.2. The basal theory for the stabilityThere are many non-linear manners when the elements losing the stability under static loads. There are many classifications based on different theories and different emphasis to the problem. Based on the usually used stability theory for the normal steel structure, the non-stability are divided into three sorts according to the performance after instability, as the balance fork instability, jump instability and extreme point instability. It is very important to distinguish the qualities of the structural instability, or it is impossible to rightly measure the structural bearing capacity.When the element studied lost the stability during the elastic-plastic period, the stability balance equation turn to the special coefficient differential equation, and the analytic value cannot be got. Therefore, it is needed to get the result through the numerical value method to most instances. The most used numerical value methods in the member analysis are divided into two sorts. One is to get the value directly. The other is to get the更多还原