钢筋混凝土柱二阶弹塑性计算方法研究

发布时间：2018-04-11 19:47

本文选题：细长柱 + 解析法　；参考：《昆明理工大学》2014年博士论文

【摘要】：钢筋混凝土柱的二阶弹塑性问题涉及到材料和几何双重非线性的耦合作用。采用有限元方法需要耗费大量时间建模,效率较低。通过对现有的数值方法和简化方法的分析,以理论推导方式,在截面上,采用由应变求内力的逆算方法来确定截面承载力和弯矩-曲率关系。这一计算过程完整地利用了钢筋和混凝土的本构关系而没有进行简化,同时解析的算法没有迭代和收敛带来的误差,因而是精确解。在杆件上,采用三种具有不同精度的方法来分析和计算钢筋混凝土柱的二阶弹塑性性能,进而提供了三种水平的设计工具。为了验证这些计算方法,利用计算结果绘制了大量的曲线,通过曲线族变化规律的合理性和曲线间的逻辑关系来判断,通过与已有方法、现行规范方法和已有试验结果的对比等方式来判断。 (1)参考欧洲规范2,得到适用于我国的极限状态截面所有可能的应变分布,这些应变与极限轴力-弯矩是一一对应关系,因而无需迭代可直接由这些应变计算截面承载力,给出了钢筋混凝土矩形和圆形截面的计算过程,得到截面的轴力-弯矩相关关系,可用于截面强度验算和短柱的配筋设计。 (2)通过引入一些中间计算参数,推导了一种新的适用范围较广的钢截面的弯矩-曲率关系的解析算法,给出了矩形和工字形截面的解析表达式,得到了轴力不变的弯矩-曲率关系曲线、轴力-弯矩相关曲线和曲率不变的轴力-弯矩曲线,这些曲线反映了截面的延性性能以及弯矩-曲率-轴力三个变量相互依存和变化的全貌。结果表明：轴力对弯矩-曲率关系的影响是很大的,轴力的存在或增加使得截面较早、较快地进入塑性阶段,从而使得弯矩承载力降低,轴力的这一影响在不同的截面形式下表现也是不同的,工字形截面比矩形受到的影响更为不利。 (3)基于钢截面的相同的计算思路,推导了钢筋混凝土矩形截面弯矩-曲率关系的解析算法,可计算用于延性分析的屈服曲率和延性系数,同样得到三个变量的关系曲线。结果表明：通常情况下钢筋混凝土截面与钢截面类似,轴力的存在是不利的,轴力使得弯矩承载能力降低,然而在小纵向压力情况下,轴力的存在是有利的,随着轴压力的增加,弯矩承载力略有提高。在大轴力作用下,截面的延性显著变差。曲率越大,轴力-弯矩值越接近截面极限承载力。 (4)基于截面弯矩-曲率关系的解析算法,推导了钢筋混凝土细长柱配筋设计和强度验算的三种方法。一是数值方法的改进Newmark法,很少的简化使这一方法具有很高的精度。二是基于正弦变形曲线假设的图解分析和计算方法,能在弯矩-曲率二维图形上直观地表示出材料非线性和几何非线性的相互作用,因较少的简化和解析的计算过程而具有较高的精度和很高的计算效率。三是基于抛物线曲率分布假设和简化的极限曲率模型的图算法,简化较多,但能够推导出直接用于手算设计的诺模图,仅需计算3个基本变量和在图形中做4条辅助线,就可进行细长柱的配筋设计和强度验算,实现了钢筋混凝土柱二阶弹塑性的简单计算。 (5)钢筋混凝土柱二阶弹塑性分析结果表明：对于双侧配筋的钢筋混凝土矩形柱子,可以近似地认为柱子极限承载力等于截面极限承载力。这一假设只有极少数情况下不成立,即长细比非常大,并且一阶偏心矩非常小。钢筋和混凝土应变的限制条件,使得截面极限状态的切线刚度远大于0,因而在轴力较大时,长细比在很大范围内变化都可能出现柱子的强度破坏。
[Abstract]:The reinforced concrete columns of two order elastic-plastic problem involves coupling of both geometric and material nonlinearity. Using the finite element method requires a lot of time modeling, low efficiency. Through the analysis of existing numerical methods and the simplified method, with theoretical derivation, in cross section, inverse calculation method to determine the relationship between force and the Moment Curvature section bearing for internal force by using strain. The calculation process of full use of the constitutive relation between steel and concrete without simplification, while parsing algorithm without error iteration and convergence brought about, so it is an exact solution. In the bar, using three methods with different accuracy analysis and the two order elastic-plastic performance calculation of reinforced concrete columns, and provides a design tool for three levels.
In order to verify these calculation methods, a large number of curves were drawn by using the results of calculation. It was judged by the rationality of curve family variation and the logical relationship between curves.
(1) refer to the European standard 2, get the limit state cross section applies to our country all possible strain distribution, the ultimate strain and axial force bending moment is one-to-one correspondence, so without iteration section bearing capacity calculation directly from these strains, the calculation process of reinforced concrete rectangular and circular cross-section are obtained axis force - section moment correlation, can be used for reinforcement design section strength calculation and the short column.
(2) calculated by introducing some parameters, deduces the algorithm of relation between moment steel section of a wide scope of the curvature of the analytical expressions of rectangular and I-shaped cross section are given, the axial force and moment invariant curvature curves of axial force, axial force and bending moment curve the bending moment and curvature invariant curve, the curve reflects the section ductility and Moment Curvature and axial force of three variables are interdependent and change the whole picture. The results show that the influence of axial force on the moment curvature relationship is great, the axial force of the existence or increase the cross section earlier, fast access to plastic stage, so as to reduce the bearing capacity of the bending moment, axial force effect in different section forms under the influence is also different, the I-shaped cross section is more unfavorable than the rectangle.
(3) steel section of the same computational thinking based on the deduced analytic algorithm of relation between moment of reinforced concrete rectangular cross section curvature ductility analysis, can be used to calculate the yield curvature and ductility coefficient, also get the relation curve of three variables. The results showed that: under normal circumstances the reinforced concrete section and steel section, axial force there is a disadvantage, the axial force bending moment bearing capacity decreased, but in the case of small vertical pressure, axial force is favorable, with the increase of axial pressure, bearing capacity increases slightly. In the role of large axial force bending moment, section ductility significantly worse. The greater curvature, axial force bending moment the value of bearing capacity is close to the ultimate.
(4) parsing algorithm based on the moment curvature relationship of the section, we derive three kinds of methods of reinforced concrete slender column reinforcement design and strength calculation. The improved Newmark method is a numerical method, a few simplified so that this method has high precision. The two is a graphic sine curve hypothesis analysis and calculation method based on the energy is clearly shown that the interaction of material nonlinear and geometry nonlinear Moment Curvature in two-dimensional graphics, and has high because of less calculation process is simplified and the analytical accuracy and high computation efficiency. Three is the graph algorithm, limit curvature model curvature distribution hypothesis and simplification based on simplified more but can be deduced directly for hand design nomograms, only needs to calculate the 3 basic variables and 4 auxiliary line in the graph, can be carried out on slender column reinforcement design and strength calculation of the steel. Simple calculation of two order elastic-plastic properties of reinforced concrete columns.
(5) reinforced concrete columns of two order elastic-plastic analysis results show that the rectangular reinforced concrete columns were reinforced, can be similar to that of the bearing force is equal to the column section bearing capacity limit. This hypothesis was not only a very few cases, the slenderness ratio is very large, and a very small eccentric moment order restrictive conditions. Strain of steel and concrete, the sectional tangent stiffness limit state is far larger than 0, so in the larger axial force, slenderness ratio in a wide range of changes are likely to destroy pillars of strength.

【学位授予单位】：昆明理工大学
【学位级别】：博士
【学位授予年份】：2014
【分类号】：TU375.3

【参考文献】