钢筋混凝土柱稳定问题的图算法

GRAPH ALGORITHM ON STABILITY PROBLEM OF REINFORCED CONCRETE COLUMNS

基于柱子曲率分布的二次抛物线假设,采用虚功原理来计算二阶偏心距,得到简化的平衡方程。对于截面抗力,考虑完整的钢筋和混凝土本构关系,采用由应变计算内力的逆解方法来计算。对于极限曲率,将精确方法与我国《混凝土结构设计规范》(GB50010-2010)中的简化方法比较和分析,提出考虑配筋率的更为合理的简化公式。通过对坐标系的设计和构思,将平衡方程所有可能的解绘制成图形,计算3个基本变量和在图形中做4条辅助线,便可进行配筋设计,为设计人员提供了一种简单高效的手算工具。

A simplified equilibrium equation is derived by assuming a quadratic parabola distribution of column curvature and using the principle of virtual work to compute the eccentricity due to second order effects. For cross-sectional resistance, the inverse method is conducted to determine the internal force from strain based on the constitutive relationships of steel and concrete. After comparing the precise method with the simplified method in Chinese Code for Design of Concrete Structures （GB50010-2010）, a more reasonable and simple formula to determine the ultimate curvature is derived, in which the influence of reinforcement ratio is taken into account. All available solutions, which satisfy the equilibrium equation, can be drawn into a graph by designing and constructing an appropriate coordinate system. For each determining of reinforcement only three basic variables and four auxiliary lines need to be calculated and drawn in the graph respectively. The graph can be used as a simple and efficient tool for concrete reinforcement design.