考虑混凝土材料变异性的超大型冷却塔随机屈曲承载力分析

ANALYSIS OF RANDOM BUCKLING BEARING CAPACITY OF SUPER-LARGE COOLING TOWERS CONSIDERING THE VARIATION OF THE PROPERTY OF CONCRETE

基于屈曲本征方程的形式解推导出随机屈曲本征值满足的概率密度演化方程。取混凝土弹性模量服从正态分布及对数正态分布,分析了超大型冷却塔随机屈曲承载力的概率密度函数、均值、标准差及可靠度。结果表明:正态分布假定时随机屈曲承载力的均值与不考虑随机性的屈曲承载力十分接近,其变异性与混凝土弹性模量的变异性相似。而对数正态分布假定时,一阶屈曲本征值偏离了正态分布,均值及变异性增大,但可靠度降低。规范关于冷却塔整体稳定安全系数的规定偏于保守。

Based on the formal solutions of the buckling eigen equation, the probability density evolution equation for the random buckling eigenvalue is derived. By assuming that the elastic modulus of concrete follows normal and logarithm normal distributions respectively, the probability density function （PDF）, mean, standard deviation and reliability of the buckling bearing capacity for a super-large cooling tower are analyzed. The results indicate that the mean buckling bearing capacity based on normal assumption is very close to the one with the deterministic parameter, and its variation is the same as the elastic modulus of concrete. For the logarithm normal assumption, however, the PDF of buckling bearing capacity deviates normal distribution, while the corresponding mean and variation increase but the reliability decreases. The safety factor for the overall buckling of cooling towers required in the design standard is relatively conservative.