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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 solution of buckling eigenvalue, the evolution equation of probability density for random buckling eigenvalues is deduced. The elastic modulus of concrete follows normal distribution and logarithmic normal distribution, and the probability density function, mean value, standard deviation and reliability of random buckling capacity of super large cooling tower are analyzed. The results show that the mean value of random buckling capacity under normal distribution assumption is close to that of buckling capacity without considering randomness, and the variability is similar to that of concrete elastic modulus. When the lognormal distribution is assumed, the first-order buckling eigenvalue deviates from the normal distribution, the mean value and the variability increase, but the reliability decreases. Regulation of the cooling tower on the overall stability and safety factor of the more conservative.