Stress evaluation of cooling towers subjected to uneven settlements with stochastic characteristics

Analytical methods to evaluate the maximum response of a rotational shell that is subjected to uneven settlements of a stochastic nature are presented. The settlements along the foundation ring are represented by a Fourier series. Each term in the series contains two coefficients: the amplitude and the phase angle. The phase angles are assumed to be random variables. Two cases are considered: when the amplitudes can be deterministically estimated, and when they are treated as random variables. In the first case, approximations of the maximum stresses in the shell are computed as a function of the standard deviations of the stresses and the predominant harmonic numbers. In the second case, the amplitude spectrum of the highest probability of occurance is obtained by the application of the maximum entropy principle that has been developed in the information sciences. Two other spectra that represent the limits of all possible spectra are generated by combining constraint equations and the maximum entropy principle.