Kye J. Han

Analysis of hyperbolic cooling towers with local imperfections

Abstract Two methods to analyse hyperbolic cooling towers with local imperfections are presented. One method relies on the finite element technique. For this a specialized finite-element program, which can model any arbitrary imperfections while retaining the advantage offered by the basically axisymmetric nature of the shell, was developed. The other method is an approximate procedure, which may be implemented with a purely axisymmetric analysis capability. The two methods are compared through numerical studies. A cooling tower shell with a bulge-type imperfection is examined under dead load and wind load conditions. It is concluded that the finite-element model presented is effective for the analysis of such shells, while the equivalent-load method may be adequate for some cases. Also, it is shown that both meridional and circumferential stress resultants may be radically influenced by a small bulge imperfection.

Quadrilateral shell element for rotational shells

Abstract A doubly curved shell element of quadrilateral shape which is suitable for the analyses of rotational shells is derived. Geometry is defined in a polar coordinate system while displacements are specified in cartesian coordinates. The element is a C° element which includes transverse shear deformations and is intended for modelling shells which follow a circular curve form in one direction.

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

Abstract 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.

Finite Element Analysis of Cylindrical Shells under Concentrated Loading

The objective of the study was to determine the most appropriate support conditions for a reinforced concrete shell panel test specimen which will adequately reproduce internal forces and moments in a prototype cylindrical shell. The goal in the experiment is to investigate a punching shear failure in the vicinity of a concentrated load. For the analysis, four computer programs were employed, SHORE-III, two versions of RONALD, and ANSYS. The SHORE-III and RONALD (rotational) analyses considered a complete cantilevered cylinder, while the ANSYS (general) model treated a cylindrical panel free along the curved edges and constrained in various ways along the longitudinal edges. Comprehensive comparative results are provided for the linear elastic loading case, which indicate the magnitude and attenuation of concentrated loading effects on cylindrical shells and panels. Also, some selected results for the panel obtained from a high performance graphic package PATRAN/ANSYS are given.

Stress analysis of hyperbolic shells of revolution with non-axisymmetrical geometric imperfections

In analyzing hyperbolic shells of revolution with non-axisymmeteric imperfections, an approximate method based on simulating the effect of imperfections by the application of fictitious normal pressure loading on the perfect shell is investigated. In the analysis of a shell of revolution with a bulge-type imperfection under non-axisymmetric loads, an efficient algorithm of applying the method is developed: the effect of individual curvature errors on stress resultants and couples are separately considered, while the interactions among various curvature errors are properly treated in the analysis by an iterative procedure. This algorithm avoids repeated analyses for non-axisymmetric loads and may be implemented with a purely axisymmetric analysis capability.A hyperbolic cooling tower shell with a bulge-type imperfection is analyzed under dead load and wind load conditions by the equivalent load method. A direct analysis of the imperfect shell is also made by a specialized finite element program. Through numerical studies, the accuracy and applicability of the equivalent load method are examined.In analyzing hyperbolic shells of revolution with non-axisymmeteric imperfections, an approximate method based on simulating the effect of imperfections by the application of fictitious normal pressure loading on the perfect shell is investigated. In the analysis of a shell of revolution with a bulge-type imperfection under non-axisymmetric loads, an efficient algorithm of applying the method is developed: the effect of individual curvature errors on stress resultants and couples are separately considered, while the interactions among various curvature errors are properly treated in the analysis by an iterative procedure. This algorithm avoids repeated analyses for non-axisymmetric loads and may be implemented with a purely axisymmetric analysis capability.