{'fraction_non_alphanumeric': 0.021011162179908074, 'fraction_numerical': 0.0, 'mean_word_length': 5.17004048582996, 'pattern_counts': {'":': 0, '<': 0, '<?xml version=': 0, '>': 0, 'https://': 0, 'lorem ipsum': 0, 'www.': 0, 'xml': 0}, 'pii_count': 0, 'substrings_counts': 0, 'word_list_counts': {'cursed_substrings.json': 0, 'profanity_word_list.json': 0, 'sexual_word_list.json': 0, 'zh_pornsignals.json': 0}}
Evaluation of Localized Stresses at Spherical Pressure Vessel-to-Column Support Junction Using Closed-Form Equations


 Spherical pressure vessels (spheres) are widely used for storing liquids and gases at high pressures. The post plates of column-supported spheres are subjected to additional loads imposed by the supporting columns. The resulting localized stresses at column-to-post plate junction are difficult to analyze using analytical methods. Numerical techniques, such as the finite element method (FEM) are generally used to analyze the local discontinuity stresses.
 In this work, a finite element parametric study is performed using a wide range of sphere geometries. The stresses at various locations around the column attachment are investigated. The influence of various loadings on the local stresses is also investigated. The internal membrane forces and bending moments obtained from the finite element model are then used to establish the dimensionless curves. A step-by-step procedure and the closed-form equations are provided to calculate membrane stresses, bending stresses and the combined stresses. A table of load factors is included to estimate the maximum vertical and horizontal loads on post plate due to wind or seismic forces. Finally, a sample problem is presented to illustrate the analysis procedure. Using this easy-to-use analysis approach, the design engineers will be able to calculate the localized stresses in sphere post plates without having to utilize the finite element method.