Part 1: Large Diameter Ratio Shell Intersections: Design of Large Diameter Ratio Shell Intersections Subjected to Pressure & External Loadings<\/b><\/p>\n
Determination of stresses at shell intersections due to pressure or external loadings is a complicated process that has been the subject of numerous research and testing projects. Design formulas and design curves have been developed by various investigators. <\/p>\n
Guidance for estimating stresses due to external loads, for nozzle diameter to vessel diameter ratios, d\/D, less than about one-half, is given in WRC 107 and WRC 297. WRC 107 is based on Bijlaard's theory for a distributed load over a rectangular area of the surface of a vessel: there is no opening in the vessel and there is no nozzle. WRC 297 is based on Prof. Steele's shell theory for a nozzle, with diameter d and thickness t, in a vessel, with diameter D and thickness T. The elastic solution is based on dimensionless parameters d\/D, D\/T and t\/T. Guidance for estimating stresses due to internal pressure, for d\/D less than about one-half, is given in WRC 383. This guidance is also based on Prof. Steele's Shell theory. <\/p>\n
With the advent of finite element analysis, an intersection may be modeled and stresses calculated with a reasonable degree of accuracy. However, the number of openings in pressure vessels may be numerous, making the routine application of finite element analysis uneconomical or impractical. Therefore, easily applied design tools are desired. <\/p>\n
Part 2: Large Diameter Ratio Shell Intersections: Parametric Finite Element Analysis of Large Diameter Shell Intersections (Internal Pressure) <\/b><\/p>\n
Cylindrical shell intersections are configurations commonly used in many industries, such as pipeline transportation, nuclear and power engineering, chemical and petrochemical engineering, aerospace, etc. Under internal pressure or external loadings, points of weakness occur at the intersection due to the presence of stress concentrations. The study of stress concentration and the influence of the geometric parameters on the maximum stresses at shell intersections due to various loadings thus have great practical value. In the past thirty years, considerable effort has been expended by stress analysts and designers all over the world in attempts to achieve a reasonable design procedure for shell intersections. WRC 386 provides guidance for the evaluation of shell and nozzle stresses due to internal pressure. However, the design formulas proposed in this Bulletin are limited to diameter ratios, d\/D, less than 0.5. For large diameter ratio (0.5 < d\/D < 1.0) shell intersections, the design procedures are still in need of improvement. In this report, a parametric study of large diameter ratio cylindrical shell intersections is performed. Sixty-nine models, which cover most of the practical cases of cylinder intersections, have been investigated. The ranges of geometric parameters included in this study are shown in Table 1. Many prior investigations, such as Widera, have shown that the stress concentration at the shell intersections can be accurately predicted by finite element analysis if the element type and the mesh density in the vicinity of the intersection are properly chosen. Therefore, the finite element method is employed in carrying out this parametric study. A cantilever model, employing a quadratic shell element is used for this project. The justification for these of this shell element rather than the 20-node 3-D element is given later on in the report. The purpose of this part of the study is to provide some data which can serve as the basis for the development of a more accurate design of large diameter ratio shell intersections under internal pressure.<\/p>\n
Part 3: Large Diameter Ratio Shell Intersections: Parametric Finite Element Analysis of Large Diameter Shell Intersections (External Loadings) <\/b><\/p>\n
Cylindrical shell intersections are configurations commonly used in many industries, such as pipeline transportation, nuclear and power engineering, chemical and petrochemical engineering, aerospace, etc. Under internal pressure or external loadings, points of weakness occur at the intersection region due to the presence of stress concentrations. The study of stress concentration and the influence of the geometric parameters on the maximum stresses at shell intersections due to various loadings thus have great practical value. In the past thirty years, considerable effort has been expended by stress analysts and designers all over the world in attempts to achieve a reasonable design procedure for shell intersections. WRC 107, which is based on Bijlaard's work, and WRC Bulletin 297, which is based on Steele's work, provides guidance for the evaluation of shell and nozzle stresses due to external loadings. However, for large diameter ratio (0.5 < d\/D < 1.0) shell intersections under internal pressure and external loadings, the design procedures are still in need of improvement. A comprehensive parametric study of large diameter ratio cylindrical shell intersections subjected to internal pressure and external loadings is being conducted. The configuration employed in this parametric study is idealized and consists of two thin shell cylinders intersecting normally with no transitions, reinforcements, or fillets in the junction region. This parametric study is divided into two phases. Phase I is for internal pressure while phase II is for external loadings. The final report for phase I is presented in Part 2 of this Bulletin. The Phase II of this project is concerned with a parametric study of large diameter ratio cylindrical shell intersections subjected to external loadings. The external loadings considered in this study are in-plane moment on the nozzle, out-of-plane moment on the nozzle, and axial force on the nozzle. The range of diameter ratios (d\/D) covered in all parts of this Bulletin is 0.333 = d\/D = 1.0. A 4-node shell element is employed in the analysis of large diameter ratio shell intersections. First, the method of determining the maximum stress of a shell intersection is determined. Next, two shell intersections with d\/D equal to 0.5 and 1.0 are analyzed and the finite element predicted maximum principal stresses are compared with the experimental data. Then, modeling parameters for all 43 finite element models are determined and all 43 finite element models are created and analyzed. Finally, the correlation equations are developed. The parametric finite element analysis of large diameter shell intersections subjected to various external loadings was investigated in this report. A 4-node shell element was employed in this analysis. It was found that: (1) The present finite element results are in excellent agreement with ORNL-1, ORNL-2 and Moffat's experimental data; therefore, it is believed that the present modeling procedure is suitable and the present finite element results are reliable, and (2) based on very long vessel and nozzle models, the FEA predicted maximum stress intensity ratios can serve as the basis of the design of shell intersections under various external loadings.<\/p>\n","protected":false},"excerpt":{"rendered":"
Large Diameter Ratio Shell Intersections: Part 1, Part 2 and Part 3<\/b><\/p>\n\n\n
\n Published By<\/td>\n Publication Date<\/td>\n Number of Pages<\/td>\n<\/tr>\n \n WRC<\/b><\/a><\/td>\n 2004<\/td>\n 67<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n","protected":false},"featured_media":697059,"template":"","meta":{"rank_math_lock_modified_date":false,"ep_exclude_from_search":false},"product_cat":[2677],"product_tag":[],"class_list":{"0":"post-697049","1":"product","2":"type-product","3":"status-publish","4":"has-post-thumbnail","6":"product_cat-wrc","8":"first","9":"instock","10":"sold-individually","11":"shipping-taxable","12":"purchasable","13":"product-type-simple"},"_links":{"self":[{"href":"https:\/\/pdfstandards.shop\/wp-json\/wp\/v2\/product\/697049","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/pdfstandards.shop\/wp-json\/wp\/v2\/product"}],"about":[{"href":"https:\/\/pdfstandards.shop\/wp-json\/wp\/v2\/types\/product"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/pdfstandards.shop\/wp-json\/wp\/v2\/media\/697059"}],"wp:attachment":[{"href":"https:\/\/pdfstandards.shop\/wp-json\/wp\/v2\/media?parent=697049"}],"wp:term":[{"taxonomy":"product_cat","embeddable":true,"href":"https:\/\/pdfstandards.shop\/wp-json\/wp\/v2\/product_cat?post=697049"},{"taxonomy":"product_tag","embeddable":true,"href":"https:\/\/pdfstandards.shop\/wp-json\/wp\/v2\/product_tag?post=697049"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}