On the buckling problem of a pressure vessel torispherical head due to internal pressure

The torispherical head of a circular cylindrical pressure vessel subjected to internal pressure can buckle if the head is very thin and the pressure is high enough. Previously, Aylward and Galletly analyzed this problem by the finite element method, considering the nonlinear prebuckling deformation. In this paper a numerical method is presented for buckling problems of the general axisymmetric shell, including consideration of its nonlinear behaviors in the prebuckling state. By using this method, the buckling problem of the torispherical head treated in Galletly's study is solved, and the results obtained by the present method are compared with Galletly's. It is found that the results coincide closely enough for practical purposes.     

Pressure testing of large-scale torispherical heads subject to knuckle buckling

Two fabricated steel torispherical heads were tested under internal pressure to determine their buckling and rupture strengths. Both models had cylindrical diameters of 192 in, knuckle radii of 32·64 in, sphere radii of 172·8 in and measured thicknesses of 0·196 in (Model 1) and 0·270 in (Model 2).For Model 1, initial buckling was noted at 58 psi. Pressurization was continued to rupture at 229 psi. During the test, 14 buckles formed and a maximum strain of 3·5% was recorded in the spherical portion of the model.For Model 2, initial buckling was noted at 106 psi. Pressurization was continued to rupture at 332 psi. During the test 14 buckles formed and maximum strains of 4·3–4·7% were recorded in the spherical portion of the model.     

Radial flexibility of welded-pad reinforced nozzles in ellipsoidal pressure vessel heads

A thin shell analysis was performed to investigate the radial flexibility of welded-pad reinforced nozzles in ellipsoidal pressure vessel heads. A comparison of the flexibility of such a nozzle to that of an integrally reinforced nozzle was made. The effect of size and thickness on flexibility was studied. A parametric study was performed for welded-pad reinforced nozzles in ASME 2:1 pressure vessel heads. Results are presented as flexibility factors which are functions of nondimensional nozzle-vessel geometries.     

Flexibility factors for nozzles in the knuckle region of dished pressure vessel heads

Nozzles in the spherical part of pressure vessel heads may be designed according to BS5500 and/or with the solutions based on the work of Bijlaard. However, no solution has been available so far if the nozzle is in the knuckle region of the pressure vessel head. Furthermore the restraint forces and moments at the nozzles and thus the stresses due to them may be reduced if the flexibility of the support at the nozzle is taken into account in the calculation. This paper reports on the flexibilities and how they can be taken into account in the design.     

Stress concentration factors for nozzles in ellipsoidal pressure vessel heads due to thrust loads

A theoretical elastic analysis of the stresses due to a thrust applied to a radial nozzle in an ellipsoidal pressure vessel head has been carried out. The nozzle can be either flush or protruding. The results, in the form of stress concentration factors and shear stress concentration factors in the ellipsoidal shells, are presented as graphs of non-dimensional shell parameters.     

Stress concentration and flexibility factor of nozzles in ellipsoidal pressure vessel heads subject to external moment

Ellipsoidal heads are commonly used as end closures for cylindrical pressure vessels in chemical and process industries. In the design of nozzles in pressure vessels, stress and flexibility of the nozzle-vessel structure are important factors to be considered. In this paper, a parametric study of radial nozzles in ellipsoidal vessel heads, when the nozzles are subjected to overturning moments, is presented. The computer program KSHEL, which is based on elastic thin shell theory, was utilized. Stress concentration factors and flexibility factors were determined and are presented as graphs of dimensionless nozzle-vessel parameters.     

Buckling under external pressure of cylinders with either torispherical or hemispherical end closures

In a number of applications, the actual boundary conditions at the ends of a cylinder are not taken into account properly when the structure is being designed against buckling. For example, in the design of submersibles the older theoretical treatments assume that bulkheads are present at the ends of the cylinders, whereas this form of construction is not always used.The purpose of the investigation described here is to study the effect of realistic boundary conditions on the elastic buckling pressure of unstiffened cylinders with torispherical or hemispherical end closures. In the present study only perfect, initially stress-free, structures are considered and their theoretical buckling pressures are obtained from a variational finite-difference program written for the digital computer.The numerical results presented were obtained from a limited parametric survey of the problem. In the main, linear buckling theory was used. However, as is shown, this can sometimes lead to unsafe predictions.The buckling pressures for the cylinders with hemispherical end closures, as predicted by the variational finite-difference technique, are also compared with a modified von Mises formula with corrections for the end closures. The agreement between the two sets of predictions was good within the range of the survey.     

Elastic buckling of,and first yielding in,thin torispherical shells subjected to internal pressure

With the aid of the non-linear shell buckling computer program BOSOR 4, the internal pressures at which elastic circumferential buckling (or wrinkling) take place in thin torispherical shells have been calculated. The maximum equivalent (or effective) stresses in the shells in the axisymmetric pre-buckled state were also obtained; from these, the pressures at which first yielding in the shells commences were determined for $\text{1 <}\text{σ}{}_{\mathrm{<mtext>yp</mtext>}}\text{E}\text{× 10}{}^3\text{< 4}$The calculations were performed for shells with $\text{diameter}\text{thickness}$ ratios of 500, 1000 and 2000; other geometric ratios, as detailed in the paper, were also varied. The computations were carried out for steel shells but the results have been presented in dimensionless form.Utilising the above results it is possible to determine whether a given torispherical end closure will buckle elastically or whether an elastic-plastic analysis of the shell is desirable. Factors which are conducive to elastic buckling are a high yield point, a low modulus of elasticity or a large value of the shell diameter-thickness ($\text{D}\text{t}$) ratio. For steel shells, elastic internal pressure buckling will occur (for some combinations of $\text{r}\text{D}$ and $\text{R}{}_{\mathrm{<mtext>S</mtext>}}\text{D}$) for $\text{D}\text{t}\text{= 2000}$ and $\text{σ}{}_{\mathrm{<mtext>yp</mtext>}}\text{E}\text{= 3 × 10}{}^{\mathrm{?3}}$. For $\text{D}\text{t}\text{= 1000}\text{and}\text{500}$, first yield always precedes elastic buckling for the parameters investigated. The failure mode for these cases is either elastic-plastic buckling or plastic collapse (an axisymmetric mode with large deformations).A comparison of the results of linear and non-linear elastic axisymmetric stress analyses of the shells shows that the linear theory sometimes underestimates the first yield pressure by considerable amounts. Limit pressures obtained from small-deflection shell theories can be too low in such cases.Also given in the paper are approximate simple expressions whereby the elastic internal buckling pressures of torispherical shells may be calculated. These expressions should be useful to designers.     

On the estimation of stress concentration and flexibility at nozzles in ellipsoidal vessel heads

The US Welding Research Council Bulletin Number 107 (WRC-107) is currently being used by many designers in the estimation of stress concentrations at nozzle-vessel junctures. The validity of the application of this design document to the case of nozzles in ellipsoidal vessel heads is studied in this paper. A number of comparisons of the stress intensity and flexibility at the nozzles between approximate approaches and the exact situation were made and discussed.     

Recent experience in pressure vessel materials irradiation

The reactor pressure vessel has been repeatedly cited as a primary concern in assessment of pressure boundary structural integrity and in planning for plant life extension programs. The life of the reactor pressure vessel will be limited by radiation-induced embrittlement; this is monitored in Westinghouse designed nuclear steam supply systems by testing samples of base metal, heat-effect-zone and weld metal in the form of Charpy V-notch, tensile, and fracture mechanics specimens which have been irradiated in surveillance capsules adjacent to the wall. The earliest reactor vessel material radiation surveillance program was the Yankee Rowe program which started in 1961. As data became available from power reactor surveillance and test reactor programs, estimates of radiation-induced changes in mechanical properties were predicted in the form of radiation damage trend curves which provide methods for calculating numerical estimates of changes in mechanical properties as a function of chemistry and fluence. For example, the proposed Revision 2 to Regulatory Guide 1.99 provides estimates of shifts in transition temperature as a function of copper and nickel content and fluence. Slight variations in chemical analyses for copper and/or nickel can result in limitation on heat-up and cool-down rates or compliance with regulatory rules, such as the PTS screening criteria. Automatic submerged arc welding was employed in the fabrication of reactor vessels in Westinghouse designed nuclear steam supply systems. The type of flux material utilized in the welding process is important because mechanical properties can differ depending upon what flux is used. This paper correlates the results from over 50 surveillance capsules with the welding practice and concludes that radiation damage trend curves can be developed for welding practice. By using trend curves based on welding practices, discrepancies in chemical analyses are eliminated and credibility is restored to structural integrity assessments.     

压力容器制造中的变形问题探究

随着时代的不断进步,压力容器在各行各业之中的应用频率越来越高.但是考虑到压力容器生产属于一项复杂的工作,其质量必定会受到诸多因素的影响,进而造成各种问题,而变形就是需要重点应对的问题.本文对压力容器制造中的变形问题进行分析,确保能满足压力容器制造要求.     

A classification system in pressure vessel production

This is the final part of a three part review. The feasibility of applying the group technology technique to the pressure vessel industry is investigated. The classifications of shape and operations are found to give considerably greater flexibility in the planning of production than classification by function. Suitable workshop layouts are discussed.     

浅谈高压储氢压力容器材料选用

高压储氢容器作为现今主流高压气态储氢方式常用的压力容器,长期在高压临氢工况下运行,本文从储氢容器的使用条件、材料性能、制造工艺、经济合理性和标准规范要求等方面介绍了高压储氢压力容器材料选用.     

In-service supervision of a prestressed concrete pressure vessel

On-line measurements of the physical state of a prestressed concrete pressure vessel, and comparison with the design predictions of the distribution of temperature, strain and stress within the concrete member and the criteria of layout, provide an efficient and economical method of operating the vessel with a high potential of safety. The requirements of instrumentation and the comparison with static calculations are discussed with reference to the prototype vessel at Seibersdorf Research Centre during the phase of construction and prestressing, the phase of the first thermal treatment (stabilization), the pressure tests and under the operating conditions of a high temperature reactor (150°C, 50 bar).