Abstract Steel storage tanks are critical components of an industrial installation due to their high seismic vulnerability and containment of hazardous materials. Failure of a which, may lead to loss of containment (LOC) triggering domino effects such as explosion, environmental pollution, loss of functionality and disruption of business. Past earthquakes have demonstrated different type of failure modes in steel storage tanks. Although there are plenty of studies related to different failure modes like elephant foot buckling or tank uplifting, there are very few efforts on the sliding behavior of tank. Large displacements caused by the tank sliding can lead to pipe detachment and release of hazardous material which might cause damage propagation. Consequently, this damage state is very important for the Quantitative Seismic Risk Assessment of industrial plants. In order to enumerate the sliding displacement of unanchored steel storage tanks, a simplified numerical model realized with OpenSees platform is proposed. The friction model used in OpenSees is calibrated with the results obtained from ABAQUS FE model. Sliding response of tanks with different D/H ratio is analyzed using the simplified model. Fragility curves for the tank sliding damage state are analytically evaluated for different D/H ratio of the tank using the “cloud method”. Finally, a parametric study is conducted in order to comprehend the influence of different parameters on the sliding behavior such as friction coefficient, tank filling level and the influence of the vertical component of ground motions.

Abstract Buckling and fatigue evaluation of braced piping supports was conducted using numerical analysis. Buckling and fatigue occurred on the piping support during vibration and static load tests. A numerical model for the evaluation was developed, and the load–displacement relationship and local strain obtained by the numerical analysis were in good agreement with experimental results. Thus, the numerical model was validated. Buckling and fatigue evaluations were subsequently conducted using the model. In the buckling evaluation, the experimental buckling load was in good agreement with that obtained by Johnson’s formula. Fatigue evaluation was conducted to investigate whether fatigue crack had occurred before the rupture on the piping support. The linear cumulative damage was calculated, suggesting the possibility of fatigue crack formation. Ductile rupture was considered to occur after the fatigue crack formation.

Abstract Failure modes of piping systems under seismic motions were discussed for several decades if the fatigue failure is dominant or there is some possibility that the plastic collapse could occur. A handful of ratchet-buckling failure observed in Pipe Fittings Dynamic Reliability Program by EPRI was frequently taken up as the evidence of the plastic collapse, and inclusion of seismic response on structures into the Primary stress evaluation for piping systems in the code evaluation was considered to be conventionally justified. Although prevention of the plastic collapse type failure is the purpose of imposing the Primary stress evaluation, the other experimental tests conducted in several countries for decades were unable to represent the plastic collapse of piping components exposed to seismic loading and the discussion was abandoned for a while. However, the drastically increased design seismic motions for nuclear power plants due to several huge earthquake occurred in Japan reminded us of exploring the fact of the plastic collapse and the necessity of the Primary stress evaluation. The load classification concept proposed by the authors introduces 3 conceptual force terms from the equation of motion to clarify the seismic loading from the aspect of the correlation of the said force terms. Based on the finding from the concept that the input force amplitude is to be evaluated for Primary stress, the gross-plastic deformation on a single cantilever with elastic-plastic analyses using multiple of single-cycle sinusoidal forcing functions was compared with the input force term. When the plastic collapse is defined as a gross-plastic deformation, the level of plastic collapse was found to be possibly anticipated with a static force evaluation that can be substitute for the conventional Primary stress evaluation with the dynamic response analysis.

Abstract In recent years, with the rapid development of solar thermal power technology in China, the key equipment molten salt storage tank is widely used. Instability is the primary failure mode for these large thin-walled structures. Thus, stability design for the molten salt storage tanks is significant. In this paper, the elastic and elastic-plastic buckling analyses of a spherical latticed shell are carried out with whole process load-deformation method considering geometric and material non-linearity. The critical buckling loads of these two analysis types are obtained from the load-deformation curve. Comparison between spherical latticed shells with channel beam and I-section beam is presented. The modeling method of finite element model for buckling analysis of latticed shell is discussed. This may provide a reference to the stability design of large scale storage tank.

Abstract In engineering, thin-walled cylindrical shells subjected to axial compression load are very sensitive to geometric imperfections and are prone to buckling. However, how to reasonably take into account the influence of geometric imperfections on the load carrying capacity of thin-walled cylindrical shells is always the bottleneck of light-weight design of these structures. In this paper, four perturbation load approach (4PLA) is adopted to consider the influence of geometric imperfections. By judging the potential buckling status of cylindrical shells, a new improved design method based on 4PLA for thin-walled cylindrical shells is proposed, in which the influence of radius-to-thickness ratio, length-to-radius ratio, Young’s modulus and material yield strength are systematically considered. Correspondingly, the buckling tests for two steel cylindrical shells with the same geometric and material parameters are conducted. Compared with the experimental results and other test results in open literatures, the superiority and safety of proposed method for the preliminary design of thin-walled cylindrical shells are validated.

Abstract Access opening is a key geometric feature of vertical vessel skirts. To ensure the structural stability of skirts, buckling strength reduction caused by openings shall be numerically evaluated. In the previous study, Buckling Strength Reduction Factor ( BSRF ) was introduced as a design factor representing the effects of openings. However BSRF is based on the elastic bifurcation buckling under axial compressive load. The relations between BSRF and practical design conditions, such as bending moment, material plasticity, and local deformation, are not yet evaluated. The purpose of this paper is to develop the buckling design method for vertical vessel skirts with access opening by investigating the relation between BSRF in consideration of practical design conditions and conventional design concepts for straight cylinder. The finite element analyses of buckling strength were conducted for cylindrical shells with and without openings under bending moments. In addition, nonlinear buckling behaviors of skirts with opening were studied by elastic-plastic analyses and limit-load analyses. These studies revealed the relation between BSRF and conventional buckling design concepts. Based on these results, a new buckling design approach which includes the application BSRF was proposed. This proposed approach provides a practical guide for buckling design of vertical vessel skirts with access opening.

Abstract For the required thickness estimation against buckling in the elevated temperature design, the external pressure chart for two kinds of ferritic steel, 2 1/4Cr-1Mo and Mod.9Cr-1Mo steel, was developed. On the basis of the guideline described in the ASME BPVC Section II, Part D, Mandatory Appendix 3 with mechanical and physical properties provided in the JSME fast reactor code, the external pressure charts for each material were constructed. The minimum stress-strain curve for evaluating the external pressure chart was applied the stress-strain equation with design yield strength, S y , provided by the JSME fast reactor code. As a result, three external pressure charts with digital values were proposed for elevated temperature design. Moreover, the rationalization effect from the current alternative was evaluated by the sample problem. This proposal resolves two issues. One is alternative use of chart for lower strength material over the 150 °C. The other is the external pressure chart above 480°C for which ferritic steels are not available.

Abstract Ellipsoidal and torispherical heads, whose geometric shapes are close, are usually used as end closures of internally pressurized vessels. In pressure vessel codes, for example, ASME BPVC Section VIII, ellipsoidal heads are designed as torispherical heads using geometric equivalency approaches. However, the difference between ellipsoidal and equivalent torispherical heads has not been studied in detail. In this paper, we first investigate the shape deviation between the two types of heads. Then we compare the elastic-plastic behaviors between ellipsoidal and equivalent torispherical heads as well as their failure modes, i.e., buckling and plastic collapse. It is found that ellipsoidal heads have more buckling resistance than equivalent torispherical heads, indicating that the current design rules for buckling failure based on the geometric equivalency approaches result in uneconomical design. Nevertheless, the shape deviation has little effect on plastic collapse pressures of ellipsoidal and equivalent torispherical heads, showing that the geometric equivalency approaches are applicable for such heads that fail by plastic collapse (bursting). In addition, the experimental and numerical results show that such heads experience geometric strengthening. The FE method considering the effect of geometric strengthening provides a good prediction about plastic collapse (bursting) pressure. However, the current design equation for bursting does not consider the effect of geometric strengthening, also leading to uneconomical design. Therefore, in order to avoid uneconomical design, we recommend that (1) with respect to the buckling of ellipsoidal heads, a new design equation be proposed rather than implementing the geometric equivalency approaches, and (2) the current design equation for bursting be deleted, and a new design equation, considering the effect of geometric strengthening, be proposed for the bursting of ellipsoidal and torispherical heads subjected to internal pressure.

The current paper examines the effects of corrosion induced wall thinning on buckling of domed closures onto cylindrical vessels. It is assumed that corrosion is axisymmetric and that the wall is corroded on inside, only. The ratio of corroded wall thickness, t c , to the non-corroded thickness, t, is varied between 0.10 ≤ t c /t ≤ 1.0. Both depth of corrosion and its meridional extend are varied during numerical calculations. Three modelling scenarios for placement of corrosion are considered: (i) corrosion confined to the knuckle, (ii) corrosion spanning evenly the knuckle and spherical parts, and (iii) patchtype area positioned at the apex. Numerical results indicate that the following factors influence buckling performance of the dome: (i) meridional position of corroded area, (ii) depth of corrosion itself, and (iii) meridional span of corroded wall. For example, wall thinning of 10 % over 10 % of meridional length causes almost 20 % drop in buckling strength. The largest drop of load carrying capacity is found when the corroded wall is at the knuckle/crown junction. Here it is shown that assessment of strength based on the collapse mechanism is not only wrong but dangerous. For the case of the corroded dome, the collapse pressure overestimates the load carrying capacity associated with asymmetric bifurcation buckling by 40 %.

This paper describes the failure of a jacketed vessel. The product pressure is 16 barg (inner vessel; D = 2200 mm) and is heated with thermal oil in the jacket (operated at 4barg). The jacket is split up in different zones which can be opened and closed separately. After a shut down, several valves were not opened properly. This resulted in blocking-in of the jacket on the top head of the vessel during the start-up and operation of the vessel. The vessel was heated to the operating temperature (±250°C), causing a pressure increase of the blocked-in thermal oil. The jacket has a wall thickness of 10 mm, and the vessel head has a wall thickness of 22 mm. Because of the pressure increase, failure occurred at a nozzle weld on the inner pressure vessel shell. This resulted in a leakage of thermal oil into the vessel. The jacket itself deformed but did not fail. Based on a detailed FE analysis, it has been concluded that failure occurred as a result of (local) buckling of the 22mm thick elliptical head (diameter of ±2.200mm). This paper describes the failure that occurred and the assessments performed to determine and validate the root cause of the failure. A level 3 assessment according to ASME VIII div 2 Part 5 (1) was used to determine if the vessel is still safe for operation.

Buckling behavior of tanks with a conical roof under harmonic settlement has been researched in this paper. A real tank in engineering is taken into account and the harmonic settlement is applied to the bottom of the tank to simulate its buckling behavior. Results show that the tank wall will be subjected to a deformation mutation when the settlement reaches a critical value. It means that compared to the conical roof, the tank wall is more vulnerable to buckling. Because of the complexity added by the grid of rafters and rings on the roof, two different simplified models are presented. For the first model, the tank’s roof is modified to an equivalent thickness based on the smeared method; for the other one, the roof is completely eliminated and its influence is represented by simply supported boundary conditions at the top of the tank wall. Analysis shows that the tank model without a roof can’t reflect buckling behavior of the real tank in engineering very well. While the model with an equivalent thickness roof can avoid this deficiency and achieve high efficiency and accuracy. It’s recommended to be applied to buckling analysis of tanks under settlement. Based on that, effects of wave numbers on the critical settlement for the three models are researched and compared. Result shows that the simplified tank model with an equivalent thickness roof presented in this paper is efficient and useful for buckling analysis of tanks with a conical roof under settlement.

The main failure mode of a large vacuum spherical tank, subjected to uniformly external pressure, is buckling of thin shell. Taking a large vacuum spherical tank with volume of 18000m 3 for research objects, the different calculation methods of buckling pressure between the ASME standard, analytic method and finite element method, were compared and analyzed. Using ANSYS software, the buckling pressure of stiffened spherical tanks were analyzed, and the optimum design of the thickness, height and quantity of stiffeners are studied. The results of analysis showed that the anti-instability ability of the large vacuum spherical tank can be improved significantly by a reasonable arrangement of stiffeners.

Thermal load is one of the most important design conditions that should be considered carefully in engineering practice. Most inner-pressure vessels suffer thermo-mechanical ratcheting or unacceptable plastic deformation under cyclic thermal stress produced by inside heat source and pressure-induced primary stress. However, thermal load is also a crucial factor for external-pressure vessels where the failure model of buckling should not be ignored. The effect of thermal load on buckling is not only thermal stress itself but also shape distortion due to thermal load. In some cases, the latter is more important. In this paper, an external-pressure thin-walled ellipsoidal head with heating jackets has been studied. The temperature of this structure is uniformly distributed along the thickness direction but changes alternately between hot and cold along the meridional direction, which will have a significant effect on buckling behavior of this typical structure. Buckling load is sensitive to initial defect and small deformation. Several comparative calculations based on nonlinear buckling analysis have been conducted and some laws are established. Finally, some useful conclusions and suggestions are proposed for engineering design.

In this study, the fundamental mechanical inelastic behavior of piping supports was investigated in order to consider an effective elastic-plastic evaluation method. High-acceleration vibration tests were conducted using the resonance shaking table installed in Central Research Institute of Electric Power Industry (CRIEPI), and the ultimate limit states of piping supports under vibration conditions were observed. Each specimen had an outer diagonal brace. Buckling or fatigue failure occurred in the vibration test. Fatigue failure did not occur in the static load test. The static and dynamic skeleton curves were in agreement with each other when the failure mode was the same. When the response load did not reach the buckling load in the vibration test, fatigue cracks occurred after the stable response. The locations of the fatigue cracks tended to be where the local buckling occurred in the static tests. In both the vibration and the static load tests, even if the load decreased after the maximum load by buckling, the reaction force of approximately one third of the maximum load was seen, and the reaction force did not become 0 kN.

It is important in the confirmation of the safety of the nuclear power plant to clarify the response behavior of a vertical cylindrical water storage tank under seismic motion. When a vertical cylindrical tank is shaken by a large earthquake, deformation of side shell due to the elephant foot buckling, the oval vibration etc. may occur. The occurrence of those deformations depends on materials, shapes, stored water level and time history of seismic motion. Then, response behavior was obtained for a condensate storage tank (CST) model under large seismic motion such as standard earthquake Ss multiplied by 2 with the elastic-plastic finite element calculation. In this calculation, dynamic water pressure and elastic-plastic characteristics of the material were taken into account. In this case, the elephant foot bulge did not occur but the oval vibration of side shell became dominant. Based on the result, we estimated the structural integrity of the tank.

Recently high grade pipeline project have been planned in hostile environment like landslide in mountain area, liquefaction in reclaimed land or the frost heave in Polar Regions. Geohazards bring large scale ground deformation and effect on the varied pipeline to cause large deformation. Therefore, strain capacity is important for the pipeline and strain based design is also needed to keep gas transportation project in safe. High grade steel pipe for linepipe tends to have higher yield to tensile (Y/T) ratio and it has been investigated that the lower Y/T ratio of the material improves strain capacity in buckling and tensile limit state. In onshore pipeline project, pipe usually transported in 12 or 18m each and jointed in the field. Girth weld (GW) is indispensable so strength matching of girth weld towards pipe body is important. In this study strain capacity of Grade X70 high strain pipe with size of 36” OD and 23mm WT was investigated with two types of experiments. One was a pipe bending test with whole pipe. The length of the specimen was approximately 8m and GW was made in the middle of joint length. A fixed internal pressure was applied during the bending test. Actual pipe situation in work was simulated and both circumferential and longitudinal stress occurred in this test. The other test was curved wide plate (CWP) test. In both tests, test pipes were cut and welded using GTAW in the first two layers and GMAW for the subsequent passes. Welding wire of TG-S62 and MG-S58P were used for GTAW and GMAW respectively to achieve over-matching girth weld considering the pipe body strength. Elliptical EDM notch was installed in the GW HAZ as simulated weld defect. In pipe bending test, buckling occurred at the intrados at 300 mm apart from the GW. 2D average compressive strain at buckling was 3.59% and this high compressive strain was considered to derive from the high strain capacity of this pipes. After the buckling, deformation concentrated to the buckling wrinkle. Test pipe broke at 35.5 degrees of pipe end rotation and the location was in base metal at the extrados opposite to the buckling wrinkle. The HAZ notch opened and CTOD was 1.44 mm and the global strain in 2D length average strain was 7.8%. In CWP test, tensile strain simply got large and pipe finally broke at global strain of 9.6% and CTOD of 15 mm. The break location was the HAZ notch. There was a significant difference in CTOD growth in HAZ between two test types. Conditions and factors that effect to these differences are argued in this paper.

Post weld heat treatment (PWHT) is often applied to welded pressure vessels and piping to increase the mechanical and metallurgical properties. During the PWHT, a pressure component made of a carbon steel to which PWHT is applied, is heated up to the temperature around 620 deg.C with +/− 25 deg.C tolerances and that elevated temperature is kept for 1 to 2 hours. The local PWHT of the vertical pressure vessel is sometimes planned at a construction site with vertical position, because of some restrictions relating to construction, such as limited access route to the vessel location, and limited space large capacity cranes. In the situation, it is important to assure the structural stability during PWHT. Except wind loads, it is considered that the stress applied in the shell during PWHT is usually not significant, however there have been no published strength criteria corresponds to the PWHT conditions. In this paper, the new elevated temperature tensile tests and constant stress creep strain tests of A516-Gr.70, a typical carbon steel material for pressure vessels, are conducted. Several examples of the numerical analysis using isochronous stress strain curve considering creep effect are presented. From the test result, the importance of the consideration of the creep deformation on the structural integrity assessment of PWHT operation is clarified.

The ASME Boiler and pressure vessel code Section VIII Division 2 and the European unfired pressure vessel code EN13445 Part 3 Design by Analysis parts dealing primarily with steel pressure vessels have been around for the last ten to fifteen years. The culmination of work on pressure vessel design by analysis address failure modes directly and are very efficient in order to guarantee that the designed and fabricated steel pressure vessels are fit for their purpose. The ASME Boiler and pressure vessel code Section X and the European codes BS EN13923 and BS EN13121 are some of the existing codes that cover design methods for composite pressure vessels. In these codes various failure criteria and damage mechanics models are possible but as such no comprehensive and robust design by analysis methods have been effectively established to encapsulate all composite pressure vessel failure modes. For instance the design of fibre-reinforced composite pressure vessels is still heavily reliant on experimental testing and prototype verification as opposed to the well-established design by analysis methods applicable to steel pressure vessels. Nonetheless a number of damage mechanics models ranging from mesoscale to microscale models have been established in other research work done on composite materials. This paper reviews the different composite pressure vessel design methods identified in the codes and standards and assesses damage mechanisms that can be used within a design by analysis context to design against possible modes of failure such as the limit load mode of failure, the progressive deformation mode of failure, the fatigue mode of failure and the buckling mode of failure. Damage mechanisms can also be used to develop criteria that allow a stress analyst deduce whether the material has failed, how it has failed and whether it has lost its capability to carry the load actions applied to it. The paper also highlights requirements for design methods based on the finite element method, and the necessary experimental validation required for different damage mechanisms leading to the different modes of failure.

Vertical vessel skirts generally have access openings. The evaluation for buckling of vertical vessel skirts shall consider the effect of the opening. On the other hand, evaluation methods of buckling in present design codes are established based on the theory for a cylindrical shell without any opening. There is no method to assess effects of openings on buckling strength. The purpose of this paper is to establish a new design method of vertical vessel skirts with access openings, by evaluating the effects of openings on buckling strength of cylindrical shells. The finite element analyses of buckling strength for cylindrical shells with and without openings were conducted by an eigenvalue analysis. A study was conducted on the effects of geometric parameters, such as skirt diameter, thickness, opening shape and application of reinforcements. The effects of openings on buckling strength were revealed by comparing the analysis results. Based on these results, the new design factor, Buckling Strength Reduction Factor (BSRF), was proposed for evaluating buckling strength. BSRF is the ratio of buckling strength of a cylindrical shell with an opening to that of a cylindrical shell without an opening. BSRF provides a practical simplified method to evaluate how an access opening affects skirt buckling strength.

Containment vessel (CV) of nuclear power plants is an important structure to prevent a significant and sudden radioactive release, however, the safety margin of the containment vessel against the internal or external pressure are not numerically clarified. The head plate is one of the components which constitute the CV boundary. In order to develop the evaluation method of the pressure toughness of the head plate at beyond design basis events, the pressure failure tests and finite element analysis of the head plates subjected to convex side pressure were performed. In the tests, non-axisymmetric deformations with local deformation concentration were observed in post buckling behavior in the case of the thin thickness head plate. In this study, to evaluate these non-axisymmetric deformations in the test, finite element analyses using detailed 3-D solid model constructed by precise dimensions of the head plates measured by 3-D scanner were performed. Moreover, FEA using simplified model with uniform or non-uniform thickness model were performed. Through a series of FEA, it was clarified the effect of each thickness pattern on post buckling non-axisymmetric deformation.