Comparison of Ellipsoidal and Equivalent Torispherical Heads Under Internal Pressure: Buckling, Plastic Collapse and Design Rules

2019 ◽  
Author(s):  
Jinyang Zheng ◽  
Keming Li ◽  
Yehong Yu ◽  
Zekun Zhang ◽  
Wenzhu Peng ◽  
...  
Keyword(s):  
Internal Pressure ◽  
Failure Modes ◽  
Bursting Pressure ◽  
Good Prediction ◽  
Plastic Collapse ◽  
Design Equation ◽  
Fe Method ◽  
Shape Deviation ◽  
Design Rules ◽  
Current Design

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.

Comparison of Ellipsoidal and Equivalent Torispherical Heads Under Internal Pressure: Buckling, Plastic Collapse and Design Rules

2020 ◽  
Vol 143 (2) ◽  
Author(s):  
Jinyang Zheng ◽  
Yehong Yu ◽  
Yehong Chen ◽  
Keming Li ◽  
Zekun Zhang ◽  
...  
Keyword(s):  
Failure Modes ◽  
Good Prediction ◽  
Plastic Collapse ◽  
Design Equation ◽  
Fe Method ◽  
Shape Deviation ◽  
Design Rules ◽  
Collapse Pressure ◽  
Current Design ◽  
The Difference

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 and EN13445-3, 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 shape deviation between the two types of heads. Then we compare elastic–plastic behaviors between ellipsoidal and equivalent torispherical heads as well as their failure modes, i.e., buckling and plastic collapse (bursting). It is found that ellipsoidal heads have more buckling resistance than equivalent torispherical heads, indicating that the current design rules for buckling of ellipsoidal heads based on the geometric equivalency approaches result in uneconomical design. In addition, experimental and numerical results show that such heads experience geometric strengthening. The finite element (FE) method considering the effect of geometric strengthening provides a good prediction of plastic collapse 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 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 bursting of ellipsoidal and torispherical heads.

Bending Capacity of Pipe Bends in Deepwater Conditions

2010 ◽  
Author(s):  
Shulong Liu ◽  
Alastair Walker ◽  
Philip Cooper
Keyword(s):  
Internal Pressure ◽  
Induction Heating ◽  
Wall Thickness ◽  
Failure Modes ◽  
Limit State ◽  
Bending Moment ◽  
External Pressure ◽  
Fe Method ◽  
Moment Capacity ◽  
Operation Conditions

Offshore pipeline systems commonly incorporate induction-heating formed bends along flowlines and in pipeline end termination assemblies and spools. In deepwater locations, the pipeline and bends are subjected to various combinations of external pressure, internal pressure, bending moment and temperature changes, during installation, and operation. Although there is a history of research into the limiting loads and failure modes of such bends and pipelines systems there is, as yet, no comprehensive guidance to enable the calculation of the maximum capacity under combined bending and external pressure loading. Conservative guidance is presented in DNV OS-F101 (2007) [1] that proposes increasing the pipe wall thickness to reduce the effect of external pressure collapse effects thus enabling bending formulations relevant to straight pipe to be used. This proposed approach leads to unfeasibly large wall thickness requirements in very deepwater applications. There is therefore a requirement for a method to design deepwater bends for installation and operation conditions with levels of safety comparable with those used in the design of straight sections of pipelines that does not depend on the requirement to increase the wall thickness to the extent proposed in the current DNV guidance. In this study, a nonlinear FE method using ABAQUS is proposed to evaluate the ultimate capacities of induction-heating formed bends. The method takes into account the combined effects of non-linear material properties, initial ovality, wall thinning/thickening, external or internal pressure, internal CRA cladding and temperature change on the ultimate moment capacity of the bend. The numerical model is validated by comparison with available published results. The method developed here is based on the limit state design formulations in the current DNV OS-F101 guidance.

Plastic Collapse and the Controlling Failure Pressures of Thin 2:1 Ellipsoidal Shells Subjected to Internal Pressure

1979 ◽  
Vol 101 (1) ◽  
pp. 64-72 ◽  
Author(s):  
G. D. Galletly ◽  
R. W. Aylward
Keyword(s):  
Internal Pressure ◽  
Strain Hardening ◽  
Failure Modes ◽  
Companion Paper ◽  
Plastic Collapse ◽  
Collapse Pressure

In the first part of the paper, plastic collapse pressures of thin 2:1 ellipsoidal shells are determined. The effects of E, σyp and strain hardening, S, on the collapse pressure are presented and discussed. The second part of the paper is concerned with the controlling failure pressures of internally pressurized 2:1 ellipsoidal shells. This involves the consideration of both plastic collapse pressures and asymmetric buckling pressures (the latter were obtained from a companion paper). Curves of the controlling failure pressures versus D/t are given for several values of σyp and S. Both aluminum and steel shells are considered. Dimensionless buckling and collapse pressures are also tabulated and some very simple formulas for both failure modes are suggested which should be useful to designers.

Cold-formed steel battened built-up columns: Experimental behaviour and verification of different design rules developed

2021 ◽  
pp. 136943322110480
Author(s):  
A.R. Dar ◽  
S. Vijayanand ◽  
M. Anbarasu ◽  
M. Adil Dar
Keyword(s):  
Failure Modes ◽  
Numerical Models ◽  
Experimental Studies ◽  
Design Standards ◽  
Uniform Compression ◽  
Design Rules ◽  
The North ◽  
Current Design ◽  
Cold Formed Steel ◽  
In The Beginning

Some of the past studies on cold-formed steel (CFS) battened built-up columns have resulted in the development of new design rules for predicting their axial strengths. However, the main drawbacks of such studies are that they are purely numerical and the numerical models developed for such parametric studies were validated using the test results on similar built-up column configurations, but not the exact ones. Therefore, experimental studies on CFS battened columns comprising of lipped channels are needed for verifying the accuracy of the proposed design rules for CFS battened columns. This paper reports an experimental study performed on CFS built-up battened columns under axial compression. Adequately spaced identical lipped channels in the back-to-back arrangement were used as chords and were connected by batten plates laterally with self-driving screws to form the built-up members. The dimensions of chords were fixed as per the geometric limits given out in the North American Specifications (NAS) for the design of CFS structural members. The sectional compactness of the chords and the overall slenderness of the built-up columns were varied by altering the thickness of the channels and height of the built-up columns, respectively. A total of 20 built-up sections were tested under uniform compression to investigate the behavioural changes in the built-up columns due to these variations. The behaviour assessment was made in terms of peak strengths, load–displacement response and failure modes of the test specimens. The current design standards on CFS structures were used to determine the design strengths and were compared against the test strengths for assessing their adequacy. Furthermore, as discussed in the beginning, the test strengths were used to verify the accuracy of the different relevant proposed design rules in the literature.

Torispherical Shells under Internal Pressure—Failure due to Asymmetric Plastic Buckling or Axisymmetric Yielding

1985 ◽  
Vol 199 (3) ◽  
pp. 225-238 ◽  
Author(s):  
G D Galletly ◽  
J Błachut
Keyword(s):  
Internal Pressure ◽  
Pressure Vessel ◽  
Shell Theory ◽  
Failure Modes ◽  
Finite Deflection ◽  
Plastic Buckling ◽  
Design Rules ◽  
Failure Pressure ◽  
Pressure Failure ◽  
Approximate Equations

In the diameter-to-thickness range 250 < D/t < 1000, internally pressurized torispherical shells can fail either by plastic buckling or by axisymmetric yielding. However, the present Code rules cater only for the axisymmetric yielding mode and they also restrict the D/t ratios to being less than 500. The rules are based on limit analysis results and these can be conservative for this problem. With regard to internal pressure buckling, there are as yet no design rules in either the American or the British pressure vessel Codes to prevent its occurrence. To provide guidance for a more accurate formulation of design rules for both of these failure modes over the range 300 < D/t < 1500, the authors have made a series of calculations to determine the values of Pcr (the internal buckling pressure) and pc (the axisymmetric yielding pressure) for perfect torispherical shells. The availability of these results, obtained with a finite-deflection shell theory, enables curves to be drawn showing when buckling is the controlling failure mode and when axisymmetric yield controls. A comparison is also made, for D/t < 600, between the controlling failure pressures mentioned above and the Drucker-Shield limit pressures. The ratio between the former and the latter varied between 1.2 and 1.8, depending on the geometry of the shell and the magnitude of the yield point, σyp. Considerable economies in the designs of many torispherical shells could, therefore, be achieved if the relevant sections of the Codes were to be modified to take advantage of the foregoing results. The controlling failure pressure curves also indicate how Code rules to prevent plastic buckling for D/t > 500 might be formulated. For the benefit of designers, the numerical values of pcr and pc were transformed, using curve-fitting techniques, into simple approximate equations. Although these equations are for perfect torispherical shells, they should be very beneficial when analysing the related problems of fabricated torispheres in practice.

Design Equations for Preventing Buckling in Fabricated Torispherical Shells Subjected to Internal Pressure

1986 ◽  
Vol 200 (2) ◽  
pp. 127-139 ◽  
Author(s):  
G D Galletly
Keyword(s):  
Internal Pressure ◽  
Failure Mode ◽  
Failure Modes ◽  
Experimental Results ◽  
Design Equation ◽  
Test Results ◽  
Theoretical Predictions ◽  
The Subject ◽  
The Difference ◽  
Empirical Constants

Design rules to prevent buckling in thin fabricated torispherical shells subjected to internal pressure are not yet available in either the American or the British pressure vessel Codes. They are the subject of the present paper and some possible design equations are suggested. The equations were obtained from the buckling equations for perfect torispheres after considering all known experimental results on fabricated models. The empirical constants in the proposed design equations depend on the type of head construction used, i.e. whether crown and segment or pressed and spun. For both types of head the equations give a factor of safety of at least 1.5. The design equation proposed for the crown and segment heads was also checked on several large vessels which had failed in service. The safety factors found for these cases were all greater than 1.7, which means that the vessels would not have buckled if the design equation had been available at the time. The other failure mode of these torispherical heads, i.e. large axisymmetric deformations leading to through-thickness yielding, is also discussed briefly. Curves are given which show that, for 300 < D/t < 500, buckling controls the failure mode in some cases and axisymmetric yielding in others. Neither the American nor the British codes recognize that buckling can occur in this D/t range but the theoretical predictions have been confirmed by experiments. However, the amount of test data is limited and more work is needed on the topic. It is also shown in the paper that, for torispherical shells with D/t ratios in the range 300 < D/t < 500, the axisymmetric limit pressures, pDS, are lower than both the internal buckling pressures and the large deflection axisymmetric yielding pressures. From this, one would expect the failure modes to be axisymmetric in this D/t range. However, as some non-symmetric buckling failures have occurred, the limit analysis predictions for the failure mode are thus not always correct. One feature of the experimental results on stainless steel torispherical shells which are reviewed in the paper is the relatively poor buckling performance of the heads tested by Kemper in comparison with similar heads tested by Stanley and Campbell. As the values of the empirical constants in the design equations are controlled by the lowest test results, the higher bucking pressures obtained by Stanley/Campbell cannot be utilized unless an adequate explanation for the difference in the two sets of results is forthcoming.

Design Rules and Failure Modes of DMFC Stack Development

2019 ◽  
Vol 26 (1) ◽  
pp. 287-294 ◽  
Author(s):  
Youngseung Na ◽  
Seong Kee Yoon ◽  
Jungkurn Park ◽  
Jun Won Suh ◽  
Inseob Song ◽  
...  
Keyword(s):  
Failure Modes ◽  
Design Rules

Experimental-Numerical Characterization of Ordinary Concrete at the Meso-Scale

2021 ◽  
Author(s):  
GIANLUCA MAZZUCCO ◽  
Beatrice Pomaro ◽  
Giovanna Xotta ◽  
Enrico Garbin ◽  
Valentina Salomoni ◽  
...  
Keyword(s):  
Yield Criterion ◽  
Plain Concrete ◽  
Point Of View ◽  
Good Prediction ◽  
Deformation Capacity ◽  
Compression Tests ◽  
Fe Method ◽  
Stress States ◽  
Meso Scale

Modeling the post-peak behaviour of brittle materials like concrete is still a challenge from the point of view of computational mechanics, due to the strong nonlinearities arising in the material behaviour during softening and the complexity of the yield criterion that may describe their deformation capacity in generic triaxial stress states. A numerical model for plain concrete in compression is formulated within the framework of the coupled elasto-plastic-damage theory. The aim is to simulate via the Finite Element (FE) method the stress-strain behaviour of concrete at the meso-scale, where local confinement effects generally characterize the cement paste under the action of the surrounding aggregates. The mechanical characterization of the components are accomplished through a specific experimental campaign. With the subsequent validation study, it is shown that a few calibration parameters give a good prediction of load strength and deformation capacity coming from real uniaxial compression tests.

Failure behavior analysis of steel strip–reinforced flexible pipe under combined tension and internal pressure

2018 ◽  
Vol 33 (6) ◽  
pp. 727-753
Author(s):  
Wei Chen ◽  
Haichao Xiong ◽  
Yong Bai
Keyword(s):  
Internal Pressure ◽  
Numerical Study ◽  
Steel Strip ◽  
Sensitivity Study ◽  
Failure Behavior ◽  
Load Path ◽  
Flexible Pipe ◽  
Fe Method ◽  
Axial Extension ◽  
The Relationship

The mechanical behaviors of steel strip–reinforced flexible pipe (steel strip PSP) under combined axial extension → internal pressure ( T→ P) load path were investigated. Typical failure characteristics of pipe samples under pure internal pressure and T→ P load path were identified in the full-scale experiments. A theoretical model for pipe under tension load was proposed to capture the relationship between axial extension of the pipe body and stress state of the steel strip. Numerical study based on finite element (FE) method was conducted to simulate the experiment process, and good agreement between FE data and experiment results were observed. Sensitivity study was conducted to study the effect of some key parameters on the pipe antiburst capacities in T→P load path; the effect of preloaded internal pressure on the pipe tensile capacity in P→T load path was also studied. Useful conclusions were drawn for the design and application of the steel strip PSP.

A Single Technically Consistent Design Formula for the Thickness of Cylindrical Sections Under Internal Pressure

2006 ◽  
Vol 129 (1) ◽  
pp. 211-215 ◽  
Author(s):  
John D. Fishburn
Keyword(s):  
Experimental Data ◽  
Internal Pressure ◽  
State Of The Art ◽  
Original Data ◽  
Pressure Vessels ◽  
Time Dependent ◽  
Design Codes ◽  
Recent Developments ◽  
Current Design ◽  
Single Formula

Within the current design codes for boilers, piping, and pressure vessels, there are many different equations for the thickness of a cylindrical section under internal pressure. A reassessment of these various formulations, using the original data, is described together with more recent developments in the state of the art. A single formula, which can be demonstrated to retain the same design margin in both the time-dependent and time-independent regimes, is shown to give the best correlation with the experimental data and is proposed for consideration for inclusion in the design codes.

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