To model the peeling phenomenon during cataract surgery and examine the effect of fluid flow during surgery, we constructed a simplified physical system and compared the case where only static pressure is applied to the adhesive thin film and the case where water flow is applied to the film by suction. From experiments with and without suctioning, the energy release rates of the adhesive thin film were calculated to be approximately 10 N/m, and no significant difference was confirmed with or without suction. We modeled the peeling phenomenon using the cohesive damage model and performed a finite element analysis considering the coupling of the fluid and membrane. The simulation results without suction were in good agreement with the theoretical values of the stress and deflection. When the water flow was applied to collide with the peeling part, the film deflection at the center became smaller, and the radial and circumferential stresses became smaller. From this result, it is shown that the stress acting on the membrane surrounding the crystalline lens can be reduced and peeling can be performed by successfully using the water flow for peeling.

We considered the Type2 pressure vessel (hereinafter, Type2) used in hydrogen refueling stations (hereinafter, HRS), a stational Composite Reinforced Pressure Vessel (hereinafter, CRPV) in which a metal layer made of high-strength low-alloy steel is wrapped with a carbon fiber reinforced plastic (hereinafter, CFRP) layer in the circumferential direction. Because Type2 is lightweight and has a long life, installation in HRS is expected. However, since no technical standards concerning design for safe use of Type2 for HRS currently exist, few Type2 have been installed in HRS in Japan. Based on these circumstances, we are developing a Technical Document on the safe use of Type2 (hereinafter, TD) to promote the installation of Type2 at HRS. In this paper, we introduce the current discussion on issuance of the TD as an industrial standard, focusing especially on the following: Type2 shall be considered a two-layer pressure vessel in which the CFRP layer shares the circumferential stress of the metal layer. The wall thicknesses of the metal layer and CFRP layer of Type2 are calculated by Design by Rule approach, but when necessary, Design by Analysis (stress analysis and fatigue analysis) can be applied. Design specification tests such as the burst test and hydraulic pressure cycle test using an actual Type2 should not be required. The hydrogen compatibility and fatigue life of the low-alloy steel used in the metal layer are evaluated in accordance with our previously-proposed methods [1]. In the fatigue analysis, the effect of autofrettage can be considered.

The determination of stress intensity factors (SIF) and crack opening area or displacements (COA or COD) is important constituent when performing the “leak before break” analysis of piping systems in NPPs. The tabulated parametrical results of their calculation are widely presented in modern scientific and normative literature. Nevertheless, there is one aspect of crack behavior, at least in thin walled pipes, which still had not obtained its due attention. We mean here the geometrically nonlinear effect, which can be the big enough to be accounted for in practical applications. It is considered in geometrically linear analysis that only the inner pressure opens the crack, and COA and SIF are directly proportional to it. SIF is presented usually as solution for infinite plate multiplied by so-called bulging factor, BF, which depends on dimensionless crack length, i.e. ratio of crack length divided on square root of product of radius, R , and wall thickness, t . Two loading factors in thin walled pipes can contribute to geometrically nonlinear behavior. The first one is axial stresses induced by value of axial force or bending moment. The second one – is the inner pressure itself. The most attention in present paper is given to influence of the axial force. With this goal the numerical models were created for pipes with different ratios of R/t (20, 30, 40, 50) and different dimensionless crack length (2, 4, 6, 8). To exclude the nonlinearity due to circumferential stress the inner pressure is kept as a very small value and dimensionless SIF and COD values are calculated with respect to axial force. To prove the correctness of choosing the finite element types, meshing, number of elements along the thickness, loading steps the auxiliary problem of nonlinear modeling of transverse beam loaded additionally by very big axial force is considered. The very good correspondence was attained. For the pipe with axial crack the careful verification of numerical model was performed by comparison with linear results existing in literature. The results obtained are presented as a percentage of difference between the linear and nonlinear results. They show that influence of geometrical nonlinearity is fairly essential to be accounted in practice and can reach for practically real cases almost 3–10%. The change of SIF in percentages due to geometrical nonlinearity for different axial stress levels and for different crack lengths can be fairly well presented as unique dependence from product of stresses, radius to thickness ratio, and square root of dimensionless crack length. The change COD in central point of crack is slightly bigger than for SIF and the same unique dependence can be formulated for COD with only exception for small cracks λ < 3.

Coke drums are thin-walled pressure vessels that experience low cycle fatigue due to thermal loadings. The delayed coking process is comprised by three major stages: heating, coking and cooling, which repeat at intervals between 20 and 48 hours. The cyclic changes of temperature increase the growth of bulges and cracks which with the passing of time, propagate and eventually cause failures due to the loss of containment. A better understanding of the phenomena of the thermal gradients and their influence on the generated stresses would reduce the effects of the damage mechanisms afflicting coke drums, for example; a continuous monitoring system could be implemented in order to control the cooling ramp to obtain a more homogeneous quenching around the cylinder of the coke drum and consequently increase its lifetime. It is been widely accepted that there is a relationship between high cooling rates in isolated zones and high axial stresses. However, this relationship has not been fully validated, since there are also been reported events of low cooling rates and high stresses. This study shows a predictable behavior (trend) that relates the spatial thermal gradients and the axial and circumferential stresses generated. A coke drum in an upgrader facility was instrumented with two arrays or grids, each of them having 24 thermocouples and 2 strain gauges in zones with distinct bulges. One arrangement was located at an inward bulge while the other was located at an outward bulge. Computational models were carried out to reproduce the behavior of the instrumented zones with their actual deformations obtained from laser scanning. Finite element models were developed using a sequentially coupled thermo-mechanical analysis to determine the transient temperature and stress distributions. The effect of the circumferential thermal gradients on the stress levels in the instrumented cylindrical sections were analyzed, considering two cases; the first of them a perfect cylinder (without deformation) and the second one considering the presence of bulges in the area of interest. The results indicate that there is a relationship between the circumferential thermal gradients [°C/m] or [°F/ft] and the axial stress levels, i.e., cold zones generate axial tensile stresses, and hot zones produce compressive axial stresses. This relationship is affected — exacerbated or counteracted — by the presence of the bulges. Additionally, the results obtained in this paper confirm those of previous investigations showing that outward bulges subject to pressure and thermal loading generate high stresses on its internal surface and low stresses on its external face whereas inward bulges produce the opposite effect.

Transverse tensile properties of the Alloy 690 steam generator tube used in Korean PWR(pressurized water reactor) nuclear power plant is one of the main properties to analyze creep rupture caused by the hoop stress in the severe accident conditions. Transverse tensile properties of steam generator tubes cannot be obtained directly machined from the tubes and it is also difficult to make miniaturized flat tensile specimens due to their geometry limitations. The ring-tensile specimens are widely used to measure the tensile properties in the circumferential direction, but membrane and bending stresses are mixed in the ring-tensile specimen during the test due to the shape of ring-tensile specimens. Therefore, obtaining the transverse tensile properties need the inverse analysis using finite element analysis and optimization process. In this study, ring-tensile tests were carried out using 3-piece loading mandrel. The stress-strain curve of ring-tensile specimen in transverse direction is derived by comparing the load-displacement curves of the finite element analysis with those of test. The load-displacement curves from tests agree well with the finite element results. Use of finite element analysis and optimization process as used in this work is effective to predict the transverse tensile properties of ring-tensile specimen.

The rigorous analysis of tube-to-tubesheet joints requires a particular attention to the transition zone of the expanded tube because of its impact on joint integrity. This transition zone is the weakest part of the joint due to the presence of high tensile residual stresses produced during the expansion process which coupled to other in-service loadings and harsh corrosive fluids results in joint failure. In fact, this zone is often subjected to stress corrosion cracking caused by intergranular attack leading to plant shutdown. Therefore, the evaluation of the residual stresses in the transition zone is of major concern during the design phase and its accurate assessment is necessary in order to achieve a reliable joint in service. In this study, a new analytical model to evaluate the residual axial and hoop stresses in the transition zone of hydraulically expanded tubes based on an elastic perfectly plastic material behavior has been developed. The model is capable of predicting the stress state under the maximum expansion pressure and after the expansion process has been completed. Three main regions are identified in the transition zone: the fully plastic region, the partially plastic region and the elastic region. Therefore, various theories have been applied to analyze the stresses and deformations neglecting the partial plastic region because of simplicity. The validation of analytical model is conducted by comparison of the results with the ones of 3D finite element models representing typical geometry and mechanical properties. The effect of reverse yielding of the expansion zone is also investigated.

The ASME Boiler and Pressure Vessel (B&PV) Code Section XI Appendix C provides analytical procedures, criteria, and evaluation methodologies used to determine acceptability for continued service for a specified evaluation time period of flawed pipe. However, Appendix C applicability to subsurface flaws and flaws located on external pipe surfaces is unclear. Appendix C as currently written suggests surface flaws are (only) on the inner pipe diameter. It is recognized that flaw solutions specific to different combinations of the type of flaw, location on component, and failure mode may not be currently available. There are also inconsistencies in the equations for determining fracture toughness for ferritic piping between circumferential and axial-oriented flaws, and the allowable applied hoop stress definitions. Furthermore, there is recent work on several topics in Appendix C that necessitate updating Appendix C. Topics include stress intensity factor (SIF) solutions for circumferential and axial through-wall flaws in cylinders, and the method of combination of bending moments and torsion for elastic-plastic fracture mode and limit load analyses when the torsion stress does not exceed 0.2 times the flow stress. This paper summarizes the proposed ASME Code Section XI Appendix C revisions that will be incorporated in the 2017 edition of the Code. The impact of revising stress intensity factor solutions for circumferential and axial through-wall cracks in cylinders is also presented. In addition to technical changes, several errata are also suggested to be corrected.

Adoption of composite reinforced pressure vessels (CRPV) into the ASME Boiler and Pressure Vessel Code represented advancement in the technology of pressure vessels. The advantage of this construction technique is that the weight of a CRPV for compressed gas service built may be reduced to about one-half conventional pressure vessel of the same capacity. The concept of hoop wrapping fibers in a plastic composite (>90% fiber fill) makes full utilization of the fiber strength as the fibers share the hoop load with a metal cylinder. With reduced hoop stresses in the metal, a substantial reduction in wall thickness is attainable. The process of adoption of this technology presented several challenges and some robust administrative hurdles. These included coordination with ASME BPV Code Section X for the composite application and Section VIII for the steel design and overall acceptance of the Case. The most vexing technical challenge was the inspection of an unfinished weld on the inside of the shell from the outside of the shell. The next challenge was to gain consensus on the testing criteria for the acceptance of finished vessels. Case 2390 was drafted in the winter of 2000 and spring of 2001 and approved for publication after nine revisions with an approval date of October 9, 2002. The Case was subsequently adopted into the body of ASME BPV Code Section VIII, Division 3 [1] (VIII-3) in the 2010 edition.

Corrosion often leads to the failure of transporting pipelines. The surface stresses on the corroded pipes are related to the failure pressure. In this paper, a double circular arc (DCA) model is developed to calculate the surface stress of the internal corroded pipes under external pressure. In addition, a critical corrosion ratio and a critical thickness-to-diameter ratio are presented to determine the location of the maximum stress. Based on the stress function method and bipolar coordinates, an analytical solution of the DCA model was obtained. And then the stress distributions on the internal and external surfaces of the corroded pipes were determined. Next, the equivalent and hoop stresses at several locations in the cross section of the corroded pipes were discussed. The calculated results were validated using finite element method (FEM). Results show that the maximum stresses vary from the internal surface to the external surface with the increase of the corrosion ratio or the thickness-to-diameter ratio. Our research provides a benchmark for approximate solutions to predict the failure pressure and assess the integrity of the corroded pipelines.

Small size longitudinal holes are common in components of high pressure vessels. In fracture mechanics evaluation, longitudinal holes have not drawn as much attention as cross-bores. However, longitudinal holes become critical at certain locations for such assessments because of high stress concentration and short distance to vessel component wall. The high stress concentration can be attributed to three parts: global hoop stress that is magnified by the existence of the hole, local stresses due to pressure in the hole, and crack face pressure. In high pressure vessel design, axisymmetric models are used extensively in stress analyses, and their results are subsequently employed to identify critical locations for fracture mechanics evaluation. However, axisymmetric models ignore longitudinal holes and therefore cannot be used to identify the critical location inside the holes. This paper is intended to highlight the importance of including longitudinal holes in fracture mechanics evaluation, and to present a quick and effective way of evaluating high stress concentration at a longitudinal hole using the combined analytical solutions and axisymmetric stress analysis results, identifying critical locations and conducting fracture mechanics evaluation.

The basic power piping creep life calculations consider the important variables of time, temperature and stress for the creep rupture properties of the unique material. Some engineering evaluations of remaining life estimate the applied stress as the design stress obtained from a conventional piping stress analysis. Other remaining life evaluations may assume that a conservative estimate of the applied stress is no greater than the hoop stress due to pressure. The creep rupture properties of the unique material are usually obtained from the base material creep rupture properties. The typical methodologies to estimate remaining life do not consider the actual applied stress due to malfunctioning supports, multiaxial stress effects, axial and through-wall creep redistribution, time-dependent material-specific weldment creep rupture properties, residual welding stresses, and actual operating temperatures and pressures. It has been determined that the initiation and propagation of Grade 91 creep damage is a function of stress to about the power of 9 at higher applied stresses. There have been many examples of malfunctioning piping supports creating unintended high stresses. When the axial stress is nearly as high as the hoop stress, the applicable corresponding uniaxial stress for creep rupture life is increased about 30%. Multiaxial stress effects in circumferential weldments (e.g., when the axial stress is nearly as high as the hoop stress) can reduce the weldment creep life to less than 1/6 th of the predicted life assuming a uniaxial stress or hoop stress due to pressure only. Since 2012, the ASME B31.1 Code has required that significant piping displacement variations from the expected design displacements shall be considered to assess the piping system’s integrity [1]. This paper discusses a strategy for an enhanced creep life evaluation of power piping circumferential weldments. Piping stresses can vary by a factor greater than 2.0. Consequently, the range of circumferential weldment creep rupture lives for a single piping system may vary by a factor as high as 40. Although there is uncertainty in the operating times at temperatures and pressures, all of the weldments within the piping system have the same time, temperatures, and pressures, so the corresponding uncertainties for these three attributes are normalized within the same piping system. Since the applied stresses are the most important weld-to-weld variable within a piping system, it is necessary to have an accurate evaluation of the applied stresses to properly rank the creep rupture lives of the circumferential weldments. This methodology has been successfully used to select the lead-the-fleet creep damage in circumferential weldments over the past 15 years.

A cylindrical steel storage tank is a cylindrical shell subjected to internal hydrostatic pressure due to the stored liquid product. The hydrostatic pressure causes the shell to experience circumferential stress. This circumferential stress can lead to the yielding of the shell if its thickness is not designed properly. The design of step-walled steel storage tanks requires the calculation of the required thickness of each shell course. A conservative way of calculating each course’s thickness is using the one-foot method (1FM). This method calculates the required thickness to withstand the hydrostatic pressure one foot above the bottom edge of the shell course under consideration. Another method, which is more refined than the 1FM, is the variable-design-point method (VDM), which finds the point in the course where the maximum circumferential stress is. VDM calculates the required shell thickness to withstand that maximum circumferential stress. However, VDM does not capture the circumferential stress resulting from the bottom edge yielding moment accurately for some thank geometries. A new linear analysis approach using thin-shell theory is presented in this paper. The approach captures the plastic yielding moment of the bottom edge accurately, and may produce more economical and safe designs than 1FM and VDM.

Cylindrical steel storage tanks are shells designed to store different types of products such as liquids or grain. The thickness of the shell is calculated to withstand the circumferential stress resulting from the hydrostatic pressure due to the stored product. A unique situation when there is no stored product leads to the vulnerability of the shell to buckle when there is wind load due to external pressure. There are two major types of buckling modes: local and general. The local buckling mode is studied analytically in various studies and is easy to mitigate. The general buckling mode can be more damaging to the tank and more costly to mitigate. The prevention of general buckling due to wind load pressure is achieved through the addition of stiffener rings. However, the stiffener rings design procedure used by various design standards has little known background. This paper reviews the current design approach’s origin and explains a semi-analytical justification for it. The unfolding of the design expressions can lead to more freedom in design variables selection leading to more economical designs.

Grade 91 steels are widely used for high temperature pipes in ultra-super-critical thermal power plants. It was recently reported that the creep damage was detected in the fine grain region within the heat affected zone (HAZ) in the welded pipes, so called “Type IV” damage. So far, studies on creep damage and life assessment methods for welded joints of the Grade 91 steel were concentrated on longitudinal welded pipes. Circumferential welded joints are also susceptible to Type IV damage due to the increase of axial thermal stress superimposed with pipe weight. In this study, the effect of additional axial stress to the axial stress produced by the internal pressure on damage and rupture property is discussed based on internal pressure creep tests adding different levels of the axial loads using the Grade 91 circumferential welded tubes. Rupture time of the circumferential welded tube decreases with increasing additional axial load level. Longitudinal cracking in the weld metal was observed in the specimens tested under lower additional load level, and Type IV cracking was observed in the specimens under higher additional load level. The stress analysis results indicate that the longitudinal stress in the HAZ increases with the axial load. Type IV cracking occurs at a certain value of a ratio of the total longitudinal stress to the circumferential stress. Under the test condition where Type IV cracking occurs, the rupture time is significantly shorter than the predicted rupture time based on the creep rupture data of the longitudinal welded tubes. The limited creep strain concept is introduced to predict the rupture time of the circumferential welded tubes by considering the effect of stress multiaxiality. Eventually, the rupture times caused by Type IV cracking of both the longitudinal and the circumferential welded tubes were accurately predicted by the limited creep strain concept.

Safe shipment and storage of nuclear reactor discharged fuel requires an understanding of how the fuel may perform under the various conditions that can be encountered. One specific focus of concern is performance during a shipment drop accident. Tests at Savannah River National Laboratory (SRNL) are being performed to characterize the properties of fuel clad relative to a mechanical accident condition such as a container drop. Unirradiated ZIRLO tubing samples have been charged with a range of hydride levels to simulate actual fuel rod levels. Samples of the hydrogen charged tubes were exposed to a radial hydride growth treatment (RHGT) consisting of heating to 400°C, applying initial hoop stresses of 90 to 170 MPa with controlled cooling and producing hydride precipitates. Initial samples have been tested using both a) ring compression test (RCT) which is shown to be sensitive to radial hydride and b) three-point bend tests which are less sensitive to radial hydride effects. Hydrides are generated in Zirconium based fuel cladding as a result of coolant (water) oxidation of the clad, hydrogen release, and a portion of the released (nascent) hydrogen absorbed into the clad and eventually exceeding the hydrogen solubility limit. The orientation of the hydrides relative to the subsequent normal and accident strains has a significant impact on the failure susceptability. In this study the impacts of stress, temperature and hydrogen levels are evaluated in reference to the propensity for hydride reorientation from the circumferential to the radial orientation. In addition the effects of radial hydrides on the Quasi Ductile Brittle Transition Temperature (DBTT) were measured. The results suggest that a) the severity of the radial hydride impact is related to the hydrogen level-peak temperature combination (for example at a peak drying temperature of 400°C; 800 PPM hydrogen has less of an impact/ less radial hydride fraction than 200 PPM hydrogen for the same thermal history) and b) for critical strains in post drying handling, storage and accident conditions the 3 point bend strain tolerance is less affected by radial hydrides than the conventional ring compression test (the radial hydride related Quasi DBTT associated with a three point bend straining is lower (better) than that measured by the ring compression tests).

Optimization calculation method determining wall thickness for large oil storage tank made of high strength steel is investigated in this paper. Taking three oil storage tanks with different volumes of 10×10 4 m 3 , 15×10 4 m 3 and 20×10 4 m 3 for examples, the wall thickness calculation methods of API 650, GB 50341, JIS B 8501 and BS EN 14015 have been analyzed and compared. Results show that as the volume of oil storage tank increases, some wall thickness calculation results of the standards have been larger than the allowable value, leading to the unreasonable distribution of the wall circumferential stress. The wall thickness calculation result applying the method of API 650 is more reasonable than other standards. While for the tanks made of high strength steel, like 12MnNiVR (GB 50341), the yield ratio of the steel has reached 0.803, which is larger than the upper limit value of API 650. In order to make up the deficiency, an optimization method based on API 650 is presented, which considers the effects of yield strength, tensile strength and yield ratio on the determination of allowable stress. Taking the 20×10 4 m 3 oil storage tank and selecting a proper welded joint efficiency, the wall thickness is calculated by the presented optimization method. The wall thickness calculation result is more reasonable and the circumferential stress distribution is more homogeneous when the safety factor of tensile strength is taken to be 2.4. Results show that the optimization method is applicable to the thickness calculation of oil storage tanks made of high strength steel.

The consideration of a geometrical nonlinearity is a common practice for the thin-walled structures. The relevance here are two well-known cases treated in ASME codes. First one is accounting for reduction of the pipe bends flexibility due to the inner pressure. The second one is the retarded increasing (and subsequent saturation) of additional local bending stress with increasing of inner pressure in a pipe with initial cross section form distortion. In both cases the rerounding effect and decreasing of local flexibilities take place. The crack can be treated as the concentrated flexibility and it is quite natural to expect that the stress intensity factor should grow nonlinearly with applied load. Two cases of SIF calculation for 1-D long axial surface crack in a pipe loaded by inner pressure are considered here: a) cross section has an ideal circular form: b) the form has a small distortion and crack is located in the place of maximal additional bending stresses. The theoretical analysis is based on: a) the well known crack compliance method [1] and b) analytical linearized solution obtained for deformation of the curved beam in case of action of fixed circumferential stress due to pressure written in the form convenient for transfer matrix method application. It was shown that for moderately deep crack (crack depth to the wall thickness ratio is 0.5 and bigger) and typical dimensions of pipes used for oil and gas transportation (radius to thickness ratio is 25–40) and loading which can reach up to 200 to 300 MPa, the effect investigated can be quite noticeable and can lead to 5–15 percent reduction of calculated SIF as compared with linear calculation. The analytical results are supported by nonlinear FEM calculation.

In the design of buried piping, resistance of the pipe-soil system to the applied vertical load is a significant design consideration. Application of a resultant vertical load perpendicular to the longitudinal pipe axis results in ovalization of the pipe, with resulting vertical pressures in the soil bedding and horizontal pressures in the soil backfill adjacent to the pipe, as well as internal forces and moments in the pipe wall. For pipes that are relatively rigid compared to the soil backfill, the developed internal forces in the pipe hoop and resulting internal moments in the wall tend to be higher than a more flexible pipe with a stiffer soil backfill. For many buried pipes, design to consider through-wall bending stress is not included and consideration of a buckling allowable is considered adequate. However, for safety-related pipes, investigation to include the through-wall bending stress is considered important. Although estimation of the internal hoop stresses in a buried pipe is relatively straight forward, several different methodologies are presented in various industry documents for calculating the through-wall bending stress due to the resulting internal moments. Recommended approaches for calculating the through-wall bending stress vary depending on the pipe material, wall thickness, wall type, deflection, burial condition and other factors. A sensitivity study comparing various theories estimating the through-wall bending stress in a buried pipe subject to external loads with a vertical resultant force is performed. The range of variables is assessed to determine the applicability of the results to typical safety-related piping. This study presents the results of the sensitivity study and provides recommendations for the calculation and incorporation of through-wall bending stress in the design of buried safety related piping.

Pipe failure under internal pressure loading is understood as due to the onset of plastic instability. Law et al. [1] extended the Considere’s construction [2], which predicts the onset of plastic instability for tensile test specimen, so that it can predict the onset of plastic instability, and thus burst of pipes under internal pressure. They noted that “It is important to note that the reduced stress and strain where instability occurs is not a result of the biaxial stress state, but of the vessel geometry where increased stress comes from both increased inner diameter and reduced wall thickness” [1]. However, they intrinsically assumed that the cylinder plane that experiences instability is in plane strain state. Considering the fact that power plant pipes are often subjected to axial force from sources such as thermal expansion/contraction or fixing, the effect of deviation from the plane strain conditions should be considered. For this purpose, the onset of plastic instability of the elastic-plastic internally pressurized 1) 2D plane strain pipe, 2) 3D pipe and 3) 3D pipe additionally subjected to axial force, were compared. The results showed that the onset of plastic instability could be monitored at the pressure when pR m −σ θ t > 0 for all the cases. Here, R m , σ θ , and t are the current mean radius, circumferential stress at mean radius and thickness at pressure p . However, the strain at this instability pressure showed non-negligible change due to presence of axial loading. On this meaning, the biaxiality affected the onset of plastic instability.

In order to assess the safety of concentric reducers and eccentric reducers, the meridian stress and circumferential stress of the reducers subjected to in-plane bending moments are calculated based on the membrane theory. Solutions of limit bending moments are derived by using the approach with the equivalent stress and engineering coefficient. The solutions for both reducers are identical, as the formulas are composed of a base term multiplied by a bending moment coefficient. The limit bending moments are dominated by the small end of the reducers. The value of limit bending moment of the reducers is 14.6% more than that of a thin wall reducing elbow with same diameter and thickness when corresponding bending coefficient λ>3.0. But comparison with a straight pipe which has the same diameter and thickness as the small end of the reducers, the limit bending moment of the reducers is 11.1% lower and the constant in the formula for the reducers is 3.6 instead of 4.0 for straight pipe. It could be dangerous to determine the limit bending moment of concentric reducers and eccentric reducers directly from the formula of limit bending moment for a thin wall pipe.