The Influence of the Bourdon Effect on Pipe Elbow

2016 ◽  
Author(s):  
Diana Abdulhameed ◽  
Samer Adeeb ◽  
Roger Cheng ◽  
Michael Martens
Keyword(s):  
Internal Pressure ◽  
Cross Section ◽  
High Stress ◽  
Bending Moment ◽  
Design Parameters ◽  
Pipeline System ◽  
Pipe Elbow ◽  
Stress Levels ◽  
Current Design ◽  
Thrust Forces

Pipe elbows are frequently used in a pipeline system to change the directions. Thermal expansion and internal pressure results in bending moments on the bends causing ovalization of the initial circular cross-section. The ability of the bend to ovalize will result in an increase in the bend flexibility when compared to straight pipes [1]. In case of bends subjected to internal pressure, the pipe will start to straighten out due to the difference between the intrados and extrados surface areas. The internal pressure causes unbalanced thrust forces tending to open up the elbow depending on its stiffness and surrounding constraints. These forces tending to cause ovalization of the cross section and causing the tendency of pipe bends to open up are termed the “Bourdon effect”. If these unbalanced thrust forces are not taken into consideration, unanticipated deformations and high stress levels could occur at the elbow location that may not be accounted for in traditional stress analysis [2]. A better understanding of the influence of the Bourdon effect on the elbow design parameters is required. Past studies have investigated the behaviour of pipe elbows under closing bending moment and proposed factors that account for the increased flexibility and high stress levels resulted from ovalization. These factors are used in the current design codes [3],[4] &[5] and known as the flexibility factor and stress intensification factor. In this investigation, pipe elbows with different nominal pipe size and various bend radiuses to internal pipe radius ratios (R/r) are studied to get a better understanding of the Bourdon effect and its influence on the pipe stresses and deformations. Differential equilibrium equations are solved to derive a mathematical model to evaluate the unbalanced thrust forces resulted from the Bourdon effect on a pipe elbow. The forces evaluated from the derived model are compared to finite element model results and showed excellent agreement. A comparison between the CSA-Z662 code and the FEA results is conducted to investigate the applicability of the stress intensification factors used in the current design code for different loading cases. The study showed that the external bending moment direction acting on the pipe has a significant effect on the distribution of stresses on the pipe elbow and significantly depending on the level of applied internal pressure.

Application of Deterministic and Probabilistic Methods in Pipeline Lateral Buckling Design

2012 ◽  
Author(s):  
Hammam Zeitoun ◽  
Maša Branković ◽  
Edwin Shim ◽  
EuJeen Chin ◽  
Benjamin Anderson
Keyword(s):  
Structural Reliability ◽  
Design Guidelines ◽  
Probabilistic Methods ◽  
Design Solution ◽  
Design Parameters ◽  
Pipeline System ◽  
Limit States ◽  
Lateral Buckling ◽  
Current Design ◽  
Subsea Pipelines

Subsea pipelines lateral buckling design has significantly evolved over the last years as more pipeline projects have moved into more challenging environments and into high temperature / high pressure (HT/HP) design application. Knowledge and understanding of pipeline lateral buckling has improved with design application resulting in refined and enhanced design approaches. Using current design approaches, it is now quite acceptable to control lateral buckle formation along the pipeline by using buckle triggers or to allow uncontrolled lateral buckles, provided that the various design limit states are satisfied. A number of design methodologies can be used to check the acceptability of uncontrolled buckling or to design for controlled buckling including deterministic, probabilistic buckle formation and full Structural Reliability Assessment (SRA) methods. Using SRA or probabilistic methods is usually an attractive design option as lateral buckling design involves dealing with a large number of uncertainties and variation in design parameters. These methods help to ensure the reliability of the proposed buckle initiation scheme. However, the use of these methods is also associated with a number of challenges such as the need to identify key parameters influencing the design and quantifying their uncertainties. Deterministic design approaches on the other hand are simpler to apply. However, they do not provide means to quantify the reliability of the proposed buckling scheme or the design risks. The choice of input parameters in a deterministic design is also relatively subjective which can possibly result in an overly conservative or unconservative design solution depending on the adopted design approach, selected design parameters and pipeline system being considered. Design guidelines and recommended practices such as SAFEBUCK (20) offer comprehensive guidelines to design for lateral buckling. However when faced with a range of complex variables, the designer needs to be aware of the effect of these parameters on the overall design. This paper describes the application of Deterministic and Probabilistic design approaches in lateral buckling design. The paper starts by describing these approaches, their advantages and limitations. The paper then explores a number of key uncertainties and variation in design parameters that the designer is faced with and its effect on the pipeline response.

Nonlinear Analysis of Pressurized Piping Elbows Subjected to Out-of-Plane Bending

2006 ◽  
Vol 306-308 ◽  
pp. 351-356 ◽  
Author(s):  
Asnawi Lubis ◽  
Jamiatul Akmal
Keyword(s):  
Finite Element Analysis ◽  
Finite Element ◽  
Internal Pressure ◽  
Cross Section ◽  
Bending Moment ◽  
Pressure Reduction ◽  
Element Analysis ◽  
Out Of Plane ◽  
Plane Bending ◽  
Reduction Effect

The behavior of piping elbows under bending and internal pressure is more complicated than expected. The main problem is that the coupling of bending and internal pressure is nonlinear; the resulting stress and displacement cannot be added according to the principle of superposition. In addition, internal pressure tends to act against the effect caused by the bending moment. If bending moment ovalise the elbow cross-section, with internal pressure acting against this deformation, then the ovalised cross section deform back to the original circular shape. It is then introduced the term “pressure reduction effect”, or in some literature, “pressure stiffening effect”. Current design piping code treats the pressure reduction effect equally for in-plane (closing and opening) moment and outof- plane moment. The aim of this paper is to present results of a detailed finite element analysis on the non-linear behavior of piping elbows of various geometric configurations subject to out-of-plane bending and internal pressure. Specifically the standard Rodabaugh & George nonlinear pressure reduction equations for in-plane closing moment are checked in a systematic study for out-of-plane moment against nonlinear finite element analysis. The results show that the pressure stiffening effects are markedly different for in-plane and out-of-plane bending.

scholarly journals Optimization of the parameters of truss beams with two posts

2021 ◽  
Vol 48 (3) ◽  
pp. 117-132
Author(s):  
A. K. Yusupov ◽  
H. M. Musеlеmov, ◽  
T. O. Ustarhanov
Keyword(s):  
Cross Section ◽  
Optimal Parameter ◽  
Bending Moment ◽  
Internal Force ◽  
Numerical Calculations ◽  
Design Parameters ◽  
Bending Moments ◽  
The Cross ◽  
Theoretical Results

Based on the theoretical results obtained in the article [17], here the analysis of the influence of various design parameters on the own weight and cost of metal of truss beams with two posts is carried out. An optimal parameter has been obtained that makes it possible to reduce the calculated bending moment in the cross section of a truss beam with two struts.Method. By equalizing the bending moments in various design sections of the truss beam, the internal force factors are reduced. The corresponding equation for optimizing the parameters of the beam has been drawn up and a formula has been obtained to determine the optimal parameter of the structure as a whole.Result. Using the example of numerical calculations, a decrease in the calculated bending moment by 14% compared to truss beams without optimization is shown.Conclusion. The proposed method and algorithm testify to the efficiency and rationality of the obtained optimal parameter of the structure as a whole.

scholarly journals Blasting and preconditioning modelling in underground cave mines under high stress conditions

2021 ◽  
Vol 121 (2) ◽  
Author(s):  
E. Córdova ◽  
I. Gottreux ◽  
A. Anani ◽  
A. Ferrada ◽  
J.S. Contreras
Keyword(s):  
Large Scale ◽  
Numerical Models ◽  
High Stress ◽  
Underground Mines ◽  
Sensitivity Analyses ◽  
Column Height ◽  
Design Parameters ◽  
Mining Technique ◽  
Initiation And Propagation ◽  
Current Design

SYNOPSIS Cave mining is an underground mass mining technique. The largest projects, which are known as 'super caves', produce hundreds of thousands of tons of ore per day, which involves large footprints with considerable column height, and have a life of mine of over 20-40 years. These operations are typically located deep, under high stresses and in competent rock masses, making initiation and propagation of the caving process harder to manage. These challenges must be confronted by optimizing the fragmentation of the orebody to achieve smaller size blocks that will result in consistent caving and improved flow of the ore from the drawpoints. To achieve better performance from the drawpoints, preconditioning is applied to fragment and damage the material required to cave. We present a proposed design for preconditioning in underground mines, considering the challenges that these large-scale mines are already facing, based on a comprehensive analysis of current design parameters, case studies, and sensitivity analyses using numerical models. Keywords: fragmentation, preconditioning, caving, blasting, structures, stresses, explosives.

Influence of Yield Strength Variability over Cross-Section to Steel Beam Load-Carrying Capacity

2005 ◽  
Vol 10 (2) ◽  
pp. 151-160 ◽  
Author(s):  
J. Kala ◽  
Z. Kala
Keyword(s):  
Yield Strength ◽  
Cross Section ◽  
Carrying Capacity ◽  
Bending Moment ◽  
Statistical Characteristics ◽  
Load Carrying Capacity ◽  
Load Carrying ◽  
Strength Variability ◽  
Hot Rolled ◽  
Hot Rolled Steel

Authors of article analysed influence of variability of yield strength over cross-section of hot rolled steel member to its load-carrying capacity. In calculation models, the yield strength is usually taken as constant. But yield strength of a steel hot-rolled beam is generally a random quantity. Not only the whole beam but also its parts have slightly different material characteristics. According to the results of more accurate measurements, the statistical characteristics of the material taken from various cross-section points (e.g. from a web and a flange) are, however, more or less different. This variation is described by one dimensional random field. The load-carrying capacity of the beam IPE300 under bending moment at its ends with the lateral buckling influence included is analysed, nondimensional slenderness according to EC3 is λ¯ = 0.6. For this relatively low slender beam the influence of the yield strength on the load-carrying capacity is large. Also the influence of all the other imperfections as accurately as possible, the load-carrying capacity was determined by geometrically and materially nonlinear solution of very accurate FEM model by the ANSYS programme.

scholarly journals Hydraulic Transients in Viscoelastic Pipeline System with Sudden Cross-Section Changes

Energies ◽  
2021 ◽  
Vol 14 (14) ◽  
pp. 4071
Author(s):  
Michał Kubrak ◽  
Agnieszka Malesińska ◽  
Apoloniusz Kodura ◽  
Kamil Urbanowicz ◽  
Michał Stosiak
Keyword(s):  
Numerical Model ◽  
Cross Section ◽  
Laboratory Data ◽  
Experimental Studies ◽  
Distribution Networks ◽  
Water Hammer ◽  
Fluid Distribution ◽  
Pipeline System ◽  
Hydraulic Transients ◽  
Single Pipe

It is well known that the water hammer phenomenon can lead to pipeline system failures. For this reason, there is an increased need for simulation of hydraulic transients. High-density polyethylene (HDPE) pipes are commonly used in various pressurised pipeline systems. Most studies have only focused on water hammer events in a single pipe. However, typical fluid distribution networks are composed of serially connected pipes with various inner diameters. The present paper aims to investigate the influence of sudden cross-section changes in an HDPE pipeline system on pressure oscillations during the water hammer phenomenon. Numerical and experimental studies have been conducted. In order to include the viscoelastic behaviour of the HDPE pipe wall, the generalised Kelvin–Voigt model was introduced into the continuity equation. Transient equations were numerically solved using the explicit MacCormack method. A numerical model that involves assigning two values of flow velocity to the connection node was used. The aim of the conducted experiments was to record pressure changes downstream of the pipeline system during valve-induced water hammer. In order to validate the numerical model, the simulation results were compared with experimental data. A satisfactory compliance between the results of the numerical calculations and laboratory data was obtained.

Front steering design guidelines formulation for e-scooters considering the influence of sitting and standing riders on self-stability and safety performance

2021 ◽  
pp. 095440702199217
Author(s):  
Milan Paudel ◽  
Fook Fah Yap
Keyword(s):  
Preventive Measures ◽  
Recent Trend ◽  
Dynamic Performance ◽  
Design Guidelines ◽  
Safety Performance ◽  
Design Parameters ◽  
Single Track ◽  
Standing Posture ◽  
Last Mile ◽  
Current Design

E-scooters are a recent trend and are viewed as a sustainable solution to ease the first and last mile problem in modern transportation. However, an alarming rate of accidents, injuries, and fatalities have caused a significant setback for e-scooters. Many preventive measures and legislation have been put on the e-scooters, but the number of accidents and injuries has not reduced considerably. In this paper, the current design approach of e-scooters has been analyzed, and the most common range of design parameters have been identified. Thereafter, validated mathematical models have been used to quantify the performance of e-scooters and relate them with the safety aspects. Both standing and seated riders on e-scooters have been considered, and their influence on the dynamic performance has been analyzed and compared with the standard 26-in wheel reference safety bicycle. With more than 80% of the accidents and injuries occurring from falling or colliding with obstacles, this paper tries to correlate the dynamics of uncontrolled single-track vehicles with the safety performance of e-scooters. The self-stability, handling, and braking effect have been considered as major performance matrices. The analysis has shown that the current e-scooter designs are not as stable as the reference safety bicycle. Moreover, these e-scooters have been found unstable within the most common range of legislated riding velocity. The results corroborate with the general perception that the current designs of e-scooters are less stable, easy to lose control, twitchy, or wobbly to ride. Furthermore, the standing posture of the rider on the e-scooter has been found dangerous while braking to avoid any disturbances such as potholes or obstacles. Finally, the front steering design guidelines have been proposed to help modify the current design of e-scooters to improve the dynamic performance, hence the safety of the e-scooter riders and the surroundings.

Effect of design parameters on stresses occurring at the tooth root in a spur gear pressed on a shaft

2021 ◽  
pp. 095440892199529
Author(s):  
Fatih Güven
Keyword(s):  
Internal Pressure ◽  
Tangential Stress ◽  
Spur Gear ◽  
Design Parameters ◽  
Interference Fit ◽  
Gear Design ◽  
Compact Design ◽  
Fit Tolerance ◽  
Moderate Stress ◽  
Good Agreement

Gears are commonly used in transmission systems to adjust velocity and torque. An integral gear or an interference fit could be used in a gearbox. Integral gears are mostly preferred as driving gear for a compact design to reduce the weight of the system. Interference fit makes the replacement of damaged gear possible and re-use of the shaft compared to the integral shaft. However, internal pressure occurs between mating surfaces of the components mated. This internal pressure affects the stress distribution at the root and bottom land of the gear. In this case, gear parameters should be re-considered to assure gear life while reducing the size of the gear. In this study, interference fitted gear-shaft assembly was examined numerically. The effects of rim thickness, profile shifting, module and fit tolerance on bending stress occurring at the root of the gear were investigated to optimize gear design parameters. Finite element models were in good agreement with analytical solutions. Results showed that the rim thickness of the gear is the main parameter in terms of tangential stress occurring at the bottom land of the gear. Positive profile shifting reduces the tangential stress while the pitch diameter of the gear remains constant. Also, lower tolerance class could be selected to moderate stress for small rim thickness.

scholarly journals Rational Choice of Reinforcement of Reinforced Concrete Frame Corners Subjected to Opening Bending Moment

Materials ◽  
2021 ◽  
Vol 14 (12) ◽  
pp. 3438
Author(s):  
Michał Szczecina ◽  
Andrzej Winnicki
Keyword(s):  
Cross Section ◽  
Bending Moment ◽  
Plasticity Model ◽  
Reinforced Concrete Frame ◽  
Moment Frame ◽  
Concrete Frame ◽  
Rational Reinforcement ◽  
Eurocode 2 ◽  
Analysis Of Results

This paper discusses a choice of the most rational reinforcement details for frame corners subjected to opening bending moment. Frame corners formed from elements of both the same and different cross section heights are considered. The case of corners formed of elements of different cross section is not considered in Eurocode 2 and is very rarely described in handbooks. Several reinforcement details with both the same and different cross section heights are presented. The authors introduce a new reinforcement detail for the different cross section heights. The considered details are comprised of the primary reinforcement in the form of straight bars and loops and the additional reinforcement in the form of diagonal bars or stirrups or a combination of both diagonal stirrups and bars. Two methods of static analysis, strut-and-tie method (S&T) and finite element method (FEM), are used in the research. FEM calculations are performed with Abaqus software using the Concrete Damaged Plasticity model (CDP) for concrete and the classical metal plasticity model for reinforcing steel. The crucial CDP parameters, relaxation time and dilatation angle, were calibrated in numerical tests in Abaqus. The analysis of results from the S&T and FE methods allowed for the determination of the most rational reinforcement details.

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