الفهرس 
IntroductionOnly 14 pages are availabe for public view
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Abstract
The research is crucial to handle the scarcity of data and guidance to design pipe bends in water, oil, and gas projects. As discussed within the literature review the collapse of straight pipes has been extensively studied in the last two decades, however, the behavior of pipe bends was always studied under internal pressure, and also the bending moment for small diameters and bend angles less than or equal to 90 degrees.
Within this study, the behavior of pipe bends under the combination of internal pressure and the bending moment has been investigated in comparison with the current methodology stated in (ASME B31.1, B31.3) [35,36].
Finally, the most challenging task all over the world for the design engineer is achieving an optimized and safe design for this crucial part (pipe bend) along the pipeline, so the need for pipe bend design will increase and it is inevitable to develop a robust and clear methodology to tackle the design of this flexible component.
Through this current detailed numerical stress analysis study conducted in this research on pipe bends with a wide range of bend angles and large diameter pipe geometry subjected to internal pressure and in-plane bending moment (closing and opening) loadings separately and in combination, to take in account the following points:
• The effect of small and large bend angles other than 90° on the value and location of maximum stress distribution along the circumference of the pipe bend.
• The effect of short (R=1D) and long (R=5D) was ignored in the SIF (P+M) of combined loadings estimated by the ASME- code.
• The effect of the direction of the applied in-plane bending moment for large diameter pipe bends and their effect on stress distribution and flexibility through the pipe wall thickness were considered as one of the main parameters that affect the behavior of pipe bends.
• The stress distribution along with the inner and outer layer through the pipe bend thickness was found to be higher by more than 33% than the mid-layer stresses addressed in the ASME B31.1- code.
To reassess the stress intensification factors used currently by the design codes (ASME B31.1, ASME B31.3) and define their limitations.
A brand new proposed stress intensification(SIFM), (SIFP+M) factors were developed within Chapter six, from this numerical analysis using the finite element method were used to conduct this study, and (ABAQUS 16.6 )software package was selected for it is a non-linear capability and ability to converge when cylinders reach the yielding limit load. In this study where pipe bends were represented in a 4-node quadrilateral shell element (S4R) form with a linear elastic material, and large deformation analysis.
To facilitate analysis, the subsequent assumptions were made:
• The objective of this research is to focus on thin-walled pipe bends with uniform thickness and without considering the residual stresses during the forming process.
• Materials are assumed to be elastic, under normal temperatures that may affect the value of stresses if decreased or increased (thermal expansion).
• Regarding the cross-section of pipe bends that encompass large deformation under internal pressure and in-plane bending moment, the large displacement analysis is taken into account.
• This study does not include the effect of valves, flanges weight, fluid weight, and self-weight of the pipeline that may lead to torsion moment on the pipe bends that tend to show different mechanical properties which will occur at the combination of both geometrical nonlinearity and material nonlinearity when they are under these combined loads.
7.2 Conclusions
Pipe bends under internal pressure undergo a cross-sectional and global deformation where the pipe bend tends to straighten out generating higher stress levels than estimated using simple beam theory.
A group of proposed models is conducted to simulate a specific case study of pipe bends that existed in a horizontal water pipeline network of 1906 Km made of carbon steel above ground of an initially circular cross-sectional seamless smooth pipe bend of uniform thickness (t) with different pipe bend diameter to thickness ratio(D/t) of range ( from 20 to 200) with a wide range of bend angles( Ø ) (from 10 to 160 degrees)and bend radii (R ) from (1D to 5D), with a fixed-loaded end condition. These proposed models are of high significance for the design of any lateral support located at the pipe bend which will affect the results.
The current design codes are addressed with pipe bends under internal pressure the same as a straight pipe. The predictive code stresses are based on Peter Barlow’s formulas with no modification to account for the increase in stresses. However, the analytical study conducted in this research using the commercial finite element package “ABAQUS” shows that the internal pressure effect ends up in an increase in stresses of pipe bend by up to 49% than that predicted by the current codes (ASME B31.1, B31.3) [35,36], which could threaten the safety of the pipeline and therefore the surrounding environment.
The FEA results show that the combined stresses evaluated using the ASME equation are un-conservative since the actual stress on the pipe bend reaches up to 1.5 times the estimated stress for a short bend radius (R=1D).
The behavior of pipe bends under in-plane bending moment has a different phenomenon affecting the stress distribution. The deformation of the cross-section depends on the direction of the bending moment based on the analytical study presented in Chapter (4).
It had been shown from the FEA results that for a bend under in-plane opening bending moment, the pipe gains stiffness with loading as a result of the oval deformed cross-section. However, the bend gains flexibility within the case of an in-plane closing bending moment since the cross-section flattens more with loading resulting in a reduction of the second moment of area.
Moreover, the FEA results show that the Von Mises stress from the closing bending moment is higher than the opening bending moment by up to 181%.
For pipe bends subjected to in-plane opening or closing bending moment, the critical section is found at the mid-length of the pipe bend where the stresses are maximum at the inner layer of the wall thickness at the crown location (Θ=90). Based on the FEA results in this study, the stresses at the inner and outer layers are found to be higher than the mid-layer stress by up to 210% which, if ignored, the pipe bend design will be unsafe. Therefore, the stresses need to be checked at the critical layer of the pipe wall thickness not just the mid-layer of the pipe. The (ASME B31.1, B31.3) [35, 36], design methodology was revisited during this study and compared to the FEA results to reassess the stress intensification factors.
The study shows that the (ASME B31.1, B31.3) [35, 36], design criteria are highly conservative for small bend angle pipes (Such as; 10 and 30 degrees). However, as the bend angles increase the (ASME) is un-conservative by up to 25% for mid-layer and may go up to 210 % for inner and outer layers.
Based on the FEA results of Chapter (4) a stress intensification factor is developed for in-plane opening and closing bending moments to evaluate the stress on the three different layers of wall thickness considered in this study. These SIF factors are based on a pipe bend with attached straight pipes having fixed-loaded end conditions.
The factors show good accuracy in comparison to the FEA results with an average error of 15%. These factors included the effect of bend angle (Ø), the direction of bending moment, and the bend radius (R) on the stresses to the formula, which were ignored from the factors proposed in the past studies and (ASME B31.1, B31.3) [35,36], design codes.
In addition to that, when the internal pressure loading is followed by an in-plane bending moment, this combination is a complex problem that needs further study since changing the ratio between both loading values alters the behavior of the bend. The effect of the ratio between the internal pressure and also the bending moment on the stress levels remains indistinct and needs further investigation.
The proposed Stress Intensification Factor SIF (P+M) is found to be unconservative, for some of the modeled pipes since it had been based on the best fit for the data points. Therefore, the standard deviation for the proposed factors is provided to enable shifting the curve ensuring conservative predictions.
7.3 Recommendations for Future Studies
1. A detailed stress analysis of the pipe bends, especially at its critical section, under the in-plane bending moment loading case, is provided here in this study. These results may be very useful, for designers as well as researchers, in gaining a deeper understanding of the structural behavior of pipe bends. Of course, further work is required to cover other aspects of the pipe bend problem, including the combined loading, and to analyze different effects, such as the effect of end constraints, despite taking into consideration the attached long straight pipe
2. The effect of residual stresses and initial geometric imperfections may affect the stresses on pipe bends starting from the forming process stage and leading to the service process stage. Therefore, future study is suggested to incorporate these parameters into the investigation and evaluate the increase in stresses generated from them.
3. The results show that adding the closing bending moment loading to internal pressure loading may increase or decrease the von mises stresses on the pipe bends, taking into consideration that the ratio between the two loadings is constant during this study. Therefore, it is recommended to consider different ratios of internal pressure to bending moment loading in future studies and this ratio could be considered as one of the variables affecting the pressure correction factors.
4. The thermal changes should be applied to the pipe bends that may cause extra pipe bend ovalization( thermal expansion) and stress variation between the three layers ( inner, mid, and outer layers) along with the thickness.