الفهرس 
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Abstract
A pipe bend’s cross-section tends to deform significantly both in and out of its plane. This shell-type behavior, characteristic of pipe bends and mainly due to their curved geometry, accounts for their greater flexibility.
This added flexibility is also accompanied by stresses and strains that are much higher than those present in a straight pipe of the same size and material, under the same loading conditions. For this reason, pipe bends are considered the critical components of a piping system. Hence, for the
purpose of designing and/or qualifying a pipeline structurally, it is useful to have a reliable estimate of their load-carrying capacity, along with a deep understanding of their structural behavior until instability, under different and combined loading conditions.
This research focuses on analyzing and solving a certain case of study of pipe bends presented in a Canadian research centre (Pipeline Integrity & Operations C-FERTechnologies, Edmonton, AB Canada).
A horizontal water pipeline network of (1906 Km) made of carbon steel above ground. After the operation of the pipeline, a sudden ground settlement of one of the pipeline supports resulted in crack initiation then crack propagation that lead to the rupture of one of the connecting vital pipe bends and leakage. This ground settlement resulted in the displacement of one of the supports subjecting the pressurized pipe bend to in-plane bending moments in different directions that were expected to lead to that collapse.
The loading on the pipe bends are found to be, firstly: the pressure during the induction of the transferred medium to the processing facility branched pipes, and followed by secondly: the in-plane bending moments (closing or opening). The effect of the two types of loading is going to be studied separately and in combination in this thesis to observe the effect of these loadings and the changes in stiffness, flexibility, stress levels, and test the link between such changes and the cross-section deformation.
Moreover, the combined loading of the internal pressure and in-plane bending results in a complex behavior than that to be solved using theoretical approaches. The bending moment tends to deform the initially circular cross-section of the bend into an oval or flattened shape for opening and closing bending moments, respectively. However, the internal pressure tends to resist the cross-sectional deformation resulted from the bending moment and tends to straighten out the pipe bend due to the generated outward forces. These two behaviours are nonlinear where the stresses cannot be added based on superposition. Past studies proposed a “Pressure reduction factor” that accounts for the reduced stress generated due to adding internal pressure to a closing in-plane bending moment. This factor is used by the current codes without modification for the case of in-plane opening bending or out-of-plane bending moments. Moreover, these factors ignored the effect of the pipe bend angle on the generated stresses which is found to be highly significant.
Focusing on the effect of that ground settlement on the behavior of large pipe bends, an extensive parametric study is conducted taking into consideration the wide selection of pipe sizes (NPS) from NPS20 (508mm) up to NPS72 (1829mm), with different bend angles (Ø) ( from 30° up to 160°),and bend radii (R), (R= 1D, 5D), to quantify the effect of bend angle (Ø) of an initially circular cross-sectional seamless smooth pipe bend of uniform thickness (t) with different pipe bend radius to thickness ratio (r/t ) (from 10 to100) on the stress distribution along with the pipe bend thickness layers (outer, mid and inner layers).
Additionally, in this research different cross-sectional dimensions are selected to develop the stress intensification factors presented in current design codes for the in-plane bending moment using large deformation finite element analysis, and the internal pressure effect combined with in-plane bending moments. Comparing the numerical analysis results presented in this thesis with ASME B31.1, B31.3 codes confirms that the ASME piping code underestimates the stresses on pipe bends under internal pressure and bending moment in both directions. However, for pure bending, the codes are conservative in some cases and un-conservative in other cases depending on the bending moment direction, the pipe bend angle, and geometry.
Finally, a tabulated comparison was done on the finite element model (FEA) results compared with currently available design codes (ASME B31.1, ASME B31.3), and the previously past proposed analytical solutions for similar pipe bends of other researchers, in addition to that a newly developed stress intensification factors (SIF) were also investigated which are beneficial for the piping industry since they consider more parameters and cover a wider range of pipe sizes and geometry.