The pipelines used to transport oil and gas from the wellheads to the distribution and refining sites can be subjected to high levels of pressure and temperature. Under such conditions, the pipelines tend to expand, but, if the expansion is inhibited, a significant compressive axial force can arise, leading to their buckling, which can occur in the horizontal or vertical plane. In this context, the objective of the present work is to analyze the upheaval buckling of pipelines, considering the internal pressure to which they are subjected during the transportation of oil and gas as its only triggering. Using the concept of effective axial force, it aims at discussing two different approaches for considering the internal pressure in buckling problems: distributed loads dependent on pipeline curvature and equivalent compressive axial forces with follower and non-follower characteristics. It also discusses the influence of using static or dynamic analysis for such approaches. Concerning the upheaval buckling itself, the work intends to analyze and compare the influence of the soil imperfection amplitudes to the influence of the friction between the pipeline and the ground in the critical loads and in the post-buckling configurations of the pipeline. Besides theoretical research, the objectives are achieved through the development of various numerical models, since geometrically-simple models, without the consideration of the interaction between the pipeline and the ground, until more complex models, with the use of contact models to detect the ground and its imperfections. The models are developed in Giraffe (Generic Interface Readily Accessible for Finite Elements) using geometrically-exact finite element models of beams, undergoing large displacements and finite rotations. Through the research, it is concluded that there is an equivalence between the application of the internal pressure as a distributed load dependent on pipeline curvature and the application of the internal pressure as a follower compressive axial force. Besides this, it is demonstrated that the type of the analysis (static or dynamic) depends on the nature of the physical system analyzed. With the aid of results presented in terms of internal pressure, classical results about the influence of the imperfection amplitudes and of the friction between the pipeline and the ground in buckling are confirmed. It is also showed that the imperfection amplitudes analyzed play a more important role in the post-buckling configurations of the pipeline than the friction.
Reinforced concrete shell elements are relevant in several civil and industrial structures. It is important to know the methods for designing and verifying such elements. In this context, the present paper aims at describing the iterative three-layer method proposed by Colombo et al. This method is based on the Model Code/1990, and it can be applied in the design of shell elements. An additional method for verifying reinforced concrete shell elements is also proposed and discussed. This one is based on the multilayer method proposed by Kollegger et al. Formulations as well as numerical examples are presented for both methods. The design proposed by Colombo et al. is verified by using the methodology based on the multilayer method. Although both methods lead to the equilibrium between applied and resistance loads using approximately the same amount of reinforcement, especially for small neutral axes in relation to the element thickness, one may conclude that the three-layer design method has limitations due to not considering strain compatibility along the thickness of the element and due to the impossibility to calculate the compression reinforcement. Although the multilayer method overcomes such limitations, it is a verification method, and more studies about its use in the design of reinforced concrete shell elements are necessary.
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