Introduction
Cylindrical pressure vessels have varied functions in our society today. When you drive into a filling station for gasoline, you encounter cylindrical pressure vessels as storage containments for the gasoline in underground burrows. Many of the people living in the countryside do not have cooking gas piped into their houses. They use cylindrical pressure vessels that contain liquefied petroleum gas. Containers of smaller sizes that serve different sizes in our households are cylindrical pressure services.
The fact is that cylindrical pressure vessels are very important, because of their varied functions. In underscoring the importance of cylindrical pressure vessels, the engineering field has developed mechanisms to analyze them in order to study the structural integrity of cylindrical pressure vessels. One of these methods is the finite element methods. As an engineering student, I could not agree more, especially after witnessing a gruesome accident after a tanker transporting liquefied petroleum gas rapture releasing its contents resulting in damage of property, loss of live ad destruction of property.
The design of most cylindrical pressure vessels features hemispherical ends on both extremes. The design is made is such a way that the internal pressure in the cylindrical pressure vessel is uniform across the entire plane. For the purposes of this paper, the material that is used to make the cylindrical pressure vessel is the EN-18C (BS-540A40) in addition to quenched and tempered steel alloys. With this in mind, I intend to perform an analysis the stress in the cylindrical pressure vessel. I will use the finite element method, with special focus on the constant string triangular element. The assumptions made in this paper are that the Poisson’s ration is 0.30 and that there is a uniform temperature in the cylindrical pressure vessel.
Stresses experienced by cylindrical pressure vessels
Longitudinal Stress
Cylindrical pressure vessels experience triaxial stresses. One of the three stresses is the longitudinal stress. This is the kind of stress that is found on the axis of those cylindrical pressure vessels that have hemispherical ends. As was introduced before, cylindrical pressure vessels are designed in a way that they have hemispherical ends. In such designs, the internal pressure acting on the walls of the cylindrical pressure vessel also acts on the hemispherical ends. The result of this is a force that pushes these ends outwardly. Longitudinal stress can be calculated using the following formula
σx=pd/4t
The longitudinal stress for the cylindrical pressure vessel is 47.1 Mpa
Circumferential Stress
Circumferential stress is a stress that occurs in cylindrical pressure vessel. Unlike the longitudinal stress that acts on the hemispherical ends, circumferential stress patterns in the azimuth direction. Circumferential stress, just like the name suggests acts on the circumference of the cylindrical pressure vessels. When this is compared to longitudinal stress, circumferential stress occurs perpendicularly to longitudinal stress, or the axis of a cylindrical pressure vessel. From the middle of the cylindrical pressure vessel, circumferential stress is exerted uniformly on the either side of the axis. The calculation of circumferential stress can be done using the following formula:
σh=pd/2t
Circumferential stress for the cylindrical pressure vessel is 94.2 Mpa
Radial Stress
Cylindrical pressure vessels undergo three types of stress. The third type of stress is the radial stress. Radial stress is exerted from the central axis of the cylindrical pressure vessel. When this pressure is compared to circumferential and longitudinal stress, radial stress is the smallest in magnitude. There is usually a tendency to disregard this type of stress because of its small nature of the magnitude. It is noteworthy that radial pressure is antagonistic and of an equal force to the gauge pressure that is experienced on the inside of the cylindrical pressure vessel. This balance is what ensures that the cylindrical pressure vessel does not collapse on either end. The radial pressure is zero when compared to the gauge pressure that is exerted on the outside of a cylindrical pressure vessel. Radial stress in a cylindrical pressure vessel can be calculated using the following formula
σr=-p/2
Reflections and Conclusion
Throughout the paper, I have underscored the importance of analyzing the stresses in cylindrical pressure vessels. This is because of the varied and sensitive functions that they perform in the society. I highlighted the accident that involved spillages of liquefied petroleum gas, leading to loses, damage of property, loss of lives and destruction of the environment. Engineering domains have come up with methods of analyzing stress in cylindrical pressure vessels. This paper focused on one of these methods, the finite element methods, with a special focus on constant strain triangular element. When a cylindrical pressure vessel is filled with pressurized contents, all the three stresses exert on the walls of the vessel. Since these stresses affect the walls of the vessel on different parts. As such it is important to understand the dynamics of these stresses in order to enhance the structural integrity of the vessel.
I have witnessed pipelines that transport petroleum, refined fuels and cooking gas from refineries to storage plants destroyed after earthquakes. When inspecting those pipelines that are not damaged, engineers use cameras that check the inside of pipelines for sutures and fractures. This is because most of the stresses act on the inside of cylindrical pressure vessels, and as such, and cracks start on the inside. Using the finite element methods and more so the constant strain triangular element, one can analyze the strains and stresses on these vessels so as to ensure that they are structurally strong. Such actions would prevent potential accidents that from my experience have adverse effects on human beings, the environment and property. Engineering has provided a way o not only create these all important vessels but to also ensure that they serve us safely.
