Stress Analysis of Thin Walled Pressure Vessels
The safe design, analysis, installation, operation, and maintenance of pressure vessels are in accordance with codes such as American Society of Mechanical Engineers (ASME) Boiler and Pressure Vessel Code. Therefore, great emphasis should be placed on analytical and experimental methods for determining their operating stresses.
Pressure vessels hold gases or liquids at a pressure substantially different from the ambient pressure. They have a variety of applications in industry, including petrochemical and energy. Pressure vessels can be any shape, but typical shapes are spheres and cylinders.
The spherical vessel is preferred for storage of high pressure fluids. For the same wall thickness, a spherical pressure vessel has approximately twice the strength of a cylindrical vessel. The distribution of stresses on the sphere’s surfaces, both internally and externally are uniform. A spherical storage has a smaller surface area per unit volume than any other shape of vessel. However, a spherical vessel is more expensive to manufacture than a cylindrical vessel.
Stress Analysis of Thin Walled Vessels
The stress in the walls of a thin-walled pressure vessel is proportional to the pressure and radius of the vessel. They are considered thin-walled when the ratio of the radius to the wall thickness is greater than 10. The failure of pressure vessels occurs when the stress state in the wall exceeds a certain criterion, emphasizing the importance of understanding and quantifying stresses in these vessels. The stress analysis of thin-walled pressure vessels involves evaluating the normal and shear stresses in the vessel walls.
For example, in a Cylindrical Pressure Vessel, the circumferential stress and axial stress are important parameters to consider. The circumferential stress is given by:
σ c = Pr / t where P is the internal pressure, r is the radius, and t is the wall thickness.
The axial stress is given by σ a = Pr / 2t, and the maximum shear stress is τc = Pr / 4t
The analysis of thin-walled pressure vessels is based on the theory of elasticity and involves assumptions such as uniform stress distribution across the wall thickness. This analysis is valid when the thickness is much less than the radius of the vessel. For example, a pressure vessel is considered thin-walled if its radius is larger than 5 times its wall thickness.
A Spherical Pressure Vessel is just a special case of a cylindrical vessel. To find σ we cut the sphere into two hemispheres. The free-body diagram gives the equilibrium condition
σ = σ a = σ h = Pr / 2t
In the spherical vessel the double curvature means that all stress directions around the pressure point contribute to resisting the pressure. Understanding the stresses developed in these vessels is crucial for ensuring their structural integrity and preventing failure. The analysis involves evaluating the normal and shear stresses in the vessel walls, taking into account the vessel’s geometry and internal pressure.
Fatigue Analysis of Thin Walled Vessels
Experience shows that fatigue cracks in such vessels are caused by cyclic thermal and pressure stresses. They typically occur at structural discontinuities and weldments. Residual stresses at weldments play a major role in the initiation and propagation of such cracks. Stress corrosion cracking and fatigue at nozzles and other structural discontinuities can be evaluated using materials science and finite element analysis.
O’Donnell Consulting Engineers Performs Stress Analysis on Vessels for Clients in Industries including Power and Petrochemical.