Compressive stresses, pressure vessels

The maximum compressive stress will occur when the vessel is not under pressure = 7.4 + 61.1 = 68.5, well below the critical buckling stress. 

Pressure vessels are subjected to other loads in addition to pressure (see Section 13.4.7) and must be designed to withstand the worst combination of loading without failure. It is not practical to give an explicit relationship for the vessel thickness to resist combined loads. A trial thickness must be assumed (based on that calculated for pressure alone) and the resultant stress from all loads determined to ensure that the maximum allowable stress intensity is not exceeded at any point. When combined loads are analyzed, the maximum compressive stress must be considered as well as the maximum tensile stress. The maximum allowable stress in compression is different from the maximum allowable stress in tension and is determined using the method given in ASME BPV Code Sec. VIII D.l Part UG-23. 

Mechanical failures occur when the part is exposed to some t5q)e of force that exceeds its capability. A part may be exposed to three different t5q)es of forces tensile, compression, and vacuum-generated stresses. Many processes require super- or subatmo-spheric pressure. In a fluoropol5mier-Iined vessel or a stand-alone vessel at elevated pressure, the walls are subjected to tensile stress. Compression stress develops in parts such as seals and gaskets where force is applied to the part, for instance, by placing it between bolted flanges. Vacuum can be a permanent or transient feature of a process and subjects a part to complex forces which could be a combination of tensile and compression. 

The maximum compressive stress (downwind side) at point X with an unguyed vessel under internal pressure and in the absence of eccentric loads is... 

Two types of stress can be present simultaneously in one plane, provided that one of the stresses is shear stress. Under certain conditions, different basic stress type combinations may be simultaneously present in the material. An example would be a reactor vessel during operation. The wall has tensile stress at various locations due to the temperature and pressure of the fluid acting on the wall. Compressive stress is applied from the outside at other locations on the wall due to outside pressure, temperature, and constriction of the supports associated with the vessel. In this situation, the tensile and compressive stresses are considered principal stresses. If present, shear stress will act at a 90° angle to the principal stress. 

Ductility is the plastic response to tensile force. Plastic response, or plasticity, is particularly important when a material is to be formed by causing the material to flow during the manufacture of a component. It also becomes important in components that are subject to tension and compression, at every temperature between the lowest service temperature and the highest service temperature. Ductility is essential for steels used in construction of reactor pressure vessels. Ductility is required because the vessel is subjected to pressure and temperature stresses that must be carefully controlled to preclude brittle fracture. Brittle fracture is discussed in more detail in Module 4, Brittle Fracture. 

Solution The stresses existing in the walls of a cylindrical vessel under pressure can be reduced to (1) the tangential or hoop stress o, (2) the radial stress Oj, and (3) the longitudinal stress Oj. For a cylinder under internal pressure, and Oj are tensile stresses while o, is a compressive stress. vessel failure. For a thick-walled vessel (i.e., where r /rj = R > 1.2) ... 

Pressure vessels commonly have the form of spheres, cylinders, cones, ellipsoids, tori, or composites of these. When the thickness is small in comparison with other dimensions (Rn/t > 10), vessels are referred to as membranes and the associated stresses resulting from the contained pressure are called membrane stresses. These membrane stresses are average tension or compression stresses. They are assumed to be uniform across the vessel wall and act tangentially to its surface. The membrane or wall is assumed to offer no resistance to bending. When the wall offers resistance to bending, bending stresses occur in addition to membrane stresses. 

This procedure is to determine the maximum allowable stress for tubular members that are subject to axial compression loadings. Tubular members may be a pressure vessel, a pipe, a silo, a stack, or any axially loaded cylinder of any kind. In addition, axial-loaded cylinders may be subjected to other load cases simultaneously. Other load cases include bending and internal or external pressure. 

For AS ME Code vessels the allowable compressive stress is Factor B. The ASME Code, factor B. considers radius and length but does not consider length unless external pressure is involved. This procedure illustrates other methods of defining critical stress and the allowable buckling stress for vessels during transport and erection as well as equipment not designed to the ASME Code. For example, shell compressive stresses are developed in tall silos and bins due to the side wall friction of the contents on the bin wall. 

Compressive stress is not significant where R /t < 200 and the vessel is designed for internal pressure only. 

The aramids fibers, however, have relatively poor shear and compression properties in a composite. Components, such as pressure vessels, that avoid these stresses make the most efficient use of aramid fiber. 

Bp = Allowable bearing pressure, PSI Do = OD of vessel shell, in Dsk = OD of skirt at base plate, in E = Modulus of elastidly, PSI Fc = Allowable compressive stress, PSI f = Load at support points. Lbs fp = Bearing pressure, PSI Ft = Allowable sttess, tension, PSI Fy = Minimum specified yield strength of skirt at design temperature, PSI... 

In addition to the simple membrane stress of the cyhnder, the shell is subjected to a radial stress due to the direct apphcation of the pressure against the wall. This is a compressive stress and is insignificant for thin walled pressure vessels when compared to the other principal stresses. But the radial stress becomes more significant as the pressure and thus the thickness is increased. 

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