Pressure vessels axial stresses

Probably the largest compound vessels built were two triple-wall vessels, each having a bore diameter of 782 mm and a length of 3048 mm designed for a pressure of 207 MPa (30,000 psi). These vessels were used by Union Carbide Co. for isostatic compaction unfortunately the first failed at the root of the internal thread of the outer component which was required to withstand the end load (40). A disadvantage of compound shrinkage is that, unless the vessel is sealed under open-end conditions, the end load on the closures has to be resisted by one of the components, which means that the axial stress in that component is high. 

Thermal Stresses. When the wak of a cylindrical pressure vessel is subjected to a temperature gradient, every part expands in accordance with the thermal coefficient of linear expansion of the steel. Those parts of the cylinder at a lower temperature resist the expansion of those parts at a higher temperature, so setting up thermal stresses. To estimate the transient thermal stresses which arise during start-up or shutdown of continuous processes or as a result of process intermptions, it is necessary to know the temperature across the wak thickness as a function of radius and time. Techniques for evaluating transient thermal stresses are available (59) but here only steady-state thermal stresses are considered. The steady-state thermal stresses in the radial, tangential, and axial directions at a point sufficiently far away from the ends of the cylinder for there to be no end effects are as fokows ... 

Wind, seismic and vibrational stresses and accumulated dead weight compression loadings primarily affect the axial stress and produce only a small effect as a result of Poisson s relationship on the circumferential stress. Therefore, the shell thickness of the upper portion of a tall vertical vessel designed to operate under either internal pressure or vacuum is determined by the circumferential stress. 

We will now consider the special problems in tall tower design which are not described in the ASME Code for Unfired Pressure Vessels. As discussed previously, circumferential stresses control the design of cylindrical vessels if external loads are of small magnitude. In tall vertical vessels, four major factors (wind load, seismic loads, dead weight and vibration) may contribute to axial stresses — in addition to axial stress produced by the operating pressure or vacuum of the vessel. 

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. 

Many investigations have been made on the low-temperature properties of aluminum alloys [1-4] however, in addition to the determination of tensile and elastic properties as a function of temperature, notched tensile properties and notched/unnotched tensile ratios were determined. The notched/unnotched ratios were determined as a function of temperature in order to evaluate the toughness, which is often referred to in terms of resistance to brittle fracture, or notch sensitivity [5-7]. A notched specimen with a stress concentration factor K oi 6.3 was selected for use in this investigation because previous axial fatigue tests of complex welded joints, and fatigue and burst tests of pressure vessels made of 301 extra full hard stainless steel exhibited excellent correlation with notched/unnotched tensile ratios obtained with this value of over a range of temperatures... 

Hechmer, J.L., and Hollinger, G.L. Three-dimensional stress criteria -summary of the PVRC project, /. Pressure Vessel TechnoL, 122, 105-109, 2000. Chattopadhyay, S., Allowable stresses for nonrectangular sections under combined axial and bending loads, /. Pressure Vessel TechnoL, 110, 188-193, 1988. 

Again, the viscoelastic solution for stress is exactly the same as the elastic solution stress. As stated earlier, in general, if the linear elastic solution for stresses for a given boundary value problem does not contain elastic constants, the solution for stresses in a viscoelastic body with equivalent geometry and equivalent loads is identical to that for the elastic body. This means that the stress analysis of most problems considered in elementary solid mechanics such as beams in bending, bars in torsion or axial load, pressure vessels, etc. will have the same solution for stress in a linear viscoelastic material as in a linear elastic material. Further, stress analysis of combined axial, bending, torsion and pressure loads can be handled easily using superposition. 

Allowable Tensile Stresses in the ASME Code Allowable External Pressure Stress and Axial Compressive Stress in the ASME Boiler and Pressure Vessel Code... 

ALLOWABLE EXTERNAL PRESSURE STRESS AND AXIAL COMPRESSIVE STRESS IN THE ASME BOILER AND PRESSURE VESSEL CODE... 

For g > 1.0, the vessel may fail by yielding and should also be checked as u cantilever beam including the axial stress effect due to the external pressure. The axial load from the external pressure is... 

Here it can be differentiated between closures attached directly to the pressure vessel and those supported by an external frame. In the first case, the pressure vessel needs to transmit the axial end load. In the other case, the axial load is carried by the frame and the pressure vessel is subjected to circumferential and radial stresses only. 

Using the cylindrical part of the pressure vessel itself to transmit the longitudinal load will normally be the more economic solution. The additional axial stress does not affect the pressure limit of the vessel significantly, since the maximum shear stress results from the circumferential and the radial stress [18]. 

Chapter BIO Thick-walled cylindrical shells under internal pressure pressure vessels within the limitation 1.2 < D/d <1.5 provided that the shell sustains the full axial stress and the material of the shell shows ductile behavior (AD2000-B10, 6.1.1) dP fmin - 2 35 3P... 

Two types of analytical models are available for dealing with cyhndrical pressure pipes. The thin wall method is the most commonly adopted solution. It is based on a simple mechanics approach and is only apphcable to vessels having a diameter-to-wall-thickness ratio of greater than 20 (Hearn, 1997). Using the thin wall method for an unconstrained, closed-end thin wall cylindrical pressure vessel, the circumferential hoop stress and longitudinal axial stress can be shown to take the form ... 

The exact calculation of radial and circumferential stresses in each layer requires the solution of N+2 linear equations in N-r2 unknowns, namely the N-H radial displacements of the layer boundaries, and the longitudinal strain of the vessel. We simplify by assuming that the internal pressure is applied only to the steel shell, and that the other layers follow the expansion of the steel. We also assume a condition of plane stress that is, no stress in the axial direction of the cylindrical vessel. We also consider the layer as being flat when layer stresses are being computed. 

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