Pressure vessels thin-walled

For many vessels, pipes, and other containers, the principal structural requirement is that the walls must withstand the pressure of the fluid in them. The calculation of the required wall thickness of thin-walljed vessels is quite simple. 

Since these forces are equal and opposite, they may be equated and solved for the thickness  

This equation describes not only the stresses in a pipe wall but also those in a cylindrical pressure vessel. j 

This approach ignores stresses in the axial direction for moderate pressures and wall thicknesses this simplification djoes not cause much error. 

Example 2.22. We wish to select a pipe with 1-ft inside diameter that can withstand an internal pressure of 1000 psig. The steel to be used has a safe 

The simultaneous solution of Eqs. (4.2) and (4.3) allows the forces and stresses in the various rods to be determined. It should be noted that even though linear elasticity is assumed, the terms for stresses do not involve the elastic constants. This is not true, however, for the strains. In the last chapter, the geometry shown in Fig. 3.25 was statically indeterminate, and to solve the problem the rods were assumed to be linear elastic. 

A simple example of a statically determinate problem is a thin-walled cylindrical pressure vessel with spherical end-caps, containing a gas or fluid exerting a pressure P. The geometry is shown in Figs. 4.3 and 4.4 the cylindrical section has a radius r, length L and thickness t, such that L r t. The cylinder is being expanded by the internal pressure and the principal axes are easily 

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A thin-walled pressure vessel is one in which the wall thickness t is small when compared to the local radius of curvature r. At a point in the wall of the vessel where the radius of curvature varies with the direction, the wall stresses are... 

In all the major industrialised countries the design and fabrication of thin-walled pressure vessels is covered by national standards and codes of practice. In most countries the standards and codes are legally enforceable. 

The maximum shear stress will depend on the sign of the principal stresses as well as their magnitude, and in a two-dimensional stress system, such as that in the wall of a thin-walled pressure vessel, the maximum value of the shear stress may be that given by putting (73 = 0 in equations 13.3 and c. 

The formulas for thin-walled pressure vessels are first-order equations and are easier to rearrange and solve for minimum thickness and maximum stress values. The thick-walled vessel formulas provide the most accurate value for the stresses in the pressure vessel wall, but solving the thin-walled equations provides comparatively accurate results and is, therefore, quite useful for preliminary design estimates. 

The cylindrical shell is frequently used in pressure vessel design. For initial designs, it is useful to calculate the stresses in a thin-walled cylindrical shell that is uniformly loaded with internal pressure. For thin-walled pressure vessel calculations to be valid, the radial stresses in the shell need to be negligible. This is usually taken to be a valid assumption when the ratio of the vessel inner radius to the wall thickness (R/t) is greater than 10. "... 

The structure of this formula can quickly be related to the thin-walled pressure vessel cylinder equation. Using the equation that calculates the stress at the center of the vessel wall, ux = P R + 0.5t)/t, and rearranging to solve for the thickness, results m. t = PR/ ux — 0.5P. The addition of the weld joint efficiency, E, and changing the coefficient before P to 0.6 results in the ASME code formula, t = PR/ SE — 0.6P), which they feel best represents the minimum wall thickness required to contain an internal pressure, P, in a cylindrical vessel having a radius, R, and made of a material with an allowable stress, S. 

ASTM Designation A 372/A 372M Standard Specification for Carbon and Alloy Steel Forgings for Thin-Walled Pressure Vessels ... 

Their design does not fall into the category of thick-walled, high-pressure vessels but rather into the field of thin-walled pressure vessels. The basic equations for thin-walled vessels under internal pressure show that the radial stress in a shell may be neglected because it is small, with a maximum... 

For thin-walled pressure vessels, both theories yield approximately the same results. 

For thin-walled pressure vessels the radial stress is so small in comparison to the other principal stresses that it can be ignored and a state of biaxial stress is assumed to exist. 

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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