Vessel walls internal stresses

All blood vessels experience internal tension under normal diastolic blood pressure. In addition to this static tension, chronic changes in wall stress that occur as a result of increases in blood pressure have been reported to lead to vascular remodeling, increased vascular wall diameter and thickness, in an attempt to restore normal values of vessel wall shear stress. Increased... 

Calculate the maximum membrane stress in the wall of shells having the shapes listed below. The vessel walls are 2 mm thick and subject to an internal pressure of 5 bar. 

Fig. 4.3-4 (ABC) gives the superimposed stress distribution in the walls of a two-layered vessel under internal pressure. It can be clearly recognized that the compressive tangential prestresses by shrink-fitting (Fig. 4.3- 4B) are decreased at the inner layer and increased at the outer layer towards a more even stress distribution (Fig. 4.3- 4 C) compared to that for a monobloc cylinder (Fig. 4.3- 4A). The theoretical fundamentals for the dimensioning of shrink-fit multilayer cylinders can be taken from [2][8][9].

Active stresses exerted by smooth muscle cells appear to increase the internal stresses that exist in vessel wall. The effects of passive and active muscular contraction on the residual stress in the wall have been considered. Their results suggest that basal muscle tone, which exists under physiological conditions, reduces the strain gradient in the arterial wall and yields a near uniform stress distribution. Increased muscular tone that accompanies elevated blood pressure tends to restore the distribution of circumferential strain in the arterial wall, and to maintain the flow-induced wall shear stress at normal levels. It appears that the active stresses exerted by smooth muscle cells may balance the tension within the vessel wall in a similar manner to the way that active fibroblast tension balances the stress in the dermis. 

Even in a thin-walled vessel the radial stress is not exactly imiform over the vessel thickness. To correct for this, the internal pressiue in the denominator of Equation 6.4 is multiplied by 1.2 to obtain a more accurate formula. Thus,... 

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. 

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... 

The ellipsoidal dished head with a major to minor axis ratio of 2 1 is popular for economic reasons, even though the theory for thin-walled vessels predicts that the head of this shape should have twice the thickness of a hemispherical head where the major and minor axes are equal. Such an ellipsoidal head used for vessels under internal pressure has the same thickness as the cylindrical shell if the same allowable stresses and joint efficiencies are applied to both parts. The 1962 ASME Code Section VIII, Division 1 gives the following equation for the thin-walled ellipsoidal dished heads with a 2 1 major to minor axis ratio ... 

Since lugs are eccentric supports they induce compressive, tensile, imd shear forces in the shell wall. The forces from the eccentric moments may cause high localized stresses that are c ombined unth stresses from internal or e.xternal pressure. In thin-walled vessels, these high local loads have been kn(rwn to physically deform the vessel wall considerably. Such deformations can cause angular rotation of the lugs, which in turn can caii.se angular rotations of the supporting steel. 

A spherical vessel is moulded from a pofymer whose one-month tensile creep compliance D(1 month) is 2 GPa . The vessel is of diameter 400 mm and wall thickness S mm. A constant internal pressure is applied to the vessel, giving rise to a tensile stress 1.6 MPa acting uniform in all directions in the plane of the vessel wall. Find (a) the change in diameter, and (b) the change in wall thickness, after 1 month of pressurization, assuming the polymer to be linearly viscoelastic with constant Poisson ratio v = 0.41. 

Yielding of the inner surface begins when the maximum shear stress is equal to the yield point shear stress. As the pressure, or force, is increased the plastic deformation penetrates farther into the vessel wall until it reaches the outer surface. At that point the entire shell has yielded. If the internal pressure is removed after the cyhnder is in plastic state, a residual stress will remain in the wall. This residual stress allows the cylinder to contain more pressure then would be possible to without it. 

There are also no decisions to make about the shape of the work chamber it must have the shape of the parts — or of the collection of parts if they are small (Figure 2.19). Enclosed vacuum machines constmcted in the early 1990s had work chambers with a cylindrical shape — for all parts. This is because the walls of a cylindrical pressure vessel can be thinner (and so cheaper and more available) to constrain a given level of internal stress (vacuum or pressure) if they are round. ... 

The l..jime hoop-siress equation indicates that the maximum stress occurs at the famer surface of the vessel. By shrink-lilting concentric shells together the inner shells are placed in residual compression so that the initial cfimpressive h(M>p stress must be relieved by the internal pressure before hoop tensile stresses are developed. Therefore the maximum hoop tensile stress as determined by Lame s relaUon-ship is apprecial>ly reduced with the result that there is a reduction of the total wall thickness retfuired l,o cnnf,ain the pressure when the vessel-wall thickness is designed with a speci/ied allowable stress. 

Results demonstrate that normal vessels experience more stresses due to applied internal loads. In the case of atherosclerotic blood vessels, the stress experienced by the vessel wall is much lowered due to the deposition of plaque material on the inner wall of the vessel. 

Results demonstrate that normal vessels experience more stresses due to applied internal loads. In the case of atherosclerotic blood vessels, the stress experienced by the vessel wall is much lowered due to the deposition of plaque material on the inner wall of the vessel. It appears that an inverse relation exists between the considered mechanical parameters and the percentage of plaque deposited on the inner vessel wall. It was further observed that the total displacement and Von Mises stress decrease nonlinearly with increasing plaque percentage. Whereas, the strain energy density decreases almost linearly with increase in plaque deposition. 

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. 

A series of utuaxial fatigue tests on unnotched plastic sheets show that the fatigue limit for the material is 10 MN/m. If a pressure vessel with a diameter of 120 mm and a wall thickness of 4 mm is to be made from this material, estimate the maximum value of fluctuating internal pressure which would be recommended. The stress intensity factor for the pressure vessel is given by K = 2hoop stress and a is the half length of an internal defect. 

A cylindrical steel pressure vessel (AlSl SAE 10.85, cold rolled) with a wall thickness of 0.1 in. and an inside diameter of 1 ft is subject to an internal pressure of 1,000 psia and a torque of 10,000 ft-lb (see Figure 2-30). What is the effective stress at point A in the wall What is the factor of safety in this design ... 

A common pressure vessel application for pipe is with internal pressure. In selecting the wall thickness of the tube, it is convenient to use the usual engineered thin-wall-tube hoop-stress equation (top view of Fig. 4-1). It is useful in determining an approximate wall thickness, even when condition (t < d/10) is not met. After the thin-wall stress equation is applied, the thick-wall stress equation given in Fig. 4-1 (bottom view) can be used to verify the design (Appendix A PLASTICS DESIGN TOOLBOX). 

The analysis of the membrane stresses induced in shells of revolution by internal pressure gives a basis for determining the minimum wall thickness required for vessel shells. The actual thickness required will also depend on the stresses arising from the other loads to which the vessel is subjected. 

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