Pressure vessels deflection

There are no hard-and-fast rules to follow in setting safety factors for any given material unless experience exists. The most important consideration is of course the probable consequences of failure. For example, a little extra deflection in an outside wall or a hairline crack in one of six internal screw bosses might not cause concern, but the failure of a pressure vessel or aircraft wing might have serious safety or product-liability implications. 

Skirt construction permits radial growth of pressure vessel due to pressure and temperature through the bending of skirt acting like a beam on an elastic foundation. The choice of proper height of the skirt support ensures that bending takes place safely. Finite-element methods can be effectively used to determine the stresses and deflections due to imposed pressure and temperature distribution. 

Figure 5.22 and 5.23 show gas pressure versus deflection, and Figs. 5.24 and 5.25 show principal stresses at normal operation. Figures 5.26 and 5.27 show principal stresses at 2.5 times the design pressure. Although this vessel layout is different in many respects to that of the Hartlepool reactor, the stress flow in many areas is identical. The stress concentrations around the boilers and at the junction between the caps and the walls are similar in both cases. However, the quantities do differ. It is because of these and some dissimilar stress contours that the final failure modes in both vessels differ. 

Fig. 5.49 High-temperature gas-coofed reactor pressure vessel and deflections...

The interior of a tube bent into a circular arc (so-called Bourdon tube) (3) is connected to the vessel to be evacuated (Fig. 3.2). Through the effect of the external air pressure the end of the tube is deflected to a greater or lesser extent during evacuation and the attached pointer mechanism (4) and (2) is actuated. Since the pressure reading depends on the external atmospheric pressure, it is accurate only to approximately 10 mbar, provided that the change in the ambient atmospheric pressure is not corrected. 

The kinetic theory of gases was first propounded by Daniel Bernoulli in 1738. It was rediscovered and worked out in detail about the middle of the nineteenth century by Kr5nig, Waterston, Maxwell, and above all by Clausius. According to the kinetic theory the molecules of a gas move in straight lines unless they are deflected from their path by impacts with other molecules or with the walls of the containing vessel. They, therefore, exert on every solid wall a pressure which is measured by the momentum which the molecules impart to the wall in unit time. As this momentum is proportional to the number of collisions per unit of timclosed vessel is proportional to the square of the velocity of its molecules. It is assumed in this that all the molecules have the same velocity. When this is not the case, the pressure can be shown to be proportional to the mean square of the velocity. In any case we may write... 

Flat Bottoms Flat bottom vertical cylindrical tanks present particular problems. The bottom must be so constructed and supported as to be completely rigid and well ventilated from the sides and underneath. This may usually be provided by I beams. The bottom shall be tack welded to the I beam so that the bottom will not flex and crack the lining when it is installed. (Reference 8, p 74). The maximum free span between I beams can be calculated on the basis that the maximum deflection under full load conditions shall not exceed the free span divided by 1000. However, in the case of vessels containing only gas at atmospheric pressure and no internal spheres, then the deflection can be as great as the distance divided by 500. It is good design to leave sufficient space between I beams to allow for maintenance perhaps enough space for a man to crawl between them. 

Recognizing that some reactor designs may be impractical or very difficult to completely validate with design formulas, ASME UG-101 offers alternative methods, such as using strain gages, deflection measurements, or pressurizing a vessel to failure, to determine the MAWP. 

The strain gage and deflection methods require the vessel to be pressurized and then released at successively higher pressures until a permanent deflection of 2% is measured. The MAWP of the vessel is established by dividing this test pressure by 2.5. 

In another type of deflection testing, the vessel is pressurized with water to the test pressure and then released. This procedure is repeated three times. The outside diameter of the vessel is measured and recorded at each successive increase and release of pressure. A vessel is considered to have passed the test if it expands to the same dimension each time it is pressurized and contracts to the same original dimension each time the pressure is released. 

The permanent deflection and burst methods of these alternative testing procedures are typically conducted at room temperature and, hence, provide maximum allowable pressure ratings for a vessel when used at room temperature. The corresponding pressure rating at an elevated temperature may be established by multiplying the calculated room temperature rating... 

Fy = minimum yield stress, shell, psi P = internal pressure, psi P,. = external pressure, psi G = gust factor, wind Kz = velocity pressure coefficient 1 = importance factor, 1.0-1.25 for vessels V = basic wand speed, mph Ks = pier spring rate, 46 fl — friction coefficient y = pier deflection, in. 

The ultimate load characteristics of structures type 1 and 2 were obtained using an ln- house computer program. This program examines a number of possible failure mechanisms In order to find the one associated with minimum potential energy of the vessel. The mechanisms are deflected In Increments, and at each step the vessel pressure which would maintain the mechanism In equilibrium Is found. Shears, deflections, prestress strains and crack sizes are output at each step so that the progressive plastic behaviour of the vessel may be monitored. Three failure criteria are recognised and overall vessel failure Is assumed to occur when one of the three Is violated. 

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