Hoop stresses

When constmction is complete, the pipeline must be tested for leaks and strength before being put into service industry code specifies the test procedures. Water is the test fluid of choice for natural gas pipelines, and hydrostatic testing is often carried out beyond the yield strength in order to reHeve secondary stresses added during constmction or to ensure that all defects are found. Industry code limits on the hoop stress control the test pressures, which are also limited by location classification based on population. Hoop stress is calculated from the formula, S = PD/2t, where S is the hoop stress in kPa (psig) P is the internal pressure in kPa (psig), and D and T are the outside pipe diameter and nominal wall thickness, respectively, in mm (in.). 

Tank Shell. Another example of where thickness is set by minimums for fabricabihty but not for strength is in small-diameter tanks. For example, a water storage tank built using a steel of an allowable stress of 20,000 psi (138 mPa), 9 ft (3 m) in diameter by 21-ft (7-m) high, requires a shell thickness to resist hoop stress of only 0.023-in. (0.58-mm) thick. However, if built to API Standard 650, the shell would be fabricated at least 0.1875-in. (4.76-mm) thick. The code requires this thickness so that when fabrication, welding, and tolerances are considered, a tank of acceptable quaUty and appearance meeting the requirements of most services in most locations is provided. 

In the large-diameter vertical cylindrical tanks, because hoop stress is proportional to diameter, the thickness is set by the hydrostatic hoop stresses. Although the hydrostatic forces increase proportionally with the depth of Hquid in the tank, the thickness must be based on the hydrostatic pressure at the point of greatest depth in the tank. At the bottom, however, the expansion of the shell owing to internal hydrostatic pressure is limited so that the actual point of maximum stress is slightly above the bottom. Assuming this point to be about 1 ft (0.305 m) above the tank bottom provides tank shells of adequate strength. The basic equation modified for this anomaly is... 

Although the coolant (river water) was at relatively low pressure, measurements revealed a residual hoop stress in the tube of approximately 9000 psi (62 MPa). The longitudinal rupture occurred as a result of these stresses after erosion had sufficiently reduced wall thickness. 

The hoop stress ct in the wall of a cylindrical pressure vessel containing gas at pressure p is given by... 

The hoop stress in the tube under the working pressure of 50 bar (5 MPa) is 5 MPa X 50 mm/5 mm = 50 MPa. Creep data indicate that, at 900°C and 50 MPa, the steel should fail after only 15 minutes or so. In all probability, then, the failure occurred by creep rupture during a short temperature excursion to at least 870°C. 

So = Maximum operating hoop stress level as determined by the Barlow formula using the maximum operating pressure. 

Figure 9.9 shows that the stress that will lead to a creep strain of 2% after one year is about 39 MPa. Substituting this into the equation as the hoop stress will give... 

Note that the ratio of the ratio of the hoop stress (pR/h) to the axial stress (pR/lh) is only 2. From the data in this question the hoop stress will be 8.12 MN/m. A plastic cylinder or pipe is an interesting situation in that it is an example of creep under biaxial stresses. The material is being stretched in the hoop direction by a stress of 8.12 MN/m but the strain in this direction is restricted by the perpendicular axial stress of 0.5(8.12) MN/m. Reference to any solid mechanics text will show that this situation is normally dealt with by calculating an equivalent stress, Og. For a cylinder under pressure Og is given by 0.5method outlined earlier. 

The nylon ring may be considered as a thick wall cylinder subjected to this internal pressure (see Appendix D). At the inner surface of the ring there will be a hoop stress, <7, and a radial stress, Cr. Benham et al. shows these to be... 

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 = 2[Pg.167]

The maximum stress in the inflated parison will be the hoop stress, ae, which is given by... 

The pipe would leak if the hoop stress caused by atmospheric pressure (0.1 MN/m ) exceed the stress in the pipe wall after 1 year. 

If the acetal ring is considered as a thick wall cylinder, then at the inner surface there will be hoop stresses and radial stresses if it is constrained in a uniform manner ... 

Longitudinal stress is the force pulling on the ends of the pipe divided by the cross sectional area of the pipe wall. The pull is p 7r r. The area of the wall is 7f (r+tp 2 7f r t, and the longitudinal stress is given by equation 9.1-3. Ifr t, then = p r/(2 f j, and the longitudinal stress is half the hoop stress (equation 9.1-4). This is the reason why hoop stress dominates over the longitudinal stress. 

For a cylindrical vessel, the radius of curvature in the axial direction is infinite, and the stress in the direction of the circumference, called the hoop stress, is... 

The conjoint action of a tensile stress and a specific corrodent on a material results in stress corrosion cracking (SCC) if the conditions are sufficiently severe. The tensile stress can be the residual stress in a fabricated structure, the hoop stress in a pipe containing fluid at pressures above ambient or in a vessel by virtue of the internal hydraulic pressure created by the weight of its contents. Stresses result from thermal expansion effects, the torsional stresses on a pump or agitator shaft and many more causes. 

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