![]() The absolute values at the inner or outer wall surfaces are the same as the internal or the external pressures. ![]() This will be investigated in detail later in this paper. In other words, the pipe is already in the compressive region prior to the external and internal pressures being equal. This means that the hoop stress transition, from tension to compression, occurs before Pi = Po. Equations 3 and 4 show the hoop stress becomes compressive with the internal and external pressure being equal (Pi = Po). However, when the internal pressure is equal to the external pressure, the hoop stress becomes compressive (see Figure 3). The hoop stress is shown to be tensile when internal pressure is greater than the external pressure. The hoop stress difference between the inner wall surface and the outer wall surface is the same as the pressure differential, Pi - Po (Equation 3 minus Equation 4). For this reason, the inside diameter is used for the hoop stress calculation when using the thick wall pipe formula. The absolute hoop stress is maximum at the inner wall surface regardless of the relationship of the internal pressure to the external pressure. įigure 2 and Figure 3 demonstrate the general characteristics of the thick wall pipe stresses along the pipe wall thickness (Equations 1 through 8). In the same way, the radial stresses at the inner and outer surfaces of the pipe wall can be expressed as shown in Equation 7 and Equation 8. When the external pressure is zero, where Po = 0, then Equation 5 and Equation 6 apply. In the same way, the hoop stress at r = b = D/2 at the pipe outer surface is represented in the Equation 4 group. ![]() By substituting a = Di/2, b = Di+2t, and r = a = Di/2 at the inner pipe surface, Equation 1 can be rewritten as the Equation 3 group. In these equations, positive stresses indicate tension, and negative stresses indicate compression. The formulas provide "exact" solutions in the elastic range for any cylindrical pipe wall thickness. The radial stress acts perpendicular to the pipe wall.įrom the equilibrium of forces (the summation of forces in each direction must be zero) and integration, the tangential or hoop stress (sh) and the radial stress (sr) can be expressed as shown (Shigley, 1983). The tangential stress is induced in the circumferential or hoop direction in the pipe wall. The longitudinal or axial stress is neglected by assuming no constraints at the ends of the pipe. A pressurized pipe develops both tangential and radial stresses in a two-dimensional cross section. Thick-wall pipe formula A French Engineer, Lame, derived a thick wall cylinder formula in 1833, using the stress system shown in Figure 1 (Blake, 1990). However, the present thin wall pipe formula yields erroneous results in cases where external pressure exists. The thin wall pipe formula's results are generally less than 5% over the exact solution provided by the thick wall pipe formula, if no external pressure exists. It provides reasonably accurate results for thin wall pipes, such as pipe having D/t ratios greater than 20. The thin wall pipe formula is simpler and easier to use in calculating the pipe wall thickness. The thick wall pipe formula gives an exact solution but requires an iterative solution to determine the required pipe wall thickness. There are two general methods for calculating the hoop stress: a thick wall pipe formula and a thin wall pipe formula. If the calculated hoop stress is greater than the allowable stress, the pipe wall thickness must be increased.įor a pipe-in-pipe design in which the inner pipe is enclosed by an outer casing pipe with the annulus pressurized or a pipe in a marine environment exposed to external hydrostatic head, the external pressure should be considered in the pipe wall thickness determination. The hoop stress must be less than the maximum allowable stress. ![]() ![]() Accounts for external pressure Jaeyoung Lee, William Rainey, Mark BrunnerĪker Engineering Wall thickness of an internally pressurized cylindrical vessel is determined by computing the hoop stress. ![]()
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