Future Work

Because of its nature as a sustained load, internal pressure is often ignored in the evaluation of piping flexibility. This tendency has been rectified recently, but is still not widely appreciated. For instance, pressure is also a cyclic load that needs to be included in the fatigue evaluation. This cyclic pressure, which is implied in Eq. (3.14), is seldom appreciated. Furthermore, pressure also has very significant effects on piping flexibility itself. Flexibility effects occur in two areas: (1) pressure elonga-tion of the piping element and (2) pressure effect on the bend flexibility factor and bend SIFs.

3.7.1  Pressure Elongation

In a pressurized pipe, the entire inside surface of the pipe sustains a uniform pressure. This pres-sure loading develops a tri-axial stress in the pipe wall. The stress component normal to the pipe wall is generally small and will be ignored in this discussion. The pipe wall is subjected to stresses Shp and

Fig. 3.9

local cold spring

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Slp in circumferential and longitudinal directions, respectively, as shown in Fig. 3.10. Stress in the circumferential direction is generally referred to as hoop stress. For practical purposes, Slp is equal to one-half of Shp, as shown in Eqs. (2.13) and (2.14). The hoop stress and the longitudinal stress gen-erate strains in all major directions. The relation between stress and strain is given by Eq. (2.8). By substituting Slp = 1/2Shp, the strains in hoop and longitudinal directions become

e_H S_hp E  QS_lp

E S_hp

E (1  05Q) (3.16)

e_L S_lp E QS_hp

E S_hp

E (05  Q) (3.17)

Elongation in the hoop direction increases the pipe diameter. This diametrical change progresses freely without creating any additional resistance to the piping system. Elongation in the longitudinal direction, on the other hand, behaves like thermal expansion. This elongation, given by Eq. (3.17), has a squeezing effect on the piping system just like thermal expansion.

The significance of the pressure elongation can be better visualized by converting it to an equivalent temperature rise [16]. Figure 3.10 shows the relationship between pressure elongation in terms of pressure hoop stress and its equivalent temperature rise, for low carbon steel pipe. For plant piping, hoop stress is normally maintained at less than 15,000 psi (103.4 MPa). In this case, pressure elonga-tion is equivalent to a temperature increase of 17.5°F (9.72°C). In view of the high temperature range normally experienced in plant piping, the effect of pressure elongation in plant piping is insignificant.

On the other hand, hoop stress in a cross-country transportation pipeline can reach 30,000 psi (206.8 MPa) or higher for high-strength pipe. The equivalent temperature of this hoop stress range can easily exceed 35°F (19.44°C), which represents a high percentage of the design temperature rise. Therefore, pressure elongation is an important factor to be considered in transportation pipeline design.

3.7.2  Potential Twisting at Bends

The longitudinal elongation discussed in the preceding section is also applicable to piping bends, but the curvature at the bends might also produce different type of deformations. One of the impres-sions that engineers would intuitively form is that the bend will tend to open when pressurized. Equa-tions have been developed for this opening rotation and are implemented in some computer programs.

This opening effect is often misquoted as the Bourdon tube effect. It has artificially generated, on

Fig. 3.10

pressure elongaTion

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82 Chapter 3

paper, much bigger twisting effects on the piping than was experienced in the field. Actually, a Bour-don tube is an arc shape tube with an oval cross-section. This oval cross-section is the key for the opening rotation. The general belief in the piping community on piping bends is that if the cross-sec-tion out-of-roundness is insignificant, the rotacross-sec-tion of the bend is not expected [17].

Detailed analyses and tests on special miter bends [18] have shown that in the elastic stress range, the bends actually close rather than open after pressurization. It starts to open only after the pressure stress exceeds the yield strength. It appears that until more rigorous theories and tests prove other-wise, the opening of the pipe bend by the pressure shall be ignored.

3.7.3  Pressure Elongation Is Self-Limiting Load

Pressure elongation is often mistreated as a sustained load because of its association with pressure, which is a sustained load. Just like thermal expansion, pressure elongation generates a displacement that is a self-limiting load. Its effect on the piping system is determined by the potential axial displace-ment of each leg of the piping. Once the displacedisplace-ment reaches the potential elongation amount, it stops regardless of whether or not the yielding occurs in the piping. This pressure elongation is gen-erally included in the flexibility analysis the same way as thermal expansion is. In general, pressure elongation is added to thermal expansion to become the total displacement load in the analysis.

3.7.4.  Pressure Effect on Bend Flexibility and SIFs

The flexibility factor and SIF at a bend are mainly caused by the ovalization of the bend cross- section. Internal pressure tends to reduce ovalization, thus reducing flexibility and stress intensifica-tion. The pressure effect on bend flexibility and SIFs has been well investigated. One of the most recognized treatments is the use of modification factors established by Rodabaugh and George [17].

These factors have been adopted by the ASME piping codes, and are summarized bellow.

In large-diameter, thin-wall elbows and bends, pressure can significantly affect the magnitudes of the flexibility factor, k, and the SIF, i. Under pressurized conditions, the value of k calculated from Eq. (3.5) should be adjusted by dividing it with

And the SIFs calculated by Eqs. (3.11) and (3.12) may be reduced by dividing them with

R = radius of the bend curvature

The use of Eqs. (3.18) and (3.19) varies from case to case. Some specifications require the applica-tion of the flexibility reducapplica-tion factor given by (3.18), but not the stress intensificaapplica-tion reducapplica-tion fac-tor given by (3.19). The rationale is that piping tends to maintain its temperature longer than it can maintain its pressure during shutdown. In other words, the stress intensification reduction factor may disappear while the piping is still under full expansion state.

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