Material 100°F 200°F 300°F 400°F 500°F
A 106 Gr.B 20.0 20.0 20.0 20.0 18.9
API 5L X52 22.0 22.0 22.0 22.0 -
A 312 Type 304 20.0 20.0 20.0 18.7 17.5
B 241 6061 T6 12.7 12.7 10.6 5.6 -
In the late 1990’s, the safety factor of 4 against ultimate strength, used in the design of B31.1 carbon steel pipe, and ASME B&PV Section VIII Division 1 pressure vessels, was reduced to 3.5. A larger safety factor SFu applies to materials less ductile than steel. For example the allowable stress for cast iron is Su/10, and the allowable stress for malleable iron is Su/5.
4.2.5 Wall Thickness Allowance
Having established the minimum required wall thickness, the designer should add a corrosion allowance and, for piping systems but not for pipelines, a fabrication tolerance.
The minimum wall thickness required by code plus allowances is then rounded up to obtain the commercial pipe size to be procured and used in construction.
It is up to the designer to select the corrosion allowance, based on experience with similar fluids, pipe materials, temperatures and flow rates (Chapter 20).
The tolerance on wall thickness depends on the pipe material specifications. For example, an ASTM A106 carbon steel pipe may be furnished 12.5% below the specified nominal pipe wall thickness. Therefore, the minimum pipe wall thickness tmin calculated by the code design equation needs to be increased by the corrosion allowance C and the fabrication tolerance f (for example with a fabrication tolerance of 12.5% on the pipe wall thickness, f=0.125). With these corrections, we now obtain the commercial pipe size to be procured:
t=(tmin+C)(1+f)
t=pipe wall thickness, is
tmin=minimum wall required by Code, in C=corrosion or threading allowance, in
f=pipe wall thickness fabrication tolerance
4.3 YIELD AND BURST PRESSURE
4.3.1 The Von Mises Yield Pressure
Applying the Von Mises criterion, yielding of the pipe wall will take place when the distortion energy reaches a certain limit value X. This can be written as
(σh−σ1)2+(σ1−σr)2+(σr−σh)2=X
We can find the limit value X through a simple tensile test. In this case, σh= σR=0 and σ1=F/A is the ratio of the applied tensile force F to the metal area A. Yielding will take place when σ1=SY, in which case the Von Mises criterion can be written as
(0−SY)2+(SY−0)2+(0−0)2=X=2SY2
By substitution, the internal pressure at which the pipe wall yields is
Py=internal pressure at onset of yield, psi
For large diameter to thickness ratio (D/t>>1) we obtain the internal pressure at the onset of yield [Cooper, Sims]
4.3.2 Burst Pressure
As the internal pressure continues to increase beyond the yield pressure Py, the pipe wall will bulge outward and reach a point of instability. In reality, the material is not perfectly uniform and this bulging does not take place exactly uniformly around the circumference but preferentially on one side of the pipe wall. The hoop strain at which instability occurs is [Cooper]
εi=n/2
εi=strain at onset of instability
n=strain coefficient, from true stress-strain equation (Chapter 3)
Soon after instability (outward bulge in pipe wall), the pipe wall ruptures. The pressure at rupture is the ultimate pressure Pu given by [Cooper]
Pu=(2 k t/D)e−n {n/[2 (3/4)(1+n)/n]}n
Pu=ultimate pressure at burst, psi t=pipe wall thickness, in k=strength coefficient, psi D=pipe outer diameter, in
For example, a 6” sch. 40 carbon steel pipe has an actual yield stress of 40 ksi, an ultimate strength of 70 ksi, a strain coefficient n=0.2, a strength coefficient k=100 ksi and an elongation at rupture of 40%. Substituting, we obtain Py= 3.9 ksi and Pu=6.2 ksi.
Compare these values with the pressure corresponding to a hoop stress equal to the ultimate strength P=2Sut/D=5.9 ksi. The difference between 6.2 ksi and 5.9 ksi is due to the fact that 2Sut/D is an approximation based on an elastic prediction of burst, ignoring plasticity.
4.4 PRESSURE DESIGN OF PLASTIC PIPE The design of plastic pipe is covered in Chapter 24.
4.5 PRESSURE DESIGN OF FITTINGS
4.5.1 Pressure Rating
The hoop stress distribution in pressurized fittings and components, such as tees, reducers, elbows, nozzles, etc., can not be expressed by a simple equation such as PD/(2t) for the hoop stress in a straight pipe. To eliminate the need for complex design calculations to size fittings, the pressure design of fittings and components relies on a simple approach: first, fittings and components must meet standard dimensions specified in the ASME B16 dimensional standards, and second, fittings and components must be pressure rated, by means of proof tests.
The fittings and components will then be assigned a pressure rating or, for butt-welded fittings (ASME B16.9), they are simply designated by the schedule number of the matching pipe. There are two methods of pressure rating: (1) The method of the ASME Boiler & Pressure Vessel (B&PV) Code and (2) the method of MSS-SP-97 and ASME B16.9. The choice between these two methods is dictated by the applicable piping design code. For example, B31.1 applies the ASME B&PV Section I method for pressure rating, while B31.3 allows the use of either the ASME B&PV Section VIII or the MSS or B16 methods in rating pipefittings and components. The ASME B&PV method for pressure rating is specified in Section I Appendix A-22 for boilers and Section VIII Division 1 Section UG101 for pressure vessels. In the rating process the fitting is subjected to a steadily increasing pressure. At one point, let’s say when the pressure has reached a value H, the fitting will start to visibly deform. The “proof yield pressure” is defined as
PY=(H/2) (SY,min/SY,tested)
PY=proof yield pressure, psi
H=test pressure at onset of visible yield, psi
Sy,min=minimum specified yield stress of the material, psi
Sy,tested=actual yield stress of the test specimen, psi
As the proof test continues, the pressure will eventually burst the fitting at a pressure we call B. In the pressure vessel rules (ASME VIII) “proof burst pressure” is the burst pressure divided by a safety factor of 5, and corrected for material properties
PB=(B/5) (Su,min/Su,tested)
PB=proof burst pressure, psi
B=burst pressure of the test specimen, psi
Su,min=minimum specified ultimate strength of the material, psi Su,test=actual ultimate strength of the test specimen, psi
When applying the boiler and pressure vessel proof burst formula to piping components, the piping design code safety factor may be used in place of 5. For example, a safety factor of 3 could be used for process piping since the allowable stress is based on Su/3. For cast iron the safety factor would be 10, and for malleable iron it would be 5.
The ratio Su,min/Su,test is meant to correct the proof burst pressure to compensate for the fact that the specimen tested is, in most cases, stronger (larger ultimate strength Su,test) than the material specification strength which is a minimum Su,min. In MSS-SP-97 or B16.9, the proof burst pressure can be based on the burst test of a single specimen, as
PB=[B/(3×1.05)] (Su,min/Su,tested)]
PB=proof burst pressure, psi
Su,min=minimum ultimate strength of the material specification, psi Su,test=actual ultimate strength of the tested pipe specimen, psi B=pressure at burst, psi
Figure 4-2 illustrates a test arrangement used to determine the pressure rating of a pipe tee. The specimen will be pressurized with water. The water pressure is then increased until the assembly bursts. If burst occurs in the tee, then the pressure at burst is B and the design pressure or rated pressure is established as a fraction of B. At times, during a burst test, the pipe extensions to which the fitting is attached will burst before the fitting itself.
If burst occurs in the pipe extensions, then the tee is stronger than the pipe and is assigned the pressure rating of the matching pipe.