A manhole interrupts the load-bearing shell of an elbow or tee, so the component is regarded as a non-standard piping fitting. The three fittings here are two 20 inch long-radius elbows, EX-23 and EZ-22, in SA-234 Gr. WP11 Cl. 1, and one 32 inch ASME B16.9 welding tee, FB-11, in SA-234 Gr. WP11 Cl. 2. Each carries a 20 inch manhole in SA-335 Gr. P11, 300 mm long, with a thick closed end representing the blind flange.
Elbows ovalise under bending, and that ovalisation raises the stress at the manhole to elbow interface. The hot temperatures on which the allowable values are based are 420 °C and 266 °C for the elbows and their manholes and 500 °C for the tee and its manhole. Forty-nine load cases were applied to the elbows in analogy with the AutoPipe output: two sustained (SUS1, SUS2), fifteen operating (OPE1 to OPE15), two occasional (OCC1, OCC2) and thirty expansion cases (EXP1 to EXP30). Separate load cases apply to the tee. The client decided to verify the three fittings by finite element analysis, assessed against ASME VIII-2 Section 5, with modifications suggested where required to reduce the stresses to acceptable levels.
Models, wall thicknesses and the assessment basis
Each fitting was modelled in three dimensions in CREO. Each model includes the complete fitting with its manhole and closed end, and parts of the connecting piping, for model accuracy and to allow proper ovalisation. On the elbows the vertical pipe section is 762 mm, 1.5 times the 508 mm outside diameter, and the horizontal end is restrained by a fixed boundary condition, directly on EX-23 and through the connecting 45° elbow, itself included in the model, on EZ-22. On the tee one of the header connections carries the fixed boundary condition and nodal forces are applied at the other two. The nodal forces are taken from the AutoPipe output. Because the finite element pipe lengths differ from the AutoPipe section lengths, those forces were first translated to the correct values by means of free body diagrams.
The stress analysis was performed for the corroded condition. Nominal wall thicknesses of 9.53 mm for the elbows and manholes and 7.92 mm for the tee were reduced for mill tolerance and corrosion allowance, giving the minimum thicknesses used in the stress analysis, 6.73 mm and 5.36 mm respectively.
Allowable values were first determined at the maximum operating temperature, a conservative approach for most load cases, and rechecked at the temperature of the specific load case wherever that value was exceeded. The allowable stress is determined in accordance with the rules of the ASME B31.3 stress code, as the minimum of UTS/3 and 2Sy/3, where UTS is the minimum ultimate tensile strength and Sy the yield stress. Local primary membrane stress is limited to 1.5·Sm,hot, occasional cases to 1.5·k·Sm with k = 1.2, and the secondary check to Sps, the lesser of 3·Sm,average and 2·Sy,average. The primary loads are pressure and weight, with plastic collapse and burst as the failure modes; the secondary loads result mainly from thermal expansion, and the failure modes are low cycle fatigue and ratcheting.
Reinforcement pads, tee manhole orientation and derivation of the SIFs and flexibilities
A reinforcement pad is required at the manhole interface to obtain acceptable stress levels: 640 mm outer diameter, measured in the symmetry plane, and 7 mm nominal thickness on the elbows, 660 mm and 7 mm on the tee. Neither B31.3 nor ASME VIII specifies a limit value for the maximum pad thickness; the applied thickness falls within the typical limit given in many engineering handbooks, tpad < 1.5·tshell. The pad is required to reduce the manhole to elbow interface stresses that result from bend ovalisation.
On the tee a vertical configuration of the manhole is applied, since a horizontal orientation of the manhole results in stress values that are too high. One modelling input had to be assumed. The crotch radius and thickness selected by the manufacturer when the B16.9 tee was designed for internal pressure were not available, so typical values of 1.3·ttee and 0.25·C were used, C being the distance from the centreline of the branch to the weld line of the header pipe and attached plain pipe. It is recommended to verify these values if possible. Crotch stresses were also checked, but are not reported with the key location results.
The same models were used to derive inputs for beam type pipe stress analysis. In-plane and out-of-plane bending moments of 10 kNm were applied to a model fixed at one end. The resulting maximum stress was multiplied by a stress concentration factor of 1.4, corresponding to a full penetration weld with sufficient NDT, divided by 2 to reference the value to a butt weld as the B31.3 code defines it, and divided by the plain pipe bending stress for the same moment. The flexibility factors were obtained by dividing the rotation of the finite element model under the same moment by the rotation of a beam element of equal length, after correcting the finite element rotations to remove the bending and twist of the attached straight pipe sections. The out-of-plane value is then multiplied by 2, since only one bend leg contributes to the bending resistance.
Code compliance, fatigue life and the derived factors
With the pads applied, all three fittings comply with ASME VIII-2. The largest stress in elbow EX-23 is 349 MPa, in expansion case EXP17, and in elbow EZ-22 348 MPa, in EXP18, being 93.2 and 93.0 percent of the 374.3 MPa secondary allowable. The tee reaches 284 MPa in operating case OPE2, 80.3 percent of its 353.9 MPa secondary allowable; its highest utilisation is in sustained case SUS1, at 107 MPa against a local primary allowable of 112.8 MPa, or 94.9 percent. On the elbows the sustained and occasional cases stay further from their limits, the highest being 160 MPa in OCC2 for EZ-22 against an occasional allowable of 179.5 MPa, or 89.1 percent.
A fatigue check was performed on the maximum cyclic stress of each fitting, using the fatigue curve of ASME VIII-2 Annex 3-F, Table 3.F.8. The stress amplitudes, half the maximum cyclic stress, are 174.5 MPa for EX-23, 174 MPa for EZ-22 and 142 MPa for the tee; with the 1.4 SCF applied, the values Sa taken to the fatigue curve are 244.3 MPa, 243.6 MPa and 198.8 MPa. The allowable number of cycles is approximately 40,000 for the two elbows and above 40,000 for the tee, in each case above the 7,000 cycles requested. The SCFs assume sufficient NDT on the welds. From a fatigue point of view the fittings are therefore fit for at least the requested number of cycles.
The factors are reported for the non-corroded condition, which is the condition B31.3 requires them to be based on. For the elbow with manhole and pad, the finite element in-plane SIF is 5.9 against the B31.3 value of 3.76 for a bend without manhole, and the out-of-plane SIF is 6.9 against 3.14. The in-plane flexibility factor is 6.0, against a finite element value of 11.2 for the same bend without a manhole; the out-of-plane factor is 10 both with and without the manhole. B31.3 gives bends a single flexibility factor, here 14.0, for both directions.
For the tee, the SIFs are 7.1 in-plane and 7.3 out-of-plane at the branch interface, against B31.3 values of 4.6 and 5.8, and 3.3 in-plane and 2.5 out-of-plane at the manhole interface, for which B31.3 gives no corresponding value. Branch to header stiffnesses of 1.1 × 10⁶ Nm/deg in-plane, 6.1 × 10⁵ Nm/deg out-of-plane and 4.5 × 10⁵ N/mm axial were determined on request, the header itself assumed as flexible as plain pipe. B31.3 gives tee fittings a flexibility factor of 1, and since that is generally a conservative assumption it is advised not to alter it.
What the project shows about qualifying non-standard fittings
A manhole raises the stress intensification at the fitting above the B31.3 values for a bend without one, and it changes the flexibility of the fitting, the in-plane flexibility factor being 6.0 with the manhole and pad against 11.2 without.
Stresses in the elbow with manhole under a 10 kNm in-plane bending moment (left) and a 10 kNm out-of-plane bending moment (right), for the corroded condition, illustrating the derivation of the stress intensification factors. Legend values in MPa.
In a flexibility calculation the branch and the manhole can be modelled either as two tee connections separated by about 1 mm, each carrying its own SIF, or as a single intersection carrying the larger SIF. Either way, the stresses calculated by a B31.3 pipe stress analysis using these SIFs and flexibility factors are not necessarily identical to those obtained in the 3D finite element analysis, because pipe loads change with the different flexibilities and because the B31.3 check differs from the ASME VIII-2 check. Should the B31.3 calculation indicate stresses in the fittings that are too large, or reaction loads significantly larger than those calculated earlier, the fitting stresses have to be recalculated.
Two measures brought the fittings within the code limits: a reinforcement pad, kept within the tpad < 1.5·tshell handbook limit, and a vertical manhole orientation on the tee. The assumed crotch radius and thickness of the tee should be verified before the qualification is treated as final.