PSI - Issue 60

Balaji Srinivasan et al. / Procedia Structural Integrity 60 (2024) 418–432 Balaji Srinivasan et al./ StructuralIntegrity Procedia 00 (2019) 000 – 000

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(1997), Chang et al. (1996) and disregards the area contribution made by the weld. For the comparison study, numerous FE analyses are performed on different d/D, D/T and t/T input variables and only a subset of these cases are reported here. Table 3 shows the list of the different FE models utilized to demonstrate the findings. Out of all eleven FE models, model #6, model #7 & model #11 are beyond the limits of STP. In Model #6, d m /D m is 0.8 which is beyond the limit of ≤ 0.7 as per Eq. (2) in Table 2. In Model #7, D m /T and t/T are beyond the limits as per Eq. (1) & Eq. (3) in Table 2 and similarly, Model #11 is beyond the limits as per Eq. (3) in Table 2.

Table 3. FE Models Dimensions and Input Parameters Model No. P (MPa) D (mm) T (mm) d (mm) t (mm)

d/D

D/T

t/T

1 2 3 4 5 6 7 8 9

2.4 2.4 2.4 2.4 2.4 2.4 2.4 2.4 2.4 2.4 2.4

2285 1142.5

27 27 27 27 27 27 27 27 27 27

609.6 609.6 609.6 609.6 609.6 609.6 609.6 609.6 609.6 609.6 609.6

15 15 15 18 15 15 27

0.263 0.533 0.670 0.265 0.262 0.800 0.298 0.258 0.252 0.150 0.138

83.630 41.315 32.852 83.630 83.630 27.519 6.879 83.630 83.630 83.630 83.630

0.556 0.556 0.556 0.400 0.667 0.556 0.052 1.000 1.500 10.00 11.00

914 2285 2285 770 2285 2285 2285 2285 2285

10.8

290

40.5 270 297

10 11

3.2. Utilization of STP Data: Appendix 3 of STP presents an extensive collection of result tables, encompassing over 24,000 finite element runs conducted throughout the study. These tables offer a detailed analysis record, furnishing valuable data for a comprehensive examination and future reference. The study meticulously documents the stress results for six distinct load cases. The load cases considered for each Finite Element (FE) model are: (a) Axial Load; (b) In-plane bending moment; (c) Out-of-plane bending moment; (d) Torsional moment; (e) Pressure and (f) Sum of all loads. For each FE model, the data includes the individual membrane stress factors for the branch and header, resulting from all load cases (a) to (e). Additionally, the data provides the stress factors for the outer and inner surfaces, considering the membrane plus bending effects for both branch and header locations. This compilation accounts for a substantial amount of data, encompassing 165,984 data points, equivalent to 4,638 rows and 38 columns. The stress factors offered in this comprehensive data set are accurately listed in Table 4, ensuring a robust foundation for further assessments and analyses. For the given branch-header configuration with the defined loads and load combinations, the stresses on the header and branch are computed from the set of equations and combination coefficients and equations provided in Appendix 2 of STP. There are different arrays of coefficients provided for determining individual membrane and membrane plus bending surface stress factors for each load combination. It is a cumbersome process to use the STP for predicting stress as it is an exhaustive procedure and care must be taken in picking correct coefficients and respective equations from the sets of data given.

Table 4. Stress Factors List and their Notations S.No

Notation

Stress factors (SF)

1 2 Membrane stress factor for the branch under axial load Membrane stress factor for the branch due to in-plane moment 3 Membrane stress factor for the branch due to out-of-plane moment Membrane stress factor for the branch due to torsional moment Membrane stress factor for the branch due to pressure Membrane stress factor for the run due to axial load Membrane stress factor for the run due to in-plane moment Membrane stress factor for the run due to out-of-plane moment Membrane stress factor for the run due to torsional moment Membrane stress factor for the run due to pressure 4 5 6 7 8 9

B-M-Axial B-M-Inplane B-M-OutPlane B-M-Torsion B-M-Pressure H-M-Axial H-M-Inplane H-M-OutPlane H-M-Torsion H-M-Pressure

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