The US code-based stress equations and load case labels used by CAESAR II for actual and allowable stresses are shown below.
The load case recommendations made by CAESAR II are usually sufficient for code compliance. CAESAR II does not recommend occasional load cases. Occasional loads are unknown in origin, and you must specify them.
Code Equation |
Allowable |
Load Type |
---|---|---|
Longitudinal Pressure Stress - Slp |
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Slp = PDo / 4tn |
Code approximation |
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Slp = PDi2 / (Do2 - Di2) |
Code exact equation (CAESAR II Default) |
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Operating Stress – unless otherwise specified |
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S = Slp + Fax/Am + Sb |
N/A |
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B31.1 (2018 Edition) |
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Sl = Slp + 0.75iMa / Z |
< Sh |
SUS |
Slp + 0.75iMa / Z + 0.75iMb / Z Where: |
< kSh |
OCC |
Se = iMc / Z |
< f[1.25(Sc + Sh) - Sl] |
EXP |
B31.1 (2020 and 2022 Editions) (Requires B31J) |
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Sl = [(|Slp + IaFax / Am| + Sb)2 + 4St2]1/2 (2020 Edition) Sl = [(Ia|Slp + Fax / Am| + Sb)2 + 4St2]1/2 (2022 Edition) Where: |
≤ Sh and ≤ kSh ≤ Sh and ≤ kSh |
SUS OCC |
Se = [(|iaFax / Am| + Sb)2 + 4St2 ]1/2 Where: |
≤ f [1.25(Sc + Sh) - Sl] |
EXP |
B31.3 |
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See the B31.3 technical discussion in the CAESAR II User's Guide for information on using B31J. |
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SL = [(Ia (|Slp + Fax / Ap|) +Sb)2 + 4St2]1/2 Where: For reduced outlet connections, use Ze instead of Z St = ltMt / 2Z |
< Sh < 1.33Sh |
SUS OCC |
Se = [(|iaFax/Ap| +Sb)2 + 4St2]1/2 Where: Sb = [(iiMi)2 + (ioMo)2]1/2 / Z Z is the section modulus computed For reduced outlet connections, use Ze instead of Z St = itMt / 2Z |
< f [1.25(Sc + Sh) - SL] |
EXP |
B31.3 Chapter IX |
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See the B31.3 Chapter IX technical discussion in the CAESAR II User's Guide for information on using B31J. |
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SL = [(Ia (|Slp + Fax / Ap|) +Sb)2 + 4St2]1/2 Where: For reduced outlet connections, use Ze instead of Z St = ltMt / 2Z |
< Sh < 1.2Sh |
SUS OCC |
Se = [(ia (|Slp + Fax / Ap|) +Sb)2 + 4St2]1/2 Sb = [(iiMi)2 + (ioMo)2]1/2 / Z Where: For reduced outlet connections, use Ze instead of Z St = itMt / 2Z |
< 1.25Sc + 0.25 Sh |
EXP |
B31.4 |
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Fully Restrained Pipe (B31.4/R) |
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Hoop: or Shoop = Pi (D-t)/2t (for D/t < 20) |
< 0.72 ESy |
SUS, OPE, OCC |
Expansion: Se = Ea(T1 − T2) |
< 0.9 Sy |
EXP |
Longitudinal: |
< 0.9 Sy |
SUS, OPE, OCC |
CAESAR II includes the thermal effect in Sb |
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Equivalent Combined: or Seq = (SH2 − SHSL + SL2 + 3St2)1/2 |
< 0.9 Sy |
SUS, OCC, OPE |
Fully Above Ground, Unrestrained Pipe (B31.4/U) |
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Hoop: or Shoop = Pi (D-t)/2t (for D/t < 20) |
< 0.72 ESy <0.90Sy when defined as Hydro (HYD) |
SUS, OCC, HYD |
Expansion: |
≤ f[1.25(Sc + Sh) - SL]
|
EXP |
Longitudinal: |
< .75Sy < .80Sy when defined as Occasional (OCC) |
SUS, OCC, HYD |
Equivalent Combined |
Not used |
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Riser and Platform for Inland Waterways (B31.4/W) |
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Hoop: or Shoop = Pi (D-t)/2t (for D/t < 20) |
< 0.6 ESy <0.90Sy when defined as Hydro (HYD) |
SUS, OCC, HYD |
Expansion: |
< 0.8 Sy |
EXP |
Longitudinal: |
< 0.8 Sy < 0.90Sy when defined as Occasional (OCC) |
SUS, OCC, HYD |
Equivalent Combined |
Not used |
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When more than one stress evaluation is used, such as checking both hoop stress and longitudinal stress, CAESAR II reports the stress pair producing the largest calculated stress/allowable stress ratio. |
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B31.4 Chapter IX (Offshore) |
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Hoop: Shoop = (Pi – Pe )D/2t (for D/t ³ 30) |
< F1Sy |
OPE, SUS, OCC |
or Shoop = (Pi – Pe )(D-t)/2t (for D/t < 30) |
< 0.9Sy |
HYD |
Longitudinal: SL = Slp + Sb +Fa/A |
< 0.8Sy |
OPE, SUS, OCC |
where |
< 0.9Sy |
HYD |
Equivalent Combined: Seq = [(SL – SH)2 + 4St2]1/2 or Seq = (SH2 - SHSL + SL2 + 3St2)1/2 |
< 0.9Sy |
OPE, SUS, OCC, HYD |
When more than one stress evaluation is used, such as checking both hoop stress and longitudinal stress, CAESAR II reports the stress pair producing the largest calculated stress/allowable stress ratio. |
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B31.4 Chapter XI (Slurry Pipes) |
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Fully Restrained Pipe (B31.4 Ch XI/R) |
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Hoop: or Shoop = Pi (D-t)/2t (for D/t < 20) |
< 0.80 ESy |
SUS, OCC, OPE |
Expansion: |
< 0.9 Sy |
EXP |
Longitudinal: |
< 0.9 Sy < 0.88 Sy when defined as Occasional (OCC) |
SUS, OPE, OCC |
CAESAR II includes the thermal effect in Sb |
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Equivalent Combined: or Seq = (SH2 − SHSL + SL2 + 3St2)1/2 |
< 0.9 Sy |
SUS, OCC, OPE |
Fully Above Ground, Unrestrained Pipe (B31.4 Ch XI/U) |
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Hoop: or Shoop = Pi (D-t)/2t (for D/t < 20) |
< 0.80 ESy <0.90Sy when defined as Hydro (HYD) |
SUS, OCC, HYD |
Expansion: |
≤ f[1.25(Sc + Sh) - SL]
|
EXP |
Longitudinal: |
< .75Sy < .88Sy when defined as occasional (OCC) |
SUS, OCC, HYD |
Equivalent Combined |
Not used |
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When more than one stress evaluation is used, such as checking both hoop stress and longitudinal stress, CAESAR II reports the stress pair producing the largest calculated stress/allowable stress ratio. |
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B31.5 |
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Sl = Slp + Fax/Am +Sb |
< Sh |
SUS |
(Sb2 + 4St2)1/2 |
< f[1.25(Sc + Sh) – Sl] |
EXP |
Fax/Am + Sb + Slp |
< kSh |
OCC |
Sb = {[(iiMi)2 + (ioMo)2]1/2} / Z |
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B31.8 (2018, 2020, and 2022 Editions) |
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Restrained Pipe |
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Longitudinal: |
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SL = Slp + Sb + Sa |
< 0.9TSy |
SUS, OPE, OCC |
CAESAR II includes the thermal effect in Sa |
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Equivalent Combined: |
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Seq = max[ |Shoop - SL| , |Shoop| , |SL| ] |
< 0.9TSy |
SUS, OPE |
< kTSy |
OCC |
|
or |
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Seq = (SL2 - SLShoop + Shoop2)1/2 |
< 0.9TSy |
SUS, OPE |
< kTSy |
OCC |
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The equivalent combined stress is valid only for straight sections of pipe. |
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Unrestrained Pipe |
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Longitudinal: |
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SL = Slp + Sb + Sa |
< 0.75TSy |
SUS, OCC |
< 0.75Sy |
HYD |
|
Expansion: |
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Se = ME/Z |
< f[1.25(Sc + Sh) - SL] where |
EXP |
Where: Shoop = PDo/2t |
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Slp = 0.3Shoop Slp = 0.5Shoop |
Restrained Pipe Unrestrained Pipe |
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Sa = Fax/Am Mb = [(0.75iiMi)2+(0.75ioMo)2]1/2 MR = [(0.75iiMi)2+(0.75ioMo)2 + Mt2]1/2 |
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Sb = Mb/Z Sb = MR/Z |
Straight pipe Fittings and components |
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ME = [(iiMi)2+(ioMo)2 + Mt2]1/2 |
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B31.8 Chapter VIII (Offshore) (2018, 2020, and 2022 Editions) |
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Hoop Stress: Sh = (Pi – Pe)D/2t, when D/t ³ 30 Sh = (Pi – Pe)(D – t)/2t, when D/t < 30 |
< F1SyT |
OPE, SUS, OCC |
Longitudinal Stress: |SL| SL = Slp + Fax/Am ± Sb Where: Slp = (Pi * Ri2 - Pe * Ro2) / (Ro2 - Ri2) Sb = {[(iiMi)2 + (ioMo)2]1/2}/Z |
< 0.8Sy |
OPE, SUS, OCC |
Equivalent Combined Stress (Tresca) (2018 edition): Seq = 2{[(SL – Sh)/2]2 + St2}1/2 |
< 0.9Sy |
OPE, SUS, OCC |
Equivalent Combined (Tresca) (2020 and 2022 editions): Seq = Maximum of absolute values of: 2{[(SL - Sh)/2]2 + St2}1/2 |
< 0.9Sy |
OPE, SUS, OCC |
Alternative Combined Stress (Von Mises) Seq = (Sh2 – SLSh + SL2 + 3St2)1/2 |
< 0.9Sy |
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Where: F1 = Hoop Stress Design Factor (Table A842.2.2-1) |
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|
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B31.9 |
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Paragraph 919.4.1.b states that analysis uses the equations of B31.1. |
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B31.12 IP |
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SL = [(Ia (|Slp + Fax / Ap|) +Sb)2 + 4St2]1/2 |
< Mf Sh < 1.33 Mf Sh |
SUS OCC |
Se = [Sb2 + 4St2]1/2 |
< f [1.25(Sc + Sh) - SL] |
EXP |
Where: Sb = [(liMi)2 + (loMo)2]1/2 / Z Z = Corroded section modulus (SUS, OCC) Z = Nominal section modulus (not corroded) (EXP) For reduced outlet connections, use Ze instead of Z. St = ltMt / 2Z |
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When using Appendix B by selecting Use Alternative Rules for Stress Range Evaluation in the Configuration Editor: |
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So = Se = [(ia (|Slp + Fax / Ap|) +Sb)2 + 4St2]1/2 |
< 1.25f (Sc + Sh) |
OPE, EXP |
Where: Sb = [(iiMi)2 + (ioMo)2]1/2 / Z Z = Nominal section modulus (not corroded) For reduced outlet connections, use Ze instead of Z. St = itMt / 2Z |
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B31.12 PL |
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Restrained Pipe |
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Longitudinal: |
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SL = Slp + Sb + Sa |
< 0.9TSy |
SUS, OPE, OCC |
CAESAR II includes the thermal effect in Sa |
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Equivalent Combined: |
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Seq = |Shoop - SL| |
< 0.9TSy |
SUS, OPE |
< kTSy |
OCC |
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Or, when Yield Stress Criterion is set to VonMises in the Configuration Editor: |
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Seq = (SL2 - SLShoop + Shoop2)1/2 |
< 0.9TSy |
SUS, OPE |
< kTSy |
OCC |
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The equivalent combined stress is valid only for straight sections of pipe. |
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Unrestrained Pipe |
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Longitudinal: |
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SL = Slp + Sa + Sb |
< 0.75TSy |
SUS, OCC |
< 0.75Sy |
HYD |
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Expansion: |
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Se = According to PL-2.6.7, expansion stress for unrestrained pipe is taken from Part IP |
< f[1.25(Sc + Sh) - SL] |
EXP |
Appendix B alternative equations are also applicable |
< f1.25(Sc + Sh) where: Or, when EXP allowable: Sc & Sh use 0.33 SuT is selected: Sc = 0.33SU |
EXP, OPE |
Where: Shoop = PDo/2t |
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Slp = 0.3Shoop Slp = 0.5Shoop |
Restrained Pipe Unrestrained Pipe |
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Sa = Fax/Am Mb = [(0.75iiMi)2+(0.75ioMo)2]1/2 MR = [(0.75iiMi)2+(0.75ioMo)2 + Mt2]1/2 |
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Sb = Mb/Z Sb = MR/Z |
Straight pipe Fittings and components |
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For restrained and unrestrained pipe, Z is the nominal section modulus (not corroded). |
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ASME SECT III CLASS 2 & 3 |
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Sl =[B1PmaxDo / 2tn] + B2Ma / Z |
< 1.5Sh |
SUS |
Se =iMc/Z |
< f(1.25Sc + 0.25Sh) + (Sh - Sl) |
EXP |
B1Slpmax + B2(Ma + Mb) / Z |
< 1.8Sh and < 1.5Sy |
OCC |
B31.1 (1967) and Navy Section 505 |
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Sl = Slp + (Sb2 + 4St2)1/2 |
< Sh |
SUS |
Se = (Sb2 + 4St2)1/2 |
< f[1.25Sc + 0.25Sh +(Sh – Sl)] |
EXP |
Slp + (Sb2 + 4St2)1/2 |
< kSh |
OCC |
GPTC |
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Slp + 0.75iMa / Z |
< Sy |
OPE |
Slp + Sb |
< 0.75SyFt |
SUS |
(Sb2 + 4St2)1/2 |
< 0.72Sy |
EXP |