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 |
Se = iMc / Z |
< f[1.25(Sc + Sh) - Sl] |
EXP |
Slp + 0.75iMa / Z + 0.75iMb / Z |
< kSh |
OCC |
B31.1 (2020 Edition) (Requires B31J) |
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Sl = [(|Slp + IaFax / Am| + Sb)2 + 4St2]1/2 Where: |
≤ Sh ≤ 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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SL = [(Ia (|Slp + Fax / Ap|) +Sb)2 + 4St2]1/2 Where: For reduced outlet connections, 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, St = itMt / 2Z |
< f [1.25(Sc + Sh) - SL] |
EXP |
B31.3 Chapter IX |
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SL = [(Ia (|Slp + Fax / Ap|) +Sb)2 + 4St2]1/2 Where: For reduced outlet connections, 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, 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 |
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] Sc and Sh are 2/3Sy. |
EXP |
Longitudinal: |
< .75Sy < .80Sy when defined as Occasional (OCC) |
SUS, OCC, HYD |
Equivalent Combined |
Not used |
|
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 |
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] Sc and Sh are 2/3Sy |
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 and 2020 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 for straight sections of pipe only. |
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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 and 2020 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 edition): 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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B31.9 |
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Paragraph 919.4.1.b states that analysis uses the equations of B31.1. |
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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 |