The US codebased 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 

Slp = PDo / 4tn 
Code approximation 

Slp = PDi2 / (Do2  Di2) 
Code exact equation (CAESAR II Default) 

Operating Stress – unless otherwise specified 

S = Slp + Fax/Am + Sb 
N/A 

B31.1 (2018 Edition) 

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) 

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 

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 

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 

Fully Restrained Pipe (B31.4/R) 

Hoop: or Shoop = Pi (Dt)/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) 

Hoop: or Shoop = Pi (Dt)/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) 

Hoop: or Shoop = Pi (Dt)/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 

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. 

B31.4 Chapter IX (Offshore) 

Hoop: Shoop = (Pi – Pe )D/2t (for D/t ³ 30) 
< F1Sy 
OPE, SUS, OCC 
or Shoop = (Pi – Pe )(Dt)/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. 

B31.4 Chapter XI (Slurry Pipes) 

Fully Restrained Pipe (B31.4 Ch XI/R) 

Hoop: or Shoop = Pi (Dt)/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) 

Hoop: or Shoop = Pi (Dt)/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 

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. 

B31.5 

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 

B31.8 (2018 and 2020 Editions) 

Restrained Pipe 

Longitudinal: 

SL = Slp + Sb + Sa 
< 0.9TSy 
SUS, OPE, OCC 
CAESAR II includes the thermal effect in Sa 

Equivalent Combined: 

Seq = max[ Shoop  SL , Shoop , SL ] 
< 0.9TSy 
SUS, OPE 
< kTSy 
OCC 

or 

Seq = (SL2  SLShoop + Shoop2)1/2 
< 0.9TSy 
SUS, OPE 
< kTSy 
OCC 

The equivalent combined stress is valid for straight sections of pipe only. 

Unrestrained Pipe 

Longitudinal: 

SL = Slp + Sb + Sa 
< 0.75TSy 
SUS, OCC 
< 0.75Sy 
HYD 

Expansion: 

Se = ME/Z 
< f[1.25(Sc + Sh)  SL] where 
EXP 
Where: Shoop = PDo/2t 

Slp = 0.3Shoop Slp = 0.5Shoop 
Restrained Pipe Unrestrained Pipe 

Sa = Fax/Am Mb = [(0.75iiMi)2+(0.75ioMo)2]1/2 MR = [(0.75iiMi)2+(0.75ioMo)2 + Mt2]1/2 

Sb = Mb/Z Sb = MR/Z 
Straight pipe Fittings and components 

ME = [(iiMi)2+(ioMo)2 + Mt2]1/2 

B31.8 Chapter VIII (Offshore) (2018 and 2020 Editions) 

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 

Where: F1 = Hoop Stress Design Factor (Table A842.2.21) 



B31.9 

Paragraph 919.4.1.b states that analysis uses the equations of B31.1. 

ASME SECT III CLASS 2 & 3 

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 

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 

Slp + 0.75iMa / Z 
< Sy 
OPE 
Slp + Sb 
< 0.75SyFt 
SUS 
(Sb2 + 4St2)1/2 
< 0.72Sy 
EXP 