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 
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) 

Sl = [(Slp + IaFax / Am + Sb)2 + 4St2]1/2 (2020 Edition) Sl = [(IaSlp + 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 

See the B31.3 technical discussion in the CAESAR II User's Guide for information on using B31J. 

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 

See the B31.3 Chapter IX technical discussion in the CAESAR II User's Guide for information on using B31J. 

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 

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 
CAESAR II includes the thermal effect in Sb 

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]

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 
CAESAR II includes the thermal effect in Sb 

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]

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, 2020, and 2022 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 only for straight sections of pipe. 

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, 2020, and 2022 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 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 

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. 

B31.12 IP 

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 

When using Appendix B by selecting Use Alternative Rules for Stress Range Evaluation in the Configuration Editor: 

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 

B31.12 PL 

Restrained Pipe 

Longitudinal: 

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

Equivalent Combined: 

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

Or, when Yield Stress Criterion is set to VonMises in the Configuration Editor: 

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

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

Unrestrained Pipe 

Longitudinal: 

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

Expansion: 

Se = According to PL2.6.7, 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 

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 

For restrained and unrestrained pipe, Z is the nominal section modulus (not corroded). 

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 