The international 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 

Stoomwezen 

Slp + 0.75iMa / Z 
< f 
SUS 
iMC / Z 
< fe 
EXP 
Slp + 0.75i(Ma + Mb) / Z 
< 1.2f 
OCC 
CODETI 

Sl = Slp + 0.75iMA / Z 
< Sh 
SUS 
iMC / Z 
< f[1.25Sc + 0.25Sh]Eh/Ec 
EXP 
Slp + 0.75iMA / Z + 0.75iMB / Z 
< kSh 
OCC 
Alternate Method: 
(Configuration switch set to TRUE) 

Sl = Slp + Fax/Am + Sb 
< Sh 
SUS 
(Sb2 + 4St2)1/2 
< f[1.25(Sl + Sh) – Sl 
EXP 
Slp + Fax/Am + Sb 
< kSh 
OCC 
Sb = {[(iiMi)2 + (ioMo)2]1/2} / Z 

Click Configuration Editor to select the method. 

Canadian Z662 

Fully restrained pipe (FAC = 1.0) 

Sh  SL This only applies if SL is negative (compression) Where: S = specified minimum yield strength T = temperature factor (Table 4.4) Sh = PDo/2tcor hoop stress Where: 
< 0.9ST 
OPE 
SL = nSh  ECa(T2T1) longitudinal stress Where: 

Buried pipe with soil restraints modeled (FAC = 0.001) 

Sh – SL + SB Where: SB = iMb/Z bending stress Where: 
< ST 
OPE 
Fully above ground (FAC = 0.0) 

Slp+Fax/Am+SB+Sh Where: Slp = PDi2/(Do2 – Di2) longitudinal pressure stress Fax = axial force Am = metal crosssectional area 
< ST 
OPE 
SE = (SB2 + 4St2)1/2 Where: 
< 0.72ST 
EXP 
0.5Sh + Sb 
< SFLT 
OCC 
Where: Sb = bending stress due to sustained and occasional loading combined F = design factor (0.800) L = location factor (Table 4.2) 

Canadian Z662 Chapter 11 

sh = (Pi – Pe)Do/2tmin 
< SyFAT 
OPE, SUS, OCC 
Seq = (sh2 + Sl2  shSl + 3t2)1/2 CAESAR II reports the largest 
< SyFBT 
OPE, SUS, OCC 
Where: Seq = Equivalent Stress (commonly referred to as Von Mises stress) sh = Hoop stress Sl = (Pi * Ri2  Pe * Ro2) / (Ro2  Ri2) The hoop stress used in the equivalent stress equation is based on nominal pipe wall thickness, but the hoop stress used in the separate code stress comparison is based on minimum wall thickness. Pi = Internal pressure Pe = External hydrostatic pressure Do = Outside pipe diameter tmin = Minimum pipe wall thickness accounting for corrosion allowance and manufacturing tolerances Sy = Specified minimum yield strength FA = Design factor (Table 11.1, column A) FB = Design factor (Table 11.1, column B) T = Temperature factor (Table 4.4) 

Sl = sax ± sb longitudinal stress Where: sax = (Pi * Ri2  Pe * Ro2) / (Ro2  Ri2) axial stress The software subtracts the Fax / Am term if the evaluation is being done on the From node and adds the term if the evaluation is being performed on the To node. Retain the sign of the term prior to adding or subtracting it. Where: Di = inside diameter of the pipe (not corroded) Fax = axial force due to all operating loads Am = metal cross sectional area sb = SIF(Mb/Z) bending stress Where: SIF = stress intensification factor Mb = resultant bending moment Z = (p/64)(Do4 – Di4)/Ro pipe section modulus t = Mt/2Z torsion stress Where: Mt = torsion moment 

Norwegian 

SI = PDi2/Eff(Do2 – Di2) + 0.75Ma/Z 
< Sh 
SUS 
iMC / Z 
< Sh + Sr  Sl 
EXP 
PmaxDi2/(Eff(Do2 – Di2) + 0.75i(Ma + Mb) / Z 
< 1.2Sh 
OCC 
Where: Sr = min(1.25Sc + .25Sh, FrRs – F2) or Fr(1.25R1 + 0.25R2) Fr = Cyclic stress range reduction factor Rs = Permissible stress for 7000 cycles R1 = Min(Sc, 0.267Rm) R2 = Min(Sh, 0.367Rm) Rm = Ultimate tensile strength at room temp 
The latter applies to temps > 370 C; 

FDBR 

Sl = Slp + 0.75iMA / Z 
< Sh 
SUS 
iMC / Z 
< f[1.25(Sc + Sh) – Sl] 
EXP 
Slp + 0.75iMA / Z + 0.75iMB / Z 
< kSh 
OCC 
BS 806 

Straight Pipe 

fc= (F2 + 4fs2)1/2 
< SAOPE 

fs = Mt(d + 2t) / 4I F = max (ft, fL) ft= pd/2t + 0.5p fL= pd2/[4t(d + t)] + (d + 2t)[(mi2 + mo2)1/2] / 2I 

Bends 

fc= (F2 + 4fs2)1/2 
< SAOPE 

fs = Mt (d + 2t) /4I F = max (ft, fL) ft = r/I * [(miFTi)2 + (moFTo)2]1/2 fs = r/I * [(miFLi)2 + (moFLo)2]1/2 

Branch Junctions 

fcb = q * [fb2 + 4fsb2]1/2 
< SAOPE 

fb = (d + t)*p*m/(2t) + r/I*sqrt[(miFTL)2 + (moFTO)2] Fsb = Mt (d + 2t) / 4I q = 1.0 except for operating cases m = geometric parameter 

SA = min[(H*Sproof ambient + H*Sproof design) 
EXP 

SA = Savg rupture at design temperature 
OPE 

SA = min[.8*Sproof, Screep rupture] 
SUS 

BS 7159 

If Sx is tensile: 

(Sx2 + 4Ss2)1/2 
< Sh 
OPE 
(Sf2+ 4Ss2)1/2 
< EffSh 
OPE 
If Sx is compressive: 

< EffSh 
OPE 

Sx 
< 1.25Sh 
OPE 
Where: Sx = PDm / 4t + [(ixiMi)2 + (ixoMo)2]1/2 / Z Ss = Sx – Fx / A If Fx / A > PDm / 4t, and it is compressive: Sf= MPDm / 2t Sf = MPDm / 2t + [(ifiMi)2 +(ifoMo)2]1/2 / Z Sf= MPDm / 2t + [(ixiMi)2 + (ixoMo)2]1/2 / Z Dm and t are always for the run pipe Eff = Ef/ Exff 
For Straight Pipe For Bends For Tees 

UKOOA 

sab(f2/r) + PDm / 4t 
< f1f2LTHS / 2.0 
OPE 
Where: sab = Axial Bending Stress due to mechanical loads f1 = Factor of Safety for 97.5% confidence limit, usually 0.85 f2 = System factor of safety, usually 0.67 r = sa(0:1) / sa(2:1) sa(0:1) = Longterm Axial Tensile Strength in absence of pressure load sa(2:1) = Longterm Axial Strength under only pressure loading LTHS = Longterm Hydrostatic Strength (hoop stress allowable) 

Det Norske Veritas (DNV) 

Hoop Stress: Sh 
< nsSMYS 
OPE, SUS, OCC 
Hoop Stress: Sh 
< nuSMTS 
OPE, SUS, OCC 
Longitudinal Stress: SL 
< nSMYS 
OPE, SUS, OCC 
Equivalent Stress: Se 
< nSMYS 
OPE, SUS, OCC 
Where: Sh = (Pi – Pe)(Dt)/2t ns = Hoop Stress Usage Factor (Tables C1 and C2) nu = Hoop Stress Bursting Factor (Tables C1 and C2) SMYS = Specified Minimum Yield Stress at Operating Temp. SMTS = Specified Minimum Tensile Strength at Operating Temp. SL = Max. Longitudinal Stress SL = SLP + Fax / Am ± Sb SLP = (Pi * Ri2  Pe * Ro2) / (Ro2  Ri2) Sb = iMb/Z Mb  Resultant bending moment n = Equiv. Stress Usage Factor (Table C4) Se = [Sh2 + SL2 – ShSL + 3t2]1/2 t = Shear stress + Torsion stress 

EN1348032017 

s1 = Pcdo/4en + 0.75iMA/Z 
< ff 
SUS 
s3 = iMc/Z 
< fa 
EXP 
s2 = Pcdo/4en + 0.75iMA/Z + 0.75iMB/Z 
< kff 
OCC 
s5 = Pcdo/4en + 0.75iMA/Z + 0.75iMC/3Z 
< fCR 
CRP 
Alternate Option: 

s1 = Pcdo/4en + SbA 
< ff 
SUS 
s3 = (SbC2 + 4StC2)1/2 
< fa 
EXP 
s2 = Pcdo/4en + SbA + SbB 
< kff 
OCC 
s5 = Pcdo/4en + SbA + [(SbC2 + 4StC2)1/2]/3 
< fCR 
CRP 
Where: 

SbA = [(iiMi)2+(ioMo)2]1/2 / Z, due to primary loads 

SbC is defined as SbA, except that it uses the range of resultant moments due to thermal expansion. 

SbB is defined as SbA, except that it uses moments due only to occasional loading. 

StC = MtC/2Z, the torsional stress due to the range of resultant moments from thermal expansion. 

en = Nominal wall thickness. 

ff, fCR = Hot allowable stress. 

fa = Allowable stress range. 

MA = Resultant moment from weight and other sustained mechanical loads (SUS) 

MB = Resultant moment from occasional or exceptional loads (OCC) 

MC = Range of resultant moments from thermal expansion and alternating loads (EXP) 

You can use s4 when the conditions of s3 are not met. See the technical discussion EN13480. 

EN134803:2017/A5:2022 

s1 = SaA + 0.75iMA/ZC 
< ff 
SUS 
s2 = Sa(A+B) + 0.75i[(MA + MB)/ZC] 
< kff 
OCC 
s3 = iaFaxC/Am + iMC/Z 
< fa 
EXP 
s5 = s1 + iaFaxC/3Am + 0.75iMC/3Z 
< fCR 
CRP 
Alternate Option: 

s1 = [(SaA + SbA)2 + 4S2tA]1/2 
< ff 
SUS 
s2 = [(Sa(A+B) + Sb(A+B))2 + 4S2t(A+B)]1/2 
< kff 
OCC 
s3 = [(iaFaxC/Am + SbC)2 + 4S2tC]1/2 
< fa 
EXP 
s5 = s1 + {[(iaFaxC/Am + [(0.75SbC)2]1/2/Z)2 + 4S2tC]1/2}/3 
< fCR 
CRP 
Where: 

SaA = iamax(FaxA/AmC, FaxA/AmC + Slp), the maximal total axial stress due to SUS 

Sa(A+B) = iamax(FaxA/AmC, FaxA/AmC + Slp, (FaxA +FaxB)/AmC, (FaxA +FaxB)/AmC +Slp), the maximal total axial stress due to SUS+OCC 

SbA = [(0.75iiMi)2 + (0.75ioMo)2]1/2/ZC, due to primary loads 

SbC = [(iiMi)2 + (ioMo)2]1/2/Z, due to thermal expansion 

Sb(A+B) is defined as SbA, except that it uses combined weight and occasional moments 

StA = itMtA/(2ZC), the torsional stress due to SUS 

St(A+B) = itMt(A+B)/(2ZC), the torsional stress due to SUS+OCC 

StC = itMtC /(2Z), the torsional stress due to EXP 

Z = uncorroded section modulus 

ZC = corroded section modulus 

Am = uncorroded crosssectional area 

AmC = corroded crosssectional area 

ff , fCR = Hot allowable stress 

fa = Allowable stress range 

MA = Resultant moment from weight and other sustained mechanical loads (SUS) 

MB = Resultant moment from occasional or exceptional loads (OCC) 

MC = Range of resultant moments from thermal expansion and alternating loads (EXP) 

You can use s4 when the conditions of s3 are not met. See the technical discussion EN13480. 

HPGSL and JPI 

Sl = Slp + Sb + Fax/Am 
< Sh 
SUS 
(Sb2 + 4St2)1/2 
< f[1.25(Sc + Sh) – Sl] 
EXP 
Slp + Sb + Fax/Am 
< kSh 
OCC 
Sl = Sb + Fax/Am 
< S 
K1P 
< 2S 
K2P 

SE = [(iiMi)2 + (ioMo)2 + (Mt)2]1/2 / Z 
< 2 Sy 
K1SR, K2SA 
< 4 Sy 
K2L, K2SR 

S is defined by the following criteria: 

For aluminum alloy and 9% nickel steel at or under room temperature 
S is the minimum value of the following: (1) 0.6SU (2) 0.9Sy 

For austenitic stainless steel and high nickel alloy steels at or over room temperature 
S is the minimum value of the following: (1) 0.6SUo (3) 0.9Syo (2) 0.6SU (4) Sy 

For other materials or temperatures 
S is the minimum value of the following: (1) 0.6SUo (3) 0.9Syo (2) 0.6SU (4) 0.9Sy 

Unspecified 
S is 0 

Where: Sc = Ambient (cold) Allowable Stress, the minimum of 0.66Syc or 0.33Suc Sh = Hot Allowable Stress, the minimum of 0.66Sy or 0.33Su Sb = bending stress, defined as (iiMi)2 + (ioMo)2]1/2 / Z SU = Tensile strength of material at design temperature SUo = Minimum tensile strength at room temperature Sy = Yield strength or 0.2% endurance strength at design temperature Syo = Minimum yield strength or 0.2% endurance strength at room temperature 

PD8010 Part 1 

Hoop Stress: Sh 
< eSy 
OPE, SUS, OCC 
Equivalent Stress: Se 
< 0.9Sy 
OPE, SUS, OCC 
Where: Sy = Specified min yield strength e = Weld joint factor Sh = P(Do2 + Di2)/(Do2  Di2) Se = [Sh2 + SL2 – ShSL + 3St2]1/2 St = MT/2Z + 2Fs/A MT= Torsional moment Fs = Shear force Unrestrained: SL = Slp +iM/Z Restrained: FAC = 1.0 (fully restrained): SL = nSh  EadT FAC = 0.001 (Buried w/soil restraints): SL = Fax/Am +Sh(1n) + Sb 

PD8010 Part 2 

Hoop Stress: Sh 
< fdhSy 
OPE, SUS, OCC 
Equivalent Stress: Se 
< fdeSy 
OPE, SUS, OCC 
Where: fdh = Hoop stress design factor per Table 2. fde = Equivalent stress design factor per Table 2. Sh = (PePi)(Do2 + Di2)/(Do2Di2) Se = [Sh2 + SL2 – ShSL + 3St2]1/2 St = Mt/2Z + iM/Z SL = Slp + iM/Z 

RCCM C&D 

Slp + 0.75iMa/Z 
< Sh 
SUS 
iMC/Z 
< f[1.25(Sc+Sh) – Sl] 
EXP 
Slpmax + 0.75i(Ma+Mb)/Z 
< 1.2Sh 
OCC 
ISO 14692 2005 

ISO 14692 2005 requires that the sum of all hoop stresses (sh, sum) and the sum of all axial stresses (sa, sum) be evaluated for all states of the piping system. CAESAR II evaluates these stresses for stress types OPE, SUS, and OCC. If the hoop stress is exceeded, the axial stress is not reported. 

Pipe: Fully Measured Envelope: 
(shl(1,1) and sal(1,1) input) 

If: sh,sum and if: sh,sum then use: sa,sum 
£ f2A1A2A3shl(2,1) £ f2A1A2A3shl(1,1) £ f2A1A2A3sal(0,1) + [(sal(1,1) – sal(0,1))/shl(1,1)] (sh,sum ) 

If: sh,sum then use: sa,sum 
³ f2A1A2A3shl(1,1) £ f2A1A2A3sal(1,1)+{[sal(2,1) – sal(1,1)]/[shl(2,1)shl(1,1)]}[sh,sum–f2A1A2A3shl(1,1)] 

Simplified Envelope: 
(shl(1,1) and sal(1,1) not input) 

sh,sum and sa,sum 
£ f2A1A2A3shl(2,1) £ f2A1A2A3sal(0,1) + [sal(2,1) – sal(0,1)]sh,sum/shl(2,1) 

Joints and Bends: Simplified Envelope (r £ 1): sh,sum and sa,sum 
£ f2A1A2A3sqs £ f2A1A2A3rsqs / 2 + (1r)sh,sum / 2 

Joints and Bends: Rectangular Envelope (r ³ 1): sh,sum and sa,sum 
£ f2A1A2A3sqs £ f2A1A2A3rsqs / 2 

Tees: Rectangular Envelope (r = 1): sh,sum and sa,sum 
£ f2A1A2A3sqs £ f2A1A2A3sqs / 2 

Where: f2 = Part Factor for Loading (default values listed from Table 3) 0.89 for Occasional ShortTerm Loads 0.83 for Sustained Loads Including Thermal Loads 0.67 for Sustained Loads Excluding Thermal Loads A1 = Partial Factor for Temperature A2 = Partial Factor for Chemical Resistance A3 = Partial Factor for Cyclic Service sqs = Qualified Stress (entered for bends, fittings, and joints) sal(0,1) = LongTerm Axial Strength at 0:1 Stress Ratio sal(1,1) = LongTerm Axial Strength at 1:1 Stress Ratio shl(1,1) = LongTerm Hoop Strength at 1:1 Stress Ratio sal(2,1) = LongTerm Axial Strength at 2:1 Stress Ratio shl(2,1) = LongTerm Hoop Strength at 2:1 Stress Ratio r = BiAxial Stress Ratio 2sal(0,1)/sqs (for simplified and rectangular envelopes) sa,sum = Sum of All Axial Stresses {(sap + sab)2 + 4x2}1/2 sh,sum = Sum of All Hoop Stresses [sh2 + 4x2]1/2 sap = Axial Pressure Stress sab = Axial Bending Stress x = Torsion Stress sh = Hoop Stress 

ISO 14692 2017 

Hoop stress: sh,sum = shp + shu shp = PDm/2tn shu = rcDfEhb(Dy/Dm)(tn/Dm) Ring bending. For buried pipe only. 

Where: rc = Rerounding coefficient For P £ 3: rc = 1  P/3 For P > 3: rc = 0 

Axial stress: sa,sum = sap ± sab + saf ± sac + sat sap = PDm/4tn For a closed, unrestrained pipe sap = n(P*Dm/2tn) For an axially restrained pipe sab = [(SIFaiMi)2 + (SIFaoMo)2]1/2/Zr Zr = ( P/32)[(D4o  D4i)/Do] saf = Fax/Ar = Fax/[P/4)(D2o  D2i)] sac = (Do/2C)/E where C = Curve radius sat = a(Tinstall  Tdesign)E 

Allowable stress: See ISO14692 and al(0:1) in the CAESAR II Users Guide. The pipe dimensions are reinforced quantities. The subscript m refers to the percentage variation. 