SECTION 5
Code Stresses
The following code stress values are supported by CAESAR II.
In This Section
Nomenclature ................................................................................ 55
US Code Stresses ......................................................................... 57
International Code Stresses .......................................................... 62
CAESAR II Verification and Validation Manual ............................. 72
Nomenclature
Use the nomenclature definitions below throughout CAESAR II unless a code section
specifically provides a different definition.
Am - Cross-sectional metal area in the pipe.
B1 - Primary stress index (component specific)
B2 - Primary stress index (component specific)
Di - Internal diameter
Dm - Mean diameter
Do - Outer diameter
dT - Change in temperature
E - Elastic modulus
f - Cyclic reduction factor
F1 - Hoop stress design factor
Fax - Axial force
FAC - A unitless factor used for a number of purposes depending on the piping code. For more
information, see the CAESAR II User's Guide.
i - Stress intensification factor
ii - In-plane stress intensification factor
io - Out-of-plane stress intensification factor
ia - Axial stress intensification factor
it -Torsional stress intensification factor
I - Sustained moment index
Ii - Sustained in-plane moment index
Io - Sustained out-of-plane moment index
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Code Stresses
Ia - Sustained axial force index
It - Sustained torsional moment index
k - Occasional load factor
Ma - Resultant moment due to weight and other sustained loadings
Mb - Resultant moment due to occasional loadings
Mc - Range of resultant moments due to expansion and displacement loadings
Mi - In-plane moment
Mo - Out-of-plane moment
Pi - Internal pressure
Pe - External pressure
R - Radius of pipe or bend
Sa - Axial stress
Sb - Bending stress
Sc - Cold allowable stress (ambient or reference temperature)
Se - Equivalent stress (von Mises or Tresca)
Sh - Hot allowable stress
Shoop - Hoop stress
Sl - Longitudinal stress
Slp - Longitudinal pressure stress
Ss - Tangential shear stress
St - Torsion stress
SU - Ultimate tensile strength
Sy - Yield stress
T - Temperature derating factor
tn - Nominal wall thickness
Z - Pipe section modulus
Ze - Effective section modulus for branch
a - Coefficient of thermal expansion
n - Poisson’s ratio
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CAESAR II Quick Reference Guide
Code Stresses
US Code Stresses
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.
Longitudinal Pressure Stress - Slp
Slp = PDo / 4tn
Code approximation
Slp = PD2i / (Do2 - Di2)
Code exact equation,
CAESAR II Default
Operating Stress – unless otherwise specified
S = Slp + Fax/Am + Sb
< N/A
B31.1
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
< Sh
SUS
B31.3
SL = [(Ia (Slp + |Fax / Ap|) +Sb)2 + 4St2]1/2
Where:
Sb = [(liMi)2 + (loMo)2]1/2 / Z
Where:
Z is the corroded section modulus
Note: For reduced outlet connections, use Ze
instead of Z.
St = ltMt / 2Z
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Code Stresses
< f [1.25(Sc + Sh) - SL]
EXP
< kSh
OCC
[B1PmaxDo / 2tn] + B2Ma / Z
< 1.5Sh
SUS
iMc/Z
< f(1.25Sc + 0.25Sh) +
Sh - Sl
EXP
B1Slpmax + B2(Ma + Mb) / Z
< 1.8Sh and < 1.5Sy
OCC
Sl = Slp + (Sb2 + 4St2)1/2
< Sh
SUS
(Sb2 + 4St2)1/2
< f[1.25Sc + 0.25Sh
+(Sh – Sl)]
EXP
Slp + (Sb2 + 4St2)1/2
< kSh
OCC
FAC|EadT – nShoop| + Shoop
< 0.9 Sy
OPE
Buried w/soil restraints modeled
(FAC = 0.001):
Only applies to OPE case if Slp +
Fax/Am is compressive.
Fax/Am – nShoop + Sb + Shoop
< 0.9 Sy
[(|iaFax/Ap| +Sb)2 + 4St2]1/2
Sb = [(iiMi)2 + (ioMo)2]1/2 / Z
Where:
Z is the section modulus computed from
nominal dimensions (not corroded).
Note: For reduced outlet connections, use Ze
instead of Z.
St = itMt / 2Z
|IaFax/Ap| + Sb + SL
Where:
Sb is defined as for sustained conditions; however, it
uses forces and moments due only to occasional
loading.
ASME SECT III CLASS 2 & 3
B31.1 (1967) and Navy Section 505
B31.4
Fully Restrained Pipe (FAC = 1.0):
58
OPE
CAESAR II Quick Reference Guide
Code Stresses
Fully Above Ground
(FAC = 0):
Only applies to OPE case if Slp +
Fax/Am is compressive.
Slp + Fax/Am + Sb + Shoop
< 0.9Sy
OPE
(Slp + Sb + Fax/Am)(1.0 – FAC)
< .75(.72)Sy
SUS
(Sb2 + 4St2)1/2
< 0.72Sy
EXP
(Slp + Sb + Fax/Am)(1.0 – FAC)
< 0.8Sy
OCC
Hoop: Shoop
< F1Sy
OPE, SUS,
OCC
Longitudinal: |Slp|
< 0.8Sy
OPE, SUS,
OCC
Equivalent: Se
< 0.9Sy
OPE, SUS,
OCC
B31.4 Chapter IX
Where:
Se = 2{[(Slp – Shoop)/2]2 + St2}1/2
Shoop = (Pi – Pe)D/2t
Slp = Sa + Sb or Sa – Sb
CAESAR II only reports the controlling stress the largest percentage of its allowable for
each load case.
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
Restrained Pipe:
As defined in section
833.1
Straight Pipe:
Max(SL, SC)
CAESAR II Quick Reference Guide
< 0.9SyT
OPE, SUS
59
Code Stresses
SL
< 0.9SyT
OCC
SC
< SyT
OCC
All other components:
SL
< 0.9SyT
Unrestrained Pipe:
As defined in section
833.1
SL
< 0.75SyT
SE
< f[1.25(Sc + Sh)] – SL
OPE, SUS,
OCC
SUS, OCC
EXP
Where:
SL = SP + Sx + SB
SP = 0.3Shoop
Restrained Pipe
SP = 0.5Shoop
Unrestrained Pipe
Sx = R / A
Straight pipe
SB = MB / Z
All other components
SB = MR / Z
MR =
[(.75iiMi)2
+(0.75ioMo)2
+
Mt2]1/2
MB = (Mi2 + Mo2)1/2
Sc = |Shoop – SL|
or
[SL2 – SLShoop + Shoop2]1/2
SE = ME / Z
ME = [(0.75iiMi)2+(0.75ioMo)2 + Mt]1/2
Where:
Sc = 0.33SUT (In the allowables)
Sh = 0.33SUT (In the allowables)
B31.8 Ch VIII
60
Hoop Stress: Shoop
< F1SyT
OPE, SUS,
OCC
Longitudinal: |SL|
< 0.8Sy
OPE, SUS,
OCC
Equivalent: Se
< 0.9Sy
OPE, SUS,
CAESAR II Quick Reference Guide
Code Stresses
OCC
Where:
F1
T
Shoop = (Pi – Pe)D/2t
Hoop Stress Design
Factor
Table
A842.22
Temp. Derating Factor
Table
841.116A
Se = 2{[(SL – Shoop)/2]2 + Ss2}1/2
The Temperature Derating Factor (T) value must be entered in the SH field in the
CAESAR II Input.
B31.11
Fully restrained pipe (FAC = 1.0):
FAC|EadT – nShoop| + Shoop
Buried w/ soil restraints (FAC = 0.001)
Fax/Am – nShoop + Sb + Shoop
Fully above ground (FAC = 0.0):
< 0.9 Sy
OPE
Only applies to OPE case if in axial
compression
< 0.9Sy
OPE
Only applies to OPE case if in axial
compression
|Slp + Fax/Am| + Sb + Shoop
< 0.9Sy
OPE
(Slp + Sb + Fax/Am)(1.0 – FAC)
< 0.75(.72)Sy
SUS
(Sb2 + 4St2)1/2
< 0.75Sy
EXP
(Slp + Sb + Fax/Am)(1.0 – FAC)
< 0.88Sy
OCC
Slp + 0.75iMa / Z
< Sy
OPE
Slp + Sb
< 0.75SyFt
SUS
(Sb2 + 4St2)1/2
< 0.72Sy
EXP
GPTC
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