US Code Stresses - CAESAR II - Installation & Upgrade

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:
Slp (OCC) is calculated using the pressure (Po) coincident with the evaluated occasional load.

< 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 = [(Ia|Slp + Fax / Am| + Sb)2 + 4St2]1/2 (2022 Edition)

Where:
Sb = [(IiMi)2 + (IoMo)2]1/2 / Z
St = ItMt / 2Z
Slp (OCC) is calculated using the pressure (Po) coincident with the evaluated occasional load.
Z = nominal section modulus

≤ Sh and ≤ kSh

≤ Sh and ≤ kSh

SUS

OCC

Se = [(|iaFax / Am| + Sb)2 + 4St2 ]1/2

Where:
Sb = [(iiMi)2 + (ioMo)2]1/2 / Z
St = itMt / 2Z
Z = nominal section modulus

≤ 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:
Sb = [(liMi)2 + (loMo)2]1/2 / Z
Z is the corroded section modulus

For reduced outlet connections, use Ze instead of Z
if you do not specify bending in/out-plane SIFs (ii and io) or
index (li and lo). Use Z if you specify bending in/out-of-plane
SIFs or index.

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
from nominal dimensions (not corroded).

For reduced outlet connections, use Ze instead of Z
if you do not specify bending in/out-plane SIFs (ii and io) or
index (li and lo). Use Z if you specify bending in/out-of-plane
SIFs or index.

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:
Sb = [(liMi)2 + (loMo)2]1/2 / Z
Z is the corroded section modulus

For reduced outlet connections, use Ze instead of Z
if you do not specify bending in/out-plane SIFs (ii and io) or
index (li and lo). Use Z if you specify bending in/out-of-plane
SIFs or index.

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:
Z is the section modulus computed
from nominal dimensions (not corroded).

For reduced outlet connections, use Ze instead of Z
if you do not specify bending in/out-plane SIFs (ii and io) or
index (li and lo). Use Z if you specify bending in/out-of-plane
SIFs or index.

St = itMt / 2Z

< 1.25Sc + 0.25 Sh

EXP

B31.4

Fully Restrained Pipe (B31.4/R)

Hoop:
Shoop = Pi D/2t (for D/t ³ 20)

or

Shoop = Pi (D-t)/2t (for D/t < 20)

< 0.72 ESy
(where E is the weld joint factor)

SUS, OPE, OCC

Expansion: Se = Ea(T1 − T2)

< 0.9 Sy

EXP

Longitudinal:
SL = nSH + Sb+ Fa/A
where
Sb = [(Mi2 + Mo2)1/2]/Z

< 0.9 Sy

SUS, OPE, OCC

CAESAR II includes the thermal effect in Sb

Equivalent Combined:
Seq = [(SL − SH)2 + 4St2]1/2

or

Seq = (SH2 − SHSL + SL2 + 3St2)1/2
where
St = Mt/2Z

< 0.9 Sy

SUS, OCC, OPE

Fully Above Ground, Unrestrained Pipe (B31.4/U)

Hoop:
Shoop = Pi D/2t (for D/t ³ 20)

or

Shoop = Pi (D-t)/2t (for D/t < 20)

< 0.72 ESy
(where E is the weld joint factor)

<0.90Sy when defined as Hydro (HYD)

SUS, OCC, HYD

Expansion:
Se = (Sb2 + 4St2)1/2
where
Sb = {[(iiMi)2 + (ioMo)2]1/2}/Z
St = Mt/2Z

≤ f[1.25(Sc + Sh) - SL]

• 2019 edition: Sc and Sh = 2/3Sy

• 2022 edition: Sc and Sh = min(2/3Sy, 1/3Su), with maximum of 20 Ksi

EXP

Longitudinal:
SL = PiD/4t + Sb + Fa/A
where
Sb = {[(iiMi)2 + (ioMo)2]1/2}/Z

< .75Sy

< .80Sy when defined as Occasional (OCC)

SUS, OCC, HYD

Equivalent Combined

Not used

Riser and Platform for Inland Waterways (B31.4/W)

Hoop:
Shoop = Pi D/2t (for D/t ³ 20)

or

Shoop = Pi (D-t)/2t (for D/t < 20)

< 0.6 ESy
(where E is the weld joint factor)

<0.90Sy when defined as Hydro (HYD)

SUS, OCC, HYD

Expansion:
Se = (Sb2 + 4St2)1/2
where
Sb = {[(iiMi)2 + (ioMo)2]1/2}/Z
St = Mt/2Z

< 0.8 Sy

EXP

Longitudinal:
SL = PiD/4t + Sb + Fa/A
where
Sb = {[(iiMi)2 + (ioMo)2]1/2}/Z

< 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 )(D-t)/2t (for D/t < 30)

< 0.9Sy

HYD

Longitudinal:

SL = Slp + Sb +Fa/A

< 0.8Sy

OPE, SUS, OCC

where
Slp = (PiRi2 - PeRo2)/(Ro2 - Ri2)
Sb = [(iiMi)2 + (ioMo)2]1/2/Z

< 0.9Sy

HYD

Equivalent Combined:

Seq = [(SL – SH)2 + 4St2]1/2

or

Seq = (SH2 - SHSL + SL2 + 3St2)1/2
where
St = Mt/2Z

< 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:
Shoop = Pi D/2t (for D/t ³ 20)

or

Shoop = Pi (D-t)/2t (for D/t < 20)

< 0.80 ESy
(where E is the weld joint factor)

SUS, OCC, OPE

Expansion:
Se = Ea(T1 − T2)

< 0.9 Sy

EXP

Longitudinal:
SL = nSH + Sb+ Fa/A
where
Sb = [(Mi2 + Mo2)1/2]/Z

< 0.9 Sy

< 0.88 Sy when defined as Occasional (OCC)

SUS, OPE, OCC

CAESAR II includes the thermal effect in Sb

Equivalent Combined:
Seq = [(SL − SH)2 + 4St2]1/2

or

Seq = (SH2 − SHSL + SL2 + 3St2)1/2
where
St = Mt/2Z

< 0.9 Sy

SUS, OCC, OPE

Fully Above Ground, Unrestrained Pipe (B31.4 Ch XI/U)

Hoop:
Shoop = Pi D/2t (for D/t ³ 20)

or

Shoop = Pi (D-t)/2t (for D/t < 20)

< 0.80 ESy
(where E is the weld joint factor)

<0.90Sy when defined as Hydro (HYD)

SUS, OCC, HYD

Expansion:
Se = (Sb2 + 4St2)1/2
where
Sb = {[(iiMi)2 + (ioMo)2]1/2}/Z
St = Mt/2Z

≤ f[1.25(Sc + Sh) - SL]

• 2019 edition: Sc and Sh = 2/3Sy

• 2022 edition: Sc and Sh = min(2/3Sy, 1/3Su), with maximum of 20 Ksi

EXP

Longitudinal:
SL = PiD/4t + Sb + Fa/A
where
Sb = {[(iiMi)2 + (ioMo)2]1/2}/Z

< .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
Sc = 0.33SU
Sh = 0.33TSU

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
(SL + Sh)/2 - {[(SL - Sh)/2]2 + St2}1/2
(SL + Sh)/2 + {[(SL - Sh)/2]2 + St2}1/2

< 0.9Sy

OPE, SUS, OCC

Alternative Combined Stress (Von Mises)
(2018 and 2020 editions):

Seq = (Sh2 – SLSh + SL2 + 3St2)1/2

< 0.9Sy

Where:

F1 = Hoop Stress Design Factor (Table A842.2.2-1)
T = Temperature Derating Factor (Table 841.1.8-1)
Sy = Specified Minimum Yield Strength

• For information on F1, T, and Sy, see Operating, sustained, and occasional load cases in the B31.8 Chapter VIII (Offshore) technical discussion.

• For the equivalent combined stress on platform piping and risers, B31.8 Chapter VIII bases the calculation of the stress components on the minimum corroded wall thickness. Pipelines use the nominal wall thickness.

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 PL-2.6.7, 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:
Sc and Sh = Values from Allowable Stress Table IX-1A

Or,

when EXP allowable: Sc & Sh use 0.33 SuT is selected:

Sc = 0.33SU
Sh = 0.33TSU

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