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 CAESAR II Quick Reference Guide 55 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 56 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 CAESAR II Quick Reference Guide 57 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 CAESAR II Quick Reference Guide 61