Study Model : Theory Vs. Caesar II
Hot Modulus @ 300 °C
@Temp = 300 °C 2
2
Thermal Force = (πD /4)Eα = 7682.75 mm x (1.8526E+005 MPa) x (
For Secondary Loads
FT = 5125326 N
) x (0.003601 mm/mm)
Thermal Axial Force
S = 667.12 N/mm2
P = AEα
For Primary Loads
S = Eα
Weight 5 m = 60.18 kg/m x 5m =2952 N Weight @ each support = 1475 N 2
Longitudinal stress from weight SLW= 1475 N/7682.75 mm = 0.192 N/mm2 2
2
2
2
2
2
Longitudinal stress from Pressure SLp= Pdi /(d0 -di ) = 1.569 N/mm2 x (273.05 ) / (273.05 -254.508 ) = 11.6653 N/mm2 Total Longitudinal stress SL = 0.192 + 11.6653 N/mm2 = 11.86 N/mm2
Corroded case Wall Thickness = 9.271 – 1.5 – (9.271x12.5%) = 6.612125 mm di = 273.05- (2xt) = 259.82575 mm. 2
Longitudinal stress from weight SLW= 1475 N/5534.608 mm = 0.2665 N/mm2 2
2
2
2
2
2
Longitudinal stress from Pressure SLp= Pdi /(d0 -di ) = 1.569 N/mm2 x (273.05 ) / (273.05 -259.82575 ) = 12.5114 N/mm2
Total Longitudinal stress S L = 0.2665 + 12.5114 N/mm2 = 12.78 N/mm2
@Temp = 250 °C 2
2
Thermal Force = (πD /4)Eα = 7682.75 mm x (1.8873E+005 MPa) x (
For Secondary Loads
FT = 4173000 N S = 543.16 N/mm2
For Primary Loads Same values as Temp. 300 °C
) x (0.002878 mm/mm)
Report 1: Use Hot Modulus (Eh1,Eh2) for Report Force & Stress Use Appendix P for Operating stress range Use Code Case 178 for sustained stress
LOAD CASE DEFINITION KEY CASE 2 (OPE) W+T1+P1 CASE 3 (SUS) W+P1
NODE
Load Case
FX
FY
FZ
MX
MY
MZ
DX
DY
DZ
(N)
(N)
(N )
(N.m.)
(N.m.)
(N.m.)
(mm.)
(mm.)
(mm.)
Rigid 2100
ANC
2(OPE)
0
-5125994
0
0
0
0
0.000
-0.000
0.000
3(OPE)
0
-4174644
0
0
0
0
0.000
-0.000
0.000
4(SUS)
0
-1475
0
0
0
0
0.000
-0.000
0.000
5(SUS)
0
-1475
0
0
0
0
0.000
-0.000
0.000
6(EXP)
0
-5124519
0
0
0
0
0.000
-0.000
0.000
7(EXP)
0
-4173168
0
0
0
0
0.000
-0.000
0.000
MAX
5125994/L2
-0.000/L2
Rigid 2110
ANC
2(OPE)
0
5123044
0
0
0
0
0.000
0.000
0.000
3(OPE)
0
4171693
0
0
0
0
0.000
0.000
0.000
4(SUS)
0
-1475
0
0
0
0
0.000
-0.000
0.000
5(SUS)
0
-1475
0
0
0
0
0.000
-0.000
0.000
6(EXP)
0
5124519
0
0
0
0
0.000
0.000
0.000
7(EXP)
0
4173168
0
0
0
0
0.000
0.000
0.000
MAX
5124519/L6
0.000/L6
Piping Code: B31.3
= B31.3 -2008, December 31, 2008
*** CODE COMPLIANCE EVALUATION FAILED *** Highest Stresses: (N./sq.mm. ) CodeStress Ratio (%) is 205.0 at Node 2110 LOADCASE: 6 (EXP) L6=L2-L4 Code Stress:
667.0 Allowable:
Axial Stress:
325.3
667.0 @Node 2110 LOADCASE: 6 (EXP) L6=L2-L4
Bending Stress:
0.0 @Node 2110 LOADCASE: 2 (OPE) W+T1+P1
Torsion Stress:
0.0 @Node 2110 LOADCASE: 2 (OPE) W+T1+P1
Hoop Stress:
26.0 @Node 2110 LOADCASE: 4 (SUS) W+P1
3D Max Intensity:
Load Case
2(OPE)
From Node
2100
805.5 @Node 2110 LOADCASE: 2 (OPE) W+T1+P1
Code Stress N./sq.mm.
Allowable Stress
To Node
N./sq.mm.
656.84
325.33
3(OPE)
533.00
4(SUS)
2110
Code Stress N./sq.mm.
Allowable Stress
Piping Code
N./sq.mm.
656.45
325.33
336.96
532.62
336.96
12.39
122.37
12.85
122.37
5(SUS)
12.39
122.37
12.85
122.37
6(EXP)
667.03
325.33
667.03
325.33
7(EXP)
543.20
336.96
543.20
336.96
B31.3
*
B31.3
*
B31.3 B31.3 B31.3
*
B31.3
*
Report 2: Use Hot Modulus (Eh1,Eh2) for Report Force & Stress Use Appendix P for Operating stress range Not use Code Case 178 for sustained stress
Piping Code: B31.3
= B31.3 -2008, December 31, 2008
*** CODE COMPLIANCE EVALUATION FAILED *** Highest Stresses: (N. /sq.mm.) CodeStress Ratio (%) is 205.0 at Node 2110 LOADCASE: 6 (EXP) L6=L2-L4 Code Stress: Axial Stress:
667.0 Allowable:
667.0 @Node 2110 LOADCASE: 6 (EXP) L6=L2-L4
Bending Stress:
0.0 @Node 2110 LOADCASE: 2 (OPE) W+T1+P1
Torsion Stress:
0.0 @Node 2110 LOADCASE: 2 (OPE) W+T1+P1
Hoop Stress: 3D Max Intensity:
Load Case 2(OPE)
325.3
From Node 2100
26.0 @Node 2110 LOADCASE: 4 (SUS) W+P1 805.5 @Node 2110 LOADCASE: 2 (OPE) W+T1+P1
Code Stress N./sq.mm.
Allowable Stress
To Node
N./sq.mm. 2110
Code Stress N./sq.mm.
Allowable Stress
Piping Code
N./sq.mm.
656.84
325.33
656.45
325.33
B31.3
*
3(OPE)
533.00
336.96
532.62
336.96
B31.3
*
4(SUS)
12.39
122.37
12.85
122.37
B31.3
5(SUS)
12.39
122.37
12.85
122.37
B31.3
6(EXP)
667.03
325.33
667.03
325.33
B31.3
*
7(EXP)
543.20
336.96
543.20
336.96
B31.3
*
Report 3: Use Hot Modulus (Eh1,Eh2) for Report Force & Stress Not use Appendix P for Operating stress range Use Code Case 178 for sustained stress
Piping Code: B31.3
= B31.3 -2008, December 31, 2008
*** CODE COMPLIANCE EVALUATION PASSED *** Highest Stresses: (N./sq.mm. ) CodeStress Ratio (%) is 10.5 at Node 2110 LOADCASE: 4 (SUS) W+P1 Code Stress:
12.8 Allowable:
Axial Stress:
122.4
667.0 @Node 2110 LOADCASE: 6 (EXP) L6=L2-L4
Bending Stress:
0.0 @Node 2110 LOADCASE: 2 (OPE) W+T1+P1
Torsion Stress:
0.0 @Node 2110 LOADCASE: 2 (OPE) W+T1+P1
Hoop Stress:
26.0 @Node 2110 LOADCASE: 4 (SUS) W+P1
3D Max Intensity:
Load Case
2(OPE)
From Node
2100
805.5 @Node 2110 LOADCASE: 2 (OPE) W+T1+P1
Code Stress N./sq.mm.
Allowable Stress
To Node
N./sq.mm.
656.84
0.00
3(OPE)
533.00
4(SUS)
2110
Code Stress N./sq.mm.
Allowable Stress
Piping Code
N./sq.mm.
656.45
0.00
0.00
532.62
0.00
12.39
122.37
12.85
122.37
5(SUS)
12.39
122.37
12.85
122.37
6(EXP)
0.00
202.96
0.00
202.96
7(EXP)
0.00
205.28
0.00
205.28
B31.3 B31.3 B31.3 B31.3 B31.3 B31.3
Report 4: Use Hot Modulus (Eh1,Eh2) for Report Force & Stress Not use Appendix P for Operating stress range Not use Code Case 178 for sustained stress
NODE
Load
FX
FY
FZ
MX
MY
MZ
DX
DY
DZ
Case
(N)
(N)
(N )
(N.m.)
(N.m.)
(N.m.)
(mm.)
(mm.)
(mm.)
Rigid ANC
2100 2(OPE)
0
-5125994
0
0
0
0
0.000
-0.000
0.000
3(OPE)
0
-4174644
0
0
0
0
0.000
-0.000
0.000
4(SUS)
0
-1475
0
0
0
0
0.000
-0.000
0.000
5(SUS)
0
-1475
0
0
0
0
0.000
-0.000
0.000
6(EXP)
0
-5124519
0
0
0
0
0.000
-0.000
0.000
7(EXP)
0
-4173168
0
0
0
0
0.000
-0.000
0.000
MAX
-
-0.000/L2
5125994/L2
Rigid ANC
2110 2(OPE)
0
5123044
0
0
0
0
0.000
0.000
0.000
3(OPE)
0
4171693
0
0
0
0
0.000
0.000
0.000
4(SUS)
0
-1475
0
0
0
0
0.000
-0.000
0.000
5(SUS)
0
-1475
0
0
0
0
0.000
-0.000
0.000
6(EXP)
0
5124519
0
0
0
0
0.000
0.000
0.000
7(EXP)
0
4173168
0
0
0
0
0.000
0.000
0.000
MAX
5124519/L6
0.000/L6
*** CODE COMPLIANCE EVALUATION PASSED *** Highest Stresses: (N./sq.mm. ) CodeStress Ratio (%) is 10.5 at Node 2110 LOADCASE: 4 (SUS) W+P1 Code Stress:
12.8 Allowable:
Axial Stress:
122.4
667.0 @Node 2110 LOADCASE: 6 (EXP) L6=L2-L4
Bending Stress:
0.0 @Node 2110 LOADCASE: 2 (OPE) W+T1+P1
Torsion Stress:
0.0 @Node 2110 LOADCASE: 2 (OPE) W+T1+P1
Hoop Stress:
26.0 @Node 2110 LOADCASE: 4 (SUS) W+P1
3D Max Intensity:
Load Case
2(OPE) 3(OPE) 4(SUS) 5(SUS) 6(EXP) 7(EXP)
From Node
2100
805.5 @Node 2110 LOADCASE: 2 (OPE) W+T1+P1
Code Stress N./sq.mm.
Allowable Stress
To Node
N./sq.mm.
656.84
0.00
533.00
Code Stress N./sq.mm.
Allowable Stress
Piping Code
N./sq.mm.
656.45
0.00
B31.3
0.00
532.62
0.00
B31.3
12.39
122.37
12.85
122.37
B31.3
12.39
122.37
12.85
122.37
B31.3
0.00
202.96
0.00
202.96
B31.3
0.00
205.28
0.00
205.28
B31.3
2110
Report 5 : Use Cold Modulus (Ec) for Report Force & Stress Not use Appendix P for Operating stress range Not use Code Case 178 for sustained stress
NODE
Load
FX
FY
FZ
MX
MY
MZ
DX
DY
DZ
Case
(N)
(N)
(N )
(N.m.)
(N.m.)
(N.m.)
(mm.)
(mm.)
(mm.)
Rigid ANC
2100 2(OPE)
0
-5628066
0
0
0
0
0.000
-0.000
0.000
3(OPE)
0
-4499159
0
0
0
0
0.000
-0.000
0.000
4(SUS)
0
-1475
0
0
0
0
0.000
-0.000
0.000
5(SUS)
0
-1475
0
0
0
0
0.000
-0.000
0.000
6(EXP)
0
-5626590
0
0
0
0
0.000
-0.000
0.000
7(EXP)
0
-4497684
0
0
0
0
0.000
-0.000
0.000
MAX
-
-0.000/L2
5628066/L2
Rigid ANC
2110 2(OPE)
0
5625115
0
0
0
0
0.000
0.000
0.000
3(OPE)
0
4496209
0
0
0
0
0.000
0.000
0.000
4(SUS)
0
-1475
0
0
0
0
0.000
-0.000
0.000
5(SUS)
0
-1475
0
0
0
0
0.000
-0.000
0.000
6(EXP)
0
5626591
0
0
0
0
0.000
0.000
0.000
7(EXP)
0
4497684
0
0
0
0
0.000
0.000
0.000
MAX
5626591/L6
0.000/L6
*** CODE COMPLIANCE EVALUATION PASSED *** Highest Stresses: (MPa
)
CodeStress Ratio (%) is 10.5 at Node 2110 LOADCASE: 4 (SUS) W+P1 Code Stress:
12.8 Allowable:
Axial Stress:
122.4
732.4 @Node 2110 LOADCASE: 6 (EXP) L6=L2-L4
Bending Stress:
0.0 @Node 2110 LOADCASE: 2 (OPE) W+T1+P1
Torsion Stress:
0.0 @Node 2110 LOADCASE: 2 (OPE) W+T1+P1
Hoop Stress:
26.0 @Node 2110 LOADCASE: 4 (SUS) W+P1
3D Max Intensity:
Load Case
2(OPE) 3(OPE) 4(SUS) 5(SUS) 6(EXP) 7(EXP)
From Node
2100
883.1 @Node 2110 LOADCASE: 2 (OPE) W+T1+P1
Code Stress
Allowable
MPa
Stress MPa
Code Stress
Allowable
MPa
Stress MPa
722.23
0.00
721.85
0.00
B31.3
533.03
0.00
532.65
0.00
B31.3
12.39
122.38
12.85
122.38
B31.3
12.39
122.38
12.85
122.38
B31.3
0.00
202.97
0.00
202.97
B31.3
0.00
205.30
0.00
205.30
B31.3
To Node
2110
Piping Code
C2 Configuration For Stress B31.3 Paragraph 319.2.3(c) Enables the software to include axial terms in the expansion stress according to Paragraph 31 9.2.3(c) of B31.3. This option has three settings, as discussed below.
No (default) - CAESAR II behaves as it always has, and axial stresses are not included in the (Expansion) Displacement Stress Range value. (This is Se in Eq. (17) of B31.3.) |Sa| + Se - The absolute value of the axial stress is added to the (Expansion) Displacement Stress Range, and the sum is reported as the (Expansion) Displacement Stress Range, Se. This selection is more conservative than ( |Sa| + Sb )2. 2 ( |Sa| + Sb ) - The absolute value for the axial stress is added to the bending term in the (Expansion) Displacement Stress Range equation (Se, Eq (17) in B31.3). This selection is less conservative than |Sa| + Se. This option is more nearly theoretically correct, and consistent with Appendix P Eqs (P17a) and (P17b).
Implement B31.3 Appendix P Activating this option implements the alternate rules in B31 .3 Appendix P. This option produces a "code compliance operating load case", with allowable stress values.
Implement B31.3 Code Case 178 Activating this option causes the program to compute t he Sustained stresses according to B31.3 Co de Case 178. ASME Website Code Case 178. Activating this option over-rides the directives for "F/A" and "torsion", since the Code Case explicitly defines how to make the Sustained Case stress calculation.
Add F/A in Stresses This option determines whether or not the axial stress term is included in the code stress computation. Setting this directive to Default causes CAESAR II to use whatever the currently active piping code recommends. Only the B31.3-type piping codes (i.e. codes where the sustained stress equation is not explicitly given) have the F/A stresses included in the sustained and occasional stress equations. The B31.1-type codes do not include the F/A stresses because the equations given explicitly in the code do not include it. The F/A stresses discussed here are not due to longitudinal pressure. These are the F/A stresses due to structural loads in the piping system itself.
Add Torsion in SL Stress Some piping codes include torsion in the sustained and occasional stresses by explicitly including it in the stress equation (i.e. B31.1), and some don't include torsion in the sustained and occasional stresses by implicitly calling for "longitudinal stresses" only (i.e. B31.3). Setting the Add Torsion in SL Stress directive to Yes forces CAESAR II to include the torsion term in those codes that don't include it already by default. Setting this directive to Default causes CAESAR II to use whatever the currently active piping code implies. In a sustained stress analysis of a very hot piping system subject to creep, it is recommended that the user include torsion in the sustained stress calculation via this parameter in the setup file.
Liberal Stress Allowable A conservative formulation of the allowable expansion stress range for many codes in CAESAR II is calculated from: SA = f ( 1.25 Sc + .25 Sh ) When the user requests that the “Liberal Allowable” be used, the difference between Sh and Sl, provided Sh > Sl, will be added to the term inside the parenthesis, i.e.
SA(Liberal) = f[ 1.25 Sc + .25 Sh + ( Sh - Sl) ] The liberal expression will only be employed when there is at least one sustained stress case in the load set. If there is more than one sustained stress case in a single problem, t hen the largest of Sl, considering all of the sustained cases, for any single element end will be chosen to subtract from Sh . Because the sustained stress varies from one pipe to another, the allowable expansion stress will also vary. By default, New Job Liberal Expansion Stress Allowable is in its computation of the expansion stress
allowable. (New models are created using this configuration setting.) Users not wishing to utilize this default setting for calculating the e xpansion can simply change the state of this check box. CAESAR II uses the liberal stress allowable setting in the configuration file
All Cases Corroded A recent version of the B31.3 piping code mentioned reducing the section modulus for sustained or occasional stress calculations by the reduction in wall t hickness due to corrosion. Several users have interpreted this to mean that the reduced section modulus should be used for all stress calculations, including expansion. This directive allows those users to apply this conservative interpretation of the code. Enabling All Cases Corroded causes CAESAR II to use the corroded section modulus for the calculation of all stress types. This method is recommended as conservative, and probably more
realistic as corrosion can significantly affect fatigue life, i.e., expansion. Disabling this directive causes CAESAR II to strictly follow the piping code recommendations, i.e. depending on the act ive piping code, some load cases will consider corrosion and some will not.
