CODE COMPLIANT PIPING SYSTEM
1CODE COMPLIANT PIPING SYSTEM
1.1 Problem definition
A stress analysis according to ASME B31.3 is to be performed on the following piping system.
Figure 2: Model by ASME B31.3
Figure 1: ROHR2 Model
1.2 References (ASME B31.3)
ASME B31.32008 Process Piping (ASME Code for Pressure Piping, B31)
Revision of ASME B31.32006, The American Society of Mechanical Engineers, New York, NY, Appendix S, pg. 282286
Apiping system with design and operating conditions is to be analyzed for primary sustained loads from gravity and pressure and for secondary expansion stresses. The pipe components are defined by ASME. The following listed values are used:

Pipe material

Outside diameter (NPS)

Inside diameter

Cross section

Section Modulus

Nominal wall thickness

Insulation thickness

Insulation density

Corrosion allowance

Bend radius

Pipe density

Unit weight

Fluid specific gravity

Number of cycles

Stress range factor ( paragraph 302.5(d))

Installation temperature

Modulus of Elasticity (Appendix C; Table C6)

Poisson's ratio (paragraph 319.3.3)

Design pressure

Design temperature

Operating pressure1

Operating temperature1

Operating pressure2

Operating temperature2

Allowable stress installation temp. (Appendix A, Table A1)

Allowable stress maximum metal temp. ( Appendix A, Table A1)

stress intensification factor (OutPlane) ( Appendix D)

stress intensification factor (InPlane) (Appendix D)
( page 322)
(page 322)
(equation 1a]
( equation 17+18])
Where:
Variable 
Description 
Unit 
Used Value 
Pipe material 
 
ASTM A 106 Grade B 

Outside diameter (NPS) 
mm 
406,4 

Inside diameter 
mm 
390.54 
3
Cross section 
mmÂ² 
9927,02 

Section Modulus 
mmÂ³ 
969992,2 

Nominal wall thickness 
mm 
9,525 

Insulation thickness 
mm 
127 

Insulation density 
kg/mÂ³ 
176 

Corrosion allowance 
mm 
1,59 

Bend radius 
mm 
609,5 

Pipe density 
kg/mÂ³ 
7833,4 

Unit weight 
kg/m 
248,3 

Fluid specific gravity 
kg/mÂ³ 
1000 

Number of cycles 
 
< 7000 

Stress range factor 
 
1 

Installation temperature 
Â°C 
21 

Modulus of Elasticity 
N/mmÂ² 
203395 

Poisson's ratio 
 
0,3 

Design pressure 
bar Ã¼ 
37,95 

Design temperature 
Â°C 
288 

Operating pressure1 
bar Ã¼ 
34,5 

Operating temperature1 
Â°C 
260 

Operating pressure2 
bar Ã¼ 
0 

Operating temperature2 
Â°C 
1 

Axial section force 
N 
 

Bending moment 
Nm 
 

Horizontal deflections 
mm 
 

Vertical deflections 
mm 
 

Horizontal support loads 
N 
 

Vertical support loads 
N 
 

Moments at supports 
Nm 
 

Pressure induced stress 
N/mmÂ² 
41,63 

Axial force 
N 
 

Bending moment (InPlane) 
Nm 
 

Bending moment (OutPlane) 
Nm 
 

Torsional moment 
Nm 
0 

Longitudinal stress 
N/mmÂ² 
 

Allowable displacement stress range 
N/mmÂ² 
205 

Allowable stress at installation temp. 
N/mmÂ² 
138 

Allowable stress at maximum metal temp. 
N/mmÂ² 
130 

stress intensification factor (OutPlane) for branch 
 
2,18 

stress intensification factor (InPlane) for branch 
 
2,62 

Flexibility stresses 
N/mmÂ² 
 
Table 1: Overview of the used variables
1.3 Model description (ROHR2)
The system has a total length of 30,5 meters. It consists of a steel pipe (ASTM A 106 Grade B) which goes 15,25 meters horizontal (Xdirection), then 6,1 meters in the vertical direction (Zaxis), finallyt 9,15 meters horizontal. Three rigid supports exists in the system. Attwo of three points (Node 10 and Node 50) anchors were entered. The third one is a sliding support, which hinders the vertical deflections. All supports have infinite stiffness . The characteristic material values (pipe density, Poisson's ratio, modulus of elasticity, mean coefficient of linear thermal expansion and basic allowable stresses) were defined new by creating a material database. The dimension of the pipe is set by the ASMEexample (Norm: ANSI B36.10; NPS16 = 406,4 mm x 9,525 mm). It has to respect the corrosion allowance (1,59 mm). The pipe has a bend radius of 609,5 mm (Norm: ANSI B 16.9; NPS16; Row 3 Design Long). The system is insulated with a 127 mm thick calcium silicate insulation (Ï = 176 kg/mÂ³). By creating the dimension with indicated parameters it results a unit pipe weight of 248,32 kg/m.
The next step to compute the system is creating additional load cases. It is necessary to define one load case of primary loads and two load cases of secondary loads. All of them had to be calculated using theory first order (don't consider nonlinear properties). The calculation of the loads and deflections of all load cases is performed with the cold modulus of elasticity. For the secondary load cases the button, axial expansion due to operating pressure, is to disabled. The acceleration due to gravity button must be include for this example.
The example proves two stress equation. The first one is called longitudinal stresses SL. In this system the internal pressure and the allowable stresses had to determinate by the operating parameters (pressure and temperature).The second equation is called flexibility stresses SE and respected in this case only the secondary loads. In fact, the still remaining liberal stresses (Ma) of the load case dead weight mustn't be regarded. As like as in the equation SL, the internal pressure and allowable stresses are determined from the operating parameters. After these changes of the ROHR2 tasks, the design and operating parameters were entered.
1.4 Result comparisons
The following figures and tables compare only two adequately points of each verification value. All results are given in the local coordinate system. The whole comparison is shown at the document R2_stresses11.ods.
1.4.1 Operating load case results 1
Figure 3: Results of node 45
Figure 4: Results of node 15
Figure 5: ROHR2 model with resulting deflections
Point 
Value 
Reference (ASME) [N] 
Rohr2 [N] 
Difference [%] 
15 
26500 
26415 
<0,33 

45 
26500 
26415 
<0,33 
Table 2: Comparison of the axial section force for node 15, 45
Point 
Value 
Reference (ASME) [Nm] 
Rohr2 [Nm] 
Difference [%] 
15 
10710 
10715 
<0,05 

45 
14900 
14804 
<0,65 
Table 3: Comparison of the Bending Moment for node 15, 45
Point 
Value 
Reference (ASME) [mm] 
Rohr2 [mm] 
Difference [%] 
15 
18,3 
18,31 
<0,06 

45 
18,3 
18,31 
<0,06 
Table 4: Comparison of the horizontal deflections for node 15, 45
Point 
Value 
Reference (ASME) [mm] 
Rohr2 [mm] 
Difference [%] 
15 
1,3 
1,33 
<2,26 

45 
13,5 
13,45 
<0,4 
Table 5: Comparison of the vertical deflections for node 15, 45
1.4.2 Operating load case results 2
Figure 7: ROHR2 model with forces
Figure 6: Support loads, node 10
Figure 8: ROHR2 model with moments
Figure 9: Support loads, node 50
Point 
Value 
Reference (ASME) [N] 
Rohr2 [N] 
Difference [%] 
10 
26500 
26415 
<0,33 

50 
26500 
26415 
<0,33 
Table 6: Comparison of the horizontal support load for node 10, 50
Point 
Value 
Reference (ASME) [N] 
Rohr2 [N] 
Difference [%] 
10 
12710 
12716 
<0,05 

50 
2810 
2722 
<3,24 
Table 7: Comparison of the vertical support load for node 10, 50
Point 
Value 
Reference (ASME) [Nm] 
Rohr2 [Nm] 
Difference [%] 
10 
21520 
21532 
<0,03 

50 
47480 
47123 
<0.7 
Table 8: Comparison of the moments at supports for node 10, 50
1.4.3 Sustained forces and stresses
Figure 10: ROHR2 model with SLstresses
Figure 12: SL results at node 20
Figure 11: SL results at node 40n
Point 
Value 
Reference (ASME) [N] 
Rohr2 [N] 
Difference [%] 
20 
3270 
3279 
<0,3 

40n 
3270 
3279 
<0,3 
Table 9: Comparison of the axial force for node 20, 40n
Point 
Value 
Reference (ASME) [Nm] 
Rohr2 [Nm] 
Difference [%] 
20 
56130 
56220 
<0,2 

40n 
2340 
2341 
<0,05 
Table 10: Comparison of the inplane Bending Moment for node 20, 40n
Point 
Value 
Reference (ASME) [N/mmÂ²] 
Rohr2 [N/mmÂ²] 
Difference [%] 
20 
99,200 
99,900 
<0,8 

40n 
46,050 
46,700 
<1,4 
Table 11: Comparison of the longitudinal stresses for node 20, 40n
1.4.4 Displacement stress range
Figure 13: ROHR2 model with SEstresses
Figure 15: SE results at node 30m
Figure 14: SE results at node 50
Point 
Value 
Reference (ASME) [Nm] 
Rohr2 [Nm] 
Difference [%] 
30m 
60250 
60735 
<0,8 

50 
92110 
91921 
<0,3 
Table 12: Comparison of the inplane Bending Moment for node 30m, 50
Point 
Value 
Reference (ASME) [N/mmÂ²] 
Rohr2 [N/mmÂ²] 
Difference [%] 
30m 
137,000 
138,200 
<0,9 

50 
79,900 
79,800 
<0,2 
Table 13: Comparison of the flexibility stresses for node 30m, 50
1.5 Conclusion
The results are generally close to the references by the appendix S example. Just single results has differences, above five percent. There are several reasons for this difference. The first one originates on the input of the new generated databank (MATDAT). The inputdata (modulus of elasticity, mean coefficient of linear thermal expansion) are entered in SIunits (kN/mmÂ², (Âµm / m) x Â°K ), but the references from ASME are given by USunits (Msi, (Âµin / in) x Â°F). As the parameters converted and additional rounded up, a difference accrued which manipulates the resultprecision. The second inaccuracy of the results is shown at point 30n (Operating load case results: Comparison of internal loads and deflections; value Î´_{V}). If the result is relative small (Î´_{V}= 0,4 mm), the relative difference will become more bigger, though the absolute difference is actually very small. In those cases the differences are negligible. Another difference consists of the stress unitconversion, which is implement in the program ROHR2. For an ASMEmaterial, which is used in this example, the basic allowable stresses in tension for metals were entered directly as USunits into the database. With these US inputdata, the stresses were issued as SIunits.
Another difference, which appears at node 30n in the comparison of the sustained forces and stresses has its origin in the SLequation. The equationterm consists of three stressparts
=Pressure induced stress
=Axial stress
=Moment induced stress
In ROHR2, the axialloads are implement as an absolute value. If the ROHR2program determines a negative axialstresses from external forces and for pressure induced stresses positive values, the axialstresses will always be added as absolute values into the SLequation. Basically this implements the idea that you cannot rely on pressure forces to compensate for dead load stresses as they may or may not be present. That condition requires, that the stresses will be added up. Apparently this approach has not been taken in the reference calculation. Consequently, the results of ROHR2 are bigger, as the results of the reference. A comparison calculation between the ASMECode and ROHR2 equation is append to SLBer.Pkt.30n.mcd.
1.6Files
R011_inch.r2w
R011_mm.r2w
R2_stresses11.ods
MATDAT.r2u
SLBer.Pkt.30n.mcd
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