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 B31.3-2008 Process Piping (ASME Code for Pressure Piping, B31)

Revision of ASME B31.3-2006, The American Society of Mechanical Engineers, New York, NY, Appendix S, pg. 282-286

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

• 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 C-6)

• 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 A-1)

• Allowable stress maximum metal temp. ( Appendix A, Table A-1)

• stress intensification factor (Out-Plane) ( Appendix D)

• stress intensification factor (In-Plane) (Appendix D)

( page 32-2)

(page 32-2)

(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 (In-Plane) Nm --- Bending moment (Out-Plane) 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 (Out-Plane) for branch --- 2,18 stress intensification factor (In-Plane) 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 (X-direction), then 6,1 meters in the vertical direction (Z-axis), 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 data-base. The dimension of the pipe is set by the ASME-example (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 SL-stresses

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 in-plane 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 SE-stresses

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 in-plane 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 data-bank (MATDAT). The input-data (modulus of elasticity, mean coefficient of linear thermal expansion) are entered in SI-units (kN/mmÂ², (Âµm / m) x Â°K ), but the references from ASME are given by US-units (Msi, (Âµin / in) x Â°F). As the parameters converted and additional rounded up, a difference accrued which manipulates the result-precision. 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 unit-conversion, which is implement in the program ROHR2. For an ASME-material, which is used in this example, the basic allowable stresses in tension for metals were entered directly as US-units into the data-base. With these US input-data, the stresses were issued as SI-units.

Another difference, which appears at node 30n in the comparison of the sustained forces and stresses has its origin in the SL-equation. The equation-term consists of three stress-parts

=Pressure induced stress

=Axial stress

=Moment induced stress

In ROHR2, the axial-loads are implement as an absolute value. If the ROHR2-program determines a negative axial-stresses from external forces and for pressure induced stresses positive values, the axial-stresses will always be added as absolute values into the SL-equation. 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 ASME-Code and ROHR2 equation is append to SL-Ber.Pkt.30n.mcd.

## 1.6Files

R011_inch.r2w

R011_mm.r2w

R2_stresses11.ods

MATDAT.r2u

SL-Ber.Pkt.30n.mcd

SIGMA Ingenieurgesellschaft mbH www.rohr2.com