The purpose of this appendix is to compare results obtained using a standard pipe stress code (CAESAR II 5.20) to those obtained using a finite element code (Abaqus) for system response to sustained loads, thermal loads, and seismic loads, and considering large displacement effects.
One concern was that a lumped mass system can’t accurately track the deflections and loads in a HDPE system. A second concern was that the small displacement theory assumed in standard piping codes may not accurately determine system response for a material with a low modulus of elasticity and high coefficient of thermal expansion, potentially leading to large displacements.
Abaqus v6.10-1 was the Finite Element Analysis (FEA) program used to check CAESAR II. The material properties were the same as presented in Chapter 4.
Before the entire piping arrangement in Chapter 4 was analyzed, a simplified example was first used to check the general differences of CAESAR II, an Abaqus 3-D model, and an Abaqus beam model. This simplified model uses the same pipe specification as Chapter 4 and is an L-shaped pipe arrangement that is 48” x 48” long, with a 6” radius elbow. The elbow is 0.616”
thick, while the pipe itself is 0.484” thick, per the requirements in the proposed code case in Chapter 3.
Figure B-1
Layout of Simplified Pipe Section
The results for +/- 4" vertical displacement at the top right node are listed in Table B-1. These results show that the Abaqus Beam and CAESAR analyses are more conservative than the full Abaqus 3D analysis.
Table B-1
Force versus Displacement
Force (lb)
Disp (in) Abaqus 3D Abaqus Beam CAESAR
-4 -31.9 -34.6 -35
0 0 0 0
4 33.7 36.5 35
A 30ºF temperature change was then applied to the model with both ends fixed. Table B-2 shows that once again the Abaqus 3D model predicts the lowest restraint reactions. CAESAR II
predicted a reaction force between the Abaqus 3-D analysis and the Abaqus beam analysis.
Finite Element Analysis Using Abaqus
Table B-2
Reaction Forces due to Δ30ºF Temperature Increase
Y - Force (lb) X - Force (lb)
CAESAR 19 19
Abaqus Beam 20.2262 20.2262
Abaqus 3D 18.3592 18.3592
The preliminary tests presented have shown that CAESAR II is consistent with a FEA analysis using beam theory and more conservative than a full 3-D model with respect to elbow flexibility.
The next step was to analyze the full piping system presented in Chapter 4 using the Abaqus beam element. Pressure design was not studied with Abaqus because it would have required a full 3-D analysis. The analysis covered gravity, thermal, and seismic loadings. The thermal analysis was performed using the tensile modulus at 70ºF, the seismic load was calculated using the tensile modulus at design temperature, and the long term deflection was calculated using the long term apparent modulus at design temperature.
Reaction forces at the restraints was chosen as a comparison method because CAESAR II manipulates the stresses per ASME Code rules. Therefore the stress output from Abaqus would not have matched the CAESAR II stress output. The position and label of all the restraints is shown in Figure B-2. The Abaqus beam model is shown in Figure B-3.
Figure B-2 Restraint Layout
Finite Element Analysis Using Abaqus
Figure B-3 Abaqus Model
The results for the gravity case are shown in Table B-3. There is a difference shown for Guides G-8 through G-11. This difference is due to the fact that the valve is modeled as a rigid element in CAESAR II, but not in the Abaqus beam model. Therefore, Abaqus is predicting a bending force in that section of the pipe which increases the load on G-9 and G-10 and decreases the load on G-8 and G-11.
Table B-3
The results for the thermal expansion case are shown in Table B-4. The agreement between Abaqus and CAESAR is excellent for this particular case. While both programs might handle the
Finite Element Analysis Using Abaqus
The results for the seismic case are shown in Table B-5. CAESAR II underpredicted the forces resulting from the seismic case detailed in Chapter 4. Based on Figure 4-5 it seems that more nodes should have been placed in the CAESAR analysis. This is something that designers should be aware of when using any lumped mass analysis program. The natural frequencies calculated
Table B-5
Results for Seismic Analysis
Seismic X-Force (lb) Y-Force (lb) Z-Force (lb)
X-Axis Guides Abaqus Caesar Abaqus Caesar Abaqus Caesar G-1 218 165 4 3
Finite Element Analysis Using Abaqus
A plot of the long term deflection due to gravity calculated by the Abaqus beam model is shown in Figure B-4. This shows a maximum deflection of 0.1”, which is greater than the 0.0175”
calculated by CAESAR. It is possible that enough nodes were not placed inbetween the valves and the supports. Additionally, the valves were modeled as point masses in Abaqus on flexible pipe, whereas in CAESAR they were modeled as rigid elements. Therefore the Abaqus model overpredicts the weight because it includes a section of pipe where the valve rests, and it also overpedicts the valve’s flexibility. An more precise comparison can be performed with a single beam model.
Figure B-4
Long Term Deflection (in) Calculated by Abaqus
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