Finite Element Analysis in PVP Design: What You Should Know
In pressure vessel and piping (PVP) design, various analysis methods are used to assess the safety and performance of systems. While hand...
Piping design and engineering play a crucial role in various industries, ensuring the safe and efficient transportation of fluids. To maintain high standards of safety and reliability, industry codes and standards are periodically updated to reflect the latest advancements and address emerging challenges. In this blog post, our experts have summarized the ASME B31.1 piping updates from 2020 and 2022 code years that affect piping engineers and stress analysts and their process for determining multi-directional stress equations.
ASME 2020 Code Edition Updates
The 2020 edition of ASME B31.1 included multi-directional Sustained Stress Indices (SSIs) and Stress Intensification Factors (SIFs) in the code equations for Sustained, Occasional, and Expansion cases. These are shown in equations 15-17 in paragraph 104.8.3 of 2022 ASME B31.1 and shown in equations 1 through 3.
SL = [ [ Ia | PDo/4tn + Fa/Ap | + [ (IiMiA)2 + (IoMoA)2 ]0.5/ Z ]2 + (ItMtA/Z)2 ]0.5 <= Sh Equation 1
SO = [ [ Ia | PoDo/4tn + Fb/Ap | + [ (IiMiB)2 + (IoMoB)2 ]0.5 / Z ]2 + (ItMtB/Z)2 ]0.5 <= kSh Equation 2
SE = [ [ | iaFc/Ap | + [ (iiMiC)2 + (ioMoC)2 ]0.5 / Z ]2 + (itMtC/Z)2 ]0.5 <= SA Equation 3
These equations replaced the single-directional equations from the 2018 B31.1 edition and should be used when calculating those factors.
ASME 2022 Code Edition Updates
Appendix D of the 2022 code edition contains a single SIF and does not differentiate between in-plane, out-of-plane, or torsional directions. The single SIF is intended to be the maximum SIF, so using the updated equations might result in reductions in stress, theoretically 25% or more. The SSIs for intersections in the pre-2022 version of B31.1 follow Equation 4, which can lead to slightly lower intensification factors.
I = MAX(0.75i, 1.0) Equation 4
I = MAX(i0.5,1) (for branch connections) Equation 5
Appendix D in the 2022 code edition includes a fascinating provision in the General Notes (b) section, allowing the utilization of ASME B31J-2017. This particular code was developed based on the insightful findings presented in the ASME B31J-20171 research paper, partly authored by Paulin Research Group. The study involved an extensive series of analyses conducted in Paulin Research Group's laboratory in Houston, TX. These analyses, performed using the advanced NozzlePRO software, focused on determining thousands of diameter and thickness ratios. Notably, the SSIs calculated using ASME B31J-2017 for intersections follow the square root of the SIF for branch connections, as portrayed in Equation 5.
Additionally, a potential source of confusion within the code is the combination of pressure stress and axial stress due to an axial force. If the axial force is negative (compressive load) the total axial stress will be reduced. PCLGold allows users to get the absolute of the axial stress due to a force (F/Ap) before adding it to the pressure stress (PDo/4tn) to produce a conservative result. PCLGold also allows users to enter different values for pressure and axial load stress intensification factors. When fatigue damage controls the life of a piping system, segregation of the SIFs can make significant differences in predicted results. Users in this case should refer to WRC 335 and make a few hand calculations on small systems with various d/D ratios to ensure the expected result occurs. This will be increasingly important as the number of cycles gets progressively larger than 40,000.
The values from ASME B31J-2017 and Appendix D in ASME B31.1 can be used if the D/T ratio is less than 100. Nonetheless, through testing, starting at when the D/T ratio equals 50, the SIFs may be under conservative due to concerns about buckling or local damage.
In this case, we recommend the use of Finite Element Analysis (FEA) for these intersections or detailing to ensure that at support locations, plane sections remain plane.
FEA Software For Easy B31 Compliance
The equations in the current (2022) ASME B31.1 code more closely resemble the equations from ASME B31.3.
With the use of ASME B31J-2017 stiffnesses to develop a more accurate set of displacements, forces and moments, and SSIs and SIFs, the computed stresses are more accurate.
The automated FEA capabilities in PRG software does not include inelastic behavior when calculating SSIs, but it does create finite element models (FEMs) that can be used to address inelastic behavior. Where large a D/T pipe is heavily loaded, we recommended taking these generated FEMs and performing buckling and nonlinear SSI calculations to verify your results.
This is particularly useful when the D/T ratio is high. Furthermore, systems can be controlled by instability due to buckling, or otherwise large compressive states due to bending, or long vertical risers.
Our most notable FEA software solutions, FEPipe and NozzlePRO, automatically compute SSI solutions based on the B31J-2017/2023 Appendix D approach. The results from a nonlinear calculation for the twice elastic slope (TES) can be compared to the B31J Table 1-1 recommendation.
FEPipe provides valuable insights into the compressive stress states experienced during elastic finite element calculations. By accurately including the loading signs in the model and reviewing the compressive stress reports, users can evaluate the magnitude and size of these stress states. Although they may not be part of a specific code evaluation procedure, these reports play a crucial role in assessing the overall integrity of the system.
additional ASCE 7 Considerations
Although everyone tends to have their own wind and seismic approaches when using loads from ASCE 7, we deem it important to note that 2022 B31 and earlier versions are considered ASD (Allowable Stress Designs) solutions. Loads from ASCE 7 are available for both ASD and LRFD (Load and Resistance Factor Design) solutions. The LRFD solution loads are 1.4 times higher than ASD loads, so wind loads computed for pressure vessel nozzles addressed by LRFD methods from pipe stress programs should be increased by 1.4 times before being used in the LRFD solution.
Stay Up-to-Date, Maintain Safety
The updates in the ASME B31.1 piping code from 2020 and 2022 have brought significant changes to the equations used in determining multi-directional stress in piping systems. These updates reflect advancements in the industry and aim to improve safety and reliability. The inclusion of Sustained Stress Indices (SSIs) and Stress Intensification Factors (SIFs) in the code equations allows for more accurate calculations. Additionally, the provisions in Appendix D to utilize ASME B31J-2017 provide further insight into diameter and thickness ratios for intersections. It is crucial for pipe engineers and stress analysts to stay up-to-date with these updates to ensure compliance with industry standards and maintain the safety and efficiency of piping systems. These updates not only ensure compliance with industry standards but also contribute to the continuous improvement of piping systems, making them safer, more efficient, and better suited to meet the evolving needs of various industries.
As technology advances and new challenges arise, the B31 piping code will continue to evolve, shaping the future of piping design and ensuring the reliability of critical infrastructure. To learn more about the latest code features available in PRG software, click here to connect with an expert today.
References
1Paulin, Anthony W., and Rodabaugh, Everett C. “Stress Intensification Factors, Stress Indices, and Flexibility Factors.” ASME Digital Collection.