A couple of FEA seismic assessments illustrate the steps involved from frequency assessment to base shear and resulting stress analysis. Results are compared to code pass/fail criteria.
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Propane Storage Sphere
File:PVE-4092, Date: Aug 10 2010, By: LB
Pressure Vessel Engineering was hired to prepare calculations for both pressure containment and supports for wind and seismic loads on a series of large propane storage spheres for Conrex. The vessel wall thickness and nozzle supports were calculated using standard ASME code calculations. The vessels supports were constructed using industry standard designs but Finite Element Analysis (FEA) was used for the analysis instead of existing design rules.
The standard design method uses an increased wall thickness at the equator of the vessel to support the additional stresses caused by the attachment of the legs. Our FEA runs for this support method verified that this design method is valid. The question raised was – “Is it possible to design a vessel where the equator of the vessel does not have to be made thicker?” After the produced design was finished, this experimental FEA report and calculation set was run to experiment with the following:
- Shorter legs – the legs are still attached to the equator plates, but not as high up. The leg to foundation pitch circle is reduced resulting in shorter legs but increasing the overturning stresses on the legs.
- Reduced leg diameter – The bottoms of the legs are reduced in diameter to the size required to support the load. This is smaller than usually used for this type of vessel but…
- Larger legs at the shell attachment – The leg size at the top was increased until the vessel stresses at the attachment were reduced to an acceptable level. A conical transition was placed between the two different sizes of leg pipe. The reduced leg diameter at the bottom has a minimal cost impact so future production is likely to be based on a straight pipe from attachment to foundation based on the larger diameter.
- Rectangular tubing cross bracing – This high strength method of cross bracing was developed by Conrex and used in the production vessel. The bracing method shown here is identical. The appendix to the FEA report shows the excellent results obtained with this design feature.
- V plate location – for this experimental report the cross bracing leg v-plates were moved from the leg to directly attach to the shell. This design change reduces twisting at the shell attachment and is one of the keys to not requiring thicker equator plates. The v plates create local stresses in the shell which are acceptable in this experimental vessel, but could be further optimized if put into production.
- All dimensions and operating conditions of the original vessel were changed for this sample to protect Conrex’s customer’s process confidentiality.
Some comments on the FEA are in order. At the time this report was first done in 2009, it was one to the largest models we had run. It was run entirely as solid elements which increased the mesh complexity but allowed study of model details impossible if a shell mesh was used. Although the model has more than 1/2 million elements and 1 1/2 million nodes, it meshes in less than 5 minutes and solve it in an additional 5 minutes. This quick response time allowed rapid experimenting with different design alternatives. Clearly a half model could have also provided the same results with shorter run times, but some of the preliminary designs we analyzed did not have symmetrical leg supports which required the full model to check for side sway effects.
The report shows the 6 load cases that were applied to the model to comply with ASME VIII-2 Table 5.3 requirements. The load cases were also based on Conrex’s field experience with hydro testing. Seismic and wind loads are from IBC 2009 for San Diego. Studying these loads by FEA provides a much greater insight into how a vessel reacts to these loads than is possible by using standard rule based design procedures. This does not invalidate the use of rule based design but allows one to go beyond the level of understanding available using them. This experimental design would not have been derived using rules based analysis.
An ASME calculation report is included which covers the scope of the shell thickness and nozzle reinforcement. Even if FEA could demonstrate savings in materials these design rules are mandatory and must be followed. The shell thickness was set to the minimum required by the code for pressure requirements. No increase in thickness was required for the equator plates for leg support loads. However the top plate was made the same thickness as the bottom plate as an inexpensive method to reduce the amount of reinforcing required.
We at Pressure Vessel Engineering Ltd are very grateful to Conrex for allowing us to post this experimental study. Conrex can be contacted at www.conrexsteel.com 416-747-4665 or firstname.lastname@example.org.
The images below are included to show standard access stairs and leg arrangements
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Frequency / Vibration Analysis
File: File:PVE-4492, Last Updated: Sept 2, 2010, By: BV
Frequency and Vibration Analysis
FEA is used for frequency and vibration analysis to determine the natural frequency of objects which cannot be obtained from classical calculations. The natural frequency can then be compared to the system resonance to ensure large amplitude oscillations will not occur. The natural frequency may also be used with building codes to determine a base shear force which can then be input to a stress analysis to validate designs subject to seismic or other oscillating conditions. A complete engineering report is available below representing a typical seismic analysis and report completed by Pressure Vessel Engineering.
Seismic Analysis of Pressure Equipment
To find the natural frequency two inputs are required, mass and stiffness. The object to be analyzed in modeled and its density (mass) and modulus of elasticity (stiffness) defined. The FEA solver then determines several displacement modes and their corresponding natural frequencies.
Pressure Vessel Engineering then uses the natural frequency provided by the FEA to determine a base shear force in accordance with building codes such as NBC, IBC, and UBC.
The base shear force is then converted to an acceleration (F = ma, both force and mass are known) and input into a stress analysis to investigate seismic loadings on the object. These stress results then either validate the design or provide insight as to how it should be revised.