Structural Flange with Gussets Design
Overview
This article outlines the design methodology used to analyze structural plate flange with Gusset. There is another article that addressed the structural flange design without gussets, and this is a continuation of that article. In this article we pick up where that article ended, because we want to add gussets in an attempt to reduce our flange thickness.
The MecaStack software includes an option for designing these structural flanges. This article details the design approach for plate flange analysis with gussets.
Example Problem
In the course of explaining each design check that is performed, we will use an actual flange design as an example to illustrate the checks. We will start with the exact same criteria, except that this time we will include gussets. The design data will be as follows:
Calculations that are Same as No Gussets
Many of the calcualtions are identical to the flange analysis without gussets that was previously performed, and so those calculations will be summarized here. The weld stress is still conservatively only considering the weld on the outside of the flange and disregarding the gusset welds. We have added a Pc calculation, which is the compressive load per bolt needed to check the gussets:
Flange Thickness
Now we need to determine the thickness of the flange. As mentioned previously to do this we ignore any seating of the gasket because we have assumed that we are either using a self-energizing gasket or some type of sealant that does not require seating. If you are using a gasket that requires seating, then this type of flange is unacceptable and you should refer to the pressure vessel code (ASME Sec. VIII, Div. 1, Appendix 2) or some comparable standard that considers gasket seating.
We determine the flange thickness by using a yield line analysis. To do this we rely upon the paper “A Yield Line Component Method for Bolted Flange Connections” by Bo Dowswell. This is a very useful paper that is written to address different prying type analysis that is encountered in structural applications. Although a structural flange is not exactly the same, it is close enough that we can apply some of it’s useful design tools. In the “Proposed Design Method” section of Dowswell it is recommended that in the AISC formula for tc that we use the yield strength rather than the ultimate, and so we have applied this recommendation.
We follow the prying method from AISC 360-22 Section 9, but we replace p with pe. There are two different yield patterns shown to the right. If the gussets are close enough together, such that xs ≤ x, then pe is equal to pg1. This assumes that the gussets are preventing the flange from rotating relative to the shell, and so the flange to shell yield line is assumed to be fixed. If xs > x then the gussets are considered to be too far apart to resist rotation completely, and so pe is based upon png2. In the png2 calculation the flange to shell yield line is assumed to be simply supported.
Using the AISC prying method with the calculated p<sub>e</sub>, the flange thickness is checked. In the article where we had no gussets, the flange was determined to be 20 mm thick. With the addition of the gussets the flange thickness should be able to be reduced, and so we have ran these calculations based upon a 12 mm thick flange.
The calculations indicate that the unity ratio is 0.98, and so the 12 mm thick barely works.
Gusset Spacing
The check for prying indicates that the 12 mm flange is adequate based upon the Unity Ratio of 0.98; however, that doesn’t provide much extra margin of safety. The xs of 72.8 mm is greater than x of 66.8 mm and so png2 is be used for the pe calculation. If we had more bolts, then the gussets would be closer together and we could make xs less than x. When xs is less than x, then the pe calculation would use pg1 and we could see a reduction in the flange thickness requirement. We will not go through that exercise here, but it is just an observation that increasing the bolts would reduce the required flange thickness.
Gusset Compression
The gussets will be checked for the maximum compressive load that is applied. This value P<sub>c</sub> was calculated previously and will be used here. The gusset compressive load will be checked per “Design Aid for Triangular Bracket Plates Using AISC Specifications” by Shilak Shakya and Sriramulu Vinnakota. A triangular bracket with a gusset is commonly used to support beams, and so we will utilize that criteria to analyze this similar situation. This method requires that the gusset be at least the t* value in Equation 15 (We refer to this as tgmin) in order to ensure that all failure is inelastic buckling. If that criteria is met we then calculate the compressive capacity of the connection (Pn) utilizing equation 22.
Gusset Tension
The gusset compression check was heavily based upon buckling and so that criteria won’t apply for the tension case. For this case we refer to “Design of Welded Structures” by Blodgett. Using the method from Blodgett we calculate the compressive load Fg on the gusset as well as the moment Mg. We then use the criteria in AISC 360-22 to evaluate the compbined axial tension and flexure.
Gusset Local Shell Stress
The gussets will distribute loads into the cylindrical shell, and so we evaluate this as a local stress concentration. This is similar to a single baseplate with triangular gussets, which is addressed in “Structural Analysis and Design of Process Equipment” 3rd Edition by Jawad and Farr. Using this reference we apply equation 12.14 to calculate the required cylindrical shell thickness. Local stress can be a problem on many flanges, and so we did modify the method in Jawad. The stress does not abruptly stop at the top of the gusset, it continues to disperse into the shell for 1.5 to 2 times the gusset height. Rather than use h, we decided to use 1.5•h, which tends to produce more realistic designs than using the more conservative h value. The Fadj factor may be used depending upon the stress code selected in MecaStack to account for the design basis (ASD vs Ultimate or LRFD).
Custom Gusset Arrangements
This entire design basis assumes that we have one gusset between each pair of bolts. If you have something different, such as one gusset every 2 bolts, then what do you do? The best option in the software at this time is to assume that if there is not 1 gusset between each pair of bolts to assume that there are not any bolts. Otherwise, you can perform a manual calculation using the Dowswell paper and determining an appropriate set of yield line patterns that need to be considered, or to utilize Finite Element Analysis.
MecaStack Structural Flange Analysis
All of the calculations we just performed are performed directly within MecaStack. You can see the output of the flange calcualtions at this link, and if you have a licensed copy of MecaStack then you can open the input file at this link.
