The flange design rules incorporated in the Code were based on a paper written in 1937 by Waters, Westrom, Rossheim, and Williams. These rules were subsequently published by Taylor Forge in 1937, and were incorporated into the Code in 1942. For all practical purposes they have been unchanged since that time. The Taylor Forge bulletin, frequently republished, is also still available, and is one of the most useful tools for flange analysis. The input and results for the Flange module are roughly modeled on the Taylor Forge flange design sheets.
The flange analysis model assumes that the flange can be modeled as stiff elements (the flange and hub) and springs (the bolts and gaskets). The initial bolt loads compresses the gasket. This load needs to be high enough to seat (deform) the gasket, and needs to be high enough to seal even when pressure is applied. The pressure load adds to the bolt load and unloads the gasket.
Analysis of a typical flange includes the following steps:
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Identify operating conditions and materials. Determine the allowable stresses for the flange material and the bolting at both ambient and operating temperatures, from the Code tables of allowable stress.
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Identify the gasket material and the flange facing type. Determine the effective width, the effective diameter of the gasket and the gasket factors from the Code charts (Tables 2-5.1 and 2-5.2).
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Calculate the required area of the bolts, from the design pressure and the gasket information. Calculate the actual area of the bolts, and make sure it is greater than the required area. Based on the bolt areas and the allowable stresses, calculate the flange design bolt loads.
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Calculate the bending moments on the flange. In each case the bending moment is the product of a load (pressure, gasket load, etc.) and the distance from the bolt circle to the point of application of the load. The final result is one bending moment for operating conditions and a second for gasket seating conditions.
The stresses on a given flange are determined entirely by the bending moment on the flange. All the loads on the flange produce bending in the same direction (i.e., counterclockwise) and this bending is resisted by the ring behavior of the flange, and in integral flanges by the reaction of the pipe.
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Calculate the hub factors and other geometry factors for the flange based on the flange type (Code Figure 2-4). The factors are found in Code figures 2-7.1, 2-7.2, 2-7.3, 2-7.4, 2-7.5, and 2-7.6. Formulae are also given in the Code so that computer software can consistently arrive at the answers that are normally selected from charts in the appendix. These formulae are implemented in the Flanges.
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Calculate the stress formula factors based on the geometry factors and the flange thickness.
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Calculate the flange stresses using the stress formula factors and the bending moments. Compare these stresses to the allowable stresses for the flange material.
The form of the stress equations is:
S = k(geometry) * M / t2
That is, a constant dependent on the flange geometry times the bending moment, divided by some thickness squared, either the thickness of the flange or the thickness of the hub.
The calculation procedures and format of results are similar to those given in "Modern Flange Design", Bulletin 503, Edition VII, published by Taylor Forge.
Flanges includes the capability to analyze a given flange under the bolting loads imposed by a mating flange. The software also takes full account of corrosion allowance. You enter uncorroded thicknesses and diameters, which the software adjusts before performing the calculations. Corrosion in treated in a special manner if indicated.
The command can also be used for two levels of flange design. The Partial option forces the software to calculate the minimum flange thickness for a given geometry. The Design option forces the software to select all of the relevant flange geometry including bolt circle, number of bolts, outside diameter, thickness, and hub geometry.
Flange Design
The defined geometry is the basis for the design performed by the software. The inside diameter, materials, pressure, gasket geometry and gasket properties remain fixed throughout the design. Beginning from this point, the software uses the following approach to design the rest of the flange:
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For slip-on type flanges, calculate the small end of the hub equal to roughly the thickness required for the design pressure
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For weld neck, slip-on, and reverse flanges, calculate the large end of the hub as the small end of the hub plus 1/16th (for small end thickness less than one inch) or 1/8th (for small end thickness greater than one inch). Then calculate a hub length equal to the small end thickness plus the minimum slope (3:1) for the hub. The effect of these choices is to design a small hub when compared with standardized flanges. This has the additional effect of keeping the moment arms and diameters (of the bolt circle and flange OD) small, and keeping the flange light. Finally, the selection of a small hub keeps the amount of machining required for the flange to a minimum.
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Select a preliminary number of bolts. This is a multiple of four based on the diameter of the flange. The algorithm chosen tends to select more and smaller bolts than would be found on standard flanges. This also has the effect of minimizing the flange outside diameter and the weight of the flange.
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Select a bolt size that will give the required bolt area for this number of bolts.
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Using this bolt size, calculate a final number of bolts based on:
The area required divided by the area available per bolt -OR-
The maximum allowed spacing between bolts of this size.
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Using this number of bolts, calculate the bolt circle based on:
The OD of the hub plus the minimum ID spacing of the bolt -OR-
The OD of the gasket face plus the actual size of the bolt -OR-
The minimum spacing distance between the bolts -OR-
For reverse flanges, the vessel OD plus the bolt ID spacing.
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Calculate the outside diameter of the flange based on the bolt circle plus the minimum edge spacing for the bolt size chosen.
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For flanges with full face gaskets, adjust the gasket and face outside diameter for the values chosen, and recalculate the moment arms for the flange.
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Select a thickness for the flange and calculate the stresses. If the stress is not equal to the allowable, adjust the thickness based on the difference between the actual and allowable stresses, and then repeat the stress calculation. Repeat until the actual stress for one of the stress components is equal to the allowable stress.
This step also applies to partial design of the flange.
