Equivalent pressure method (also known as Kellogg's method) tries to calculate a pressure whose effect on the flange is equivalent to that of axial and bending loads. Then the equivalent pressure is added to the internal design pressure and the total pressure is compared with the pressure-temperature rating (for standard flanges) or is used in ASME VIII Div.1 App.2 calculations (for non-standard and sometimes standard flanges) to work out the bolt loads. But the method is believed to be overly conservative, as the calculated equivalent pressure is "artificially" high. Well explained in Tony's attached article.
Bolt stress limit (the method which has been in ASME B31 Mechanical Design Committee) is even less accurate.
Blick's method (also known as equivalent axial force) is a simpler method and gives reasonable results, but is still conservative.
Koves, on the other hand, suggests another method which seems to be more accurate than the above methods. Koves' method recognizes the non-uniform load distribution due to bending moments and takes the flange flexibility into account to some extent. The method gives more realistic results while it is conservative enough and complies with FEA. Beware that tortional flexibility and effect of bolt holes are neglected in this method.
One is Flange Checks - Auxiliary Data Area in classic piping spreadsheet, which provide equivalent pressure Peq(so called Kellogg method) and ASME SECTION III NC 3658.3.
Another is supplied in Flange Leakage/Stress by selecting the Main Menu option ANALYSIS-FLANGES.
Chapter 11 Equipment Component and Compliance 11-15
Flange Leakage/Stress Calculations
The Flange Leakage/Stress Calculations are started by selecting the Main Menu option ANALYSIS-FLANGES
The stress calculation methods are from the following sources:
ASME Section VIII Division 1 Appendix 2, Rules for Bolted Flange Connections With Ring Type Gaskets including the consideration for the effect of external piping loads
ANSI B16.5 Rating Tables, Peq
The CAESAR II Flange Leakage Calculation
ASME SECTION III
ASME NC-3658.3 Calculation for B16.5 Flanged Joints with High Strength Bolting Method
The analysis method for Service Level A has been implemented in CAESAR II.
CAESAR II considers any moments Mfs developed during a non-Occasional Load Case to be evaluated by the equation (12).
CAESAR II considers any moments developed during an Occasional Load Case to be Mfd, effectively doubling flange capacity for Occasional loadings, to be evaluated by evaluation (13).
Level B is almost same as Level A except the limitation of pressure against rated pressure.
Unfortunately, CAESAR II does not address Level C service limits, but you can easily calculate it manually.
Piping external loading criteria for bolted flanged connections
(a) Guidelines
Allowable forces and moments (for static equipment nozzle)
(b) Bolt-Stress Limits
ML =(C/4) (Sb*Ab - P*AP)
where
SB=the bolt stress
Ab=the total bolt area
P =the internal pressure
Ap=the area to outside of gasket contact
ML=the moment to produce flange leakage
C=the bolt-circle diameter
Blick method
Blick, R. G., “Bending Moments and Leakage at Flanged Joints,”
Petroleum Refiner, 1950, p. 385.
M<G*Ab*Sb/4-p*p*G²/2*(G/8+b*m)
Checking for gasket crushing:
M<p*G³/16+p*G²*y*n/2-G*Ab*Sb/4
where
Ab=Bolt area
Sb=Allowable bolt stress
G=Gasket min diameter(Gasket reaction diameter)
y=Gasket seating stress
m=gasket factor
n=Gasket width
p=design pressure
b=effective gasket width
(c) Equivalent-Pressure Method
Kellogg method
Design of Piping Systems
Copyright The M.W. Kellogg Company, 1941, 1956
Revised Second Edition (the last one) 1977
Peq=P+4F/piG²+16M/piG³
It makes sense to follow NC-3658.1(b) "the Design Pressure used for the calculation of H […] shall be replaced by a flange design pressure =P+Peq", rather than consider P+Peq as design pressure.
The reason is based on Kellogg that mention “[…] analysis and experience which indicates that, with a properly preightened flange, the bolt load changes very little when a moment is applied, whereas the gasket loading changes appreciably.” That means Kellogg team expectations were to have external loads transmitted to gasket loads rather than to affect W pretightening load, and their Peq concept is a measure of this effect.
Including Peq only in H (or better said only in HD and consequently in H) means indirectly to consider
HG=W-H= W-Pi/4*G^2*(P+ 16*M/Pi/G^3+4*F/Pi/G^2)
=W-Pi/4*G^2*P-F-4*M/G
which is in line with Kellogg approach/ theory of plates. "
(d) Equivalent-Axial-Force Method
(1) Rodabaugh, E. C., and Moore, S. E., “Evaluation of the Bolting and Flanges of ANSI B16.5 Flanged Joints, ASME Part A Design Rules”,
ORNL/Sub/2913-C, Oak Ridge National Laboratory, Oak Ridge, TN,
1976.
Feq =4M/G and check flange integrity
(2) EN 13445 Annex G/EN 1951-1
Feq =4M/d3e and check flange integrity
where
d3e=equivalent bolt circle
(e) Finite-Element Method
(f) Recommended Approach
The most efficient approach for evaluating leakage is to evaluate the flange as a structural system.
The flexibility of the flange gaskets and bolts must be modeled to accurately predict the gasket and bolt loads resulting from pres-sure and external loads. The flange can be analyzed by using the shell-and-plate theory solution, which is consistent with the current ASME Code approach.
The effect of axial loads on a flange joint can be handled the same way as the axial pressure thrust term in the current ASME method. The axial force is simply added to the axial-pressure-thrust force, and the ASME design procedure is followed for the computation of flange moments. Using the ASME nomenclature,
HD = 0.785B2P + FA
where
FA= the axial applied force
P=the design pressure
B=the inside diameter of flange
HD=the axial force in the flange neck
External moments are more difficult to handle. The loading is not axisymmetric and cannot be addressed as easily as the axial forces. However, the ASME design approach assumes axisymmetric behavior. Therefore, the problem is to evaluate the effect of exter-nal-moment loading on the flange joint and develop a correction to be applied to the axisymmetric analysis. This is addressed by analytically solving for the forces acting on a ring flange, as a result of an external moment; then comparing it with the axisym-metric force solution.
An external applied moment is assumed to create a linear stress distribution in the flange neck. This moment can be reduced to a linear-distributed load. Therefore, a moment correction factor, FM , can be defined that adjusts for the torsional resistance of the flange to external-moment loads. Using the relationship between
the shear and elastic moduli, G=E/2(1+v), gives the following:
FM =1/[1 +J/2(1 + n)I], where J and I are parameters related flange configurations and rigidity.
The greater the torsional resistance, relative to the bending resis-tance, the less the induced circumferential bending stress and corresponding flange rotation as a result of the external moment.
The preceding equation is an exact solution for compact-ring flanges, where bending is primarily carried by the ring. When circumferential bending or flange rotation limits the design, the equation may be applied directly. Finite-element analysis of loose-ring flanges subjected to both an axisymmetric axial force and a harmonically varying force agree with the preceding equation. Note that the correction can be significant; for example, a rectangular ring flange may be in error by a factor of two or more.
Using the terminology of Section VIII, Division 1, external moments and forces can be included in the design by defining the operating design moment as follows:
HD = 0.785B2P + FA + 4FMME/G
HG = (2b)(3.14GmP)
HT = 0.785(G2- B2)P
Mo = HDhD + HThT + HGhG
ASME Section VIII Division 1
Bsmax=2a+6t/(m+0.5)
When the bolt spacing exceeds 2a + t, multiply MO by the bolt spacing correction factor BSC for calculating flange stress
Bsc={Bs/(2a+t)}^0.5
Bs: bolt spacing. The bolt spacing may be taken as the bolt circle circumference divided by the num-ber of bolts or as the chord length between adjacent bolt locations
a: nominal bolt diameter
t: flange thickness
TEMA
Bmax=2db+6t/(m+0.5)
Bsc=(Bs/Bmax)^0.5
Controlling the load is essential to ensuring the gasketed joint will seal properly. Previous Sealing Sense articles have examined the types of gaskets to use, how flange finish affects gasket sealing and major pitfalls to avoid to properly assemble a gasketed joint. However, regardless of the type of gasket, controlling the load is probably the most important criteria for getting a gasketed joint to seal. A big problem is the load on the gasket cannot be measured directly and easily during installation.
However, applied torque on the flange bolts can be measured and controlled and is one of the most frequently used methods to control gasket load. This article explores bolt torque and the major considerations for converting measurable bolt torque into the gasket load necessary to seal a flanged connection.(latest edition of ASME Section VIII division 2)
Companion Guide to the ASME Boiler & Pressure Vessel Code, Second Volume, Second Edition, Second /Chapter 40 BOLTED-FLANGE JOINTS AND CONNECTIONS
EN 1591 and EN 13445 Annex G
Alternative Design Rules for Flanges.
The New European Flange Design Method: Theory, Advantages, Comparison With Taylor Forge and DIN — Future Developments
Paper no. PVP2006-ICPVT-11-93151 pp. 125-134
<http://dx.doi.org/10.1115/PVP2006-ICPVT-11-93151> http://dx.doi.org/10.1115/PVP2006-ICPVT-11-93151
ASME 2006 Pressure Vessels and Piping/ICPVT-11 Conference (PVP2006-ICPVT-11)
July 23–27, 2006 , Vancouver, BC, Canada
Sponsor: Pressure Vessels and Piping Division
Volume 2: Computer Technology
ISBN: 0-7918-4753-5
References
Links
Leakage from the gasket