"PA" (pressure x area) load is
frequently misunderstood. This can sometimes
lead to serious errors in calculating main anchor
design loads. Some common misconceptions are
shown below, as well as the correct expression for
"PA" load is based on the
corrugation sidewall annulus area: WRONG
is the most serious misconception since it can
lead to gross under prediction of the bellows
"PA" load and grossly underdesigned
main anchors. See Figure "a" below.
"PA" load is based on the bellows ID
misconception can lead to underdesigned
anchors, since it ignores the contribution of
corrugation sidewall load to total
"PA" load. See figure "b"
"PA" load is based on the bellows OD
misconception can lead to over predicting the
bellows "PA" since it gives too much
credit to corrugation sidewall pressure load.
See figure "c" below.
"PA" load is based on the bellows
mean diameter: CORRECT
pressure vs load tests on bellows have shown
the mean (or pitch) diameter of the bellows to
give very accurate results in predicting
bellows pressure thrust. A brief rationale for
bellows effective area based on mean diameter
is given in para IV. See figure "d"
TID Fluid Area:
reasonably apparent that in a system with a
bellows the pipe internal fluid pressure load is
not balanced by pipe longitudinal tensile forces
and must be restrained by external forces. It can
also be seen that if the bellows ID exceeds the
pipe ID, an additional pressure force will be
transmitted through the pipe as a compression load
which must also be externally restrained. Hence
one component of the total bellows thrust load is
based on the bellows ID.
ID Area =
can also be visualized that internal pressure
acting on the sidewall of the corrugation would
tend to spread the corrugation out in the
longitudinal direction, and this load must be
restrained by an external reaction force. As an
approximation consider a 1" wide radial strip
cut out of a corrugation.
a fixed ended beam with uniform load, RID =
one half of the corrugation sidewall load is
carried in tension at the crest of the
corrugation. The other half it transmitted through
the neck of the corrugation as a compressive
force. This force must be resisted by the external
main anchors and results in a (generally) small
longitudinal compressive stress in the pipe.
Effective Area =
But ID + h = mean dia. = Dm
Therefore, Sidewall Effective Area =
| Total Effective Thrust Area:
area + Sidewall area
more precise development of corrugation sidewall
load and an equation for bellows effective thrust
area is given in the Appendix. A comparison on 5
sample problems of typical bellows dimensions,
including one extreme case of OD/ID ratio, shows
that the percent error involved in using the mean
diameter approximation is generally less than 1%
and only 1 1/2% in the extreme example.