In CAEPIPE Version 5.1E (Mar 14, 2002) a change to the
program states:
Presently pressure expansion (Bourdon effect)
is treated as thermal expansion and applied to expansion (T) and operating
(W+P+T) load cases. If an environment variable BOURDONP is set (i.e. set
BOURDONP=y), pressure expansion is not treated as thermal expansion (i.e.
pressure expansion is treated as pressure expansion and applied to sustained
(W+P) and operating (W+P+T) load cases).
Treating a pressure caused stress as a thermal expansion-like stress may
seem incorrect to some analysts, but treating pressure expansion as a
load similar to thermal expansion is the correct interpretation of the
type of load and the failure mode related to that type of load. Pressure
expansion causes displacement (secondary) stresses and leads to a fatigue
failure. Hoop pressure (PD/2t) and longitudinal pressure (PD/4t) type
stresses are sustained (primary) stresses, but pressure expansion, if
the piping is unrestrained would not cause any displacement (secondary)
stresses. Restraining the pipe, as in introducing more than one anchor
or an intermediate support opposed to the direction of pressure expansion,
causes stresses from the introduction of that restraint. A simple illustration
is shown below:
Shown are two weightless piping layouts. Note the layout
on the left has a single anchor and when pressurized will expand as shown
to the dashed line configuration. Sustained load stresses due to hoop
and longitudinal pressure exist, but no additional stresses due to pressure
expansion exist. However, note what happens when an additional anchor
is introduced, restraining the piping pressure expansion in the right
hand layout. The deformed shape is indicative that stresses exist due
to the "restraint of free end displacement" in addition to the
hoop and longitudinal pressure stresses. These pressure expansion stresses
are displacement (secondary) stresses and should be treated in a similar
manner to thermal expansion stresses.
Note also, the Bourdon effect, which tries open elbows or curved members
when such are pressurized, is a pressure expansion effect and should be
treated the same way that simple pressure expansion as discussed above
is, i.e., the Bourdon effect causes displacement (secondary) stresses.
Further note that Pressure expansion was usually ignored prior to the
use of computer aided analysis techniques because most piping analyzed
was metallic, typically steel, piping. It was ignored because the amount
of pressure expansion was normally small compared to thermal expansion,
i.e., typically less than 10 percent. However, with low modulus materials,
such as nonmetallics (plastics), the amount of pressure expansion can
be significant and may need to be considered in the analysis of piping
systems made from such materials.
Editor's Note: Since version 3.32 (4/22/1992)
CAEPIPE has been treating pressure expansion as a secondary load (similar
to thermal expansion) and applying it to thermal and operating load cases.
This is the default behavior of CAEPIPE (even now).
However, a few users want to treat pressure expansion as a primary load
and apply it to the sustained and operating load cases because finite
element programs and other piping programs do it this way. Starting v5.1E,
these users (with some effort by setting an environment variable) can
alter CAEPIPE's behavior (i.e., treat pressure expansion as a primary
load) to suit their needs. Please see the second para. above in this article
for how to set the variable.
Author: Mr. Ron Haupt, P. E., of Pressure Piping Engineering (www.ppea.net) is
a member of several piping code committees (B31, B31.1, B31.3, BPTCS, and others).
He consults with us in the capacity of Nuclear QA Manager.
Question: How are limit stops handled in dynamic analysis (response spectrum, time history, harmonic)? We noticed that the displacements in the results for dynamic cases could be higher (e.g., 108.45 mm) than those input for limits at the limit stops (e.g., 50 mm and -70 mm). Results indicate that a limit stop has "not reached." Please explain.
Reply: Dynamic
analysis in Caepipe is performed using mode superposition which is a linear
process whereas analysis of limit stops is a nonlinear process. It is
not possible to include nonlinearities in dynamic analysis. As an approximation
only, nonlinearities are "sort of" indirectly included in dynamic
analysis by using the stiffness associated with them from the first operating
case (W+P1+T1) during modal analysis.
In the case of limit stops, if a limit is reached during the first operating
case, then the associated stiffness is used in modal analysis. If a limit
is not reached, then the limit stop is ignored in modal analysis. Even
if a limit is reached and the stiffness is used in modal analysis, it
is still not possible to use the actual limits (upper and lower) in modal
analysis.
In the example mentioned, the limits are not reached in the first operating
case. This status is used in modal analysis and subsequently in dynamic
case analysis. So, in effect, this limit stop is not used.
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