Relief valves are used in piping systems to provide an
outlet for those situations when pressure builds up beyond that desired
for safe operation.
The escaping fluid creates a jet force which is transferred through the
pipng system. This force must be resisted by the pipe supports if the
pipe is incapable of resisting the force internally. The magnitude of
the force is usually given by the valve manufacturer. It can be easily
calculated however, for those situations where the valve vents to the
atmosphere.
ANSI B31.1 recommends the following method for calculating this force.
F = DLF ( MV/32.2 + PA) (English units)
F = DLF ( MV+ PA/10^6) (SI units)
V = SQRT(50,113 (ho - a)/(2b - 1) ) (English units)
V = SQRT(2.0085 (ho - a)/(2b - 1) ) (SI units)
P = (M/A) (b - 1)/b SQRT(48.33 (ho - a)/(2b - 1)) - Pa (English units)
P = (M/A) (b - 1)/b SQRT((1.995 x 10^12) (ho - a)/(2b - 1)) - Pa (SI units)
where
F = Discharge force (lb., N)
DLF = Dynamic load factor (dimensionless), see discussion below
M = Mass flow rate from valve x 1.11 (lbm/s, kg/s)
V = Fluid exit velocity (ft/s, m/s)
P = Static gauge pressure at discharge (psi, N/m^2)
A = Discharge flow area (in^2, mm^2)
Pa = Atmospheric pressure (psi, N/m^2)
ho = Stagnation enthalpy of pipe fluid (Btu/lbm, J/kg)
a, b are as given below:
| a | b (dimensionless) | ||
| Steam Condition | Btu/lbm | J/kg | |
| Wet, <90% quality | 291 | 675,411 | 11 |
| Saturated, > 90% quality | 823 | 1,910,183 | 4.33 |
| Superheated | 831 | 1,928,751 | 4.33 |
The American Society of Mechanical Engineers (ASME)
B31 Code for Pressure Piping was developed with the expectation that piping
system designers would be familiar with the concept of flexibility. For
this reason the B31 Codes never described or discussed in any depth the
intention of either performing a flexibility analysis or the results expected
therefrom. The flexibility equation, also referred to as the thermal expansion
or displacement stress equation,
SE = SQRT(Sb^2 + 4 St^2)
was incorporated into the 1955 Edition of B31.1 in
Section 6, Chapter 3, Expansion and Flexibility. In 1955 the B31.1 book
had different sections for different applications, i.e., Section 1 for
power piping, Section 2 for industrial gas and air piping, Section 3 for
refinery and oil transportation piping, Section 4 for district heating
piping, and Section 5 for refrigeration piping. But prior to 1955, in
1952, the B31.8 Gas Transmission and Distribution Piping book was published,
initiating the publication of the separate applications books we have
today, i.e., B31.1 Power Piping, B31.3 Process Piping, B31.4 Liquid Transportation
Piping, B31.5 Refrigeration Piping, and B31.9 Building Services Piping.
Each of these applications books, when published, incorporated the flexibility
equation following a B31 code model outline developed in the 1950's. B31.8
also incorporated the flexibility equation even though B31.8 did not follow
the model outline owing to the fact that B31.8 was published prior to
the development of the B31 model outline.
The allowable flexibility stress-range for the 1955 Edition of B31.1 was
based on the expectation of elevated temperature operation and ductile
behavior, and first introduced the concept of self-springing or shakedown
to ASME pressure component design. Generally, the flexibility allowable
stress-range was permitted to approach two times yield. However, the pipeline
codes, B31.4 and B31.8, never adopted the twice yield allowable stress-range
(shakedown) concept because it was expected that pipelines would experience
nonductile behavior. Code revisions over the years since 1955 have not
served to clarify the concept of flexibility and in many ways have obscured
it. For example, B31.1 deleted a stress equation which implied the methodology
typically used for flexibility design.
The purpose of performing a flexibility analysis is to determine that,
barring interferences and assuming a supportable geometry, the anchor-to-anchor
piping configuration (layout) is acceptable. Adequate flexibility is required
to avoid an expansion (or contraction) induced fatigue failure and to
limit anchor loads on equipment. A flexibility analysis typically (and
traditionally) evaluates the range of stresses encountered by piping system
service startup and shutdown. It is generally assumed that the startup-shutdown
stress-range will bound the other thermal expansion or displacement stress-ranges.
The piping flexibility is evaluated between equipment and structural anchors
without locating any intermediate supports. Weight stresses, then, would
not be known. It is presumed that the intermediate supports for weight
and other loads can be added after determining that a piping system has
adequate flexibility without significantly increasing the flexibility
stress-ranges. This is reflected in the circa. 1955 B31 books having an
allowable thermal expansion stress-range
SA = f(1.25Sc + 0.25Sh)
and permitting an additional thermal expansion stress-range allowance
of Sh - SL, when the stresses due to weight and other sustained loads,
SL, were known.
After the flexibility analysis has determined that the piping has adequate
flexibility, using the allowable thermal expansion or displacement stress-range,
SA, then span tables and/or engineeringjudgement is used to locate intermediate
supports for weight and other loads. If the thermal displacements at a
proposed support point are negligible (i.e., very small), then a rigid
support can be located at that point. If the vertical thermal displacements
are significant at locations where weight supports are proposed, springs
(variable or constant) can be used. If the lateral thermal displacements
are significant at locations where lateral supports are proposed, gapped
supports usually can be used. By use of support types that offer minimal
restraint throughout the startup-shutdown excursion, the flexibility stress-range
is not significantly increased and could be expected to be bounded by
the additional thermal expansion allowance, Sh - SL. (Editor's note: Sh
- SL is available in CAEPIPE as an Analysis Option (under Code) "Use
liberal allowable stresses," for certain piping codes).
The entire flexibility design and analysis process assures that the effects
of fatigue due to thermal expansion, or more generally the restraint of
free-end displacements, are minimized. However, some caution in performing
the flexibility analysis is necessary to see that other frequently occurring
normal and abnormal operating condition stress-ranges do not envelope
the startup-shutdown stress-range or to see that supports do not unduly
restrain the load induced expanding (or contracting) piping system.
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.
Update: As this method
is from an older edition of A58.1, we recommend that you refer to ASCE-7,
2002 edition for the latest guideline for calculating g-loads.
Piping should be designed for earthquake-induced forces. Either ANSI A58.1
or the Uniform Building Code (UBC) may be used for calculating the g-load
(or static seismic coefficient).
The following is a simplified method based on ANSI/ASCE A58.1-1988 ("Minimum
Design Loads for Buildings and Other Structures"). Piping is assumed
to be equivalent to equipment thus giving a force coefficient, Cp as 0.3
(Table 25).
For the proper method:
1. First, based on the map below (Contiguous 48 States+Alaska/Hawaii/Puerto
Rico), identify the seismic zone and its corresponding coefficient (Z).
| Seismic Zone Coefficient | Z |
| 4 | 1.0000 |
| 3 | 0.7500 |
| 2 | 0.3750 |
| 1 | 0.1875 |
| 0 | 0.1250 |
2. Determine the Importance Factor, I.
| Type of piping Factor | I |
| Piping required in an emergency or piping with contents representing significant hazard to human life | 1.5 |
| Other piping | 1.0 |
3. Calculate the g-load as (0.3*Z*I). The equation is
Fp = 0.3*Z*I*Wp, where
Fp = Design Inertia force, and
Wp = Weight of piping including insulation and contents.
Assumptions and Exclusions:
1. Earthquake restraints may be omitted from the following installations:
a. Gas piping less than 1 inch inside dia.
b. Piping in boiler and mechanical rooms less than 1.25 inch inside dia.
c. All other piping, except that containing hazardous fluids, less than
2.5 inch inside dia.
2. Individual hangers less than 12 inches in length may be considered
as seismic restraints.
Example:
For a power plant required to operate in an emergency, located in Anchorage,
Alaska, calculate the design earthquake load coefficient for piping required
to operate the plant.
1. From the map below, seismic zone is 4, from the table above, corresponding
coefficient is 1.0.
2. For piping required to operate in an emergency, the Importance factor
is 1.5.
3. Calculate the coefficient,
Fp = 0.3*1.0*1.5*Wp
Fp = 0.45*Wp
The coefficient, 0.45, needs to be applied independently in the desired
horizontal/vertical directions. See map below for US seismic zones.
How does CAEPIPE analyze internally?
CAEPIPE computes the Design inertia force for each direction and applies
it as an occasional load. From the example above, assume we applied 0.45g
in X, Y and Z directions. CAEPIPE internally applies an X acceleration
(of 0.45g) first and solves the case. This procedure is then applied independently
to the accelerations in Y and Z directions.
The above procedure results in three sets of solutions (displacements,
element forces and moments, and support loads) to accelerations in X,
Y and Z directions, which are typically combined in some manner. In CAEPIPE,
two directional combination methods are available: SRSS (Square root of
sum of squares) and ABS (Absolute). The SRSS summation method employed
in Acceleration (static seismic) load case and other simplified dynamic
analysis methods, such as response spectrum method, is statistically based.
In the SRSS method, displacements, element forces and moments, and support
loads from the three X, Y and Z accelerations are squared individually
and added. The square roots of these respective sums are the displacement,
element force and moment, and support load at the given node. In the ABS
method, all absolute values of displacements, element forces and moments,
and support loads are added to get the total displacement and support
load. The resulting stresses are added to Sl (Sustained stress) and shown
under Occasional stresses (Sl+So).
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