Whenever the user enters weight, operating or occasional loads, the program generates a variety of load cases designed to satisfy the ASME Section VIII Division 2 Code requirements. Weight, primary, operating, thermal, occasional and “range” load cases and allowables are established as needed. The user will find the results of this activity in the tabulated reports in the left pane of the output window.
• ASME Overstressed Areas
• Highest Primary Stress Ratios
• Highest Shakedown Stress Ratios
• Highest Fatigue Stress Ratios
• Highest Occasional Stress Ratios
If the stresses in each of these reports are less than the given allowables, then at least one portion of the Codes requirements have been satisfied. The load cases set up by the program are described in detail in the “FE/Pipe Load Case Report.”
Always review the graphical results along with the necessary tabular results! Graphical results that “make sense” are a confirmation that the tabular finite element results are correct. Incorrect or invalid tabular results are almost always accompanied by incorrect, inconsistent or invalid graphical results, and graphical errors are much easier to spot!
Finite element results are directly comparable to WRC 107 or WRC 297. Membrane stresses in WRC 107 or WRC 297 are directly comparable to Pl type membrane stresses from a finite element calculation. Membrane plus bending stresses from WRC 107 and WRC 297 are directly comparable to a (Pl+Pb+Q) outer-fiber stress from a finite element calculation, and peak stresses (those that include a “stress concentration factor”) are directly comparable to a Pl+Pb+Q+F alternating peak stress from a finite element program.
With respect to the piping codes, (Pl) from ASME Section VIII Division 2 is approximately equivalent to the sustained stress from a pipe stress program, and (Pl+Pb+Q+F) is equivalent to the expansion stress from a pipe stress program. (Although the sustained stress from a pipe stress program can be interpreted many ways – see
“Background for the ASME Nuclear Code Simplified Method for Bounding Primary Loads in Piping Systems” by S.E. Moore and E.C. Rodabaugh.)
The following caveats should be noted:
1) Elastic instability due to external pressure and loads is not covered explicitly by the Section VIII Division 2 Rules. Nor are they covered by the B31 piping code rules. The user must recognize conditions where elastic instability can be a problem. Most common vessel and thin-walled piping geometries are not subject to elastic instability providing they are designed in accordance with the Code for external pressure. For large openings subject to heavy loads, and where diameter-to-thickness ratios exceed 100 and external pressure is a design criteria the designer is urged to exercise caution. The full version of FE/Pipe has several techniques available for evaluating elastic instability.
2) The ASME Section VIII Division 2 Code provides additional rules (See 4-136.7) for simplified elastic/plastic analyses. The rules of Section 4-136.7 allow the analyst to apply considerably larger secondary loads to nozzles without violating the Codes rules, its intent, or the Code desired safety factor against failure. This evaluation capability is typically NOT used in design. Should the user wish to take advantage of Code rules, which may permit extremely high secondary loads applied over a limited number of cycles, he should contact his software representative.
3) Occasional loads that may contribute to cyclic failures should be evaluated in terms of contribution to a cycle life fraction. Options are available to perform this type of evaluation if the need should exist; for example, the occasional loads are due to vibrations.
The following gives a brief discussion of the calculated stresses and allowables.
Primary (Sustained) Membrane Stresses: Pl < (1.5)(k)(Smh) Primary Bending Stresses: Qb < (3.0)(Smh)
Secondary Stresses: Pl+Pb+Q < (3.0)(Smavg) < 2Sy Peak (Fatigue, or Expansion) Stresses: Pl+Pb+Q+F < Sa < f (1.25(Sc+Sh) < (C) N-0.2
Pl Local membrane stress due to weight and pressure – sustained, or primary loads.
k Occasional load factor. 1.0 – weight and pressure, 1.2 – occasional.
Smh Hot allowable stress
Pl+Pb+Q Secondary stress on inner and outer fibers due to both the “range” of stresses and the sum of the primary and secondary stresses. (The range calculation insures elastic shakedown, and the sum of primary and secondary stresses insures that incremental straining per the Bree diagram will not occur.)
Smavg The average of the material hot and cold allowables.
Sy The material yield average yield strength.
Pl+Pb+Q+F Peak stresses on the inner or outer fibers due to the “range” of stresses. This stress will cause a fatigue crack to occur.
Sa Allowable from the ASME Section VIII Division 2, Appendix 5 allowable stress curve.
Note that this value is computed based on an allowed number of operating load cycles. If not given this value defaults to 7000 cycles, a value selected by one of the original piping code developers, A.R.C. Markl, and used in most piping programs worldwide today.
f Cyclic reduction factor based on the number of cycles. “f” usually starts at “1.0” for 7000 cycles. The empirical expression f = 6N-0.2 can be substituted for “f:”.
Sc Piping Code – Cold allowable stress.
Sh Piping Code – Hot allowable stress.
C Constant used in Markl’s equation for allowable fatigue strength of materials. The value most commonly used for low carbon steels is 245,000 psi.
Typical “primary,” “secondary,” and “fatigue” stress reports are shown below.
Highest Primary Stress Ratios
Pl+Pb+Q 3(Smavg) Primary+Secondary (Outer) Load Case 2
Each of the reported stresses corresponds with the individual items discussed above. Output is organized on a
“region” basis. Two typical regions are shown, although usually there are more. Additional regions exist for thickened, or self-reinforcing nozzles, nozzles with repads, etc. In each case the stress for all regions in the model must satisfy the Codes requirements. Each reported stress has associated with it a “plot reference.” The “plot reference” can be used to review the distribution of the reported stress over the entire surface of the geometry. In general the stresses that are computed by a finite element calculation are very local. Only a small region of the model should show to be red, (or highly stressed). This is the desired stress condition. Very small, high stress regions plastically deform a small volume of material and redistribute their load to the relatively large elastic volume surrounding them. These types of “higher” localized stresses are safe and serve only as a potential site for a fatigue crack initiation. If a high, secondary stress is distributed broadly over the geometry then it becomes less
“safe.” Large regions of red are, in general, significantly worse than small, local regions. The plots below illustrate.
Figure 1 – Broadly Distributed Stress Zones – The governing stress for the design is distributed over a significant part of the diameter, that is, greater than 50% of the total circumference.
Figure 2 – Local Stress Zones – The governing stress for the design is distributed over a fairly small part of the diameter, that is, much less than 50% of the total circumference.
Structural output is grouped under longitudinal and circumferential plates, depending on the cross section selected.
Each plate has a region described in the output as SCR. The stresses reported in this region are the plate stresses that are adjacent to a weld zone. SCR stands for Stress Concentration Region. SCR regions exist for plates along the outside edges of the plate that is adjacent to another construction.