Pipe Stress Analysis: Basic Concepts
Such "back and forth" design iterations between layout and stress departments continue until a suitable layout and support scheme is arrived at, resulting in significant increase in project execution time, which, in turn, increases project costs.
This delay in project execution is further aggravated in recent years as operating pressures and temperatures are increased in operating plants to increase plant output; increased operating pressures increase pipe wall thickness, which, in turn, increase piping stiffness further; increased operating temperatures, applied on such "stiffer" systems, increase pipe thermal stresses and support loads. So, it is all the more important to make the piping layout flexible at the time of routing by piping designers.
The "Design by Color" product "checkSTRESS" from SST (different from CAEPIPE) for AutoCAD, CATIA, Autoplant, PDMS, Cadmatic, etc. can be used to substantially reduce the number of design iterations between the piping layout and stress departments, resulting in huge time savings during design.
Basic Pipe Stress Concepts for Piping Designers
It mainly consists of internal pressure and dead-weight. Dead-weight is from weight of pipes, fittings, components such as valves, operating fluid, test fluid, insulation, cladding, lining etc.
Internal design/operating pressure develops uniform circumferential stresses in the pipe wall, based on which pipe wall thickness is determined during the process/P&ID stage of plant design such that "failure by rupture" is avoided. In addition, internal pressure develops axial stresses in the pipe wall. These axial pressure stresses vary only with pressure, pipe diameter and wall thickness, all three of which are pre-set at the P&ID stage and hence these axial pressure stresses cannot be reduced by changing the piping layout or the support scheme.
On the other hand, dead-weight causes the pipe to bend (generally downward) between supports and nozzles, producing axial stresses in the pipe wall (also called "bending stresses"); these bending stresses linearly vary across the pipe cross-section, being tensile at either the top or bottom surface and compressive at the other surface. If the piping system is not supported in the vertical direction (i.e., in the gravity direction) excepting at equipment nozzles, bending of the pipe due to dead-weight may develop excessive stresses in the pipe and impose large loads on equipment nozzles, thereby increasing the susceptibility to "failure by collapse".
Various international piping codes impose limits, also called "allowable stresses for sustained loads", on these axial stresses generated by dead-weight and pressure in order to avoid "failure by collapse".
For the calculated axial stresses to be below such allowable stresses for sustained loads, it may be necessary to support the piping system vertically. Typical vertical supports to carry dead-weight are:
- Resting steel supports,
- Rod hangers,
- Variable spring hangers, and
- Constant support hangers.
Two examples are presented in this Tutorial to illustrate how piping can be supported by spring hangers and resting steel supports to comply with the code requirements for sustained loads.
Thermal Load (also referred as Expansion Load):
It refers to the "cyclic" thermal expansion/contraction of piping as the system goes from one thermal state to another thermal state (for example, from "shut-down" to "normal operations" and then back to "shut-down"). If the piping system is not restrained in the thermal growth/contraction directions (for example, in the axial direction of a straight pipe), then for such cyclic thermal load, the pipe expands/contracts freely; in this case, no internal forces, moments and resulting stresses and strains are generated in the piping.
On the other hand, if the pipe is "restrained" in the directions it wants to thermally deform (such as at equipment nozzles and pipe supports), such constraint on free thermal deformation generates cyclic thermal stresses and strains throughout the system as the system goes from one thermal state to another. When such calculated thermal stress ranges exceed the "allowable thermal stress range" specified by various international piping codes, then the system is susceptible to "failure by fatigue". So, in order to avoid "fatigue failure" due to cyclic thermal loads, the piping system should be made flexible (and not stiff). This is normally accomplished as follows:
- Introduce bends/elbows in the layout, as bends/ elbows "ovalize" when bent by end-moments, which increases piping flexibility.
- Introduce as much "offsets" as possible between equipment nozzles (which are normally modeled as anchors in pipe stress analysis).
For example, if two equipment nozzles (which are to be connected by a pipeline) are in line, then the straight pipe connecting these nozzles is "very stiff". On the other hand, if the two equipment are located with an "offset", then their nozzles will have to be connected by an "L-shaped" pipeline which includes a bend/elbow; such "L-shaped" pipeline is much more flexible than the straight pipeline mentioned above.
- Introduce expansion loops (with each loop consisting of four bends/elbows) to absorb thermal growth/contraction.
- Lastly, introduce expansion joints such as bellows, slip joints etc., if warranted.
In addition to generating thermal stress ranges in the piping system, cyclic thermal loads impose loads on static and rotating equipment nozzles. By following one or more of the steps from (a) to (d) above and steps (e) and (f) listed below, such nozzle loads can be reduced.
- Introduce "axial restraints" (which restrain pipe in its axial direction) at appropriate locations such that thermal growth/contraction is directed away from equipment nozzles, especially critical ones.
- Introduce "intermediate anchors" (which restrain pipe movement in the three translational and three rotational directions) at appropriate locations such that thermal deformation is absorbed by regions (such as expansion loops) away from equipment nozzles.
This type of load is imposed on piping by occasional events such as earthquake, wind etc. To protect piping from wind (which normally blows in horizontal plane), it is normal practice to attach "lateral supports" to piping systems. During an earthquake, the earth may also move vertically. To protect piping against both horizontal and vertical movement during earthquake, some of the resting supports may be made as "integral 2-way vertical and lateral restraints".
Fortunately, to carry sustained loads, normally vertical supports (as those listed under the Section titled "Sustained Load" above) are required. To withstand static seismic ‘g’ loads, "integral 2-way vertical and lateral restraints" are required. Generally, some of the vertical weight supports can be modified as "integral 2-way vertical and lateral restraints". On the other hand, for thermal loads, zero supports give zero stresses. So, thermal stresses and equipment nozzle loads will normally decrease as the number of supports goes down. Axial restraints and intermediate anchors are recommended only to direct thermal growth away from equipment nozzles.
Model the piping system in CAEPIPE (either directly inside CAEPIPE, or by using one of SST’s data translators to import the piping model) and follow the steps shown in the CAEPIPE Tutorial to learn the basics of operating CAEPIPE to create and analyze a model and review its results. Once all the data is in, Analyze. Now, review Results.
Step2: Studying Thermal Stress results for the Initial Layout
Review first stress contour plot for thermal stresses. The plot is color-coded such that "blue" region denotes areas with the least stress ratios (where stress ratio equals to actual computed stress divided by allowable thermal stress), "green" region with higher stress ratios, "yellow" region with even higher stress ratios, and "red" region with the highest stress ratios. Intermediate areas between these distinct colors will be of "bluish-green", "greenish-yellow" and "orange" colors.
Since thermal stresses generated are directly dependent on how "flexible" the layout is, it may be necessary to make the layout as "flexible" as possible (by including bends, offsets, loops etc.) to reduce thermal stresses. So, the goal is to arrive at a "flexible" layout for which thermal stress ratios remain within "blue" to "yellow" range and not get into "orange" and "red" zones. For a more "flexible" layout, even "yellow" zone may be avoided.
Step 3: Finalizing Layout to meet Thermal Stress criteria
In case thermal stress ratios exceed "yellow" zone (i.e., "orange" and "red" zones appear in one or more areas of the piping system), it is important to study the deformed shape for "thermal" load case in order to understand how the piping deforms for "pure thermal" load (where only temperature change is considered). By studying such deformed shape, it is possible to arrive at a layout with appropriate bends, offsets and loops and/or with appropriately located axial restraints/intermediate anchors such that thermal stress ratios do not exceed "yellow" zone. This process may require several iterations on layout and/or locations for axial restraints/intermediate anchors.
Step 4: Studying Results for Sustained Load
After finalizing piping layout under Steps 2 and 3 for thermal loading, the next task is to support the system vertically to carry its own deadweight under operating condition. In this connection, first review stress contour plot shown in color codes from "blue" to "red" (as in Step 2 above) for sustained stress ratios generated by deadweight and pressure for the system without any vertical supports (excepting those provided by equipment nozzles and intermediate anchors introduced in Step 3 above).
The goal is to arrive at a vertical support scheme consisting of (a) resting steel supports, (b) rod hangers, (c) variable spring hangers and (d) constant support hangers, at appropriate locations (where such pipe supports can be attached to adjacent concrete/steel structures, platforms etc.) so that stress contour plot for sustained stress ratios avoids "orange" and "red" zones and remains within "blue to yellow" range.
Step 5: Finalizing Vertical Supports to carry Sustained Load
In case sustained stresses exceed "yellow" zone in one or more areas of the piping system, study the deformed shape provided by CAEPIPE for sustained load case in order to understand how the piping responds to its own deadweight. Next, identify pipe locations where the pipe can be vertically supported by the support types listed under Step 4 above. Based on this input, vertically support the piping such that sustained stresses do not exceed "yellow" zone. This step may require a number of analysis iterations with several different locations for weight supports.
In case resting steel supports are selected to provide vertical support for piping under sustained load, it is to be made sure that piping continues to rest on such steel supports even during operating condition (= weight + pressure + thermal) and does not lift off from these supports. If pipe lifts up at any of these resting supports during operating condition, then that support does not carry any pipe weight and hence will not serve its purpose. Similarly, at rod hanger locations, the tendency of piping should be to deform downward for operating load case, so that the rod hangers carry the pipe weight under tension. On the other hand, if pipe lifts up at any of the rod hangers, then that rod hanger goes into compression thereby not carrying the weight of the piping during operating condition. Whether the pipe weight is being carried during operation by resting steel supports and/or rod hangers (both types are mathematically modeled as one-way vertical Limit Stops in CAEPIPE) or whether the pipe lifts up at those support locations is shown in the report titled "Status of Limit Stops – Operating Load". The goal is to make sure the status is shown as "Reached" at all vertical Limit Stops for Operating Load case.
Step 6: Studying Results for Static Seismic "g" Load
After arriving at a final layout with an acceptable pipe support scheme under Steps 2 to 5 for thermal and sustained loads, the next task is to protect piping against large horizontal and vertical movements that could occur due to static seismic "g" load. This can be accomplished by replacing some of the weight supports with "integral 2-way vertical and lateral restraints".
In this regard, review stress contour plot for occasional stresses generated by deadweight, pressure and static seismic "g" load shown in color codes from "blue" to "red" (as in Step 2 above).
The goal is to replace some of the weight supports (for example, resting supports) located in the "yellow" to "red" zones with "integral 2-way vertical and lateral supports", so that stress contour plot for occasional stresses avoids "orange" and "red" zones and remains within "blue to yellow" range.
Step 7: Finalizing 2-way Vertical and Lateral Restraints to withstand Static Seismic "g" Load
In case occasional stresses exceed "yellow" zone in one or more areas of the piping system, study the deformed shape provided by CAEPIPE for occasional load case in order to understand how the piping responds to static seismic "g" load. Next, identify those weight support locations (for example, resting supports) in the "yellow" to "red" zones where the pipe can also be laterally supported and replace those weight supports with "integral 2-way vertical and lateral restraints", such that occasional stresses do not exceed "yellow" zone. This step may require a number of analysis iterations with several different locations for "integral 2-way vertical and lateral restraints".
Step 8: Meeting Allowable Loads at Nozzles / Anchors
After locating relevant supports (a) to minimize thermal stresses, (b) to carry weight of the piping during operation, and (c) to withstand static seismic "g" load, the calculated loads at nozzles/anchors in the Support Load Summary need to be checked. If the calculated loads at nozzles/anchors exceed the corresponding Allowable Loads, by studying the deformed shapes provided by CAEPIPE for different load cases, it is possible to further modify the layout and/or support scheme such that the calculated loads at nozzles/anchors do not exceed the Allowable Loads.
As a minimum, the above said Nozzle Load compliance should be carried out forOperating Load case.
Any such changes made to the layout and/or support scheme at this stage (i.e., at Step 8) should not adversely affect the stresses for thermal, sustained and occasional load cases (i.e. all the 3 stress contour plots should continue to avoid "orange" and "red" zones and remain within "blue to yellow" range). This process may require several iterations on layout and/or support scheme.
- 4" NB/Sch. 40: Between nodes 10 and the first reducer
- 6" NB/Sch. 40: Between the first reducer and the second reducer and ending at node 90
- 8" NB/Sch. 40: Between nodes 90 and anchor node 130
- T = 470°F