DEMM Engineering & Manufacturing
PIPING STRESS ANALYSIS FOR INDUSTRIAL MANUFACTURING PLANTS
INTRODUCTION
Piping systems are usually complex and challenging. Thermal movements in many piping systems are significant and constraints on the thermal movements resulted in high stresses. Piping stress analysis done on piping to ensure the stresses, reaction loads and deflections due to pressure, temperature, weight, dynamic loads and others are within safe and reliable limits. Spans of piping supports, the selection and placing of supports, and other piping tasks have usually been done using rules of thumbs or rough tables or charts. However, all these should be checked and verified carefully using piping stress analysis based on calculated stresses, reaction forces, displacement, and equipment nozzle analysis. This article discusses piping stress analysis with focus on practical notes and useful guidelines.
SUSTAINED VS. SELF-LIMITING
The stress generated by thermal expansion or contraction is assumed to be self-limiting theoretically. This is quite differently from the sustained stress caused by weight or pressure. For instance, considering weight loads, when the stress reaches the yield point of the material and the piping section entirely yields, the stress increases by a relatively small amount, but the displacement could increase by a large amount due to plastic deformation. At this situation, the strain is so large that it results in a gross deformation in the system. Therefore, sustained stress is generally limited to values lower than the yield strength of the material, say 60 or 70 percent of it.
The case of self-limiting stress is different. When the piping is subject to thermal movements or other displacement load, the mechanism of balance shifts to the strain. The strain always corresponds with the amount of expansion, contraction or displacement. For instance, when the strain corresponding to the displacement exceeds the yield strain, it stays there without any further abrupt movement. This position fixing nature is called self-limiting. The stress due to thermal movement is self-limiting stress. Self-limiting stress usually does not break ductile pipe in one application of the load; the mode of failure is nearly always fatigue requiring many cycles of applications; and the fatigue failure depends on stress range, measured from the lowest stress to the highest stress.
LOAD CASES
Load cases include operational cases, sustained cases, expansion cases and hydro-test case. It is possible to have higher stresses in some load cases when compared to the operational loads. The allowable stresses as per codes are also different. It is therefore necessary to check and verify all possible load cases in order to ensure the piping under study is safe and reliable.
Sustained case stresses are due to the axial loads, bending moment, and internal pressure. Sustained case focuses on the loads of pressure, weight (of all masses), and similar. Failure in this case usually indicates the lack of sufficient number of supports, or insufficient thickness to contain the internal pressure (hoop stress).
The operating case takes into account the actual loads on the piping including the ones for the attached equipment, anchors, supports, guides, or limit stops. Temperature, weight, pressure and operational loads is combined to mimic the real life operating scenario.
Expansion case is considered specifically to study the thermal expansion/contraction of the piping under the temperature effect. Failure often occurs due to high stresses at or near the fixed points (zero displacements) or where the thermal movements are restricted.
In the hydro-test case, the piping is filled with water and exposed to a pressure that is 1.25 times or 1.5 times the operational pressure. For many piping, density of water is more than the density of operating fluid and the test pressure is obviously more than operational pressure; therefore, the stresses at this case can be higher than operational cases.
CODES & REQUIREMENTS
Different piping code asked for different set of checks and verifications. Code stresses and allowable stresses have been different in various codes and specifications. In Addition, there can be specific specifications or requirements for a facility or a plant. An example is sometimes maximum stress ratio of 0.75 or 0.8 are requested. This is to provide an additional 20-25 percent margin on the top of applicable code allowable stresses. As another example, sometimes, maximum axial displacement is asked to be limited to 50 mm, 60 mm or 70 mm. This is to limit float or overall axial displacement of piping.
SUPPORTS, GUIDES & GAPS
Thermal stresses in a piping system are actually because of restriction in piping elastic deformations and support loads. If a piping system is allowed to expand or contract freely and there is no support restriction or inherent piping restriction due to its configuration or other reasons, the thermal stresses would be low even for large thermal gradient.
Resting supports have commonly provided for many piping. A good aspect of these supports is they let piping to have movements (such as thermal movements) without restricting support loads, therefore, stresses and support loads are not very high. However, in many cases, some restraining supports whether in the form of guide or others are needed to keep piping static or dynamic movements under control. One reason might be to increase the natural frequencies and prevent uncontrolled vibration of piping.
To ensure the free movement of the piping in unrestrained directions, guides and other types of supports are generally provided with gaps. These gaps usually range from 2 mm to 4 mm. However, there have been special supports with permitted gap of 10 mm, 15 mm, 20 mm or even more. An example is a special clamp type support where the bolt hole is provided with slots to allow movements in the required direction and the bolts are also provided with special washer springs to let such a movement. The gap on this type of support can be somewhere between 15 mm, 20 mm or 25 mm in the designated direction which could be lateral or axial. When lateral option is used, the support acts as a guide with a large gap. Such a special support can be used in places where lateral thermal movements of around or below 20 mm is expected, restricting the movement causes high stresses and support loads, and at the same time a guide support is needed for other reasons such as the modal analysis and increasing the natural frequency.
The gaps on those supports located close to the connecting equipment and machineries need attention. Particularly gaps at the first support from the equipment need special attention. A detailed analysis may show that initially assigned gaps are too large or too small. These gaps often are optimized based on detailed simulations and studies.
FRICTION IN PIPING SUPPORTS
Friction is a major factor in piping stress analysis, and it should nearly always be considered in such analysis. Support friction is important in many areas. This type of friction is important in estimating the potential axial movement of piping, particularly long piping. It also has significant effect on piping systems connected to equipment, machineries and rotating equipment. Inclusion of the friction effect in the analysis significantly increases the complexity of calculation. In fact, it introduces nonlinearity to the system and this can affect many aspects of the analysis such as the convergence of the solution, numerical accuracy, time and man-hours needed for the analysis and others.
COMPLICATED CASES OF PACKAGES
Different parts of the piping systems in a plant or facility may be provided by different companies or manufacturers. The piping from a package then will be connected to the piping of the facility at the package skid edge connection. A problem arises for the piping stress analysis of these twodifferent scope of piping and specifically how to simulate the piping within each scope considering that there is a shared tie-in or boundary condition at the skid edges of the package.
A typical approach may specify that the support near the skid edge connection be an anchor. An allowable load at the skid edge connection anchor point is also specified. The rationale for this approach is that the skid edge anchor is a means of isolating the flexibility response of the package piping and facility piping from each other. There are several factors that make this approach inaccurate in many packages. Also, the resulting piping analysis from this approach will be overly conservative meaning high cost and possibly longer schedule.
The best approach for the flexibility analysis in areas where there is a shared responsibility for the piping scope is that both parties need to simulate a sufficient part of the piping that is outside of their analysis scope. The piping stress principles describing how the piping system will respond due to changes in pressure and temperature does not recognize the arbitrary boundary at the point where responsibility changes. The response of the overall system should be calculated accurately. For complex packages, regular updates on the piping progress and deviations due to site conditions are necessary. The overall success relies on all parties involved making adjustments in their area of responsibility considering factors in the control of the other party.