Global coordinates are used most often when dealing with piping models. Global coordinates are used to define the model and review nodal results. Even though element stresses are defined in terms of axial and bending directions, which are local coordinate system terms, local coordinates are rarely used. A typical piping analysis scenario is:
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A decision is made as to how the global coordinate system for the piping model will align with the plant coordinate system. Usually, one of the two horizontal axes is selected to correspond to the North direction. However, if this results in a majority of the system being skewed with respect to the global axes, you should consider realigning the model. It is best to have most of the system aligned with one of the global coordinate axes.
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The piping system is then assigned node points at locations where: there is a change in direction, a support, a terminal point, a point of cross section change, a point of load application, or any other point of interest.
After you assign the nodes, define the piping model using the delta dimensions as dictated by the orientation of the global coordinate system. Use Break, List, Rotate, Duplicate, and the Direction Cosines to construct the model.
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After verifying the input, confirming the load cases, and analyzing the model, output review commences.
Output review involves checking various output reports to ensure the system responds within certain limits. These checks include:
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Checking that operating displacements make sense and are within any operational limits to avoid ponding. Displacements, being nodal quantities, are reviewed in the global coordinate system. There is no local coordinate system associated with nodes. For the model defined in Figures 7 and 8, the operating displacements are shown in Figure 15 below.
Figure 15 - Operating Displacements
This report shows the movements of all of the nodes in the model, in each of the six degrees of freedom, in the global coordinate system.
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Checking that the restraint loads for the structural load cases are reasonable. This includes ensuring that the restraints can be designed to carry the computed load. Restraints being nodal quantities are reviewed in the global coordinate system. There is no local coordinate system associated with restraints. For the model defined in Figures 7 and 8, the operating / sustained restraint summary is shown in Figure 16 below.
Figure 16 - Operating / Sustained Restraint Summary
This report shows the loads on the anchor at 10 and the nozzle at 50, for all six degrees of freedom, for the two selected structural load cases, in the global coordinate system.
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Checking the code cases for codes stress compliance. Typically, the code stress is compared to the allowable stress for each node on each element. Occasionally, when there is an overstress condition, a review of axial, bending, and torsion stresses are necessary. These stresses axial, bending, and torsion are local coordinate system terms, and therefore relate to the element’s local coordinate system. For the model defined in Figures 7 and 8, a portion of the sustained stress report is shown in Figure 17 below.
Figure 17 - Sustained Stress Report
These reports provide sufficient information to evaluate the pipe elements in the model, to ensure proper behavior and code compliance. However, the analyst’s job is not complete, loads and stress must still be evaluated at terminal points, where the piping system connects to equipment or vessel nozzles. Depending on the type of equipment or nozzle, various procedures and codes are applied. These include API-610 for pumps and WRC-107 for vessel nozzles, as well as others. In the case of API-610 and WRC-107, a local coordinate system specific to these codes is employed. These local coordinate systems are defined in terms of the pump or nozzle/vessel geometry.
When the equipment coordinate system aligns with the global coordinate system of the piping model, the nozzle loads from the restraint report (node 50 in Figure 14) can be used in the nozzle evaluation. However, when the equipment nozzle is skewed as it is in the case of node 50 in Figure 14, the application of the loads is more difficult. In this case, it is best to use the loads from the element’s force/moment report, in local coordinates. The only thing to remember here is to flip the signs on all of the forces and moments, because the element force/moment report shows the loads on the pipe element, not on the nozzle. For the element FROM node 40 to node 50, the local element force/moment report is shown in Figure 18 below.
Figure 18 - Local Element Force/Moment Report
Because the correlation between the pipe model’s coordinate systems and those of equipment codes API and WRC are often times tedious and error prone, CAESAR II provides an option in its equipment modules to acquire the loads on the nozzle directly from the static output. Select the node and the load case; CAESAR II acquires the loads and rotates them into the proper coordinate system as defined by the applicable equipment code. You really do not have to be concerned with the transformation from global to local coordinates, even for skewed components. This is illustrated below, in Figure 19. In this figure, the API-610 nozzle loads at node 50 have been acquired by clicking Select Loads by Job/Load Case.
Notice that the loads shown in Figure 19 are in the CAESAR II global coordinate system. This can be easily verified by comparing these values to those in the restraint summary for the operating load case as shown previously in Figure 16.
Figure 19 - API-610 Nozzle Load Acquisition
In the corresponding output report for this API-610 analysis, both the global and API local loads are reported. This is shown below in Figure 20.
Figure 20 - API-610 Nozzle Output Report Segments
Notice in Figure 20, that each report segment indicates which values are related to the global coordinate system and which are related to the local API coordinate system.