TPi January 2019

Computer analysis vs engineering theory One way to gain additional confidence in any application’s results is to start with simple models. Perform a few tests on the component or analysis and confirm that the results simulate the actual system reasonably well. For these simplistic models, we can manually apply the engineering theory to check the results. Let us start with that cantilever pipe and look at the static and dynamic results to see how they compare with the manual predictions. Statically apply a 1000-Newton horizontal load to a 15-metre-long, 10" STD wall pipe cantilever. We predict that the deflection should be 82.9 millimetres [1] (Figure 1). Dynamically, let us determine the natural frequencies of this beam. We predict that the first five natural frequencies will be 1.18, 7.39, 20.72, 40.63 and 67.16 hertz [2] (Figure 2). Note that the natural frequencies come in pairs due to the symmetrical nature of the cantilever model. The results match closely with the expectations. There will always be slight differences because the application considers shear deformation whereas empirical formulas do not account for it. We can see that it is possible to match the results with the theory, but this model is not representative of a real piping system. As we expand the model and add in more geometry, it becomes harder to use simple beam theory to check the results. We can always do some simple model checks on boundary conditions and equilibrium, but for a more thorough test we need standard example models to compare with the results or industry benchmarks.

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design section. For comparison, the loads, deflections and stresses are averaged from commercial programs. Therefore, aligning with these values will provide more confidence of a program’s accuracy against other applications. Bentley’s AutoPIPE ® Connect Edition v11.03.00.08, for example, can be used to analyse these benchmarks. Note that the published results in Appendix S match only earlier versions of the code. This discrepancy is due to changes to the material properties in 2012. To simplify the modelling and utilise the library values for material properties, we applied the 2010 code year. While it is possible to use a later code year, the material properties would have to be manually entered to align with those used when this assessment was first published. The first example, S301, is intended to illustrate the rules and definitions in Chapter II, Part 5, Flexibility and Support; and the stress limits of para. 302.3.5. The S302 example (Figures 3 and 4) is intended to illustrate the analysis of a piping system where a portion of the piping lifts off at least one +Y support in at least one operating condition. The emphasis describes the effect this removal of support has on determining anticipated sustained conditions. Note that using the 2014 ASME B31.3 design code and later, AutoPIPE can assess the effect of support lift off automatically in a single analysis run by a different static analysis set. Since the code year for this analysis is 2010, it was necessary to remove the support manually and run two analyses. The S303 example (Figure 5) is intended to illustrate the flexibility analysis required for a piping system designed for more than one operating condition. It also experiences a “reversal of moments” between any two anticipated operating conditions.

Industry standard benchmarks and examples

Three such example models are provided in Appendix S of ASME B31.3. [3] The simple examples in this appendix are intended to illustrate the application of the piping code’s

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January 2019 TUBE PRODUCTS INTERNATIONAL