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In addition, P-delta with large displacements enables engineers to more accurately calculate stresses and reactions in layouts where flexible piping exhibits catenary behavior. Following is a simple example illustrating the effects of P-delta with large displacements which users can easily reproduce with their own piping stress program. Pipe section OD 6.625" wall thickness .188", A106-B, fluid contents specific gravity 1.0 (water), no insulation. 80 ft. span of unsupported pipeline divided into 5 ft. segments. Anchors on each end have moment releases with rigid fixity in all 3 translational directions. That is, anchors are rigid in global X, Y, and Z direction with no rotational restraint stiffness (aka "pinned" support).
Vertical displacements displayed below for weight case only (selfweight including fluid). Right-side window is weight case with consideration of P-delta with large displacements with max vertical displacement of -8.69". Left-side window are displacement results from the same weight case, but ignoring P-delta effects, with a calculated max vertical displacement of -41.5", which is what older generation legacy piping stress programs will report. With a long flexible pipeline like this, there is catenary behavior that needs to be accounted for in which axial load is being distributed to the anchors to help support the pipeline. P-delta with large displacements accounts for this real-world catenary behavior which made quite a difference in this example.
Vertical deflection results without P-delta large displacements Vertical deflections with consideration of P-delta large displacements
Even though the GR weight case includes by default Insulation, cladding, and lining, in this example there were no insulation, cladding, or lining loads defined or assigned, only Dead selfweight and Fluid contents load.
Using the same long span model, we load sequenced an additional Modal case to be based on the end state of the GR-PD load case, which is the weight case analyzed with P-delta large displacements. On the left window we have Modal results from the default unstressed Modal case. On the right window we have have results from the load sequenced Modal case which includes the effects of P-delta large displacements. Consideration of P-delta with large displacements made a 300%+ difference in fundamental period/frequency results. The catenary behavior of the long flexible pipeline distributed axial load to the anchors, and P-delta accounted for changes in pipeline stiffness due to those axial loads.
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