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CSiPlant offers P-Delta analysis, including P-Delta with large displacements. P-Delta analysis, also known as second-order geometric nonlinearity, involves the equilibrium and compatibility relationships of a structural system loaded about its deflected configuration. It also accounts for real world changes to element stiffness due to axial loads, as tension loads increase lateral stiffness of elements, while compression loads reduce lateral stiffness. The tightening of guitar strings is a good example of P-delta effects changing element stiffness. These changes in element stiffness affect piping and frame resistances to lateral loads.   

P-Delta analysis has been a near-mandatory requirement in structural design codes for many years due to the importance of its effects in design calculations. However, piping stress models have traditionally ignored P-Delta effects, possibly because most older generation piping stress software programs are incapable of P-Delta analysis.

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FRP/GRP piping and jacketed pipes are are also susceptible to buckling from compression load buildbuilt-up compressive load due to axial friction. Piping ball joints, flexible hoses, and swivel joints can involve large displacements which need to be properly accounted for in design calculations. 

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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


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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