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.
P-Delta analysis has been a 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.
Although P-delta effects can have a significant effect on some plant piping layouts, P-Delta analysis with large displacements can be particularly important in analysis of buried and seabed pipelines where lateral or upheaval buckling is a design concern. In the widely referenced paper, “About upheaval and lateral buckling of embedded pipelines”, author Dr. K. Peters emphasizes that rigorous analysis of upheaval and lateral buckling requires “second order solutions” (aka P-delta analysis), and he warns that “piping programs not able to produce second order solutions may not be used in solving upheaval or lateral buckling problems."
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 6.65" 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.
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 other 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.
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, not unlike the effect of tightening a guitar string.
You can create this example with your own piping stress program and compare with CSiPlant by downloading a free fully-functional trial license by clicking the "Trial" link here https://www.csiamerica.com/products/csiplant
The CSiPlant model we used can be downloaded here P-Delta Large Displacement Catenary Example.cpdb