Nonlinear P-delta effects in piping/pipeline stress analysis

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.  

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 since 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 soil friction causes built-up compression forces that can make lateral or upheaval buckling 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."

FRP/GRP piping and jacketed pipes are are also susceptible to buckling from built-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. 

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 ("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 long span 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.

Below is the Modal load case which is load sequenced to be based on the end state of the GR-PD load case which includes the effects of P-Delta with large displacements.

Consideration of P-delta effects with CSiPlant requires only a couple of mouse clicks and a small amount of additional analysis time for a typical model, so there’s no reason not to consider P-delta effects to ensure more realistic design calculations. You can create the example above with your own piping stress program and compare with CSiPlant. Download a free fully-functional CSiPlant 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

We welcome users of other piping stress software to compare results from their program to results from CSiPlant. If your piping stress program is incapable of properly considering second order P-delta effects, then results may not be realistic in some (many?) designs, particularly with analysis of buried and subsea pipelines.