It's Finally Springtime! Applying Nonuniform Hydraulic Pressure Using FEMAP
- John Parsons
- May 17, 2025
- 4 min read
Updated: May 18, 2025
It has finally stopped snowing in upstate New York; that means it is officially springtime.
I think we can all agree that the best type of pool is one owned by your kindly neighbor.
Let's examine the cable tension load in a high-end on-ground or above-ground wooden swimming pool using FEMAP/NX Nastran.
Crestwood On-Ground Pool www.crestwoodpools.com
High-end on-ground or above-ground wooden swimming pools rely on stainless steel cables to hold back the hydraulic pressure generated by the water in the pool.
Let's look at an 18-foot (5.486-meter) diameter pool that is filled with 3.6 feet (about 1 meter) of water.
Because this pool is round, we can take advantage of its symmetry and look at only a single board on the circumference of the pool. The geometry for this model can be downloaded directly from this article.
Notice that the geometry has been split so that we can apply constraints and connect the cables to the solid board.
We can mesh the solid cedar board in this model using solid linear elements that have a modulus of elasticity of 884,730 psi and a Poisson's ratio of 0.35.
The cables are meshed as rod elements that have a modulus of elasticity of 2.3E7 psi and a Poisson's ratio of 0.3.
To constrain our cross section of the pool, we have:
1) Applied an X-axis symmetry constraint along the length of the board.
2) Applied a Z-axis constraint to the inner edge of the board.
3) Created a new coordinate system (Coordinate System 2) that is rotated +1.45 degrees from the global coordinate system. This new coordinate system aligns with the start of the three cables. The start of each cable is constrained in the X-axis of Coordinate System 2.
4) Created a new coordinate system (Coordinate System 3) that is rotated -1.45 degrees from the global coordinate system. This new coordinate system aligns with the end of the three cables. The end of each cable is constrained in the X-axis of Coordinate System 3.
To connect our rod elements to our solid linear elements, we added Rigid Body Elements (RBE2) using the Mesh > Connect > Closest Link command. Please note that the nodes on the rod elements were precisely located adjacent to the nodes of the solid linear elements. These RBE2 elements will be connected in all degrees of freedom except Rz; this allows the rod elements to expand and contract freely.
Now, let's get to the true purpose of this article: how to fill this pool with water, which is significantly cheaper than paying your local municipality.
Let's make a new coordinate system named "Fluid Loading" and place it at the waterline of the pool. We can use the Load on Surface command to apply a pressure load to all surfaces below the waterline. For this pressure load, we will select Variable in the Method box. This will bring up the "Advanced Load Method" dialog box.
The variable for this equation-based load will be "!x"; this represents the distance from the origin of the Fluid Loading coordinate system along the X-axis. We will multiply "!x" by 0.036127, the density of water in lb/in^3. Please be careful with units. This model is in inches, so the units work out well, but this will not always be the case. Lastly, set your Definition Coordinate System to the newly created "Fluid Loading" coordinate system.
With a variable pressure load such as this, it is best to double-check that it has been applied properly to the model. You can create a contour plot of the pressure load using the Model > Output > From Load command.
It looks like our hydraulic pressure load was applied correctly and our constraints appear to be grounded, so let's solve our model using the NX Nastran solver.
This linear model solves in under 6 seconds.
Let's view our results.
The pool wall displaces less than 1/4 inch radially with the water load applied.
The peak tension in the bottommost cable is 2,054.2 lbf.
The maximum principal stress in the cedar board is only 370 psi.
The 1/4-inch cable that we selected for this pool is rated for a tensile load of 6,400 lbs; this cable looks like a good selection for the hydraulic pressure generated by the water in the pool.
For those who are curious, I set up a similar FE model using ANSYS. In this FE model, the board was modeled with shell elements, and the connection between the cable and board was modeled with frictionless contact. The ANSYS software identified the peak tension in the bottommost cable as 2,061.5 lbf, resulting in a difference of less than 0.36% from the results obtained using FEMAP/NX Nastran.
Let's review what we learned.
1) The weather in upstate NY is rarely good and owning a pool may not be a great investment.
2) Applying hydraulic pressure is fairly simple in FEMAP using equation-based loading. (Please note that there are other ways to apply nonuniform pressure loads, such as data tables and data maps within FEMAP; we will cover these in the future.)
3) Taking advantage of symmetry and using constraints wisely can create a grounded and very efficient FE-model.
Thank you for taking the time to read this article. Please let me know if you have any additional questions or ideas for future articles.
John Parsons
Analyst
MESim LLC
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