Tension only Structure with Hydrostatic Loads

[bigmig]

We are designing a large swimming pool, for lack of a better description, where the walls of the pool are a fabric membrane that contains the fluid. The pool is on the order of 10' deep. Without going into the specifics of what the supporting structure is, I'm having nightmares about solving membrane problem. The membrane is wrapped around a support at the pool base and pool top. The membrane goes over these top and bottom supports, turns a 90 degree turn, and is then attached to a "fixed" support. Directly between these two top and bottom points is a roller, that prevents the membrane from bowing out in one big bulge. With the roller, it now bows out in two varying sized bulges.

The supports are steel pipes that span between larger, primary structure.

I have attached a sketch to clarify.

I am trying to size the supports (top, roller and bottom)without buying a non geometric linearity FEA modeling program, or by performing matrix analysis. Any suggestions on how to simplify this, or a hint on a cheap cable modeling program would be great.

 

[bigmig]

BAretired, thanks for your efforts on this problem. I think that ignoring the vertical component is too conservative. As the membrane reaches the support, it may be totally horizontal, meaning you would be ignoring 100% of the load at this location.

In addition the vertical component is not constant, which is why the membrane forms a curve. A free body at any segment of the membrane in the curved area shows widely varying vertical and horizontal vectors. The vector addition of each of these comes up with a similar tension in the entire system which may increase when load is added to it, but is the same amount from end to end.

chicopee, the entire concept is that the membrane DOES bulge.

A better way to look at things is to make the following conservative assumptions:

1. The water column load is rectangular, not triangular, so the curve is a perfect arch with equal water pressures normal to the surface. The load on each bay would be the average water pressure. The statics for this problem are straightforward.

2. The membrane will stretch under load, pretensioning the upper bay. The stretch will change the deflected shape and tensions through-out. An iteration would find this.

3. The membrane will slip over the middle sheave, changing the deflected shape and tensions throughout until equilibrium is achieved. Another iteration would find this.

4. Leverage effects will multiply loads on the top and bottom purlins by a factor of upto 2x (assumes membrane bows so far, that it creates a hairpin shape over the top and bottom rollers. Since the final deflected shape is unknown, I can assume the worst case (factor of 2) for preliminary design.

 

[bigmig]

BAretired,

Sorry for the confusion in my latest reply....what I meant to say was that ignoring the vertical component would lead to portions of the curve being ignored at the VERTICAL surface, not the horizontal.
Sorry again.

 

[BAretired]

bigmig,

I was not suggesting that the vertical components of pressure be ignored in the final analysis...only as a first approximation.

When pressure is applied normal to the surface of the membrane in its deflected position, the membrane will be in pure tension throughout its length as noted by paddingtongreen. But without knowing the size of the bulge, the vertical component of pressure acts on an unknown area.

Just as a point of interest, why not eliminate the middle support and introduce one single bulge from top to bottom? The tension could be controlled by varying the initial amount of slack in the membrane.

BA

 

[Compositepro]

The middle support will significantly reduce the tension in the membrane. However, it should not be in the middle but 1/3 span up from the bottom. The fabric in these membranes can have a higher tensile strength than steel.

http://www.splashpools.com/Splash_Pools_Manuals.asp

 

[bigmig]

Compositepro is right. As soon as we eliminate the middle support the fabric drapes steeply, increasing the force on the top and bottom purlins. The increases are substantial.

BAretired, by assuming and equal pressure distribution over a span (average pressure at the depth of the span) we know the bulge, and the tension in the membrane based on the elasticity properties of the membrane (given in the manufacturer's cut sheet).

The problem I have now is that the bulge is a function of elasticity, AND membrane translation as it slides over the middle support. Both of which change the geometry and therefore the tension. The entire process iterates to stability. We built a real life model this weekend to better understand it. Now I just have to find a methodolgy that iterates elasticity and translation simultaneously and I will have it solved.

 

[fmorales9475]

I am a little confused with your post, it seem that you are looking at a liner pool which are not very common but for example in Miami, fl the biggest pool 500,000 gal is a liner pool. There are system already in the market for liner pools. Why are you starting for cero... I am a Florida resgisted PE and a CPC which is a Commercial Pool Contractor...

 

[btrueblood]

Interesting post. I provide some food for thought, but no answers here:

Fabric is not a perfect membrane, it has two directions of orthogonality.

About halfway down this page is picture of a freestanding membrane pool that doesn't require purlins for support:

http://sites.google.com/site/grandmaisonavendre/

Partly because the shape is circular (and the shape of the sidewall is controlled by the cut of the fabric), and partly because the top of the pool is a float.

This page (below) shows a system like what the OP is describing, but without a center support purlin.

Both show a differing degree of bulge. One would presume that the degree of bulging is due to differences in supports, and also the degree to which the distribution of stress (laterally vs. vertically) is engineered into the fabric.

 

[bigmig]

fmorales: My pool is 10' deep, holds 500,000 barrels, 300' across and can be assembled and disassembled in only a couple days. If you know of a liner company that can hold that, and a PE to back it up I would love to see their website. What are the specifications on the type of liner you use? Have you ever built a liner pool with a 10' head using that liner?

 

[hokie66]

A pool liner and a tension membrane are two entirely different things.