Find stress on strap of vinyl

[zjn12385]

I am trying to calculate the stress applied to a 1' x 2' piece of vinyl. The vinyl is welded to the bottom of an above ground pool and is used to hold the leg support, which holds up the side of the pool, in place. There is a leg support every 4'. A picture of the pool can be found at www.splashpools.com. I think I've figured out how to calculate the force exerted on the side of the pool, but I don't know how this stress transfers to the leg support. The leg inserts into a SS tube, which sits inside the top white vinyl sleeve, and can pivot. I assumed that the strap could be modeled like a wire connecting the leg to a fixed wall and then summed the moments about the point at which the leg connects to the strap.

The height of the top rail is 51.5".
The horizontal distance from the pool side to where the leg sits on the ground is 9".
The leg is propped up 2" by a plastic block.
I assumed that the rounded portion of the pool was equivalent to a circle with a 13" radius and that the rest of the wall is completely vertical.
The pool normally has 4' of water in it.

 

[nvn]

zjn12385: Why did you sum moments about the ground-level connecting pin (i.e., about the point at which the leg connects to the vinyl buttress strap via stainless steel rings and a connecting pin)? What did that accomplish?

Instead, sum horizontal forces. The horizontal compressive force, Fx, applied to the top of the buttress leg, is equal to the vinyl buttress strap tensile force. Assume the vinyl buttress strap is horizontal. Once you obtain this vinyl buttress strap tensile force, divide it by the vinyl buttress strap cross-sectional area [A = (305 mm)*t, where t = vinyl strap thickness], to obtain the vinyl buttress strap stress. Afterwards, sum moments about the ground-level connecting pin, to obtain the vertical tensile force applied to the pool wall.

Now the question becomes, what is the value of Fx? This is possibly a rather difficult question, and depends on how much of the hydrostatic force on the swimming pool wall is (a) carried directly by membrane tension in the bottom sheet (floor) of the swimming pool, and (b) carried by membrane tension in the adjacent pool walls (via the pool-sleeve steel top rail). Any horizontal hydrostatic force not carried directly by the pool floor, nor by the adjacent pool walls, is the horizontal force transmitted to the buttress legs, which is equal to the tensile force in the vinyl buttress straps.

 

[zjn12385]

What did it accomplish? Not a darn thing. I had forgotten that forces act uniformly across an object so I wasn't sure how to combine the forces.

I used the equation F = 0.5*(rho)*g*(H2^2 - H1^2)/cos(theta) to calculate the hydrostatic forces acting on the pool wall, where
(rho) = density
g = acceleration due to gravity
H2 = the depth of the water at the bottom of the area the hydrostatic forces are acting upon
H1 = the depth of the water at the top of the area the hydrostatic forces are acting upon
(theta) = the angle between the y-axis and the pool wall

I modeled the rounded portion of the pool wall like an 80-sided polygon and used Google SketchUp to figure out my horizontal and vertical distances for each section. I then multiplied each section's force by the cos(90 - theta) in order to get the horizontal component of each force and summed these all together. I also assumed that each footstrap supported a 4 ft section of the pool wall. I calculated a horizontal force of approximately 2000 lbf acting on each 4 ft section of the pool wall.

I was using the above as Fx at the top of the leg. From your previous post, nvn, I assume this is incorrect, but then how do I calculate the distribution of the horizontal force between the pool floor and the footstraps? Also, how do I calculate the stress on a section of the pool wall due to the hydrostatic force acting in the z-direction when the section is being held rigid by equal but opposing forces acting in the +/- x-direction and +/- y-direction?

 

[nvn]

zjn12385: I would think the horizontal hydrostatic force acting on the pool wall, per unit of wall length, is f = 0.5*rho*g*(h2^2 - h1^2)*cos(theta), where theta = angle between a vertical axis and the pool wall. But perhaps I do not understand your coordinate system (CS). Is the vertical axis of your CS the y axis? Or the z axis? (And your CS axis perpendicular to the long pool wall is the x axis, right?)

Unfortunately, you will not be able to compute the force applied to the steel tube buttress leg (nor the vinyl buttress strap) using hand calculations, because the problem is statically indeterminate. Therefore, you will need to either (a) measure the tensile force in the vinyl buttress strap using a spring scale, or (b) perform a finite element analysis (FEA) of the pool (using a pool quarter model). Ansys is probably generally the best FEA program (although you can use any FEA software). You cannot perform the FEA calculations yourself, because your given problem involves plate analysis.

I think you might be able to assume the soil horizontal coefficient of friction (COF), mu, is zero. However, this assumption is something to be contemplated, to determine if mu = 0 is conservative or not, for this analysis. But unless you hear otherwise, go ahead and assume mu = 0. Also, assume the soil surface is rigid.

You will need the tensile modulus of elasticity (E), and Poisson ratio (nu), for your particular vinyl material or fabric. And it will be good if you have the fabric tensile yield strength (Sty). You will also need all cross-sectional dimensions, and the vinyl thickness(es), both for the pool and for the vinyl buttress strap. Do you have all of this data yet, which you could post? Preferably use standard units (N, mm, MPa).

 

[zjn12385]

If I understand that equation correctly, then it finds the force that is perpendicular to the plane it is acting on. You are correct that this would produce the horizontal force on the vertical wall of the pool. But once you reach the rounded portion of the pool wall, the hydrostatic force is no longer horizontal (unless I'm wrong). This is why I multiplied the hydrostatic force by the cos(90-theta) to find the resulting horizontal force. For the vertical portion of the wall, I said theta equaled 90, effectively canceling it out.

y-axis: height of pool
x-axis: parallel to the pool wall
z-axis: direction of hydrostatic force (out of pool)

I do not have access to a FEA program. Who can I consult with that could help me out?

I do not have the data you requested on hand, but I will try to post it later.

 

[nvn]

zjn12385: Angle theta is defined as, theta = angle between y-axis and the pool wall. Therefore, the horizontal hydrostatic force on the pool, per unit of wall width, is as I listed in post 4, regardless of whether the pool wall is vertical or not.

Post the data described in post 4 whenever you obtain it, and then allow a few weeks thereafter for a response.

 

[zjn12385]

Sorry for the wait. I had been searching for that data, but came up empty handed so I tried calculating it myself. I tested the vinyl material with a Tinius Olsen Tensile Machine and came up with the following values. The material is stronger in the machine direction than it is across the width of the roll.

Width of Roll:
Modulus of Elasticity = 366.27 MPa
Poisson's Ratio = 0.29
Tensile Yield Strength = 1842 N

Machine Direction:
Modulus of Elasticity = 557.58 MPa
Poisson's Ratio = 0.12
Tensile Yield Strength = 1918.8 N

I haven't been able to find anything to compare these values to, so let me know if they seem incorrect. The thickness of the material for both the strap and the pool is approximately 0.762 mm and the thickness at the welds is approximately 1.397 mm.

I am not sure what cross sections to give you. The pool is made up of several panels that are welded together; do you need to know the dimensions of each panel and how they fit together? I am primarily concerned with the stresses across the welds, specifically where the buttress straps connect to the pool floor and where the light blue top strip of the pool wall is folded back on itself and welded. I am hoping to be able to simulate these stresses on a 101.6 mm x 787.4 mm welded test sample for quality control.

 

[nvn]

zjn12385: The cross section information you provided for the pool walls and floor, and buttress strap, is adequate. We need the dimensions of each pool panel (i.e., walls and floor). I think I do not need to know how the panels fit together, so skip that. We also need the cross-sectional dimensions of the steel tube top rail (inside the pool top sleeve), and the cross-sectional dimensions of the steel tube buttress leg.

The shape of the buttress leg is a U shape. If the two upright sides of the U are slanted, somewhat like the sides of a V, then we need to know the angle of the upright, measured from the U base axial centerline. E.g., the sides of a true U (nonslanted uprights) would be 90 deg (i.e., perpendicular to the U base).

We also need the centerline distance between the U upright upper tips.

Also, you can give us the centerline bend radius of the U corners, if you wish, although it is not required. If you omit this bend radius, we can assume a sharp angle (miter).