Stress calculations for acrylic

[bigfish2000]

I need a formula for deriving the required material thickness for an acrylic panel.

The project will involve an acrylic window for a large aquarium. I have included a dimensional rendering.

The maximum design stress must be maintained at or below 800PSI.

The maximum water pressure inside the aquarium will be 2.6662 PSI above atmospheric.

The panel will be used in a vertical position as detailed in the rendering.

The load force (wet) will be on the concave side.

The panel will have concrete support along all four edges as outlined in gray. The viewing portion is shown translucent in the rendering.

The mechanical properties of acrylic are as follows.

Tensile strength: 10,000 PSI
Elongation, Rupture: 4.2%
Modulus of Elasticity: 400,000 PSI

Flexural Strength: 16,500 PSI
Modulus of Elasticity: 475,000 PSI

Compressive Strength: 18,000 PSI
Modulus of Elasticity: 430,000 PSI

Shear Strength: 9,000 PSI

Impact Strength .4ft lbs/in

Rockwell hardness: M-94

If you need any additional information please let me know.

Thank you for the assistance.

 

[AlephZero]

If you think about a horizontal "slice" one inch deep at the bottom, the water pressure is about 2.7 psi (that's about right for 6 feet of water). So the force pushing the panel outwards is 2.7 psi x 1 inch x 120 inches width = 324 pounds.

So if you want to limit the stress to 800 psi, you need a total thickness of 324/800 = 0.4 inches of acrylic, i.e a 0.2 inch thick plate (because there are two sides resisting the force).

Note, that is a very over-simplified calculation. You would also need to consider the stress in the joint between the bottom of the acrylic sheet and the base of the tank, which is a much more complicated issue. Personally I would do a stress analysis using a computer model (i.e. finite element analysis), rather than trying to find a "formula"