Calculate the thickness of a plate to withstand a specified uniform pressure

In summary: The thickness of the sheet will have a large impact on the deflection. The thinner the sheet, the more deflection it will have.The deflection under 100kPa of pressure will be 1.6mm for a 0.5" sheet.
  • #1
Plat
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In exploring the feasibility of constructing a vacuum chamber, I am trying to calculate the thickness of rectangular polycarbonate sheet needed to withstand 100kPa of pressure, given dimensions of 30.5cm by 61cm (12 by 24 inches) and clamped edges.

I have found some calculators that will tell me the deflection given different thicknesses, but what I really need to know is whether actual failure will occur and how much safety margin in thickness will be required to reduce this possibility.

I have found values of Young's modulus to be 13.5 - 21.4 GPa and Poisson's ratio to be 0.3182 - 0.3487 for polycarbonate.I am aware that constructing and using such a chamber presents safety risks and, if I do it, I want it to be as safe as possible and take all responsibility for it.
 
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  • #2
Will this be used just once, or will it be cycled? (Is fatigue an issue or not?) What do you know about the stress-strain curve for this material? Is it brittle, ductile, or what?
You say clamped edges, but absolute rigid clamping is a fiction; just how clamped will it be?
There are a thousand questions that need to be addressed, and this is not a good to start your engineering practice.
 
  • #3
I agree however I am not an engineer, that's why I'm asking.
 
  • #4
The full thickness of the sheet will be comprised of two thinner sheets solvent laminated together. Thus, the chamber will have an inner and outer layer of polycarbonate, with the inner and outer layers alternately overlapping each other at the corners so that the force under pressure is never held only by a bond. The front and back ends will be capped by double-layer sheets which completely overlap the edges where they are located.

So the edges will be solvent-bonded together.

For example, assuming a thickness of 0.5" for each single sheet, the dimensions of each sheet needed to fit together as I have described are as follows:

In inches:

12 x 18 Quantity = 4
13 x 18 Quantity = 4
13 x 14 Quantity = 4

I have calculated a maximum deflection of 1.6mm for a 30cm x 45cm x 2.54cm sheet under 100kPa with simple edge support, which seems reasonable. With my fixed edges, it should actually be much less than that.
 
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What is the formula for calculating the thickness of a plate to withstand a specified uniform pressure?

The formula for calculating the thickness of a plate to withstand a specified uniform pressure is t = (P * d) / (2 * σ), where t is the thickness of the plate, P is the specified uniform pressure, d is the plate's diameter, and σ is the material's yield strength.

What is the significance of calculating the thickness of a plate to withstand a specified uniform pressure?

Calculating the thickness of a plate to withstand a specified uniform pressure is important in engineering and construction, as it ensures that the plate will be able to withstand the expected pressure without deforming or failing.

What factors affect the thickness of a plate to withstand a specified uniform pressure?

The factors that affect the thickness of a plate to withstand a specified uniform pressure include the material's yield strength, the diameter of the plate, and the specified pressure. Other factors such as temperature and external forces may also play a role.

How accurate is the calculation of the thickness of a plate to withstand a specified uniform pressure?

The accuracy of the calculation depends on the accuracy of the input values, such as the material's yield strength and the specified pressure. It is important to use precise and reliable data in order to obtain an accurate result.

Are there any limitations to using the formula for calculating the thickness of a plate to withstand a specified uniform pressure?

Yes, there are some limitations to this formula. It assumes that the plate is perfectly circular and that the pressure is evenly distributed. It also does not take into account factors such as stress concentrations or the effects of temperature. As such, it should be used as a general guideline and other factors should be considered in the design process.

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