# Calculating Material Thickness

1. Mar 18, 2013

### anonME

Right now I am working on a small project. I have a board (made of PVC) that is nearly 3ft long (1ft wide) and supported on each end. Mounted to the board will be various items. To save money and weight I am looking to calculate the minimum thickness I need so that the board can support everything and remain rigid without snapping/sagging/breaking.

Unfortunately I am a little rusty from my college days in regards to how to calculate this.

Any tips or help would be greatly appreciated.

2. Mar 19, 2013

### nvn

anonME: If this is unplasticized, rigid polyvinyl chloride (uPVC), I guess you could assume the allowable flexural stress is Sfa = 18 MPa, at room temperature. Therefore, I guess you could compute the required thickness of your specified board (stress-wise) using t = 0.50(P^0.5), where t = board thickness (mm), and P = total weight, in units of newtons (N), of objects placed on board.

You can include 60 % of the board self weight in parameter P. uPVC density is rho = 1400 kg/m^3.

I think uPVC flexural modulus of elasticity is Ef = 2800 MPa. Therefore, your board midspan deflection, in mm, would be, y = 224.0*P/(t^3), where P = total applied load (N), as defined above, and t = board thickness (mm).

Both of the above equations apply only to the specific dimensions and material given in post 1.

Using the above equations, I currently think you might find that deflection governs over stress.

Last edited: Mar 20, 2013