Stacking sequence & moment of inertia

[vinhermes]

Hello,

Quick question fairly simple for most of you but I am confused.

In the following sentences, please assume that E is the Young Modulus (MPa), I the second moment of inertia (mm4), t the thickness in mm and h the distance of the ply from the neutral axis.

To determine the EI value of a laminate, that allows one to improve the stacking sequence, one obvioulsy needs to know the E value( which I am happy to determine) but also the I value.

I know that it can be assumed as the sum of the ((Ei^3/12)+(tihi)2.

Which makes it very easy to find. But I am actually making a spreadsheet, that I will post if some of you need once finished and checked, and I can't find the relative height of a ply from the neutral axis. At least I can't make the process automatic as

Do you see my problem? Basically the NA is at half the laminate thickness but the height depends on the n° of ply and the thickness of the ply.

Is there a mean to find the I from a baseline (say the inner ply) and then convert it as a usual I from a neutral axis?

I hope I have been clear enough for you to help me.

Thanks a lot by advance. Vincent

 

[Onda]

You need to find the position of neutral axis and then using the Huygens theorem you could find the Inertia relative to Neutral axis.
To find the neutral axis of a set of layers:
Assuming a strip of one units width:
Sum(E*thk*1*thk)/Sum(E*thk*1)

In the attached spreadsheet you can find an example.

Onda

 

[vinhermes]

Thank you so much. My spreasheet for the skins is ready. i will include the cores as soon as possible and post it as I am sure this could serve other persons. I double check it with the Bureau veritas free software and so far so good.

Onda, thanks a lot. Vincent