# How to calculate Young's modulus of layered cross section

Given a rectangular prism that is composed of various horizontal layers made of different materials, how can one calculate the modulus of elasticity? Currently the materials used and their respective ratios have not been specified. We wish to determine this information using the results of trying to find the modulus.

Nidum
Gold Member
If in the end you want to work out stresses and deflections a piecewise method is needed using the individual Young's moduli of the different layers .

SteamKing
Staff Emeritus
Homework Helper
Given a rectangular prism that is composed of various horizontal layers made of different materials, how can one calculate the modulus of elasticity? Currently the materials used and their respective ratios have not been specified. We wish to determine this information using the results of trying to find the modulus.
It depends on what you are trying to accomplish.

If you want to calculate the bending stresses in a beam made of this layered material, there is a way to calculate a weighted-modulus if you know the moduli of the individual components.

Other than this, we'll need further information.

The end goal is to calculate the buckling load of the overall material. Given a specific list of materials and their elastic moduli, is it possible to mathematically set up a process to find the modulus of the overall structure?

I have looked into the Rule of Mixtures, but I am not sure if it is applicable here.

Nidum
Gold Member
An expression can be derived for a beam of specific dimensions and layer construction but there are difficulties in arriving at a truly meaningful value .

In a laminated beam the strength and flexibility of the bond between layers has to be included .

Could someone please elaborate on the procedure and how someone should go about it?

Chestermiller
Mentor
Given a rectangular prism that is composed of various horizontal layers made of different materials, how can one calculate the modulus of elasticity? Currently the materials used and their respective ratios have not been specified. We wish to determine this information using the results of trying to find the modulus.
You assume that, since all the layers are glued together, they all experience the same in-plane strain. Once you know the strains, you can calculate the stresses in each layer, and average these to get the average modulii. If it is a uniaxial unconstrained deformation, you first solve for the strain that makes the average transverse stress zero, and then determine the average axial stress.

Information like this should be available in the Composite literature.

Chet