How to Calculate Young's Modulus

Young's modulus is a measure of the stiffness of an elastic material and may also be referred to as the tensile modulus or elastic modulus. There are actually several different elastic moduli, but the term "elastic modulus" usually refers to Young's modulus unless otherwise specified. Young's modulus can be calculated from the tensile stress and tensile strain, and it can also be measured experimentally.

Things You'll Need

• Scientific calculator

Instructions

1. Define Young's modulus mathematically. This can be given as E = s/t where E is the value of Young's modulus, s is the tensile stress and t is the tensile strain. The higher the value of Young's modulus, the stiffer the material.

2. Calculate the tensile stress of a cross section. Tensile stress can be given as s = F/Ao where s is the tensile strain, F is the force that is applied to the material and Ao is the original area of the cross section before the force was applied.

3. Express the tensile strain. This gives t = dL/Lo where t is the tensile strain, dL is the change in the object's length and Lo is the object's length before applying the stress.

4. Derive Young's modulus experimentally. By substituting the values obtained in step 3 into the equation for Young's modulus, we have:
   E = s/t = (F/Ao) / (dL/Lo) = (FLo) / (Ao/dL).
   Young's modulus is therefore expressed in terms of force per unit area, typically pascals.

5. Use Young's modulus to calculate the force that an object exerts when it is under a given strain. From step 4, we have:
   F = E(Ao)(dL)/Lo.

References

• Engineering ToolBox