# Calculate Modulus of Elasticity

#### Hazard007

Hi, need help with an equation.
A titanium bar 8.75 mm in diameter will stretch from a 150 mm length to a 150.5 mm length when a force of 23 kN is exerted. Calculate the modulus of elasticity of the alloy.
My lecture teacher has not provided a formula regarding how to calculate the modulus of elasticity, apart from a strain formula. I've tried individually to work it out and its my final question. Very much appreciated if i can get a response.

#### studiot

This is really Physics, but here you go

The elastic modulus is also called Young's Modulus and usually given the symbol E

$$\displaystyle E = \frac{{Stress}}{{Strain}}$$

Now

$$\displaystyle Stress = \frac{{Force}}{{X\sec tionArea}}$$

and

$$\displaystyle Strain = \frac{{ChangeofLength}}{{OriginalLength}}$$

Since you have the force and the rod diameter you can calculate the (tensile) stress.

Also since you have the original length and the extension (change of length) you can calculate the strain.

#### Hazard007

Thank you, i worked it out.
So you stress= F/A= 23x10^3/[3.14/4 (8.75 x 10 ^-3) ^2]
= 382.49 MPa
strain= 150.5-150/ 150 = 3.33x 10 ^-3

E= 382.49x 10^6/
3.33x 10^-3
= 115 x 10^9 or 115 GPa

Well done.