A steel bar 100 mm long and having a square cross section 20 mm on an edge is pulled in tension with a load of 89,000 N and experiences an elongation of 0.10 mm. Assuming that the deformation is entirely elastic, calculate the elastic modulus of steel. Give your answer in GPa

The elastic modulus of steel is 222.5 GPa.

Explanation:

Elastic modulus = stress/strain

Stress = Force (F) / area (A)

Strain = extension (e) / length (L)

Elastic modulus = FL/Ae

F = 89,000 N

L = 100 mm = 100/1000 = 0.1 m

A = side of square^2 = (20/1000) ^2 = 0.02^2 = 4*10^-4 m^2

e = 0.1 mm = 0.1/1000 = 1*10^-4 m

Elastic modulus of steel = 89,000*0.1/4*10^-4 * 1*10^-4 = 8900/4*10^-8 = 222.5*10^9 Pa = 222.5 GPa