Question

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

Answer 1

The elastic modulus of steel is 222.5 GPa.

Step-by-step 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