A mild steel rod of 14 mm diameter and 154 mm length elongates 0.025 mm under an axial pull of 10 kN. What is the Young's modulus of the material?

Concept:

Hook's Law:

σ = E × ϵ 

σ = E × \(\frac{δ l}{l}\)

δl = \(\frac{σ × l}{E}\)

Elongation in the rod when an axial force is applied is given by:

\(δ L = \frac{{PL}}{{AE}}\)

where,

δl = Elongation, σ = Maximum stress, E = Modulus of Elasticity, l = length of bar, P = axial Pull

Calculation:

Given,

Diameter of rod (d) = 14 mm = 1.4 cm, Length of rod (L) = 154 mm = 15.4 cm

Elongation of rod (δl) = 0.025 mm = 0.0025 cm

Axial Pull (P) = 10 KN

Elongation in the rod when an axial force is applied, \(δ L = \frac{{PL}}{{AE}}\)

⇒ \(E = \frac{{PL}}{{\delta L × A}}\)

⇒ \(E = \frac{{10000 × 154}}{{0.025 × \frac{\pi }{4} × {14^2}}}\)

E = 400207 N/mm2

E = 4 ×10⁵ N/mm2