Question

A steel rod has a radius of 10mm and a
length of 1m. A 100KN force stretches it
along its length. Calculate (a) stress (b)
elongation and (c) percentage strain on the
rod. Y of steel is 2.4x1012 dyne/cm

Answer 1

given a steel rod:
Radius = r = 10 mm = 0.010 m.
Length L = 1 m.
Tensile Force = F = 100 kN.
Young's Modulus = Y = 2.0 &* 10¹¹ Nm⁻²

a) Stress = Force/cross sectional area
σ = F / A
= 100,000 /(π 0.010²) Pa
= 318.309 MPa

b) Y = (F/A) / (ΔL/L)
Elongation ΔL = L F / (A Y)
= L σ / Y
= 1 * 318.309 * 10⁶ / 2.0 * 10¹¹ m
= 1.591 mm

c) Percentage elongation : ΔL/L * 100 = 0.1591 %