Total extension

Question

A steel bar is 900 mm long; its two ends are 40 mm and 30 mm in diameter and the length of each rod is 200 mm. The middle portion of the bar is 15 mm in diameter and 500 mm long. If the bar is subjected to an axial tensile load of 15 kN, find its total extension. Take E = 200 GN/ m² (G stands for giga and 1G = 10⁹).

Answer 1

Load, P = 15kN

Area, A₁ = (Π/4) × 40² = 1256.6 mm² = 0.001256 m²

Area, A₂ = (Π/4) × 15² = 176.7 mm² = 0.0001767 m²

Area, A₃ = (Π/4) × 30² = 706.8 mm² = 0.0007068 m²

Lengths: L₁ = 200mm = 0.2m, L₂ = 500mm = 0.5m and L₃ = 200mm = 0.2m

Total extension of the bar:

Let δL₁, δL₂ and δL₃, be the extensions in the parts 1, 2 and 3 of the steel bar respectively. Then,

Total extension of the bar

= 0.0002454 m 

= 0.2454 ram

Hence total extension of the steel bar = 0.2454 mm.