Question

A rectangular bar of uniform cross-section 4 cm × 2.5 cm and of length 2 m is hanging vertically from a rigid support. lt is subjected to axial tensile loading of 10KN. Take the density of steel as 7850 kg/m³. And E = 200 GN/m². Find the maximum stress and the elongation of the bar.

Answer 1

Data given,cross sectional area A = 4 cm. × 2.Scm.

length L = 2m

axial load

P = 10KN

 density of steel 

ρ = 7850 Kg/m³

E = 200 GN/m²

Since δL = PL/AE + ρL²/2E

= (10 × 10³ × 2)/(4 × 2.5 × 10^–4 × 200 × 10⁹)

+ (7850 × 9.81 × 2²)/(2 × 200 × 10⁹)

= 0.0001 m

= 0.1 mm

stress (σ_max) = E × strain

= 200 × 10⁹ × δL/L =200 × 10⁹ × (0.0001/2) 

= 10.08 mpa