Find out maximum stress and elongation of the bar:

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

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

length   L = 2m

axial load

P = I0KN

Density of steel     σ= 7850 Kg/m3

E = 200 GN/m2

As                        δL = PL/AE +   L²/2E

= (10 × 103 × 2)/(4 × 2.5 × 10^-4  × 200 × 10⁹) + (7850 × 9.81 × 22)/(2 × 200 × 10⁹)

10 kN

= 0.0001 m                                                             

= 0.1 mm stress
( σ _max) = E × strain

= 200 × 10⁹  ×  δ L/L =200 × 10⁹  × (0.0001/2) = 10.08 mpa  .......ANS