Answer to Question #127818 in Mechanical Engineering for Arthur

Question

A uniaxial steel bar is initially 250mm in length with a square cross-section of 50mm x 50mm. The modulus of elasticity is 200 GPa and a poisson's ratio is 0.32 Determine the change in dimensions of the bar when carrying tensile load of 600kn.

Answer 1

Steel bar:

Length(L)=250mm, bredth(B)=50mm and Height(H )=50mm

Modulus of elasticity(E)=200GPa=2x10⁵ N/mm²

Poissons ratio( μ)=0.32

Tensile Load(P)= 600000 N

$Change in length(\Delta L)=\frac{PL}{AE}$

$\Delta L=\frac{600000\times 250}{50\times 50\times 200000}=0.3mm$

Strain along length(e_L)=(change in length)/(Length)=0.3/250=1.2x10^-3

Change height(ΔH)=change in bredth(ΔB)=-(μxe_L)xH=-0.0192mm(-ve sign indicates reduction in dimension)