Question

At a particular point in a structural member a two dimensional stress system exists where sigma x=60N/mm^2 sigma y=-40N/mm^2 and shear stress (xy) =50N/mm^2 if young's modulus =200000N/mm^2 and poisson's ratio =0.3 calculate the direct strain in the x and y directions and the shear strain at the point.

Answer 1

x=60N/mm²

y=-40N/mm²

xy=50N/mm²

E=200000N/mm²

v=0.3

$\epsilon_x=\frac{\sigma_x-v\sigma_y}{E}$

=$\frac{60+0.3*40}{200000}$

=3.6*10^-4N/mm²

$\epsilon_y=\frac{\sigma_y-v\sigma_x}{E}$

=$\frac{-(40+0.3*60)}{200000}$

=2.9*10^-4N/mm²