Answer to Question #297676 in Mechanical Engineering for Harsh

Question #297676

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.

1
Expert's answer
2022-02-17T05:09:03-0500

x=60N/mm2

y=-40N/mm2

xy=50N/mm2

E=200000N/mm2

v=0.3

ϵx=σxvσyE\epsilon_x=\frac{\sigma_x-v\sigma_y}{E}

=60+0.340200000\frac{60+0.3*40}{200000}

=3.6*10-4N/mm2

ϵy=σyvσxE\epsilon_y=\frac{\sigma_y-v\sigma_x}{E}

=(40+0.360)200000\frac{-(40+0.3*60)}{200000}

=2.9*10-4N/mm2

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