Question

Electrical strain gauges were applied to a notched specimen to determine the stresses in the notch. The results were εx=0.0019 and εy=0.00072. Find σx and σy if the material is made of carbon steel where E=200GPa, Sy=360 MPa.

Answer 1

Answer:

$\sigma_x=451.8MPa$

$\sigma_y=265.99MPa$

Explanation:

$\varepsilon _x=0.0019$

$\varepsilon _y=0.00072$

Poission's ratio for steel =0.28

We know that

$\varepsilon _x=\dfrac{\sigma _x}{E}-\mu\dfrac{\sigma _x}{E}$

$\varepsilon _y=\dfrac{\sigma _y}{E}-\mu\dfrac{\sigma _x}{E}$

Now by putting the values

$0.0019=\dfrac{\sigma _x}{200\times 1000}-0.28\dfrac{\sigma _y}{200\times 1000}$

$0.00072=\dfrac{\sigma _y}{200\times 1000}-0.28\dfrac{\sigma _x}{200\times 1000}$

So $\sigma_x=451.8MPa$

$\sigma_y=265.99MPa$