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

`\sigma_x=451.8MPa`

`\sigma_y=265.99MPa`

Step-by-step explanation:

`\varepsilon _x=0.0019`

`\varepsilon _y=0.00072`

Poission's ratio for steel =0.28

We know that

`\varepsilon _x=(\sigma _x)/(E)-\mu(\sigma _x)/(E)`

`\varepsilon _y=(\sigma _y)/(E)-\mu(\sigma _x)/(E)`

Now by putting the values

`0.0019=(\sigma _x)/(200* 1000)-0.28(\sigma _y)/(200* 1000)`

`0.00072=(\sigma _y)/(200* 1000)-0.28(\sigma _x)/(200* 1000)`

So
`\sigma_x=451.8MPa`

`\sigma_y=265.99MPa`