## Chapter 1

## Q. 1.22

## Step-by-Step

## Verified Solution

It is plane stress problem where,

\varepsilon_x=\frac{0.05}{100}=0.005 mm / mm , and

\varepsilon_y=\frac{0.01}{50}=0.0002 mm / mmSubstituting in Eq. (1.231),

\sigma_x =\frac{E}{1-\mu^2}\left(\varepsilon_x+\mu \varepsilon_y\right)=\frac{200000}{1-0.3^2}(0.0005+0.3 \times 0.0002) =123.07 MPa

\sigma_y =\frac{E}{1-\mu^2}\left(\varepsilon_y+\mu \varepsilon_x\right)

=\frac{200000}{1-0.3^2}(0.0002+03 \times 0.0005) =76.92 MPa