Problem $1$: $[$Required$]$

The strain rosette is mounted on a beam. The following readings are obtained for each gauge: ${}_a$

$=480{10}^{-6}i\frac{n}{i}n,{}_b=200{10}^{-6}i\frac{n}{i}n,{}_c=75{10}^{-6}i\frac{n}{i}n.$ Determine $($a$)$ the in$-$plane principal

stresses and their orientation, and $($b$)$ the maximum in$-$plane shear stress and average normal stress.

Show on a properly oriented state of stress block. Use Mohr's circle to determine the principal

stresses. $($NOTE: $E=29,000$ksi,$v=0\mathrm{.}32,G=11,000$ksi $)$