During experiments, strain gages $($which measure the strain along their axis$)$ are often

used to determine the state of strain in a test specimen. All the in$-$plane strain

components can be found by using three gages in a so$-$called rosette as shown.

a$)$ Find ${}_x,{}_y$ and ${}_{xy}$ if the measured strain gage values are ${}_1=0\mathrm{.}0001,{}_2=0\mathrm{.}0005,$

${}_3=0\mathrm{.}0002.$ Draw an exagerated sketch of a deformed block of material.

b$)$ Suppose that all out$-$of$-$plane strains are zero. Use Mohr's circle to find the

principal strains and principal directions and the maximum in$-$plane shear strain.

Draw the rotated physical element in each case.