MEB$2024/$ MFB$2024$

$4.$ The $45$ strain rosette shown in FIGURE Q$4$ is mounted on a machine element. The following readings are obtained from each gauge: ${}_a=650({10}^{-6}),,{}_b=-300({10}^{-6}),$ and ${}_c=480({10}^{-6}).$

a$.$ Determine the state of strain, ${}_x,{}_y$ and ${}_{xy}$ at that point.

$[6$ marks$]$

b$.$ Using strain transformation equations, determine:

i$.$ the in$-$plane principal strains and their orientation.

$[5$ marks$]$

ii$.$ the average strain, maximum in$-$plane shear strain and its orientation.

$[5$ marks$]$

c$.$ Sketch a Mohr's circle and label the results obtained in part $($b$).$

$[4$ marks$]$