$($a$)$ Derive the equations expressing the elastic strains in $xYZ$ directions in terms of elastic stresses,

elastic modulus, and Poisson's ratio for a cube element.

$($b$)$ For the system of stresses shown below, calculate the strains in $x,Y$ and Z directions.

$)$

${}_1,x,100$

${}_2,y,75$

${}_3,z,200$derive the equations expressing the elastic strains in XYZ directions in terms of elastic stresses, elastic modulus, and poisons ratio for the cube element