Problem $3(9$ points$)$

$3\mathrm{.}1$ A steel bar with a diameter of $12$ mm is subjected to a direct shear test. The maximum force applied before failure in the single shear condition is recorded as $5000$ kg $.$ Calculate the shear stress in the steel bar under single shear.

$3\mathrm{.}2$ If the same bar is subjected to double shear, and the maximum force applied before failure is $8000$ kg $,$ calculate the shear stress in the double shear condition.

$3\mathrm{.}3$ A wood specimen with dimensions, parallel to the applied force, $50$ mm x $50$ mm is tested for shear strength parallel to the grain. The maximum load applied before failure is $1500$ kg $.$ Calculate the shear strength of the wood.