Question # $6$

Please refer to the figure below. A load $P$ is supported by a steel pin that has been inserted in a wooden member hanging from a ceiling. Note that $c$ is the vertical distance from the base of the wooden block to the center of the pin. The yield stress of wood is $65$ MPa in tension, $10$MPa in shear, and $70$MPa in bearing, while the yield stress of steel is $110$MPa in shear. Take $b=50mm,c=80mm,$ and $d=20mm.$ Considering all possible failure mechanisms $($wherever appropriate$),$ determine the allowable load $P,$ if a factor of safety of at least $2\mathrm{.}0$ is required for both steel pin and wood member.