The $d=16-$mm$-$diameter solid rod passes through a $D=21-$mm$-$diameter hole in the support plate. When a load $P$ is applied to the rod, the rod head rests on the support plate. The support plate has a thickness of $b=10mm.$ The rod head has a diameter of $a=32mm,$ and the head has a thickness of $t=10mm.$ The shear stress in the rod head cannot exceed $145$MPa, the punching shear stress in the support plate cannot exceed $110$MPa, and the bearing stress between the rod head and the support plate cannot exceed $135$MPa. Determine the maximum value of $P_{\text{m}\text{a}\text{x}}$ that can be supported by the structure.

Answer: $P_{\text{m}\text{a}\text{x}}=kN$