A flat rod of width $b-60mm$ and thickness $t-10mm$ is working in tension with a load P: The rod is attached to the support by a pin of diameter $d,$ which is the same size as the hole in it$.$ The tensile safety stress in the net cross$-$section of the rod is $140$MPa, the shear safety stress in the pin is $80$MPa, and the safety stress of the contact surface between the pin and the rod is $200$MPa.

Determine the pin diameter $d$ at which the $P$ load will be greatest.

Determine the value of the Pmats load corresponding to this value of the diameter.