A standard ISO metric thread for a screw with a nominal diameter d $=10$mm and a pitch P $=1\mathrm{.}5$mm has a tread friction factor $=0\mathrm{.}12.$ Determine the following items:

a$)$ The pitch diameter $,$

b$)$ The stress diameter and the stress area $,$

c$)$ The thread angle,

d$)$ The thread friction angle,

e$)$ The thread friction torque for a screw force $=27\mathrm{.}5$kN

f$)$ The total tightening torque for a screw head diameter of du $=1\mathrm{.}3$d and a head factor $=0\mathrm{.}15.$