PROBLEM $2$:

Three $100-$mm$-$by$-150$mm planks arranged together are supported by

bolts $0\mathrm{.}4m$ apart. Load $P$ as shown causes a maximum flexural

stress of $12$MPa. The bolts are tightened to a tension of $140$

MPa, and the coefficient of friction between the planks is $0\mathrm{.}40.$

Assume the shear between the planks is transmitted by friction

only.

a$.$ What is the value of load $P$ in $kN?$

b$.$ Determine the maximum bolt diameters $($mm$).$