$9$

Required Information

Two full$-$sized a $c-mm$ boords are nailed to $8bc-mm$ board and the resulting beam that is subjected to o vertical shear of $1500N.$ Knowing thot the sllowable shesring force in esch nail is $135N,$ detemine the allowable spocing sthat can be used between each poir of nsils. Asume $=45mm,b=45mm$ and $c=90mm.$

Moment of Inertia

The centroidsl moment of inertio of the cross$-$section, about the $z-$sxis, is given as $z_z=90\frac{(135{)}^3}{12}(m{m}^4)=18\mathrm{.}453{10}^{-6}(m^4)$ First moment of area

z

For the cutout generated by cutting through only the nails, the first moment of the ares obout the $z-$axis is given as $Q_z=459045(m{m}^3)=1,823{10}^{-4}(m^3)$

Allowable spacing

The sllowable spscing of the nsils is $,(mm$ and is a