A simply supported beam with span, $L=5m,$ is subjected to a uniformly distributed load of intensity, w $(k\frac{N}{m}),$ refer to Fig. $2$a$.$ The $400mm$ deep composite beam was constructed by bonding together $50mm$ thick timber laminates $($plates$),$ each of the full $200mm$ width and $5m$ length, as shown in Fig. $2$b$.$ The width of the beam is also $200mm.$ Epoxy resin used has a shear capacity and bending capacity of $20$MPa and $100$MPa, respectively. Assume the thickness of epoxy resin to be insignificant. Timber plates used are of C$16$ grade of shear and bending capacity of $1\mathrm{.}6$MPa and $8$MPa, respectively.

a$.$ Determine the maximum uniformly distributed load, $w$ that can be carried by the beam assuming that the failure is governed only by the shear capacity. le shear stress reaching the shear capacity.