A $20-$ft simply supported wood beam, having the measured dimensions of $9\mathrm{.}5in.17\mathrm{.}5in.,$ is subjected to a uniformly distributed load of $1\mathrm{.}75\frac{k}{f}t($not including the beam self$-$weight$).$ The adjusted allowable flexural strength of the wood is taken as $1\mathrm{.}13$ksi, and the corresponding flexural modulus is $1296$ksi. The beam will be strengthened by externally side$-$ bonded steel plates $($Yield stress $=50$ksi, modulus of elasticity $=29,000$ksi, factor of safety $=1\mathrm{.}67)$ as shown below.

$1-$Determine the minimum thickness of the steel plates so that beam stresses$/$strains do not exceed the allowable stress$/$strain$.$

$2-$Calculate the percent decrease in the beam maximum deflection resulting from the stren

gthening scheme.