Problem $1-$ Fire analysis of a timber beam

A simply supported timber $($glue$-$lam$)$ beam, $150mm600mm$ in cross section $($C$/$S$),$ is

exposed to a standard ASTM$-$E$119$ fire burning for $60$ minutes, followed by decay at

$625\frac{C}{?}$ hour. The beam, $6m$ in span, is subjected to dead and live loads of $4k\frac{N}{m}$ and $6$

$k\frac{N}{m}$ respectively, and the top of the beam is protected by a supporting deck. Assume the

bending strength $(F_b)=16\mathrm{.}55$MPa, charring rate is $0\mathrm{.}655m\frac{m}{m}in,$ duration load factor for

fire $(k_d)=0\mathrm{.}8,k_{20}=1\mathrm{.}15$ and Vol. factor $C_V=0\mathrm{.}85,$

$($a$)$ Calculate the strength of the beam at $60$ minutes using effective $\frac{C}{S}$ method

$($b$)$ Calculate the strength of the beam at $60$ minutes using reduced properties method

$($c$)$ Calculate the strength of the beam at $60$ minutes using reduced properties, with corner

rounding, method

$($d$)$ Determine fire resistance of the beam using "correlation method" by assuming that the

beam exposed to standard fire only $($no decay phase$).$