Problem $1-$ Fire analysis of a $RC$ beam

A concrete beam of span $6m$ is exposed to a standard ASTM$-$E$119$ fire burning for $120$ minutes,

followed by decay at $625C/$hour$.$ The beam size is $200mmx450mm$ and the top surface is

protected from fire by the concrete floor slab. The beam has four $25mm$ diameter reinforcing

bars at four corners and the clear cover to the reinforcing bars is $40mm.$ The stirrups are of $10$

$mm$ dimensions and the compressive and tensile strength of concrete and steel are $40$MPa and

$400$MPa respectively.

$($a$)$ Calculate the flexural capacity of the concrete beam after $120$ minutes. Use Wickstrom's

method for calculating the temperatures in rebars and concrete.

$($b$)$ Repeat the analysis using Kodur et al$.$ approach $*.$

$($c$)$ Plot the fire and rebar temperatures in a graph $($both from $($a$)$ and $($b$)).$