Problem No$.2$ Flexural strength in Steel Design $($Answere with complete solution completely thanks..$)$

A simply supported beam having a simple span of $8$ m must support a uniformly distributed service load of $10$ kn$/$m including its own weight.

A$36$ steel is used.

Properties of the steel beam:

$A=10452m{m}^2,t_w=10\mathrm{.}03mm,Z_x=2196{10}^{3}m{m}^3$

$d=598\mathrm{.}68mm,F_y=248$MPa,$r_x=231\mathrm{.}39mm$

$b_f=177\mathrm{.}93mm,I_x=562{10}^{6}m{m}^4,$

$t_y=12\mathrm{.}33mm,I_y=12{10}^{6}m{m}^4,$

a$.$ Determine the allowable bending stress using elastic design $($ASD$).$

b$.$ Determine the safe uniform live load it could support using ASD method due to its flexural strength.

c$.$ Determine the safe uniform live load it could support using plastic design method due to its flexural strength. $U=1\mathrm{.}2DL+1\mathrm{.}6LL$