Problem$-1$: The beam shown below in Figure$-1$ is simply supported at $A,$ continuous over

support $C$ and is free at $D$; the beam is partially restrained at $A,$ fully restrained at $C$ and

unrestrained at $D$ for the purpose of lateral global buckling. Downward loads of $4F^{*}$ and

$F^{*}$ acts at the top of flange where $F^{*}=25kN.$ Check whether the hot rolled I $-$ section

$($Figure$-2)$ provided for this beam is adequate for segments ABC and CD for both

local buckling and global buckling considerations. Assume $f_y=250$MPa.

$d=206\mathrm{.}2mm$

$b_f=203\mathrm{.}9mm$

$t_f=12\mathrm{.}5mm$

$t_W=8\mathrm{.}0mm$

$S_x=568{10}^{3}m{m}^3$

$I_y=17\mathrm{.}7{10}^{6}m{m}^4$

$J=320{10}^{3}m{m}^4$

$I_W=166{10}^{9}m{m}^6$

FIGURE$-2$