A beam has $9\mathrm{.}0$ m span and carry two intermediate point load in addition to self$-$ weight.

The beam is laterally restrained at the ends and at the point loads only. Check the

resistance capacity of the beam for the grade S$275$ steel and for the trial cross$-$section

given below. $(25$ pts $)$

Try a $45719182$ UB in grade S$275$ steel

From section property tables:

$h,=460\mathrm{.}0mm,b,=191\mathrm{.}3mm,t_w,=9\mathrm{.}9mm$

$t_f,=16\mathrm{.}0mm,r,=10\mathrm{.}2m{m}^2,i_z,=4\mathrm{.}23c{m}^3$

$i_y,=18\mathrm{.}8cm,A,=104c{m}^2,W_{pl,y},=1830c{m}^3$

$I_z,=1870c{m}^4,I_y,=37100c{m}^4,I_w,=0\mathrm{.}922d{m}^6$

$\frac{c_f}{t_f},=5\mathrm{.}03,\frac{c_w}{t_w},=41\mathrm{.}2,$