in steel design use $2015$ code answer completely with solutions ty $($:

A W $2148$ beam is simply supported on a span $7m.$ The beam is laterally supported at its ends and subjected to a uniform service dead load of $7k\frac{N}{m}$

$($including the weight of the bea$)$ ans a service live load of $3\mathrm{.}1k\frac{N}{m},$ respectively. If $Fy=345$MPa, deter mine the available strength for LRFD and ASD.

Properties of W $2148$

$d=523mm$

$b_f=207mm$

$t_f=8\mathrm{.}89mm$

$t_w=10\mathrm{.}9mm$

$Z_y=244({10}^3)m{m}^3,l_x=399({10}^6)m{m}^4,r_y=42\mathrm{.}2mm$

$J=334({10}^3)m{m}^4,l_y=16\mathrm{.}1({10}^6)m{m}^4,r_{ts}=52\mathrm{.}1mm$

$J=334({10}^3)m{m}^4,I_y=16\mathrm{.}1({10}^6)m{m}^4,r_{ts}=52\mathrm{.}1mm$

$h_0=513mm,S_x=1520({10}^3)m{m}^3,z_5=1750>$

$h_o=513mm$

$C_w=1060({10}^9)m{m}^4$

$S_y=156({10}^3)m{m}^3$

$z_X=1750{10}^{3}m{m}^3$