QUESTION $1-$ CLO$3$

$20$ Points

A simply$-$supported beam with a span length of $L=7m,$ width of $b=400mm,$ total depth of $h=600$

mm $,$ and tension steel depth of $d=530mm,$ carries a uniform service load of $(w)k\frac{N}{m}$ including its

own weight. Materials strengths are $f_c^{\text{'}}=30$MPa,$f_y=420$MPa, and $E_s=200$GPa. The beam is

reinforced with $4$ No$.25$ tension reinforcing bars.

Determine the nominal moment strength $(M_n)$ of the beam section.

Determine the yield moment $(M_y)$ of the beam section.

Determine the service uniform load $(w)$ that will cause yielding of tension steel.