QUESTION $3-$ CLO$3$

$20$ Points

A rectangular beam made using concrete with $f^{\text{'}}c=42$MPa and steel with $f_y=420$MPa has a width $b$

$=500mm,$ and effective depth of $d=440mm,$ and a total depth of $h=500mm.$ The concrete modulus

of rupture $f_r=3\mathrm{.}6$MPa. The elastic moduli of the concrete and steel are, respectively, $E_c=28,000$

MPa and $E_s=200,000$MPa. The tensile steel consists of four No$.36$ bars.

Determine the cracking moment of the beam $(M_{cr})$

Find the service load moment $(M_s)$ that causes stress in the concrete in compression of $0\mathrm{.}6f_c.$

Compute the nominal moment strength $(M_n)$ of the beam.