A short column shown below is subjected to an eccentric loading. A uniaxial bending is caused about $y$ axis. The material strengths are $f_y=60$ksi and $f_c^{\text{'}}=5$ksi. The Young's modulus of steel is $29000$ ksi $.$

$A_{st}=6No.9$ bars

$($a$)$ Determine the balanced failure point, i$.$e$.,P_b$ and $M_b.$

$($b$)$ Determine a combination of $P$ and $M$ with $c={50}^{\text{'}\text{'}}$ that can lead to the column failure. Also calculate the corresponding $e.$ Discuss if the failure is governed by compression failure of concrete or tension failure of rebars.