$(1)$ A circular concrete column has a diameter of $100$ cm and a height of $450cm.,f_c^{\text{'}}=350$

$kg\frac{f}{c}{m}^2.$

$($a$)$ If the column is subjected to an axial compression $P=1000tf,$ calculate the total

axial deformation of the column after three years of concrete creep. Neglect the

shrinkage deformation. The creep coefficient after three years $C_t$ is calculated by

Eq$.(1\mathrm{.}11)$ of the lecture notes. The ultimate creep coefficient $C_u=2\mathrm{.}0.$ The column

does not have any reinforcement.

$($b$)$ On the basis of $($a$),24$ D$36($#$11)$ longitudinal steel bars are added to the column.

Calculate the total axial deformation of the column after three years of concrete

creep and the change of the stress in the steel bars and concrete due to concrete

creep.

$($c$)$ Based on previous calculations, discuss the effect of adding steel bars on the

long$-$term total axial deformation of the column.