Question

A square column of size $400mm$ is subjected to ultimate concentric axial force of $1200kN$. The grade of material used are $M25$ and $Fe415$. The area of steel to be provided assuming zero eccentricity is:

• A. $850m{m}^2$
• B. $1120m{m}^2$
• C. $1280m{m}^2$
• D. $790m{m}^2$

Answer 1

The correct option is A $850m{m}^2$

Size of column $=400mm\times 400mm$
Axial load, $P_u=1200kN$
For concentric load,
$P_u=0.45f_{ck}{A}_c+0.75f_y{A}_{sc}$
$1200\times {10}^3=0.45\times 25({400}^2-A_{sc})+0.75\times 415A_{sc}$
$1200000=1800000+300A_{sc}$
$A_{sc}$ comes out to be negative. Hence concrete is self sufficient to bear the ultimate axial load.

Hence, we will provide the reinforcement equal to the minimum longitudinal reinforcement provided for column criteria.

Area of concrete required to resist direct stress
$A_c^{{}^{\prime }}=\frac{P_u}{0.45\times f_{ck}}$
$=\frac{1200\times {10}^3}{0.45\times 25}$
$A_c^{{}^{\prime }}=106666.67m{m}^2$
$\therefore$ Area of steel to be provided $=0.8$ % of $A_c^{{}^{\prime }}$
$=\frac{0.8}{100}\times 106666.67$
$=853.333m{m}^2$