Question

An RCC short column (with lateral ties) of rectangular cross-section of 250 mm x 300 mm is reinforced with four numbers of 16 mm diameter longitudinal bars. The grades of steel and concrete are Fe 415 and M 20, respectively. Neglect eccentricity effect. Considering limit state of collapse in compression (IS : 456 :2000), the axial load carrying capacity of the column (in kN, up to one decimal place), is _______.

• A. 918.1

Answer 1

The correct option is A 918.1
In the question, the column is defined as a short column. Also, it is mentioned that the eccentricity shall be neglected.

Considering limit state of collapse in compression and the permissible axial strain as 0.002, the stress in concrete $=0.45f_{ck}$

and stress in steel
$=0.87f_{y}forFe250$
$=0.79f_{y}forFe415$
$=0.75f_{y}forFe500$

The above stresses in steel are derived from stress strain curve of different grade of steel.
The axial load capacity of column neglecting eccentricity effect

$=0.45f_{ck}{A}_c+0.75f_y{A}_{sc}$

$A_c=250\times 300-4\times \frac{\pi }{4}\times {16}^2$
$=74195.75m{m}^2$

$A_{sc}=4\times \frac{\pi }{4}\times {16}^2=804.25m{m}^2$

axial load capacity

$=0.45\times 20\times 74195.75+0.75\times 415\times 804.25$
= 918084 N
= 918.08 kN