# How to Calculate The Load Carrying Capacity of a Column?

The load carrying capacity of a column is the maximum load that the column can support without failing.

**It is calculated based on the following factors:**

- The area of the column
- The compressive strength of the concrete
- The yield strength of the steel reinforcement
- The slenderness ratio of the column

### The most common formula for calculating the load carrying capacity of a column is as follows:

Pu = 0.4fck * Ac + 0.67fy * Asc

The load carrying capacity of a column is the maximum load that the column can support without failing. It is calculated based on the following factors:

- The area of the column
- The compressive strength of the concrete
- The yield strength of the steel reinforcement
- The slenderness ratio of the column

### The most common formula for calculating the load carrying capacity of a column is as follows:

`Pu = 0.4fck * Ac + 0.67fy * Asc`

*Where:*

- Pu is the load carrying capacity of the column
- fck is the characteristic compressive strength of the concrete
- Ac is the area of the concrete in the column
- fy is the yield strength of the steel reinforcement
- Asc is the area of the steel reinforcement in the column

The slenderness ratio of the column is a measure of how slender the column is, and it can affect the load carrying capacity of the column. For slender columns, the load carrying capacity is reduced.

Once the load carrying capacity of the column has been calculated, it is important to compare it to the actual load that the column will be carrying. If the actual load is greater than the load carrying capacity, then the column is undersized and will need to be redesigned or strengthened.

### Here is an example of how to calculate the load carrying capacity of a column:

**Given:**
* Column size: 300mm x 450mm
* Concrete grade: M25
* Steel grade: Fe415
* Number of 16mm diameter reinforcement bars: 6
**Calculation:**
* Area of concrete (Ac): 300mm x 450mm = 135,000mm^2
* Area of steel (Asc): 6 * (pi/4) * 16^2 = 1884mm^2
* Load carrying capacity (Pu): 0.4 * 25 * 135,000 + 0.67 * 415 * 1884 = 6,500,000N
Therefore, the load carrying capacity of the column is 6,500,000N, or 650kN.

It is important to note that this is just a simplified example. In practice, there are many other factors that need to be considered when calculating the load carrying capacity of a column, such as the boundary conditions, the type of loading, and the presence of any imperfections in the column.

## Example: The Load Carrying Capacity

Calculate the load-carrying capacity of a column that is carrying an ultimate axial load of 650KN. The size of the column is 230mm х380mm. The column has 4nos. of 16mm. dia. bars. Use M25 & Fe415 steel.

### Given data:

Breadth = b = 230mm.

Depth =D = 380mm.

No. of rebars = 4nos.

Dia. of main bar = d = 16mm.

fck = 25N/mm²

fy= 415N/mm².

*Calculation:*

Load carrying capacity is calculated by the formula [as per IS-456 (2000)]

Pu = 0.4fck*Ac + 0.67fy*Asc

*Where,*

Pu = Load carrying capacity.

fck = Characteristic compressive strength of concrete.

Ac = Area of concrete.

fy = Grade of steel.

Asc = Area of the main reinforcement.

*Now,*

◆. Area of concrete

Ac = [Ag – Asc]

*Where,*

Ag = Gross sectional area of the column.

Ag = [breadth х depth]

` = [230mm.х 380mm.]`

Ag = 87,400 mm².

◆. The sectional area of steel

Asc = [(area of 1 bar) х No. of bars]

```
= [(πd² ÷ 4) х 4nos.]
= [(3.142 х 16² ÷ 4) х 4nos.]
= [201.09 х 4nos.]
```

Asc.= 804.4 mm².

*Area of concrete*

Ac = [Ag – Asc]

```
= [ 87,400 - 804.4]
Ac = 86596.6mm².
```

Pu = [0.4fck*Ac + 0.67fy*Asc]

```
= [(0.4 х 25 х 86596.6 ) + (0.67 х415 х804.4)]
= [ 865,966 + 2,23,663.4]
```

Pu = 1,089,629.4N

To get the above result in KN, we have to multiply the value by 10⁻³

Pu = [1,089,629.4 х 10⁻³]

Pu = 1089.6KN > 650KN & hence safe.✔

*◆. Check for minimum reinforcement:*

Asc% = [Asc ÷ Ag] х 100

` = [804.4 ÷ 87400] х 100`

Asc% = 0.92% > 0.8% & hence safe ✔