Calculating the size of columns is essential in structural engineering. Accurate dimensions ensure the stability and durability of buildings. This guide explains how to find the dimensions of columns with a practical example.

Given Data

• Total Load Over the Column: 1650KN = 1650 x 10³N
• Concrete Grade: M30
• Steel Grade: Fe415

Factored Load Calculation

The factored load is calculated using the formula:

Pu = 1.5 x Total Load

Pu = 1.5 x 1650KN

Pu = 2475KN = 2475 x 10³N

Formula to Find Column Size

According to IS code:

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

Where:

• Pu: Ultimate Load = 2475 x 10³N
• fck: Characteristic Compressive Strength of Concrete = 30 N/mm²
• fy: Yield Strength of Steel = 415 N/mm²
• Ac: Sectional Area of Concrete
• Asc: Sectional Area of Steel

Steel Percentage

Let us provide 1.5% steel in the column.

Asc = 1.5% of Ac = 0.015Ac

Now substitute the values:

2475 x 10³N = [0.4 x 30 x Ac + 0.67 x 415 x 0.015Ac]

2475 x 10³N = [12Ac + 4.171Ac]

2475 x 10³N = 16.171Ac

Ac = 2475 x 10³N ÷ 16.171N/mm²

Ac = 153.05 x 10³ mm²

Ac = 1,53,051 mm²

Square Column Calculation

If the column is square-shaped:

L x B = L²

L² = 153051mm²

L = √153051mm²

L = 391.21mm

By rounding off, the final size of the square column will be:

400mm x 400mm

Rectangular Column Calculation

In residential buildings, the column breadth is typically 225mm (9″) to match the wall width.

Option 1:

L x 225mm = 153051mm²

L = 153051mm² ÷ 225mm

L = 680.2mm

The rectangular column size will be 225mm x 680mm

Option 2:

If the column width is 300mm (12″):

L = 153051mm² ÷ 300mm

L = 510mm

The column size will be 300mm x 510mm

Conclusion:

✅ This method is perfect for residential buildings (G+1, G+2).

🚫 For multi-storeyed buildings, lateral loads (wind, earthquake) and slenderness effects must also be considered.

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