How to Find Column Dimension | Column Size Calculation

Size of column can not be taken arbitrary, column dimension should be decided based on load combination grade of steel and concrete.

Even though standard size of column are taken for minimum suitable size of column for particular building. Correct approach to decide size of column is to use IS code recommended formula.

Column size is decided by the following column size formula given by IS 456:2000.

Pu = 0.4 f_ck A_c + 0.67 f_y A_sc

Where,

• Pu = Ultimate Load on Column
• f_ck = Characteristics compressive strength of concrete
• A_c = Sectional Area of Concrete
• f_y = Yield strength of steel
• A_sc = Area of Steel Reinforcement
• A_c = A_g – A_sc
• A_sc = 0.01 A_g (A_g =  Gross Area of Column)
• A_c = 0.99 A_g

Example of Column Size Calculation

Example 1

Let us learn how to design a column to support axial load of 600 KN by using M20 grade of concrete and Fe 500 steel grade.

From the given condition,

Pu = 600 KN,
f_ck = 20 N/mm²,
f_y = 500 N/mm²,

Assume,
Steel = 1% and
Factor of Safety = 1.5

P_u = 0.4 f_ck A_c + 0.67 f_y A_sc
1.5 x 600 x 10³ = 0.4 x 20 x (0.99 A_g) + 0.67 x 500 x (0.01 A_g)
A_g = 79858 mm²

For the square column,

A_g = (size of column)²

Size of Column = √79858 = 282.59 mm

Provide square column of size 285 mm x 285 mm

A_g = Provided = 81225 mm²

A_sc = 0.01 A_g = 0.01 x 81225 = 812.25 mm²

Provide 8 Nos of 12 mm Dia steel with actual area of steel = 905 mm²

The size of the column for 600 KN load is 285 mm x 285 mm (12″ x12″)

Example 2

Design a column to support 1650 KN of load on the structure with M30 grade of concrete and Fe 415 grade of steel.

From the given condition,

Pu = 1650 KN,
f_ck = 30 N/mm²,
f_y = 415 N/mm²,

Assume,
Steel = 1.5% and
Factor of Safety = 1.5

Factored Load = 1.5 X 1650 = 2475 KN

P_u = 0.4 f_ck A_c + 0.67 f_y A_sc
2475 x 10³ = 0.4 x 30 x (0.985 A_g) + 0.67 x 415 x (0.015 A_g)
A_g = 153051 mm²

Either we can design the column as square column or a rectangle column

• Square column

For square column,

A_g = (size of column)²

Size of Column = √153051 = 391.21 mm

Provide square column of size 400 mm x 400 mm

A_g = Provided = 160000 mm²

A_sc = 0.01 A_g = 0.01 x 160000 = 1600 mm²

Provide 8 Nos of 16 mm Dia steel with actual area of steel = 1608 mm²

The size of the column for 1650 KN load is 400 mm x 400 mm (16″ x 16″)

• Rectangular column

For rectangular column,

A_g = length X breadth

In building column we take width of the column equal to size of wall so that column is not protruded inside home and matches the wall surface.

Generally, the width of column is selected as 9″ or 225 mm and sometimes 12″ or 300 mm

Taking the width of column as 9″

A_g = L X B

153051 = L X 225
L = 153051 / 225
L = 680.2 mm

Provide a rectangle column of size 225 mm x 680 mm

OR

Taking width of column as 12″

A_g = L X B

153051 = L X 300
L = 153051 / 300
L = 510 mm

Provide rectangle column of size 300 mm x 510 mm

A_g = Provided = 153000 mm²

A_sc = 0.01 A_g = 0.01 x 160000 = 1530 mm²

Provide 8 Nos of 16 mm Dia steel with actual area of steel = 1608 mm²

The size of rectangle column for 1650 KN load is 225 mm X 680 mm (9″ X 27″) or 300 mm x 510 mm (12″ x 20″)