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/mm^{2},

f_{y} = 500 N/mm^{2},

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 10

^{3}= 0.4 x 20 x (0.99 A

_{g}) + 0.67 x 500 x (0.01 A

_{g})

**A**

_{g}= 79858 mm^{2}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 mm^{2}

A_{sc} = 0.01 A_{g} = 0.01 x 81225 = **812.25 mm ^{2}**

Provide** 8 Nos of 12 mm Dia** steel with actual area of steel = **905 mm ^{2}**

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/mm^{2},

f_{y} = 415 N/mm^{2},

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 10

^{3}= 0.4 x 30 x (0.985 A

_{g}) + 0.67 x 415 x (0.015 A

_{g})

**A**

_{g}= 153051 mm^{2}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 mm^{2}

A_{sc} = 0.01 A_{g} = 0.01 x 160000 = **1600 mm ^{2}**

Provide** 8 Nos of 16 mm Dia** steel with actual area of steel = **1608 mm ^{2}**

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 mm^{2}

A_{sc} = 0.01 A_{g} = 0.01 x 160000 = **1530 mm ^{2}**

Provide** 8 Nos of 16 mm Dia** steel with actual area of steel = **1608 mm ^{2}**

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″)**

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