# How To Calculate Cutting Length of Stirrups for Beam and Column

## How To Calculate Cutting Length of Stirrups

Different shapes of rings/Links/stirrups have varying cutting length. Today here, we are going to learn “How to calculate the cutting length of Stirrups for various shapes”.

Remember, The transverse bars provided in the column is known as Ties, and the transverse bars provided in the beam is known as Stirrups. But on-site; generally, we use the same term stirrup for both mounts.

Stirrups are used in beam to counteract shear failure and to hold the longitudinal bars in position.

## Method for Calculating Cutting Length of Stirrups

1. Study the size of a beam or column on drawings
2. Check the diameter of the bar given for stirrups (Mostly 8mm diameter is used for stirrups)
3. Subtract the clear cover or concrete cover.
4. Calculate the total perimeter/outer length for stirrup by deducting concrete cover.
5. Then add hook-length to the outer length of the stirrup
6. Now Subtract the Length of bends

Formula

Cutting Length of Stirrup = Perimeter of stirrup shape + Hook Length – Bend length

## Important Formulas

Perimeter of Rectangle = 2( Length + Width )

Perimeter of Square = 4 × Side Length

Circumference/ perimeter of Circle = 2лr or лd ( Where R = radius, d = Diameter)

## Example

There is a typical diagram of stirrup for a better understanding of concrete cover, length, width, hook and bend.

In the stirrup shown in the image above have concrete cover around it, 5 bands at 4 corners and 2 hooks.

A = A is the length of the stirrup in the horizontal direction.

B = B is the length of the stirrup in the vertical direction.

## Standard Length of Hook and Bend

Hook length = 9d or 75 mm (for One hook)

Bend Length for 45° = 1d

Bend Length for 90° = 2d

Bend Length for 135° = 3d (Where d = Diameter of Bar)

## Cutting Length of Rectangular Stirrup

The rectangular shape is most common and generally used for beam and column at many structures. This shape column and beam have rectangular shape stirrups.

Considering

Rctangular Column of Size = 300 mm × 600 mm

Diameter of bar used for Stirrup = 8 mm

Concrete Cover = 25 mm

Step1 – Deduct Concrete Cover

A = 300 – 25 – 25 = 250

B = 600 – 25 – 25 = 550

Step2 – The perimeter of stirrup = 2(L + W) = 2(250 + 550) = 1600 mm

Step3 – Hook Length

There are two hooks in this stirrup hence the total length of hook = 9d + 9d = 18d

Step4 – Bend Length

From the figure shown above, there are 3 bends at 90° and 2 bends at 135°

Total Bend Length = 3 × 2d + 2 × 3d = 6d + 6d = 12d

Cutting Length of rectangular stirrup = Perimeter + Hook Length – Bend length.

= 2 × (250 + 550) + 18 × 8 – 96

= 1648 mm or 1.648 meter

Also, Read – How to Calculate Unit Weight of Steel Bars?

## Cutting Length of Square Stirrup

The square shape is also the most common and generally used for beam and column at several structures. This shape column and beam have square shape stirrups.

Considering

Square Column of Size = 300 mm × 300 mm

The diameter of the bar used for stirrup = 8 mm

Concrete Cover = 25 mm

1. Deduct Concrete Cover

A = 300 – 25 – 25 = 250

B = 300 – 25 – 25 = 250

2. Perimeter of Square Stirrup = 4 × 200 = 1000

3. Total Hook Length = 9d + 9d = 18d

4. Bend Length

From the figure shown above, there are 3 bends at 90° and 2 bends at 135°

Total Bend Length = 3 × 2d + 2 × 3d = 6d + 6d = 12d

Cutting Length of Square stirrup = Perimeter + Hook Length – Bend length.

= 4 × 250 + 18 × 8 – 12 × 8

= 1048 mm say 1.048

## Cutting Length of Circular Stirrup

Considering

Circular Column of Diameter = 300 mm

The diameter of the bar used for Stirrup = 8 mm

Concrete Cover = 50 mm

1. Deduct Concrete Cove = 300 -50 = 250 mm

2. Circumference (perimeter) of stirrup = лd = л × 250 = 785.39 say 785 mm

3. Hook Length = 9d + 9d = 18d = 18 × 8 = 144 mm

4. Bend length

There are two bends at 135°

So total bend length = 3d +3d = 6d = 6 × 8 = 48

Cutting Length of Circular stirrup = Perimeter/Circumference + Hook Length – Bend Length

= 785 + 144 – 48

= 881 mm or 0.88 meter

## Cutting Length of Triangular Stirrup

Considering

Circular Column of Diameter = 230 mm × 230 mm

The diameter of the bar used for stirrup = 8 mm

Concrete Cover = 25 mm

1. Deducting Concrete Cover

A = 230 – 25 – 25 = 180 mm

B = 230 – 25 – 25 = 180 mm

2. Perimeter of Triangular Stirrup

By Pythagoras theorem

Hypotenuse2 = Base2 + Height2

H2 = 602 + 1802

H = √( 602 + 1802)

H = 189.7 say 190 mm

The perimeter of stirrup = 2 × H + Base = 2 × 190 × 180 = 560 mm

3. Hook Length = 9d + 9d = 18d

4. Band Length

There are 4 bens at 135°

Total Bend Length = 4 × 3d = 12d

Cutting Length of Triangular stirrup = Perimeter + Hook Length – Bend length

= 560 + 144 – 96

= 608 mm or 0.608 meter

## Cutting Length of Diamond Stirrup

Considering

Rctangular Column of Size = 350 mm × 350 mm

Diameter of bar used for Stirrup = 8 mm

Concrete Cover = 25 mm

1. Deduct concrete cove from all side

A = 350 – 25 -25 = 300 mm

B = 350 -25 – 25 = 300 mm

2. The perimeter of the stirrup

By Pythagoras theorem

Hypotenuse2 = Base2 + Height2

H2 = 1502 + 1502

H = √( 1502 + 1502)

H = 212.13 say 212 mm

The perimeter of diamond stirrup = 4 × H = 4 × 212 = 848 mm

3. Total Hook Length = 9d +9d = 18d

4. Bend Length

From the above figure diamond stirrup have 3 bends at 90° and 2 bends at 135°.

Total Bend Length = 2 × 3d + 2 × 3d = 12d

Cutting Length of Diamond Stirrup = Perimeter + Hook Length – Bend Length

= 848 + 144 – 96

= 896 mm or 0.896 meter

## Cutting Length of Helical Stirrup

A spiral stirrup is similar to circular stirrup except for hook.

Considering

Circular Column of Diameter = 600 mm

The diameter of the bar used for stirrup = 8 mm and pitch 150 mm

Concrete Cover = 50 mm

Deducting Concrete Cover = 600 – 25 – 50 = 550 mm

Perimeter of stirrup

Circumference of circle = πd = π × 550 = 1727.87 mm or 1.73

Numbers of spiral = Total Length/pitch + 1 = 9000/150 + 1 = 61 numbers

Length of Spiral Stirrup or Ring = Number of spiral × Length of one Spiral

= 60 × 1.73

=  103.8 say 104  meters.

We can also calculate the cutting length of spiral Stirrup by the formula given below.

Cutting Length of Helical Stirrup = n√(C2 + P2)

Where

n = Numbers of Spiral

C = Circumference of one spiral

P = Pitch

L = n√c2 + p2

N = H/p = 9/0.15 = 60

C = лD = л × 0.55 = 1.727 say 1.73 meter

P = 150 mm or 0.15 meter

L = n√c2 + p2

L = 150√1.732 + 1502

L = 60 × 1.736

L = 104.16 say 104 meter

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